From 8939a55653c636358b22e5ed58acd493560546d7 Mon Sep 17 00:00:00 2001
From: Mark Olesen <Mark.Olesen@esi-group.com>
Date: Mon, 5 Oct 2020 12:30:41 +0200
Subject: [PATCH 1/3] ENH: relocate blockMesh polyMesh generation into library
 (for code reuse)

STYLE: adjust blockMesh advanced/non-advanced options

- make -merge-points "non-advanced" (for better exposure)
- make -write-obj "advanced" (-write-vtk is preferred)
---
 .../mesh/generation/blockMesh/addCellZones.H  |  88 +-----------
 .../mesh/generation/blockMesh/blockMesh.C     |  73 +++-------
 .../blockMesh/handleCyclicPatches.H           |  22 +++
 .../generation/blockMesh/mergePatchPairs.H    |  42 +++---
 src/mesh/blockMesh/blockMesh/blockMesh.C      |  12 +-
 src/mesh/blockMesh/blockMesh/blockMesh.H      |  36 +++--
 .../blockMesh/blockMesh/blockMeshCreate.C     | 128 +++++++++++++++++-
 7 files changed, 225 insertions(+), 176 deletions(-)
 create mode 100644 applications/utilities/mesh/generation/blockMesh/handleCyclicPatches.H

diff --git a/applications/utilities/mesh/generation/blockMesh/addCellZones.H b/applications/utilities/mesh/generation/blockMesh/addCellZones.H
index eca57f2ed4..7cec1b4541 100644
--- a/applications/utilities/mesh/generation/blockMesh/addCellZones.H
+++ b/applications/utilities/mesh/generation/blockMesh/addCellZones.H
@@ -1,87 +1 @@
-// Set any cellZones
-// Note cell labelling unaffected by previous mergePatchPairs
-
-{
-    const label nZones = blocks.numZonedBlocks();
-    if (nZones)
-    {
-        Info<< nl << "Adding cell zones" << endl;
-
-        // Map from zoneName to cellZone index
-        HashTable<label> zoneMap(nZones);
-
-        // Cells per zone.
-        List<DynamicList<label>> zoneCells(nZones);
-
-        // Running cell counter
-        label celli = 0;
-
-        // Largest zone so far
-        label freeZoneI = 0;
-
-        for (const block& b : blocks)
-        {
-            const word& zoneName = b.zoneName();
-            const label nCellsInBlock = b.cells().size();
-
-            if (zoneName.size())
-            {
-                const auto iter = zoneMap.cfind(zoneName);
-
-                label zonei;
-
-                if (iter.found())
-                {
-                    zonei = *iter;
-                }
-                else
-                {
-                    zonei = freeZoneI++;
-
-                    Info<< "    " << zonei << '\t' << zoneName << endl;
-
-                    zoneMap.insert(zoneName, zonei);
-                }
-
-
-                // Fill with cell ids
-
-                zoneCells[zonei].reserve
-                (
-                    zoneCells[zonei].size() + nCellsInBlock
-                );
-
-                const label endOfFill = celli + nCellsInBlock;
-
-                for (; celli < endOfFill; ++celli)
-                {
-                    zoneCells[zonei].append(celli);
-                }
-            }
-            else
-            {
-                celli += nCellsInBlock;
-            }
-        }
-
-        List<cellZone*> cz(zoneMap.size());
-        forAllConstIters(zoneMap, iter)
-        {
-            const word& zoneName = iter.key();
-            const label zonei = iter.val();
-
-            cz[zonei] = new cellZone
-            (
-                zoneName,
-                zoneCells[zonei].shrink(),
-                zonei,
-                mesh.cellZones()
-            );
-        }
-
-        mesh.pointZones().resize(0);
-        mesh.faceZones().resize(0);
-        mesh.cellZones().resize(0);
-        mesh.addZones(List<pointZone*>(), List<faceZone*>(), cz);
-    }
-}
+#warning File removed - left for old dependency check only
diff --git a/applications/utilities/mesh/generation/blockMesh/blockMesh.C b/applications/utilities/mesh/generation/blockMesh/blockMesh.C
index 0eec9f01b8..b510d91170 100644
--- a/applications/utilities/mesh/generation/blockMesh/blockMesh.C
+++ b/applications/utilities/mesh/generation/blockMesh/blockMesh.C
@@ -77,7 +77,6 @@ Usage
 #include "foamVtkInternalMeshWriter.H"
 #include "attachPolyTopoChanger.H"
 #include "polyTopoChange.H"
-#include "emptyPolyPatch.H"
 #include "cyclicPolyPatch.H"
 #include "cellSet.H"
 
@@ -85,7 +84,7 @@ Usage
 #include "OSspecific.H"
 #include "OFstream.H"
 
-#include "Pair.H"
+#include "wordPair.H"
 #include "slidingInterface.H"
 
 using namespace Foam;
@@ -122,7 +121,8 @@ int main(int argc, char *argv[])
     argList::addBoolOption
     (
         "write-obj",
-        "Write block edges and centres as obj files and exit"
+        "Write block edges and centres as obj files and exit",
+        true  // (old) mark as advanced option. -write-vtk is preferred
     );
     argList::addOptionCompat("write-obj", {"blockTopology", 1912});
 
@@ -135,9 +135,9 @@ int main(int argc, char *argv[])
     argList::addBoolOption
     (
         "merge-points",
-        "Geometric (point) merging instead of topological merging "
-        "(slower, fails with high-aspect cells. default for 1912 and earlier)",
-        true  // mark as an advanced option
+        "Geometric point merging instead of topological merging"
+        " [default for 1912 and earlier]."
+        // NOTE: " Slower, fails with high-aspect cells."
     );
     argList::addBoolOption
     (
@@ -164,6 +164,9 @@ int main(int argc, char *argv[])
     // Remove old files, unless disabled
     const bool removeOldFiles = !args.found("noClean");
 
+    // Write cellSets
+    const bool writeCellSets = args.found("sets");
+
     // Default merge (topology), unless otherwise specified
     blockMesh::mergeStrategy strategy(blockMesh::DEFAULT_MERGE);
 
@@ -329,56 +332,22 @@ int main(int argc, char *argv[])
     }
 
 
-    Info<< nl << "Creating polyMesh from blockMesh" << endl;
+    // Ensure we get information messages, even if turned off in dictionary
+    blocks.verbose(true);
 
-    polyMesh mesh
-    (
-        IOobject
+    autoPtr<polyMesh> meshPtr =
+        blocks.mesh
         (
-            regionName,
-            meshInstance,
-            runTime
-        ),
-        pointField(blocks.points()),  // Copy, could we re-use space?
-        blocks.cells(),
-        blocks.patches(),
-        blocks.patchNames(),
-        blocks.patchDicts(),
-        "defaultFaces",               // Default patch name
-        emptyPolyPatch::typeName      // Default patch type
-    );
+            IOobject(regionName, meshInstance, runTime)
+        );
 
+    polyMesh& mesh = *meshPtr;
 
-    // Handle merging of patch pairs. Dictionary entry "mergePatchPairs"
+    // Merge patch pairs (dictionary entry "mergePatchPairs")
     #include "mergePatchPairs.H"
 
-    // Set any cellZones
-    #include "addCellZones.H"
-
-
-    // Detect any cyclic patches and force re-ordering of the faces
-    {
-        bool hasCyclic = false;
-        for (const polyPatch& pp : mesh.boundaryMesh())
-        {
-            if (isA<cyclicPolyPatch>(pp))
-            {
-                hasCyclic = true;
-                break;
-            }
-        }
-
-        if (hasCyclic)
-        {
-            Info<< nl << "Detected cyclic patches; ordering boundary faces"
-                << endl;
-            const word oldInstance = mesh.instance();
-            polyTopoChange meshMod(mesh);
-            meshMod.changeMesh(mesh, false);
-            mesh.setInstance(oldInstance);
-        }
-    }
-
+    // Handle cyclic patches
+    #include "handleCyclicPatches.H"
 
     // Set the precision of the points data to 10
     IOstream::defaultPrecision(max(10u, IOstream::defaultPrecision()));
@@ -386,7 +355,7 @@ int main(int argc, char *argv[])
     Info<< nl << "Writing polyMesh with "
         << mesh.cellZones().size() << " cellZones";
 
-    if (args.found("sets") && !mesh.cellZones().empty())
+    if (writeCellSets && !mesh.cellZones().empty())
     {
         Info<< " (written as cellSets too)";
     }
@@ -400,7 +369,7 @@ int main(int argc, char *argv[])
             << exit(FatalError);
     }
 
-    if (args.found("sets"))
+    if (writeCellSets)
     {
         for (const cellZone& cz : mesh.cellZones())
         {
diff --git a/applications/utilities/mesh/generation/blockMesh/handleCyclicPatches.H b/applications/utilities/mesh/generation/blockMesh/handleCyclicPatches.H
new file mode 100644
index 0000000000..eb79d02de2
--- /dev/null
+++ b/applications/utilities/mesh/generation/blockMesh/handleCyclicPatches.H
@@ -0,0 +1,22 @@
+// Detect any cyclic patches and force re-ordering of the faces
+{
+    bool hasCyclic = false;
+    for (const polyPatch& pp : mesh.boundaryMesh())
+    {
+        if (isA<cyclicPolyPatch>(pp))
+        {
+            hasCyclic = true;
+            break;
+        }
+    }
+
+    if (hasCyclic)
+    {
+        Info<< nl << "Detected cyclic patches; ordering boundary faces" << endl;
+
+        const word oldInstance = mesh.instance();
+        polyTopoChange meshMod(mesh);
+        meshMod.changeMesh(mesh, false);
+        mesh.setInstance(oldInstance);
+    }
+}
diff --git a/applications/utilities/mesh/generation/blockMesh/mergePatchPairs.H b/applications/utilities/mesh/generation/blockMesh/mergePatchPairs.H
index 2c94bcc0fa..be551d01f6 100644
--- a/applications/utilities/mesh/generation/blockMesh/mergePatchPairs.H
+++ b/applications/utilities/mesh/generation/blockMesh/mergePatchPairs.H
@@ -1,6 +1,6 @@
 // Handle merging of patch pairs
 {
-    List<Pair<word>> mergePatchPairs;
+    wordPairList mergePatchPairs;
 
     // Read in a list of dictionaries for the merge patch pairs
     if
@@ -14,19 +14,19 @@
         // Create and add point and face zones and mesh modifiers
         List<pointZone*> pz(mergePatchPairs.size());
         List<faceZone*> fz(3*mergePatchPairs.size());
-        List<cellZone*> cz(0);
+        List<cellZone*> cz;
 
-        forAll(mergePatchPairs, pairI)
+        forAll(mergePatchPairs, pairi)
         {
             const word mergeName
             (
-                mergePatchPairs[pairI].first()
-              + mergePatchPairs[pairI].second()
-              + name(pairI)
+                mergePatchPairs[pairi].first()
+              + mergePatchPairs[pairi].second()
+              + name(pairi)
             );
 
             // An empty zone for cut points
-            pz[pairI] = new pointZone
+            pz[pairi] = new pointZone
             (
                 mergeName + "CutPointZone",
                 0,
@@ -34,11 +34,11 @@
             );
 
             // Master patch
-            const word masterPatchName(mergePatchPairs[pairI].first());
+            const word masterPatchName(mergePatchPairs[pairi].first());
             const polyPatch& masterPatch =
                 mesh.boundaryMesh()[masterPatchName];
 
-            fz[3*pairI] = new faceZone
+            fz[3*pairi] = new faceZone
             (
                 mergeName + "MasterZone",
                 identity(masterPatch.size(), masterPatch.start()),
@@ -48,11 +48,11 @@
             );
 
             // Slave patch
-            const word slavePatchName(mergePatchPairs[pairI].second());
+            const word slavePatchName(mergePatchPairs[pairi].second());
             const polyPatch& slavePatch =
                 mesh.boundaryMesh()[slavePatchName];
 
-            fz[3*pairI + 1] = new faceZone
+            fz[3*pairi + 1] = new faceZone
             (
                 mergeName + "SlaveZone",
                 identity(slavePatch.size(), slavePatch.start()),
@@ -62,7 +62,7 @@
             );
 
             // An empty zone for cut faces
-            fz[3*pairI + 2] = new faceZone
+            fz[3*pairi + 2] = new faceZone
             (
                 mergeName + "CutFaceZone",
                 2,
@@ -78,30 +78,30 @@
         attachPolyTopoChanger polyMeshAttacher(mesh);
         polyMeshAttacher.setSize(mergePatchPairs.size());
 
-        forAll(mergePatchPairs, pairI)
+        forAll(mergePatchPairs, pairi)
         {
             const word mergeName
             (
-                mergePatchPairs[pairI].first()
-              + mergePatchPairs[pairI].second()
-              + name(pairI)
+                mergePatchPairs[pairi].first()
+              + mergePatchPairs[pairi].second()
+              + name(pairi)
             );
 
             // Add the sliding interface mesh modifier
             polyMeshAttacher.set
             (
-                pairI,
+                pairi,
                 new slidingInterface
                 (
-                    "couple" + name(pairI),
-                    pairI,
+                    "couple" + name(pairi),
+                    pairi,
                     polyMeshAttacher,
                     mergeName + "MasterZone",
                     mergeName + "SlaveZone",
                     mergeName + "CutPointZone",
                     mergeName + "CutFaceZone",
-                    mergePatchPairs[pairI].first(),
-                    mergePatchPairs[pairI].second(),
+                    mergePatchPairs[pairi].first(),
+                    mergePatchPairs[pairi].second(),
                     slidingInterface::INTEGRAL, // always integral
                     false,
                     intersection::VISIBLE
diff --git a/src/mesh/blockMesh/blockMesh/blockMesh.C b/src/mesh/blockMesh/blockMesh/blockMesh.C
index 3df87de8d2..04db49d80c 100644
--- a/src/mesh/blockMesh/blockMesh/blockMesh.C
+++ b/src/mesh/blockMesh/blockMesh/blockMesh.C
@@ -109,15 +109,23 @@ Foam::blockMesh::blockMesh
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-bool Foam::blockMesh::valid() const
+bool Foam::blockMesh::valid() const noexcept
 {
     return bool(topologyPtr_);
 }
 
 
-void Foam::blockMesh::verbose(const bool on)
+bool Foam::blockMesh::verbose() const noexcept
 {
+    return verboseOutput;
+}
+
+
+bool Foam::blockMesh::verbose(const bool on) noexcept
+{
+    bool old(verboseOutput);
     verboseOutput = on;
+    return old;
 }
 
 
diff --git a/src/mesh/blockMesh/blockMesh/blockMesh.H b/src/mesh/blockMesh/blockMesh/blockMesh.H
index 4227b3de06..d08a475585 100644
--- a/src/mesh/blockMesh/blockMesh/blockMesh.H
+++ b/src/mesh/blockMesh/blockMesh/blockMesh.H
@@ -226,10 +226,10 @@ public:
 
         //- Construct from IOdictionary for given region
         //  Default is topological merging.
-        blockMesh
+        explicit blockMesh
         (
             const IOdictionary& dict,
-            const word& regionName,
+            const word& regionName = polyMesh::defaultRegion,
             mergeStrategy strategy = mergeStrategy::DEFAULT_MERGE
         );
 
@@ -255,10 +255,10 @@ public:
             }
 
             //- True if the blockMesh topology exists
-            bool valid() const;
+            bool valid() const noexcept;
 
-            //- Reference to point field defining the blockMesh
-            //  these points have not been scaled by scaleFactor
+            //- Reference to point field defining the blockMesh.
+            //  These points are \b not scaled by scaleFactor
             const pointField& vertices() const;
 
             //- Return the blockMesh topology as a polyMesh
@@ -279,8 +279,8 @@ public:
             //- The scaling factor used to convert to metres
             scalar scaleFactor() const;
 
-            //- The points for the entire mesh
-            //  these points have been scaled by scaleFactor
+            //- The points for the entire mesh.
+            //  These points \b are scaled by scaleFactor
             const pointField& points() const;
 
             //- Return cell shapes list
@@ -299,16 +299,26 @@ public:
             label numZonedBlocks() const;
 
 
-        // Edit
+    // Verbosity
 
-            //- Enable/disable verbose information about the progress
-            void verbose(const bool on=true);
+        //- Verbose information?
+        bool verbose() const noexcept;
+
+        //- Enable/disable verbose information about the progress
+        //  \return old value
+        bool verbose(const bool on) noexcept;
 
 
-        // Write
+    // Mesh Generation
 
-            //- Writes edges of blockMesh in OBJ format.
-            void writeTopology(Ostream&) const;
+        //- Create polyMesh, with cell zones
+        autoPtr<polyMesh> mesh(const IOobject& io) const;
+
+
+    // Write
+
+        //- Writes edges of blockMesh in OBJ format.
+        void writeTopology(Ostream& os) const;
 };
 
 
diff --git a/src/mesh/blockMesh/blockMesh/blockMeshCreate.C b/src/mesh/blockMesh/blockMesh/blockMeshCreate.C
index 4e8dad0cc6..8d93b69b87 100644
--- a/src/mesh/blockMesh/blockMesh/blockMeshCreate.C
+++ b/src/mesh/blockMesh/blockMesh/blockMeshCreate.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -28,6 +28,7 @@ License
 
 #include "blockMesh.H"
 #include "cellModel.H"
+#include "emptyPolyPatch.H"
 
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
@@ -270,4 +271,129 @@ void Foam::blockMesh::createPatches() const
 }
 
 
+// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
+
+Foam::autoPtr<Foam::polyMesh>
+Foam::blockMesh::mesh(const IOobject& io) const
+{
+    const blockMesh& blkMesh = *this;
+
+    if (verboseOutput)
+    {
+        Info<< nl << "Creating polyMesh from blockMesh" << endl;
+    }
+
+    auto meshPtr = autoPtr<polyMesh>::New
+    (
+        io,
+        pointField(blkMesh.points()),   // Copy, could we re-use space?
+        blkMesh.cells(),
+        blkMesh.patches(),
+        blkMesh.patchNames(),
+        blkMesh.patchDicts(),
+        "defaultFaces",                 // Default patch name
+        emptyPolyPatch::typeName        // Default patch type
+    );
+
+
+    // Set any cellZones
+    const label nZones = blkMesh.numZonedBlocks();
+
+    if (nZones)
+    {
+        polyMesh& pmesh = *meshPtr;
+
+        if (verboseOutput)
+        {
+            Info<< "Adding cell zones" << endl;
+        }
+
+        // Map from zoneName to cellZone index
+        HashTable<label> zoneMap(2*nZones);
+
+        // Cells per zone
+        List<DynamicList<label>> zoneCells(nZones);
+
+        // Running cell counter
+        label celli = 0;
+
+        // Largest zone so far
+        label freeZonei = 0;
+
+        for (const block& b : blkMesh)
+        {
+            const word& zoneName = b.zoneName();
+            const label nCellsInBlock = b.cells().size();
+
+            if (zoneName.size())
+            {
+                const auto iter = zoneMap.cfind(zoneName);
+
+                label zonei = freeZonei;
+
+                if (iter.found())
+                {
+                    zonei = *iter;
+                }
+                else
+                {
+                    zoneMap.insert(zoneName, zonei);
+                    ++freeZonei;
+
+                    if (verboseOutput)
+                    {
+                        Info<< "    " << zonei << '\t' << zoneName << endl;
+                    }
+                }
+
+
+                // Fill with cell ids
+
+                zoneCells[zonei].reserve
+                (
+                    zoneCells[zonei].size() + nCellsInBlock
+                );
+
+                const label endOfFill = celli + nCellsInBlock;
+
+                for (; celli < endOfFill; ++celli)
+                {
+                    zoneCells[zonei].append(celli);
+                }
+            }
+            else
+            {
+                celli += nCellsInBlock;
+            }
+        }
+
+        List<cellZone*> cz(zoneMap.size());
+        forAllConstIters(zoneMap, iter)
+        {
+            const word& zoneName = iter.key();
+            const label zonei = iter.val();
+
+            cz[zonei] = new cellZone
+            (
+                zoneName,
+                zoneCells[zonei].shrink(),
+                zonei,
+                pmesh.cellZones()
+            );
+        }
+
+        pmesh.pointZones().resize(0);
+        pmesh.faceZones().resize(0);
+        pmesh.cellZones().resize(0);
+        pmesh.addZones(List<pointZone*>(), List<faceZone*>(), cz);
+    }
+
+
+    // Merge patch pairs, cyclic must be done elsewhere
+    // - requires libdynamicMesh
+
+    return meshPtr;
+}
+
+
 // ************************************************************************* //

From 1d08ed9be2551bdfbeedeb0edb3980501c9b7af8 Mon Sep 17 00:00:00 2001
From: Mark Olesen <Mark.Olesen@esi-group.com>
Date: Mon, 5 Oct 2020 12:36:19 +0200
Subject: [PATCH 2/3] ENH: support arc edge specification with origin point

- The arc will frequently enclose an angle less than 180 degrees.
  For the case, it is possible to define the arc by its endpoints
  and its centre (origin) point. For example,

      arc 0 1 origin (0 0 0);

  When defined in the way, any discrepancy in the arc radius for the
  endpoints is resolved by adjusting the origin to ensure that the
  average radius is satisfied.

  It is also possible to specify a \em flatness factor as a multiplier
  of the radius. For example,

      arc 0 1 origin 1.1 (0 0 0);

ENH: minor code cleanup for block edges

ENH: expose point appending as polyList::concat
---
 .../blockEdges/BSplineEdge/BSpline.C          |   2 +-
 .../blockEdges/BSplineEdge/BSpline.H          |  21 +-
 .../blockEdges/BSplineEdge/BSplineEdge.C      |  22 +-
 .../blockEdges/BSplineEdge/BSplineEdge.H      |  19 +-
 .../blockMesh/blockEdges/arcEdge/arcEdge.C    | 231 ++++++++++++++----
 .../blockMesh/blockEdges/arcEdge/arcEdge.H    |  95 +++++--
 src/mesh/blockMesh/blockEdges/bezier/bezier.C |   8 +-
 src/mesh/blockMesh/blockEdges/bezier/bezier.H |  17 +-
 .../blockEdges/blockEdge/blockEdge.C          |  25 +-
 .../blockEdges/blockEdge/blockEdge.H          |  58 +++--
 .../blockEdges/blockEdge/blockEdgeI.H         |   6 +-
 .../blockEdges/lineDivide/lineDivide.H        |  12 +-
 .../blockMesh/blockEdges/lineEdge/lineEdge.C  |  20 +-
 .../blockMesh/blockEdges/lineEdge/lineEdge.H  |  19 +-
 .../blockEdges/polyLineEdge/polyLine.C        |  82 +++++--
 .../blockEdges/polyLineEdge/polyLine.H        |  49 ++--
 .../blockEdges/polyLineEdge/polyLineEdge.C    |   8 +-
 .../blockEdges/polyLineEdge/polyLineEdge.H    |  18 +-
 .../projectCurveEdge/projectCurveEdge.C       |  28 ++-
 .../projectCurveEdge/projectCurveEdge.H       |  27 +-
 .../blockEdges/projectEdge/projectEdge.C      |  23 +-
 .../blockEdges/projectEdge/projectEdge.H      |  20 +-
 .../blockEdges/splineEdge/CatmullRomSpline.C  |   2 +-
 .../blockEdges/splineEdge/CatmullRomSpline.H  |  19 +-
 .../blockEdges/splineEdge/splineEdge.C        |  22 +-
 .../blockEdges/splineEdge/splineEdge.H        |  21 +-
 26 files changed, 575 insertions(+), 299 deletions(-)

diff --git a/src/mesh/blockMesh/blockEdges/BSplineEdge/BSpline.C b/src/mesh/blockMesh/blockEdges/BSplineEdge/BSpline.C
index 39d3b99b8c..29957a0ceb 100644
--- a/src/mesh/blockMesh/blockEdges/BSplineEdge/BSpline.C
+++ b/src/mesh/blockMesh/blockEdges/BSplineEdge/BSpline.C
@@ -134,7 +134,7 @@ Foam::point Foam::BSpline::position
 Foam::scalar Foam::BSpline::length() const
 {
     NotImplemented;
-    return 1.0;
+    return 1;
 }
 
 
diff --git a/src/mesh/blockMesh/blockEdges/BSplineEdge/BSpline.H b/src/mesh/blockMesh/blockEdges/BSplineEdge/BSpline.H
index e9da49bcdc..00f77df5b0 100644
--- a/src/mesh/blockMesh/blockEdges/BSplineEdge/BSpline.H
+++ b/src/mesh/blockMesh/blockEdges/BSplineEdge/BSpline.H
@@ -6,6 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
+    Copyright (C) 2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -77,21 +78,12 @@ class BSpline
 :
     public polyLine
 {
-    // Private Member Functions
-
-        //- No copy construct
-        BSpline(const BSpline&) = delete;
-
-        //- No copy assignment
-        void operator=(const BSpline&) = delete;
-
-
 public:
 
     // Constructors
 
         //- Construct from components
-        BSpline
+        explicit BSpline
         (
             const pointField& knots,
             const bool notImplementedClosed = false
@@ -100,15 +92,16 @@ public:
 
     // Member Functions
 
-        //- Return the point position corresponding to the curve parameter
+        //- The point position corresponding to the global curve parameter
         //  0 <= lambda <= 1
         point position(const scalar lambda) const;
 
-        //- Return the point position corresponding to the local parameter
-        //  0 <= lambda <= 1 on the given segment
+        //- The point position corresponding to the local lambda (0-1)
+        //- on the given segment
         point position(const label segment, const scalar lambda) const;
 
-        //- Return the length of the curve
+        //- The length of the curve
+        //  \note NotImplemented
         scalar length() const;
 };
 
diff --git a/src/mesh/blockMesh/blockEdges/BSplineEdge/BSplineEdge.C b/src/mesh/blockMesh/blockEdges/BSplineEdge/BSplineEdge.C
index 81c3ab24ee..af5e4d89ed 100644
--- a/src/mesh/blockMesh/blockEdges/BSplineEdge/BSplineEdge.C
+++ b/src/mesh/blockMesh/blockEdges/BSplineEdge/BSplineEdge.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2014-2016 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -27,9 +27,9 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "BSplineEdge.H"
+#include "polyLine.H"
 #include "addToRunTimeSelectionTable.H"
 
-
 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
 
 namespace Foam
@@ -59,7 +59,10 @@ Foam::blockEdges::BSplineEdge::BSplineEdge
 )
 :
     blockEdge(points, start, end),
-    BSpline(appendEndPoints(points, start, end, internalPoints))
+    BSpline
+    (
+        polyLine::concat(points[start_], internalPoints, points[end_])
+    )
 {}
 
 
@@ -73,13 +76,16 @@ Foam::blockEdges::BSplineEdge::BSplineEdge
 )
 :
     blockEdge(dict, index, points, is),
-    BSpline(appendEndPoints(points, start_, end_, pointField(is)))
+    BSpline
+    (
+        polyLine::concat(points[start_], pointField(is), points[end_])
+    )
 {
-    token t(is);
-    is.putBack(t);
+    token tok(is);
+    is.putBack(tok);
 
-    // discard unused start/end tangents
-    if (t == token::BEGIN_LIST)
+    // Discard unused start/end tangents
+    if (tok == token::BEGIN_LIST)
     {
         vector tangent0Ignored(is);
         vector tangent1Ignored(is);
diff --git a/src/mesh/blockMesh/blockEdges/BSplineEdge/BSplineEdge.H b/src/mesh/blockMesh/blockEdges/BSplineEdge/BSplineEdge.H
index e04434c593..68eefdab87 100644
--- a/src/mesh/blockMesh/blockEdges/BSplineEdge/BSplineEdge.H
+++ b/src/mesh/blockMesh/blockEdges/BSplineEdge/BSplineEdge.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2014-2016 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -77,20 +77,20 @@ public:
         //- Construct from components
         BSplineEdge
         (
-            const pointField&,
-            const label start,
-            const label end,
+            const pointField& points,   //!< Referenced point field
+            const label start,      //!< Start point in referenced point field
+            const label end,        //!< End point in referenced point field
             const pointField& internalPoints
         );
 
-        //- Construct from Istream, setting pointsList
+        //- Construct from Istream and point field.
         BSplineEdge
         (
             const dictionary& dict,
             const label index,
             const searchableSurfaces& geometry,
-            const pointField&,
-            Istream&
+            const pointField& points,   //!< Referenced point field
+            Istream& is
         );
 
 
@@ -100,11 +100,12 @@ public:
 
     // Member Functions
 
-        //- Return the point position corresponding to the curve parameter
+        //- The point position corresponding to the curve parameter
         //  0 <= lambda <= 1
         virtual point position(const scalar) const;
 
-        //- Return the length of the spline curve (not implemented)
+        //- The length of the spline curve
+        //  \note NotImplemented
         virtual scalar length() const;
 };
 
diff --git a/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.C b/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.C
index 7c614b8829..698fec2a8d 100644
--- a/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.C
+++ b/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.C
@@ -6,6 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
+    Copyright (C) 2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -43,10 +44,15 @@ namespace blockEdges
 
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
-Foam::coordSystem::cylindrical Foam::blockEdges::arcEdge::calcAngle()
+void Foam::blockEdges::arcEdge::calcFromMidPoint
+(
+    const point& p1,
+    const point& p3,
+    const point& p2
+)
 {
-    const vector a = p2_ - p1_;
-    const vector b = p3_ - p1_;
+    const vector a = p2 - p1;
+    const vector b = p3 - p1;
 
     // Find centre of arcEdge
     const scalar asqr = a & a;
@@ -55,7 +61,7 @@ Foam::coordSystem::cylindrical Foam::blockEdges::arcEdge::calcAngle()
 
     const scalar denom = asqr*bsqr - adotb*adotb;
 
-    if (mag(denom) < VSMALL)
+    if (mag(denom) < ROOTVSMALL)
     {
         FatalErrorInFunction
             << denom
@@ -64,44 +70,120 @@ Foam::coordSystem::cylindrical Foam::blockEdges::arcEdge::calcAngle()
 
     const scalar fact = 0.5*(bsqr - adotb)/denom;
 
-    point centre = 0.5*a + fact*((a ^ b) ^ a);
+    const point centre = p1 + 0.5*a + fact*((a ^ b) ^ a);
 
-    centre += p1_;
+    // Position vectors from centre
+    const vector r1(p1 - centre);
+    const vector r2(p2 - centre);
+    const vector r3(p3 - centre);
 
-    // Find position vectors w.r.t. the arcEdge centre
-    const vector r1(p1_ - centre);
-    const vector r2(p2_ - centre);
-    const vector r3(p3_ - centre);
+    const scalar mag1(mag(r1));
+    const scalar mag3(mag(r3));
 
-    // Find angle (in degrees)
-    angle_ = radToDeg(acos((r3 & r1)/(mag(r3) * mag(r1))));
+    vector arcAxis(r1 ^ r3);
+
+    // The radius from r1 and from r3 will be identical
+    radius_ = mag(r3);
+
+
+    // Determine the angle
+    angle_ = acos((r1 & r3)/(mag1*mag3));
 
     // Check if the vectors define an exterior or an interior arcEdge
     if (((r1 ^ r2) & (r1 ^ r3)) < 0.0)
     {
-        angle_ = 360.0 - angle_;
+        angle_ = constant::mathematical::twoPi - angle_;
     }
 
-    vector arcAxis;
-
-    if (angle_ <= 180.0)
+    if (angle_ <= constant::mathematical::pi)
     {
-        arcAxis = r1 ^ r3;
-
-        if (mag(arcAxis)/(mag(r1)*mag(r3)) < 0.001)
+        if (mag(arcAxis)/(mag1*mag3) < 0.001)
         {
             arcAxis = r1 ^ r2;
         }
     }
     else
     {
-        arcAxis = r3 ^ r1;
+        arcAxis = -arcAxis;
     }
 
-    radius_ = mag(r3);
+    // Corresponding local cylindrical coordinate system
+    cs_ = coordSystem::cylindrical(centre, arcAxis, r1);
+}
 
-    // The corresponding local cylindrical coordinate system (radians)
-    return coordSystem::cylindrical("arc", centre, arcAxis, r1);
+
+void Foam::blockEdges::arcEdge::calcFromCentre
+(
+    const point& p1,
+    const point& p3,
+    const point& centre,
+    bool adjustCentre,
+    scalar rMultiplier
+)
+{
+    // Position vectors from centre
+    const vector r1(p1 - centre);
+    const vector r3(p3 - centre);
+
+    const scalar mag1(mag(r1));
+    const scalar mag3(mag(r3));
+
+    const vector chord(p3 - p1);
+
+    const vector arcAxis(r1 ^ r3);
+
+    // The average radius
+    radius_ = 0.5*(mag1 + mag3);
+
+    // The included angle
+    angle_ = acos((r1 & r3)/(mag1*mag3));
+
+    // TODO? check for 180 degrees (co-linear points)?
+
+    bool needsAdjust = false;
+
+    if (adjustCentre)
+    {
+        needsAdjust = !equal(mag1, mag3);
+
+        if (!equal(rMultiplier, 1))
+        {
+            // The min radius is constrained by the chord,
+            // otherwise bad things will happen.
+
+            needsAdjust = true;
+            radius_ *= rMultiplier;
+            radius_ = max(radius_, (1.001*0.5*mag(chord)));
+        }
+    }
+
+    if (needsAdjust)
+    {
+        // The centre is not equidistant to p1 and p3.
+        // Use the chord and the arcAxis to determine the vector to
+        // the midpoint of the chord and adjust the centre along this
+        // line.
+
+        const point newCentre =
+        (
+            (0.5 * (p3 + p1))                   // mid-chord point
+          + sqrt(sqr(radius_) - 0.25 * magSqr(chord))
+          * normalised(arcAxis ^ chord)         // mid-chord -> centre
+        );
+
+        //// Info<< nl << "Adjust centre. r1=" << mag1 << " r3=" << mag3
+        ////     << " radius=" << radius_ << nl
+        ////     << "angle=" << radToDeg(angle_) << ' '
+        ////     << coordSystem::cylindrical(centre, arcAxis, r1) << nl;
+
+        // Recalculate - do attempt to readjust
+        calcFromCentre(p1, p3, newCentre, false);
+    }
+    else
+    {
+        // Corresponding local cylindrical coordinate system
+        cs_ = coordSystem::cylindrical(centre, arcAxis, r1);
+    }
 }
 
 
@@ -110,17 +192,35 @@ Foam::coordSystem::cylindrical Foam::blockEdges::arcEdge::calcAngle()
 Foam::blockEdges::arcEdge::arcEdge
 (
     const pointField& points,
+    const point& origin,
     const label start,
-    const label end,
-    const point& pMid
+    const label end
 )
 :
     blockEdge(points, start, end),
-    p1_(points_[start_]),
-    p2_(pMid),
-    p3_(points_[end_]),
-    cs_(calcAngle())
-{}
+    radius_(0),
+    angle_(0),
+    cs_()
+{
+    calcFromCentre(points[start_], points[end_], origin);
+}
+
+
+Foam::blockEdges::arcEdge::arcEdge
+(
+    const pointField& points,
+    const label start,
+    const label end,
+    const point& midPoint
+)
+:
+    blockEdge(points, start, end),
+    radius_(0),
+    angle_(0),
+    cs_()
+{
+    calcFromMidPoint(points[start_], points[end_], midPoint);
+}
 
 
 Foam::blockEdges::arcEdge::arcEdge
@@ -133,41 +233,82 @@ Foam::blockEdges::arcEdge::arcEdge
 )
 :
     blockEdge(dict, index, points, is),
-    p1_(points_[start_]),
-    p2_(is),
-    p3_(points_[end_]),
-    cs_(calcAngle())
-{}
+    radius_(0),
+    angle_(0),
+    cs_()
+{
+    point p;
+
+    token tok(is);
+    if (tok.isWord())
+    {
+        // Can be
+        //   - origin (0 0 0)
+        //   - origin 1.2 (0 0 0)
+
+        scalar rMultiplier = 1;
+
+        is >> tok;
+        if (tok.isNumber())
+        {
+            rMultiplier = tok.number();
+        }
+        else
+        {
+            is.putBack(tok);
+        }
+
+        is >> p;  // The origin (centre)
+
+        calcFromCentre(points_[start_], points_[end_], p, true, rMultiplier);
+    }
+    else
+    {
+        is.putBack(tok);
+
+        is >> p;  // A mid-point
+
+        calcFromMidPoint(points_[start_], points_[end_], p);
+    }
+
+    // Debug information
+    #if 0
+    Info<< "arc " << start_ << ' ' << end_
+        << ' ' << position(0.5) << ' ' << cs_
+        // << " radius=" << radius_ << " angle=" << radToDeg(angle_)
+        << nl;
+    #endif
+}
 
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
 Foam::point Foam::blockEdges::arcEdge::position(const scalar lambda) const
 {
+    #ifdef FULLDEBUG
     if (lambda < -SMALL || lambda > 1 + SMALL)
     {
-        FatalErrorInFunction
-            << "Parameter out of range, lambda = " << lambda
-            << abort(FatalError);
+        WarningInFunction
+            << "Parameter out of range, lambda = " << lambda << nl;
     }
+    #endif
 
     if (lambda < SMALL)
     {
-        return p1_;
+        return points_[start_];
     }
-    else if (lambda > 1 - SMALL)
+    else if (lambda >= 1 - SMALL)
     {
-        return p3_;
+        return points_[end_];
     }
 
-    // The angle is degrees, the coordinate system in radians
-    return cs_.globalPosition(vector(radius_, degToRad(lambda*angle_), 0));
+    return cs_.globalPosition(vector(radius_, (lambda*angle_), 0));
 }
 
 
-Foam::scalar Foam::blockEdges::arcEdge::length() const
+Foam::scalar Foam::blockEdges::arcEdge::length() const noexcept
 {
-    return degToRad(radius_*angle_);
+    return (radius_*angle_);
 }
 
 
diff --git a/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.H b/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.H
index 8db6fcaa97..459b6a70f0 100644
--- a/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.H
+++ b/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2017 OpenCFD Ltd.
+    Copyright (C) 2017-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -28,7 +28,32 @@ Class
     Foam::blockEdges::arcEdge
 
 Description
-    Defines the arcEdge of a circle in terms of 3 points on its circumference
+    A blockEdge defined as an arc of a circle.
+
+    The arc is normally defined by its endpoints and a point on
+    its circumference, typically a midpoint. For example,
+    \verbatim
+    points ((1 0 0) (0 1 0));
+
+    arc 0 1 (0.707107 0.707107 0);
+    \endverbatim
+    The arc can enclose an angle greater than 0 and less than 360 degrees.
+
+    The arc will frequently enclose an angle less than 180 degrees.
+    For the case, it is possible to define the arc by its endpoints and its
+    centre (origin) point. For example,
+    \verbatim
+    arc 0 1 origin (0 0 0);
+    \endverbatim
+    When defined in the way, any discrepancy in the arc radius for the
+    endpoints is resolved by adjusting the origin to ensure that the average
+    radius is satisfied.
+
+    It is also possible to define a \em flatness factor as a multiplier of
+    the calculated radius. For example,
+    \verbatim
+    arc 0 1 origin 1.1 (0 0 0);
+    \endverbatim
 
 SourceFiles
     arcEdge.C
@@ -56,26 +81,41 @@ class arcEdge
 :
     public blockEdge
 {
-    // Private data
-
-        // Begin, mid, end points
-        point p1_, p2_, p3_;
-
-        //- The arc angle (in degrees)
-        scalar angle_;
+    // Private Data
 
         //- The arc radius
         scalar radius_;
 
+        //- The arc angle (radians)
+        scalar angle_;
+
         //- The local cylindrical coordinate system
         coordSystem::cylindrical cs_;
 
 
     // Private Member Functions
 
-        //- Calculate the angle, radius and axis
-        //  \return the cylindrical coordinate system
-        coordSystem::cylindrical calcAngle();
+        //- Calculate angle, radius, cylindrical coordinate system
+        //- from end points and the given point on the circumference
+        void calcFromMidPoint
+        (
+            const point& p1,        //!< Start point
+            const point& p3,        //!< End point
+            const point& p2         //!< Point on circumference
+        );
+
+        //- Calculate angle, radius, cylindrical coordinate system
+        //- from end points and the given origin.
+        //  Optionally adjust centre to accommodate deviations in the
+        //  effective radius to the end-points
+        void calcFromCentre
+        (
+            const point& p1,        //!< Start point
+            const point& p3,        //!< End point
+            const point& centre,    //!< Centre
+            bool adjustCentre = false,  //!< Adjust centre
+            scalar rMultiplier = 1      //!< Adjust radius by this factor
+        );
 
         //- No copy construct
         arcEdge(const arcEdge&) = delete;
@@ -92,23 +132,34 @@ public:
 
     // Constructors
 
-        //- Construct from components
+        //- Construct from components, given the origin of the circle
         arcEdge
         (
-            const pointField& points,
-            const label start,
-            const label end,
-            const point& pMid
+            const pointField& points,   //!< Referenced point field
+            const point& origin,    //!< The origin of the circle
+            const label start,      //!< Start point in referenced point field
+            const label end         //!< End point in referenced point field
         );
 
-        //- Construct from Istream setting pointsList
+        //- Construct from components, using a point on the circumference
+        arcEdge
+        (
+            const pointField& points,   //!< Referenced point field
+            const label start,      //!< Start point in referenced point field
+            const label end,        //!< End point in referenced point field
+            const point& midPoint   //!< A point on the circumference
+        );
+
+        //- Construct from Istream and point field.
+        //  The Istream can specify either a point on the circumference,
+        //  or with a tag to specify the origin.
         arcEdge
         (
             const dictionary& dict,
             const label index,
-            const searchableSurfaces& geometry,
-            const pointField& points,
-            Istream&
+            const searchableSurfaces& geometry, // unsed
+            const pointField& points,   //!< Referenced point field
+            Istream& is
         );
 
 
@@ -122,7 +173,7 @@ public:
         point position(const scalar lambda) const;
 
         //- The length of the curve
-        scalar length() const;
+        scalar length() const noexcept;
 };
 
 
diff --git a/src/mesh/blockMesh/blockEdges/bezier/bezier.C b/src/mesh/blockMesh/blockEdges/bezier/bezier.C
index b1b884d32a..cac55d1ba3 100644
--- a/src/mesh/blockMesh/blockEdges/bezier/bezier.C
+++ b/src/mesh/blockMesh/blockEdges/bezier/bezier.C
@@ -26,6 +26,7 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "bezier.H"
+#include "polyLine.H"
 #include "SubList.H"
 #include "addToRunTimeSelectionTable.H"
 
@@ -66,7 +67,10 @@ Foam::blockEdges::bezier::bezier
 )
 :
     blockEdge(dict, index, points, is),
-    control_(appendEndPoints(points, start_, end_, pointField(is)))
+    control_
+    (
+        polyLine::concat(points[start_], pointField(is), points[end_])
+    )
 {}
 
 
@@ -94,7 +98,7 @@ Foam::point Foam::blockEdges::bezier::position(const scalar lambda) const
 Foam::scalar Foam::blockEdges::bezier::length() const
 {
     NotImplemented;
-    return 1.0;
+    return 1;
 }
 
 
diff --git a/src/mesh/blockMesh/blockEdges/bezier/bezier.H b/src/mesh/blockMesh/blockEdges/bezier/bezier.H
index b1f14dab27..5feaeb4139 100644
--- a/src/mesh/blockMesh/blockEdges/bezier/bezier.H
+++ b/src/mesh/blockMesh/blockEdges/bezier/bezier.H
@@ -63,7 +63,7 @@ class bezier
 :
     public blockEdge
 {
-private:
+    // Private Data
 
         //- Control points
         pointField control_;
@@ -89,20 +89,20 @@ public:
         //- Construct from components
         bezier
         (
-            const pointField& points,
-            const label start,
-            const label end,
-            const pointField& control
+            const pointField& points,   //!< Referenced point field
+            const label start,      //!< Start point in referenced point field
+            const label end,        //!< End point in referenced point field
+            const pointField& control   //!< The control points
         );
 
-        //- Construct from Istream
+        //- Construct from Istream and point field.
         bezier
         (
             const dictionary& dict,
             const label index,
             const searchableSurfaces& geometry,
-            const pointField&,
-            Istream&
+            const pointField& points,   //!< Referenced point field
+            Istream& is
         );
 
 
@@ -117,6 +117,7 @@ public:
         point position(const scalar lambda) const;
 
         //- Return the length of the curve
+        //  \not NotImplemented
         scalar length() const;
 };
 
diff --git a/src/mesh/blockMesh/blockEdges/blockEdge/blockEdge.C b/src/mesh/blockMesh/blockEdges/blockEdge/blockEdge.C
index 01621e08c8..a49880b121 100644
--- a/src/mesh/blockMesh/blockEdges/blockEdge/blockEdge.C
+++ b/src/mesh/blockMesh/blockEdges/blockEdge/blockEdge.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -28,6 +28,7 @@ License
 
 #include "blockEdge.H"
 #include "blockVertex.H"
+#include "polyLine.H"
 
 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
 
@@ -104,32 +105,22 @@ Foam::autoPtr<Foam::blockEdge> Foam::blockEdge::New
 }
 
 
-// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
+// * * * * * * * * * * * * * Static Member Functions * * * * * * * * * * * * //
 
 Foam::pointField Foam::blockEdge::appendEndPoints
 (
-    const pointField& points,
+    const pointField& pts,
     const label start,
     const label end,
-    const pointField& otherKnots
+    const pointField& intermediate
 )
 {
-    pointField allKnots(otherKnots.size() + 2);
-
-    // Start/end knots
-    allKnots[0] = points[start];
-    allKnots[otherKnots.size() + 1] = points[end];
-
-    // Intermediate knots
-    forAll(otherKnots, knotI)
-    {
-        allKnots[knotI+1] = otherKnots[knotI];
-    }
-
-    return allKnots;
+    return pointField(polyLine::concat(pts[start], intermediate, pts[end]));
 }
 
 
+// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
+
 Foam::tmp<Foam::pointField>
 Foam::blockEdge::position(const scalarList& lambdas) const
 {
diff --git a/src/mesh/blockMesh/blockEdges/blockEdge/blockEdge.H b/src/mesh/blockMesh/blockEdges/blockEdge/blockEdge.H
index 30d09f00f1..dd48cba834 100644
--- a/src/mesh/blockMesh/blockEdges/blockEdge/blockEdge.H
+++ b/src/mesh/blockMesh/blockEdges/blockEdge/blockEdge.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -24,6 +24,12 @@ License
     You should have received a copy of the GNU General Public License
     along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
 
+Namespace
+    Foam::blockEdges
+
+Description
+    A namespace for various blockEdge types.
+
 Class
     Foam::blockEdge
 
@@ -46,13 +52,10 @@ SourceFiles
 namespace Foam
 {
 
-// Forward declaration of friend functions and operators
-
+// Forward Declarations
 class blockEdge;
-
 Ostream& operator<<(Ostream&, const blockEdge&);
 
-
 /*---------------------------------------------------------------------------*\
                          Class blockEdge Declaration
 \*---------------------------------------------------------------------------*/
@@ -61,24 +64,29 @@ class blockEdge
 {
 protected:
 
-    // Protected data
+    // Protected Data
 
+        //- The referenced point field
         const pointField& points_;
 
+        //- Index of the start point
         const label start_;
+
+        //- Index of the end point
         const label end_;
 
 
     // Protected Member Functions
 
         //- Return a complete point field by appending the start/end points
-        //  to the given list
+        //- to the given list
+        //  \deprecated(2020-10) use polyLine::concat
         static pointField appendEndPoints
         (
-            const pointField&,
-            const label start,
-            const label end,
-            const pointField& otherKnots
+            const pointField& points,   //!< Referenced point field
+            const label start,      //!< Start point in referenced point field
+            const label end,        //!< End point in referenced point field
+            const pointField& intermediate  //!< Intermediate points (knots)
         );
 
 
@@ -110,18 +118,18 @@ public:
         //- Construct from components
         blockEdge
         (
-            const pointField& points,
-            const label start,
-            const label end
+            const pointField& points,   //!< Referenced point field
+            const label start,      //!< Start point in referenced point field
+            const label end         //!< End point in referenced point field
         );
 
-        //- Construct from Istream setting pointsList
+        //- Construct from Istream and point field.
         blockEdge
         (
             const dictionary& dict,
             const label index,
-            const pointField&,
-            Istream&
+            const pointField& points,   //!< Referenced point field
+            Istream& is
         );
 
         //- Clone function
@@ -133,8 +141,8 @@ public:
             const dictionary& dict,
             const label index,
             const searchableSurfaces& geometry,
-            const pointField&,
-            Istream&
+            const pointField& points,
+            Istream& is
         );
 
         //- Class used for the read-construction of
@@ -174,10 +182,10 @@ public:
 
     // Member Functions
 
-        //- Return label of start point
+        //- Index of start point
         inline label start() const;
 
-        //- Return label of end point
+        //- Index of end point
         inline label end() const;
 
         //- Compare the given start and end points with this curve
@@ -201,22 +209,22 @@ public:
         //  - -1: same edge, but different orientation
         inline int compare(const label start, const label end) const;
 
-        //- Return the point position corresponding to the curve parameter
+        //- The point position corresponding to the curve parameter
         //  0 <= lambda <= 1
         virtual point position(const scalar) const = 0;
 
-        //- Return the point positions corresponding to the curve parameters
+        //- The point positions corresponding to the curve parameters
         //  0 <= lambda <= 1
         virtual tmp<pointField> position(const scalarList&) const;
 
-        //- Return the length of the curve
+        //- The length of the curve
         virtual scalar length() const = 0;
 
         //- Write edge with variable backsubstitution
         void write(Ostream&, const dictionary&) const;
 
 
-    // Ostream operator
+    // Ostream Operator
 
         friend Ostream& operator<<(Ostream&, const blockEdge&);
 };
diff --git a/src/mesh/blockMesh/blockEdges/blockEdge/blockEdgeI.H b/src/mesh/blockMesh/blockEdges/blockEdge/blockEdgeI.H
index a781be5f96..6aab3064f0 100644
--- a/src/mesh/blockMesh/blockEdges/blockEdge/blockEdgeI.H
+++ b/src/mesh/blockMesh/blockEdges/blockEdge/blockEdgeI.H
@@ -49,10 +49,8 @@ inline int Foam::blockEdge::compare(const label start, const label end) const
     {
         return -1;
     }
-    else
-    {
-        return 0;
-    }
+
+    return 0;
 }
 
 
diff --git a/src/mesh/blockMesh/blockEdges/lineDivide/lineDivide.H b/src/mesh/blockMesh/blockEdges/lineDivide/lineDivide.H
index acd035602d..1c58386a0f 100644
--- a/src/mesh/blockMesh/blockEdges/lineDivide/lineDivide.H
+++ b/src/mesh/blockMesh/blockEdges/lineDivide/lineDivide.H
@@ -6,6 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
+    Copyright (C) 2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -46,6 +47,7 @@ SourceFiles
 namespace Foam
 {
 
+// Forward Declarations
 class blockEdge;
 
 /*---------------------------------------------------------------------------*\
@@ -54,7 +56,7 @@ class blockEdge;
 
 class lineDivide
 {
-    // Private data
+    // Private Data
 
         pointField points_;
 
@@ -67,18 +69,18 @@ public:
         //- Construct from components
         lineDivide
         (
-            const blockEdge&,
-            const label ndiv,
+            const blockEdge& cedge,
+            const label nDiv,
             const gradingDescriptors& gd = gradingDescriptors()
         );
 
 
     // Member Functions
 
-        //- Return the points
+        //- The points
         const pointField& points() const;
 
-        //- Return the list of lambda values
+        //- The list of lambda values
         const scalarList& lambdaDivisions() const;
 };
 
diff --git a/src/mesh/blockMesh/blockEdges/lineEdge/lineEdge.C b/src/mesh/blockMesh/blockEdges/lineEdge/lineEdge.C
index 713d9bec15..203f16220a 100644
--- a/src/mesh/blockMesh/blockEdges/lineEdge/lineEdge.C
+++ b/src/mesh/blockMesh/blockEdges/lineEdge/lineEdge.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -71,11 +71,21 @@ Foam::blockEdges::lineEdge::lineEdge
 
 Foam::point Foam::blockEdges::lineEdge::position(const scalar lambda) const
 {
-    if (lambda < -SMALL || lambda > 1+SMALL)
+    #ifdef FULLDEBUG
+    if (lambda < -SMALL || lambda > 1 + SMALL)
     {
-        FatalErrorInFunction
-            << "Parameter out of range, lambda = " << lambda
-            << abort(FatalError);
+        WarningInFunction
+            << "Parameter out of range, lambda = " << lambda << nl;
+    }
+    #endif
+
+    if (lambda < SMALL)
+    {
+        return points_[start_];
+    }
+    else if (lambda >= 1 - SMALL)
+    {
+        return points_[end_];
     }
 
     return points_[start_] + lambda * (points_[end_] - points_[start_]);
diff --git a/src/mesh/blockMesh/blockEdges/lineEdge/lineEdge.H b/src/mesh/blockMesh/blockEdges/lineEdge/lineEdge.H
index b44b3ab14a..1bbc9d67ce 100644
--- a/src/mesh/blockMesh/blockEdges/lineEdge/lineEdge.H
+++ b/src/mesh/blockMesh/blockEdges/lineEdge/lineEdge.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -51,12 +51,10 @@ namespace blockEdges
                           Class lineEdge Declaration
 \*---------------------------------------------------------------------------*/
 
-
 class lineEdge
 :
     public blockEdge
 {
-
 public:
 
     //- Runtime type information
@@ -66,15 +64,20 @@ public:
     // Constructors
 
         //- Construct from components
-        lineEdge(const pointField&, const label start, const label end);
+        lineEdge
+        (
+            const pointField& points,   //!< Referenced point field
+            const label start,      //!< Start point in referenced point field
+            const label end         //!< End point in referenced point field
+        );
 
-        //- Construct from Istream with a pointField
+        //- Construct from Istream and point field.
         lineEdge
         (
             const dictionary& dict,
             const label index,
             const searchableSurfaces& geometry,
-            const pointField&,
+            const pointField& points,   //!< Referenced point field
             Istream& is
         );
 
@@ -85,11 +88,11 @@ public:
 
     // Member Functions
 
-        //- Return the point position corresponding to the curve parameter
+        //- The point position corresponding to the curve parameter
         //  0 <= lambda <= 1
         point position(const scalar) const;
 
-        //- Return the length of the curve
+        //- The length of the curve
         scalar length() const;
 };
 
diff --git a/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLine.C b/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLine.C
index 0703696698..42f6a74db6 100644
--- a/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLine.C
+++ b/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLine.C
@@ -6,6 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
+    Copyright (C) 2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -26,16 +27,41 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "polyLine.H"
+#include "SubList.H"
+
+// * * * * * * * * * * * * * Static Member Functions * * * * * * * * * * * * //
+
+Foam::tmp<Foam::pointField> Foam::polyLine::concat
+(
+    const point& p0,
+    const pointField& intermediate,
+    const point& p1
+)
+{
+    auto tresult = tmp<pointField>::New(intermediate.size() + 2);
+    auto& result = tresult.ref();
+
+    // Intermediate points (knots)
+    SubList<point>(result, intermediate.size(), 1) = intermediate;
+
+    // Start/end points (knots)
+    result.first() = p0;
+    result.last() = p1;
+
+    return tresult;
+}
+
 
 // * * * * * * * * * * * * Protected Member Functions  * * * * * * * * * * * //
 
 void Foam::polyLine::calcParam()
 {
-    param_.setSize(points_.size());
+    lineLength_ = 0;
+    param_.resize(points_.size());
 
     if (param_.size())
     {
-        param_[0] = 0.0;
+        param_[0] = 0;
 
         for (label i=1; i < param_.size(); i++)
         {
@@ -48,23 +74,34 @@ void Foam::polyLine::calcParam()
         {
             param_[i] /= lineLength_;
         }
-        param_.last() = 1.0;
-    }
-    else
-    {
-        lineLength_ = 0.0;
+        param_.last() = 1;
     }
 }
 
 
-
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
 Foam::polyLine::polyLine(const pointField& ps, const bool)
 :
     points_(ps),
-    lineLength_(0.0),
-    param_(0)
+    lineLength_(0),
+    param_()
+{
+    calcParam();
+}
+
+
+Foam::polyLine::polyLine
+(
+    const point& start,
+    const pointField& intermediate,
+    const point& end,
+    const bool
+)
+:
+    points_(polyLine::concat(start, intermediate, end)),
+    lineLength_(0),
+    param_()
 {
     calcParam();
 }
@@ -101,19 +138,20 @@ Foam::label Foam::polyLine::localParameter(scalar& lambda) const
     // Search table of cumulative distances to find which line-segment
     // we are on.
     // Check the upper bound.
+    // Too small to bother with a binary search...
 
-    label segmentI = 1;
-    while (param_[segmentI] < lambda)
+    label segment = 1;
+    while (param_[segment] < lambda)
     {
-        segmentI++;
+        ++segment;
     }
-    segmentI--;   // We want the corresponding lower bound
+    --segment;   // We want the corresponding lower bound
 
     // The local parameter [0-1] on this line segment
     lambda =
-        (lambda - param_[segmentI])/(param_[segmentI+1] - param_[segmentI]);
+        (lambda - param_[segment])/(param_[segment+1] - param_[segment]);
 
-    return segmentI;
+    return segment;
 }
 
 
@@ -151,8 +189,8 @@ Foam::point Foam::polyLine::position
         return points_.last();
     }
 
-    const point& p0 = points()[segment];
-    const point& p1 = points()[segment+1];
+    const point& p0 = points_[segment];
+    const point& p1 = points_[segment+1];
 
     // Special cases - no calculation needed
     if (mu <= 0.0)
@@ -163,11 +201,9 @@ Foam::point Foam::polyLine::position
     {
         return p1;
     }
-    else
-    {
-        // Linear interpolation
-        return points_[segment] + mu*(p1 - p0);
-    }
+
+    // Linear interpolation
+    return points_[segment] + mu*(p1 - p0);
 }
 
 
diff --git a/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLine.H b/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLine.H
index e720812201..b7bf40e8af 100644
--- a/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLine.H
+++ b/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLine.H
@@ -6,6 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
+    Copyright (C) 2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -52,26 +53,16 @@ namespace Foam
                           Class polyLine Declaration
 \*---------------------------------------------------------------------------*/
 
-
 class polyLine
 {
-    // Private Member Functions
-
-        //- No copy construct
-        polyLine(const polyLine&) = delete;
-
-        //- No copy assignment
-        void operator=(const polyLine&) = delete;
-
-
 protected:
 
-    // Protected data
+    // Protected Data
 
         //- The control points or ends of each segments
         pointField points_;
 
-        //- The real line length
+        //- The real (total) line length
         scalar lineLength_;
 
         //- The rational (0-1) cumulative parameter value for each point
@@ -81,11 +72,11 @@ protected:
     // Protected Member Functions
 
         //- Precalculate the rational cumulative parameter value
-        //  and the line-length
+        //- and the line-length
         void calcParam();
 
         //- Return the line segment and the local parameter [0..1]
-        //  corresponding to the global lambda [0..1]
+        //- corresponding to the global lambda [0..1]
         label localParameter(scalar& lambda) const;
 
 
@@ -94,30 +85,50 @@ public:
     // Constructors
 
         //- Construct from components
+        explicit polyLine
+        (
+            const pointField& points,   //!< The poly-line points
+            const bool notImplementedClosed = false
+        );
+
+        //- Construct from begin, intermediate, end points
         polyLine
         (
-            const pointField&,
+            const point& start,             //!< The start point
+            const pointField& intermediate, //!< The intermediate points
+            const point& end,               //!< The end point
             const bool notImplementedClosed = false
         );
 
 
+    // Static Member Functions
+
+        //- Concatenate begin, intermediate and end points
+        static tmp<pointField> concat
+        (
+            const point& start,             //!< The start point
+            const pointField& intermediate, //!< The intermediate points
+            const point& end                //!< The end point
+        );
+
+
     // Member Functions
 
         //- Return const-access to the control-points
         const pointField& points() const;
 
-        //- Return the number of line segments
+        //- The number of line segments
         label nSegments() const;
 
-        //- Return the point position corresponding to the curve parameter
+        //- The point position corresponding to the curve parameter
         //  0 <= lambda <= 1
         point position(const scalar) const;
 
-        //- Return the point position corresponding to the local parameter
+        //- The point position corresponding to the local parameter
         //  0 <= lambda <= 1 on the given segment
         point position(const label segment, const scalar) const;
 
-        //- Return the length of the curve
+        //- The length of the curve
         scalar length() const;
 };
 
diff --git a/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLineEdge.C b/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLineEdge.C
index c350a82322..9a1b014fee 100644
--- a/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLineEdge.C
+++ b/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLineEdge.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -48,11 +48,11 @@ Foam::blockEdges::polyLineEdge::polyLineEdge
     const pointField& ps,
     const label start,
     const label end,
-    const pointField& otherPoints
+    const pointField& intermediate
 )
 :
     blockEdge(ps, start, end),
-    polyLine(appendEndPoints(ps, start_, end_, otherPoints))
+    polyLine(ps[start_], intermediate, ps[end_])
 {}
 
 
@@ -66,7 +66,7 @@ Foam::blockEdges::polyLineEdge::polyLineEdge
 )
 :
     blockEdge(dict, index, ps, is),
-    polyLine(appendEndPoints(ps, start_, end_, pointField(is)))
+    polyLine(ps[start_], pointField(is), ps[end_])
 {}
 
 
diff --git a/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLineEdge.H b/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLineEdge.H
index 9eb6690143..bcce9c738e 100644
--- a/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLineEdge.H
+++ b/src/mesh/blockMesh/blockEdges/polyLineEdge/polyLineEdge.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -77,19 +77,19 @@ public:
         //- Construct from components
         polyLineEdge
         (
-            const pointField&,
-            const label start,
-            const label end,
-            const pointField& otherPoints
+            const pointField& points,       //!< Referenced point field
+            const label start,      //!< Start point in referenced point field
+            const label end,        //!< End point in referenced point field
+            const pointField& intermediate  //!< The intermediate points
         );
 
-        //- Construct from Istream
+        //- Construct from Istream and point field.
         polyLineEdge
         (
             const dictionary& dict,
             const label index,
             const searchableSurfaces& geometry,
-            const pointField&,
+            const pointField& points,       //!< Referenced point field
             Istream& is
         );
 
@@ -100,11 +100,11 @@ public:
 
     // Member Functions
 
-        //- Return the point position corresponding to the curve parameter
+        //- The point position corresponding to the curve parameter
         //  0 <= lambda <= 1
         point position(const scalar lambda) const;
 
-        //- Return the length of the curve
+        //- The length of the curve
         scalar length() const;
 };
 
diff --git a/src/mesh/blockMesh/blockEdges/projectCurveEdge/projectCurveEdge.C b/src/mesh/blockMesh/blockEdges/projectCurveEdge/projectCurveEdge.C
index 08fa1186a5..f6f182207a 100644
--- a/src/mesh/blockMesh/blockEdges/projectCurveEdge/projectCurveEdge.C
+++ b/src/mesh/blockMesh/blockEdges/projectCurveEdge/projectCurveEdge.C
@@ -59,7 +59,7 @@ Foam::projectCurveEdge::projectCurveEdge
     geometry_(geometry)
 {
     wordList names(is);
-    surfaces_.setSize(names.size());
+    surfaces_.resize(names.size());
     forAll(names, i)
     {
         surfaces_[i] = geometry_.findSurfaceID(names[i]);
@@ -83,6 +83,14 @@ Foam::projectCurveEdge::projectCurveEdge
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
+Foam::point
+Foam::projectCurveEdge::position(const scalar) const
+{
+    NotImplemented;
+    return point::max;
+}
+
+
 Foam::tmp<Foam::pointField>
 Foam::projectCurveEdge::position(const scalarList& lambdas) const
 {
@@ -101,8 +109,8 @@ Foam::projectCurveEdge::position(const scalarList& lambdas) const
     }
 
 
-    tmp<pointField> tpoints(new pointField(lambdas.size()));
-    pointField& points = tpoints.ref();
+    auto tpoints = tmp<pointField>::New(lambdas.size());
+    auto& points = tpoints.ref();
 
     const point& startPt = points_[start_];
     const point& endPt = points_[end_];
@@ -149,10 +157,11 @@ Foam::projectCurveEdge::position(const scalarList& lambdas) const
 
 
     // Upper limit for number of iterations
-    const label maxIter = 10;
+    constexpr label maxIter = 10;
+
     // Residual tolerance
-    const scalar relTol = 0.1;
-    const scalar absTol = 1e-4;
+    constexpr scalar relTol = 0.1;
+    constexpr scalar absTol = 1e-4;
 
     scalar initialResidual = 0.0;
 
@@ -258,4 +267,11 @@ Foam::projectCurveEdge::position(const scalarList& lambdas) const
 }
 
 
+Foam::scalar Foam::projectCurveEdge::length() const
+{
+    NotImplemented;
+    return 1;
+}
+
+
 // ************************************************************************* //
diff --git a/src/mesh/blockMesh/blockEdges/projectCurveEdge/projectCurveEdge.H b/src/mesh/blockMesh/blockEdges/projectCurveEdge/projectCurveEdge.H
index 1e6ca665ee..7f939b9d58 100644
--- a/src/mesh/blockMesh/blockEdges/projectCurveEdge/projectCurveEdge.H
+++ b/src/mesh/blockMesh/blockEdges/projectCurveEdge/projectCurveEdge.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2016 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -46,6 +46,7 @@ SourceFiles
 namespace Foam
 {
 
+// Forward Declarations
 class pointConstraint;
 
 /*---------------------------------------------------------------------------*\
@@ -81,13 +82,13 @@ public:
 
     // Constructors
 
-        //- Construct from Istream setting pointsList
+        //- Construct from Istream and point field.
         projectCurveEdge
         (
             const dictionary& dict,
             const label index,
             const searchableSurfaces& geometry,
-            const pointField& points,
+            const pointField& points,   //!< Referenced point field
             Istream& is
         );
 
@@ -98,24 +99,18 @@ public:
 
     // Member Functions
 
-        //- Return the point positions corresponding to the curve parameters
+        //- The point position corresponding to the curve parameter
         //  0 <= lambda <= 1
-        virtual point position(const scalar) const
-        {
-            NotImplemented;
-            return point::max;
-        }
+        //  \note NotImplemented
+        virtual point position(const scalar) const;
 
-        //- Return the point positions corresponding to the curve parameters
+        //- The point positions corresponding to the curve parameters
         //  0 <= lambda <= 1
         virtual tmp<pointField> position(const scalarList&) const;
 
-        //- Return the length of the curve
-        virtual scalar length() const
-        {
-            NotImplemented;
-            return 1;
-        }
+        //- The length of the curve
+        //  \note NotImplemented
+        virtual scalar length() const;
 };
 
 
diff --git a/src/mesh/blockMesh/blockEdges/projectEdge/projectEdge.C b/src/mesh/blockMesh/blockEdges/projectEdge/projectEdge.C
index 8259bc77ed..16b99b1bbf 100644
--- a/src/mesh/blockMesh/blockEdges/projectEdge/projectEdge.C
+++ b/src/mesh/blockMesh/blockEdges/projectEdge/projectEdge.C
@@ -26,13 +26,12 @@ License
 
 \*---------------------------------------------------------------------------*/
 
-#include "searchableSurfacesQueries.H"
 #include "projectEdge.H"
-#include "unitConversion.H"
-#include "addToRunTimeSelectionTable.H"
 #include "pointConstraint.H"
+#include "searchableSurfacesQueries.H"
 #include "OBJstream.H"
 #include "linearInterpolationWeights.H"
+#include "addToRunTimeSelectionTable.H"
 
 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
 
@@ -146,8 +145,8 @@ Foam::projectEdge::position(const scalarList& lambdas) const
     }
 
 
-    tmp<pointField> tpoints(new pointField(lambdas.size()));
-    pointField& points = tpoints.ref();
+    auto tpoints = tmp<pointField>::New(lambdas.size());
+    auto& points = tpoints.ref();
 
     const point& startPt = points_[start_];
     const point& endPt = points_[end_];
@@ -161,10 +160,11 @@ Foam::projectEdge::position(const scalarList& lambdas) const
 
 
     // Upper limit for number of iterations
-    const label maxIter = 10;
+    constexpr label maxIter = 10;
+
     // Residual tolerance
-    const scalar relTol = 0.1;
-    const scalar absTol = 1e-4;
+    constexpr scalar relTol = 0.1;
+    constexpr scalar absTol = 1e-4;
 
     scalar initialResidual = 0.0;
 
@@ -270,4 +270,11 @@ Foam::projectEdge::position(const scalarList& lambdas) const
 }
 
 
+Foam::scalar Foam::projectEdge::length() const
+{
+    NotImplemented;
+    return 1;
+}
+
+
 // ************************************************************************* //
diff --git a/src/mesh/blockMesh/blockEdges/projectEdge/projectEdge.H b/src/mesh/blockMesh/blockEdges/projectEdge/projectEdge.H
index 1c3d180d7f..44c9d143d8 100644
--- a/src/mesh/blockMesh/blockEdges/projectEdge/projectEdge.H
+++ b/src/mesh/blockMesh/blockEdges/projectEdge/projectEdge.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2016 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -46,6 +46,7 @@ SourceFiles
 namespace Foam
 {
 
+// Forward Declarations
 class pointConstraint;
 
 /*---------------------------------------------------------------------------*\
@@ -84,13 +85,13 @@ public:
 
     // Constructors
 
-        //- Construct from Istream setting pointsList
+        //- Construct from Istream and point field.
         projectEdge
         (
             const dictionary& dict,
             const label index,
             const searchableSurfaces& geometry,
-            const pointField& points,
+            const pointField& points,   //!< Referenced point field
             Istream& is
         );
 
@@ -101,20 +102,17 @@ public:
 
     // Member Functions
 
-        //- Return the point positions corresponding to the curve parameters
+        //- The point position corresponding to the curve parameter
         //  0 <= lambda <= 1
         virtual point position(const scalar) const;
 
-        //- Return the point positions corresponding to the curve parameters
+        //- The point positions corresponding to the curve parameters
         //  0 <= lambda <= 1
         virtual tmp<pointField> position(const scalarList&) const;
 
-        //- Return the length of the curve
-        virtual scalar length() const
-        {
-            NotImplemented;
-            return 1;
-        }
+        //- The length of the edge
+        //  \note NotImplemented
+        virtual scalar length() const;
 };
 
 
diff --git a/src/mesh/blockMesh/blockEdges/splineEdge/CatmullRomSpline.C b/src/mesh/blockMesh/blockEdges/splineEdge/CatmullRomSpline.C
index a8ee8c1d71..bfa0aaf27b 100644
--- a/src/mesh/blockMesh/blockEdges/splineEdge/CatmullRomSpline.C
+++ b/src/mesh/blockMesh/blockEdges/splineEdge/CatmullRomSpline.C
@@ -134,7 +134,7 @@ Foam::point Foam::CatmullRomSpline::position
 Foam::scalar Foam::CatmullRomSpline::length() const
 {
     NotImplemented;
-    return 1.0;
+    return 1;
 }
 
 
diff --git a/src/mesh/blockMesh/blockEdges/splineEdge/CatmullRomSpline.H b/src/mesh/blockMesh/blockEdges/splineEdge/CatmullRomSpline.H
index c78803d9d3..27093f9cbd 100644
--- a/src/mesh/blockMesh/blockEdges/splineEdge/CatmullRomSpline.H
+++ b/src/mesh/blockMesh/blockEdges/splineEdge/CatmullRomSpline.H
@@ -6,6 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
+    Copyright (C) 2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -79,21 +80,12 @@ class CatmullRomSpline
 :
     public polyLine
 {
-    // Private Member Functions
-
-        //- No copy construct
-        CatmullRomSpline(const CatmullRomSpline&) = delete;
-
-        //- No copy assignment
-        void operator=(const CatmullRomSpline&) = delete;
-
-
 public:
 
     // Constructors
 
         //- Construct from components
-        CatmullRomSpline
+        explicit CatmullRomSpline
         (
             const pointField& knots,
             const bool notImplementedClosed = false
@@ -102,15 +94,16 @@ public:
 
     // Member Functions
 
-        //- Return the point position corresponding to the curve parameter
+        //- The point position corresponding to the curve parameter
         //  0 <= lambda <= 1
         point position(const scalar lambda) const;
 
-        //- Return the point position corresponding to the local parameter
+        //- The point position corresponding to the local parameter
         //  0 <= lambda <= 1 on the given segment
         point position(const label segment, const scalar lambda) const;
 
-        //- Return the length of the curve
+        //- The length of the curve
+        //  \note NotImplemented
         scalar length() const;
 };
 
diff --git a/src/mesh/blockMesh/blockEdges/splineEdge/splineEdge.C b/src/mesh/blockMesh/blockEdges/splineEdge/splineEdge.C
index 048d19878b..5494d4ed88 100644
--- a/src/mesh/blockMesh/blockEdges/splineEdge/splineEdge.C
+++ b/src/mesh/blockMesh/blockEdges/splineEdge/splineEdge.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -27,9 +27,9 @@ License
 \*---------------------------------------------------------------------------*/
 
 #include "splineEdge.H"
+#include "polyLine.H"
 #include "addToRunTimeSelectionTable.H"
 
-
 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
 
 namespace Foam
@@ -59,7 +59,10 @@ Foam::blockEdges::splineEdge::splineEdge
 )
 :
     blockEdge(points, start, end),
-    CatmullRomSpline(appendEndPoints(points, start, end, internalPoints))
+    CatmullRomSpline
+    (
+        polyLine::concat(points[start_], internalPoints, points[end_])
+    )
 {}
 
 
@@ -73,13 +76,16 @@ Foam::blockEdges::splineEdge::splineEdge
 )
 :
     blockEdge(dict, index, points, is),
-    CatmullRomSpline(appendEndPoints(points, start_, end_, pointField(is)))
+    CatmullRomSpline
+    (
+        polyLine::concat(points[start_], pointField(is), points[end_])
+    )
 {
-    token t(is);
-    is.putBack(t);
+    token tok(is);
+    is.putBack(tok);
 
-    // discard unused start/end tangents
-    if (t == token::BEGIN_LIST)
+    // Discard unused start/end tangents
+    if (tok == token::BEGIN_LIST)
     {
         vector tangent0Ignored(is);
         vector tangent1Ignored(is);
diff --git a/src/mesh/blockMesh/blockEdges/splineEdge/splineEdge.H b/src/mesh/blockMesh/blockEdges/splineEdge/splineEdge.H
index a5519ec883..3ac595cbac 100644
--- a/src/mesh/blockMesh/blockEdges/splineEdge/splineEdge.H
+++ b/src/mesh/blockMesh/blockEdges/splineEdge/splineEdge.H
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2019 OpenCFD Ltd.
+    Copyright (C) 2019-2020 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -30,6 +30,10 @@ Class
 Description
     A blockEdge interface for Catmull-Rom splines.
 
+See also
+    BSpline
+    CatmullRomSpline
+
 SourceFiles
     splineEdge.C
 
@@ -77,19 +81,19 @@ public:
         //- Construct from components
         splineEdge
         (
-            const pointField&,
-            const label start,
-            const label end,
+            const pointField& points,   //!< Referenced point field
+            const label start,      //!< Start point in referenced point field
+            const label end,        //!< End point in referenced point field
             const pointField& internalPoints
         );
 
-        //- Construct from Istream, setting pointsList
+        //- Construct from Istream and point field.
         splineEdge
         (
             const dictionary& dict,
             const label index,
             const searchableSurfaces& geometry,
-            const pointField&,
+            const pointField& points,   //!< Referenced point field
             Istream&
         );
 
@@ -100,11 +104,12 @@ public:
 
     // Member Functions
 
-        //- Return the point position corresponding to the curve parameter
+        //- The point position corresponding to the curve parameter
         //  0 <= lambda <= 1
         virtual point position(const scalar) const;
 
-        //- Return the length of the spline curve (not implemented)
+        //- The length of the spline curve
+        //  \note NotImplemented
         virtual scalar length() const;
 };
 

From 121c69ef2ea396c6d58824049dcaf86e684eb85d Mon Sep 17 00:00:00 2001
From: Mark Olesen <Mark.Olesen@esi-group.com>
Date: Mon, 5 Oct 2020 12:48:54 +0200
Subject: [PATCH 3/3] TUT: use new 'arc' specification in several tutorials

- in most cases this eliminates manually calculation of circumferential
  points.

TUT: improve parameterization of sphere blockMeshDict

- allow separate parameterization of radius, ratio of inner to outer,
  and the number of divisions in x/y/z and radial directions
---
 .../cylinder/system/blockMeshDict             |  93 +++++----
 .../oscillatingCylinder/system/blockMeshDict  |  25 +--
 .../compartmentFire/system/blockMeshDict.m4   |  16 +-
 .../system/blockMeshDict                      |  67 +++---
 .../RAS/squareBendLiq/system/blockMeshDict    |  63 +++---
 .../squareBend/system/blockMeshDict           |  63 +++---
 .../squareBendLiq/system/blockMeshDict        |  63 +++---
 .../chargedWire/system/blockMeshDict          |  16 +-
 .../cylinder/system/blockMeshDict             | 117 ++++++-----
 .../SRFSimpleFoam/mixer/system/blockMeshDict  |  85 ++++----
 .../offsetCylinder/system/blockMeshDict       | 195 +++++++++---------
 .../cylinder2D/system/blockMeshDict.main      |  69 +++----
 .../simpleFoam/bump2D/system/blockMeshDict    |  10 +-
 .../pipeCyclic/system/blockMeshDict           |  25 ++-
 .../squareBend/system/blockMeshDict           |  63 +++---
 .../cylinder/system/blockMeshDict             | 116 ++++++-----
 .../blockMesh/sphere/system/blockMeshDict     |  84 ++++----
 .../blockMesh/sphere7/system/blockMeshDict    | 156 +++++++-------
 .../system/blockMeshDict                      | 129 ++++++------
 .../refineFieldDirs/system/blockMeshDict      |  30 +--
 .../plateHole/system/blockMeshDict            |  16 +-
 21 files changed, 786 insertions(+), 715 deletions(-)

diff --git a/tutorials/basic/potentialFoam/cylinder/system/blockMeshDict b/tutorials/basic/potentialFoam/cylinder/system/blockMeshDict
index ac3995c8dc..ceb0865644 100644
--- a/tutorials/basic/potentialFoam/cylinder/system/blockMeshDict
+++ b/tutorials/basic/potentialFoam/cylinder/system/blockMeshDict
@@ -16,6 +16,10 @@ FoamFile
 
 scale   1;
 
+// Front/back locations
+zmin -0.5;
+zmax 0.5;
+
 vertices #codeStream
 {
     codeInclude
@@ -25,34 +29,39 @@ vertices #codeStream
 
     code
     #{
-        pointField points(19);
-        points[0]  = point(0.5, 0, -0.5);
-        points[1]  = point(1, 0, -0.5);
-        points[2]  = point(2, 0, -0.5);
-        points[3]  = point(2, 0.707107, -0.5);
-        points[4]  = point(0.707107, 0.707107, -0.5);
-        points[5]  = point(0.353553, 0.353553, -0.5);
-        points[6]  = point(2, 2, -0.5);
-        points[7]  = point(0.707107, 2, -0.5);
-        points[8]  = point(0, 2, -0.5);
-        points[9]  = point(0, 1, -0.5);
-        points[10] = point(0, 0.5, -0.5);
-        points[11] = point(-0.5, 0, -0.5);
-        points[12] = point(-1, 0, -0.5);
-        points[13] = point(-2, 0, -0.5);
-        points[14] = point(-2, 0.707107, -0.5);
-        points[15] = point(-0.707107, 0.707107, -0.5);
-        points[16] = point(-0.353553, 0.353553, -0.5);
-        points[17] = point(-2, 2, -0.5);
-        points[18] = point(-0.707107, 2, -0.5);
+        // sin(45), cos(45)
+        const scalar sqrt05 = sqrt(0.5);
 
-        // Duplicate z points
-        label sz = points.size();
-        points.setSize(2*sz);
-        for (label i = 0; i < sz; i++)
+        pointField points
+        ({
+            /* 0*/ {0.5, 0, $zmin},
+            /* 1*/ {1, 0, $zmin},
+            /* 2*/ {2, 0, $zmin},
+            /* 3*/ {2, sqrt05, $zmin},
+            /* 4*/ {sqrt05, sqrt05, $zmin},
+            /* 5*/ {sqrt05/2, sqrt05/2, $zmin},
+            /* 6*/ {2, 2, $zmin},
+            /* 7*/ {sqrt05, 2, $zmin},
+            /* 8*/ {0, 2, $zmin},
+            /* 9*/ {0, 1, $zmin},
+            /*10*/ {0, 0.5, $zmin},
+            /*11*/ {-0.5, 0, $zmin},
+            /*12*/ {-1, 0, $zmin},
+            /*13*/ {-2, 0, $zmin},
+            /*14*/ {-2, sqrt05, $zmin},
+            /*15*/ {-sqrt05, sqrt05, $zmin},
+            /*16*/ {-sqrt05/2, sqrt05/2, $zmin},
+            /*17*/ {-2, 2, $zmin},
+            /*18*/ {-sqrt05, 2, $zmin}
+        });
+
+        // Duplicate z points for zmax
+        const label sz = points.size();
+        points.resize(2*sz);
+        for (label i = 0; i < sz; ++i)
         {
             const point& pt = points[i];
-            points[i+sz] = point(pt.x(), pt.y(), -pt.z());
+            points[i + sz] = point(pt.x(), pt.y(), $zmax);
         }
 
         os  << points;
@@ -76,22 +85,24 @@ blocks
 
 edges
 (
-    arc 0 5 (0.469846 0.17101 -0.5)
-    arc 5 10 (0.17101 0.469846 -0.5)
-    arc 1 4 (0.939693 0.34202 -0.5)
-    arc 4 9 (0.34202 0.939693 -0.5)
-    arc 19 24 (0.469846 0.17101 0.5)
-    arc 24 29 (0.17101 0.469846 0.5)
-    arc 20 23 (0.939693 0.34202 0.5)
-    arc 23 28 (0.34202 0.939693 0.5)
-    arc 11 16 (-0.469846 0.17101 -0.5)
-    arc 16 10 (-0.17101 0.469846 -0.5)
-    arc 12 15 (-0.939693 0.34202 -0.5)
-    arc 15 9 (-0.34202 0.939693 -0.5)
-    arc 30 35 (-0.469846 0.17101 0.5)
-    arc 35 29 (-0.17101 0.469846 0.5)
-    arc 31 34 (-0.939693 0.34202 0.5)
-    arc 34 28 (-0.34202 0.939693 0.5)
+    // Inner cylinder
+    arc  0  5 origin (0 0 $zmin)
+    arc  5 10 origin (0 0 $zmin)
+    arc  1  4 origin (0 0 $zmin)
+    arc  4  9 origin (0 0 $zmin)
+    arc 19 24 origin (0 0 $zmax)
+    arc 24 29 origin (0 0 $zmax)
+    arc 20 23 origin (0 0 $zmax)
+    arc 23 28 origin (0 0 $zmax)
+    // Intermediate cylinder
+    arc 11 16 origin (0 0 $zmin)
+    arc 16 10 origin (0 0 $zmin)
+    arc 12 15 origin (0 0 $zmin)
+    arc 15  9 origin (0 0 $zmin)
+    arc 30 35 origin (0 0 $zmax)
+    arc 35 29 origin (0 0 $zmax)
+    arc 31 34 origin (0 0 $zmax)
+    arc 34 28 origin (0 0 $zmax)
 );
 
 boundary
diff --git a/tutorials/combustion/XiDyMFoam/oscillatingCylinder/system/blockMeshDict b/tutorials/combustion/XiDyMFoam/oscillatingCylinder/system/blockMeshDict
index cc11d554db..ee3b75f0be 100644
--- a/tutorials/combustion/XiDyMFoam/oscillatingCylinder/system/blockMeshDict
+++ b/tutorials/combustion/XiDyMFoam/oscillatingCylinder/system/blockMeshDict
@@ -73,21 +73,22 @@ blocks
 
 edges
 (
-    arc  8  9 (-3.46410161513775 2 0)
-    arc  9 10 (-4                0 0)
-    arc 10 11 (-3.46410161513775 2 0)
-    arc 11 13 ( 0                4 0)
-    arc 13 12 ( 4                0 0)
-    arc 12  8 ( 0               -4 0)
+    arc  8  9 origin (0 0 0)
+    arc  9 10 origin (0 0 0)
+    arc 10 11 origin (0 0 0)
+    arc 11 13 origin (0 0 0)
+    arc 13 12 origin (0 0 0)
+    arc 12  8 origin (0 0 0)
 
-    arc 26 27 (-3.46410161513775 2 1)
-    arc 27 28 (-4                0 1)
-    arc 28 29 (-3.46410161513775 2 1)
-    arc 29 31 ( 0                4 1)
-    arc 31 30 ( 4                0 1)
-    arc 30 26 ( 0               -4 1)
+    arc 26 27 origin (0 0 1)
+    arc 27 28 origin (0 0 1)
+    arc 28 29 origin (0 0 1)
+    arc 29 31 origin (0 0 1)
+    arc 31 30 origin (0 0 1)
+    arc 30 26 origin (0 0 1)
 );
 
+
 defaultPatch
 {
     name    frontAndBack;
diff --git a/tutorials/combustion/fireFoam/LES/compartmentFire/system/blockMeshDict.m4 b/tutorials/combustion/fireFoam/LES/compartmentFire/system/blockMeshDict.m4
index 30801ad7b5..e54dee9a38 100644
--- a/tutorials/combustion/fireFoam/LES/compartmentFire/system/blockMeshDict.m4
+++ b/tutorials/combustion/fireFoam/LES/compartmentFire/system/blockMeshDict.m4
@@ -153,15 +153,15 @@ blocks
 
 edges
 (
-    arc 4 5 (0 0 -R_burner)
-    arc 5 6 (R_burner 0 0)
-    arc 6 7 (0 0 R_burner)
-    arc 7 4 (-R_burner 0 0)
+    arc 4 5 origin (0 0 0)
+    arc 5 6 origin (0 0 0)
+    arc 6 7 origin (0 0 0)
+    arc 7 4 origin (0 0 0)
 
-    arc 24 25 (0 H_box -R_burner)
-    arc 25 26 (R_burner H_box 0)
-    arc 26 27 (0 H_box R_burner)
-    arc 27 24 (-R_burner H_box 0)
+    arc 24 25 origin (0 H_box 0)
+    arc 25 26 origin (0 H_box 0)
+    arc 26 27 origin (0 H_box 0)
+    arc 27 24 origin (0 H_box 0)
 );
 
 boundary
diff --git a/tutorials/compressible/rhoPimpleFoam/RAS/externalCoupledSquareBendLiq/system/blockMeshDict b/tutorials/compressible/rhoPimpleFoam/RAS/externalCoupledSquareBendLiq/system/blockMeshDict
index d638986f2e..4aa031189d 100644
--- a/tutorials/compressible/rhoPimpleFoam/RAS/externalCoupledSquareBendLiq/system/blockMeshDict
+++ b/tutorials/compressible/rhoPimpleFoam/RAS/externalCoupledSquareBendLiq/system/blockMeshDict
@@ -16,36 +16,39 @@ FoamFile
 
 scale   0.001;
 
+zmin -25;
+zmax 25;
+
 vertices
 (
-    // front-plane: z = +25mm
+    // front-plane:
     // inlet region
-    (   -50  25   25)           // pt 0
-    (     0  25   25)           // pt 1
-    (   -50  75   25)           // pt 2
-    (     0  75   25)           // pt 3
+    (   -50  25   $zmax)    // pt 0
+    (     0  25   $zmax)    // pt 1
+    (   -50  75   $zmax)    // pt 2
+    (     0  75   $zmax)    // pt 3
     // outlet region
-    (  -500 -75   25)           // pt 4
-    (     0 -75   25)           // pt 5
-    (  -500 -25   25)           // pt 6
-    (     0 -25   25)           // pt 7
+    (  -500 -75   $zmax)    // pt 4
+    (     0 -75   $zmax)    // pt 5
+    (  -500 -25   $zmax)    // pt 6
+    (     0 -25   $zmax)    // pt 7
     // bend mid-points
-    (    25   0   25)           // pt 8
-    (    75   0   25)           // pt 9
-    // back-plane: z = -25mm
+    (    25   0   $zmax)    // pt 8
+    (    75   0   $zmax)    // pt 9
+    // back-plane:
     // inlet region
-    (   -50  25   -25)          // pt 0 + 10
-    (     0  25   -25)          // pt 1 + 10
-    (   -50  75   -25)          // pt 2 + 10
-    (     0  75   -25)          // pt 3 + 10
+    (   -50  25   $zmin)    // pt 0 + 10
+    (     0  25   $zmin)    // pt 1 + 10
+    (   -50  75   $zmin)    // pt 2 + 10
+    (     0  75   $zmin)    // pt 3 + 10
     // outlet region
-    (  -500 -75   -25)          // pt 4 + 10
-    (     0 -75   -25)          // pt 5 + 10
-    (  -500 -25   -25)          // pt 7 + 10
-    (     0 -25   -25)          // pt 8 + 10
+    (  -500 -75   $zmin)    // pt 4 + 10
+    (     0 -75   $zmin)    // pt 5 + 10
+    (  -500 -25   $zmin)    // pt 7 + 10
+    (     0 -25   $zmin)    // pt 8 + 10
     // bend mid-points
-    (    25   0   -25)          // pt 8 + 10
-    (    75   0   -25)          // pt 9 + 10
+    (    25   0   $zmin)    // pt 8 + 10
+    (    75   0   $zmin)    // pt 9 + 10
 );
 
 blocks
@@ -59,16 +62,16 @@ blocks
 
 edges
 (
-   // block 2
-   arc  1  8  ( 17.678  17.678  25)
-   arc 11 18  ( 17.678  17.678 -25)
-   arc  3  9  ( 53.033  53.033  25)
-   arc 13 19  ( 53.033  53.033 -25)
-   // block 3
-   arc  7  8  ( 17.678  -17.678  25)
-   arc 17 18  ( 17.678  -17.678 -25)
-   arc  5  9  ( 53.033  -53.033  25)
-   arc 15 19  ( 53.033  -53.033 -25)
+    // block 2
+    arc  1  8  origin (0 0 $zmax)
+    arc  3  9  origin (0 0 $zmax)
+    arc 11 18  origin (0 0 $zmin)
+    arc 13 19  origin (0 0 $zmin)
+    // block 3
+    arc  7  8  origin (0 0 $zmax)
+    arc  5  9  origin (0 0 $zmax)
+    arc 17 18  origin (0 0 $zmin)
+    arc 15 19  origin (0 0 $zmin)
 );
 
 boundary
diff --git a/tutorials/compressible/rhoPimpleFoam/RAS/squareBendLiq/system/blockMeshDict b/tutorials/compressible/rhoPimpleFoam/RAS/squareBendLiq/system/blockMeshDict
index 165f4e9b23..366520c4bb 100644
--- a/tutorials/compressible/rhoPimpleFoam/RAS/squareBendLiq/system/blockMeshDict
+++ b/tutorials/compressible/rhoPimpleFoam/RAS/squareBendLiq/system/blockMeshDict
@@ -16,36 +16,39 @@ FoamFile
 
 scale   0.001;
 
+zmin -25;
+zmax 25;
+
 vertices
 (
-    // front-plane: z = +25mm
+    // front-plane:
     // inlet region
-    (   -50  25   25)           // pt 0
-    (     0  25   25)           // pt 1
-    (   -50  75   25)           // pt 2
-    (     0  75   25)           // pt 3
+    (   -50  25   $zmax)    // pt 0
+    (     0  25   $zmax)    // pt 1
+    (   -50  75   $zmax)    // pt 2
+    (     0  75   $zmax)    // pt 3
     // outlet region
-    (  -500 -75   25)           // pt 4
-    (     0 -75   25)           // pt 5
-    (  -500 -25   25)           // pt 6
-    (     0 -25   25)           // pt 7
+    (  -500 -75   $zmax)    // pt 4
+    (     0 -75   $zmax)    // pt 5
+    (  -500 -25   $zmax)    // pt 6
+    (     0 -25   $zmax)    // pt 7
     // bend mid-points
-    (    25   0   25)           // pt 8
-    (    75   0   25)           // pt 9
-    // back-plane: z = -25mm
+    (    25   0   $zmax)    // pt 8
+    (    75   0   $zmax)    // pt 9
+    // back-plane:
     // inlet region
-    (   -50  25   -25)          // pt 0 + 10
-    (     0  25   -25)          // pt 1 + 10
-    (   -50  75   -25)          // pt 2 + 10
-    (     0  75   -25)          // pt 3 + 10
+    (   -50  25   $zmin)    // pt 0 + 10
+    (     0  25   $zmin)    // pt 1 + 10
+    (   -50  75   $zmin)    // pt 2 + 10
+    (     0  75   $zmin)    // pt 3 + 10
     // outlet region
-    (  -500 -75   -25)          // pt 4 + 10
-    (     0 -75   -25)          // pt 5 + 10
-    (  -500 -25   -25)          // pt 7 + 10
-    (     0 -25   -25)          // pt 8 + 10
+    (  -500 -75   $zmin)    // pt 4 + 10
+    (     0 -75   $zmin)    // pt 5 + 10
+    (  -500 -25   $zmin)    // pt 7 + 10
+    (     0 -25   $zmin)    // pt 8 + 10
     // bend mid-points
-    (    25   0   -25)          // pt 8 + 10
-    (    75   0   -25)          // pt 9 + 10
+    (    25   0   $zmin)    // pt 8 + 10
+    (    75   0   $zmin)    // pt 9 + 10
 );
 
 blocks
@@ -60,15 +63,15 @@ blocks
 edges
 (
     // block 2
-    arc  1  8   (17.678  17.678  25)
-    arc 11 18   (17.678  17.678 -25)
-    arc  3  9   (53.033  53.033  25)
-    arc 13 19   (53.033  53.033 -25)
+    arc  1  8  origin (0 0 $zmax)
+    arc  3  9  origin (0 0 $zmax)
+    arc 11 18  origin (0 0 $zmin)
+    arc 13 19  origin (0 0 $zmin)
     // block 3
-    arc  7  8   (17.678  -17.678  25)
-    arc 17 18   (17.678  -17.678 -25)
-    arc  5  9   (53.033  -53.033  25)
-    arc 15 19   (53.033  -53.033 -25)
+    arc  7  8  origin (0 0 $zmax)
+    arc  5  9  origin (0 0 $zmax)
+    arc 17 18  origin (0 0 $zmin)
+    arc 15 19  origin (0 0 $zmin)
 );
 
 boundary
diff --git a/tutorials/compressible/rhoSimpleFoam/squareBend/system/blockMeshDict b/tutorials/compressible/rhoSimpleFoam/squareBend/system/blockMeshDict
index 165f4e9b23..366520c4bb 100644
--- a/tutorials/compressible/rhoSimpleFoam/squareBend/system/blockMeshDict
+++ b/tutorials/compressible/rhoSimpleFoam/squareBend/system/blockMeshDict
@@ -16,36 +16,39 @@ FoamFile
 
 scale   0.001;
 
+zmin -25;
+zmax 25;
+
 vertices
 (
-    // front-plane: z = +25mm
+    // front-plane:
     // inlet region
-    (   -50  25   25)           // pt 0
-    (     0  25   25)           // pt 1
-    (   -50  75   25)           // pt 2
-    (     0  75   25)           // pt 3
+    (   -50  25   $zmax)    // pt 0
+    (     0  25   $zmax)    // pt 1
+    (   -50  75   $zmax)    // pt 2
+    (     0  75   $zmax)    // pt 3
     // outlet region
-    (  -500 -75   25)           // pt 4
-    (     0 -75   25)           // pt 5
-    (  -500 -25   25)           // pt 6
-    (     0 -25   25)           // pt 7
+    (  -500 -75   $zmax)    // pt 4
+    (     0 -75   $zmax)    // pt 5
+    (  -500 -25   $zmax)    // pt 6
+    (     0 -25   $zmax)    // pt 7
     // bend mid-points
-    (    25   0   25)           // pt 8
-    (    75   0   25)           // pt 9
-    // back-plane: z = -25mm
+    (    25   0   $zmax)    // pt 8
+    (    75   0   $zmax)    // pt 9
+    // back-plane:
     // inlet region
-    (   -50  25   -25)          // pt 0 + 10
-    (     0  25   -25)          // pt 1 + 10
-    (   -50  75   -25)          // pt 2 + 10
-    (     0  75   -25)          // pt 3 + 10
+    (   -50  25   $zmin)    // pt 0 + 10
+    (     0  25   $zmin)    // pt 1 + 10
+    (   -50  75   $zmin)    // pt 2 + 10
+    (     0  75   $zmin)    // pt 3 + 10
     // outlet region
-    (  -500 -75   -25)          // pt 4 + 10
-    (     0 -75   -25)          // pt 5 + 10
-    (  -500 -25   -25)          // pt 7 + 10
-    (     0 -25   -25)          // pt 8 + 10
+    (  -500 -75   $zmin)    // pt 4 + 10
+    (     0 -75   $zmin)    // pt 5 + 10
+    (  -500 -25   $zmin)    // pt 7 + 10
+    (     0 -25   $zmin)    // pt 8 + 10
     // bend mid-points
-    (    25   0   -25)          // pt 8 + 10
-    (    75   0   -25)          // pt 9 + 10
+    (    25   0   $zmin)    // pt 8 + 10
+    (    75   0   $zmin)    // pt 9 + 10
 );
 
 blocks
@@ -60,15 +63,15 @@ blocks
 edges
 (
     // block 2
-    arc  1  8   (17.678  17.678  25)
-    arc 11 18   (17.678  17.678 -25)
-    arc  3  9   (53.033  53.033  25)
-    arc 13 19   (53.033  53.033 -25)
+    arc  1  8  origin (0 0 $zmax)
+    arc  3  9  origin (0 0 $zmax)
+    arc 11 18  origin (0 0 $zmin)
+    arc 13 19  origin (0 0 $zmin)
     // block 3
-    arc  7  8   (17.678  -17.678  25)
-    arc 17 18   (17.678  -17.678 -25)
-    arc  5  9   (53.033  -53.033  25)
-    arc 15 19   (53.033  -53.033 -25)
+    arc  7  8  origin (0 0 $zmax)
+    arc  5  9  origin (0 0 $zmax)
+    arc 17 18  origin (0 0 $zmin)
+    arc 15 19  origin (0 0 $zmin)
 );
 
 boundary
diff --git a/tutorials/compressible/rhoSimpleFoam/squareBendLiq/system/blockMeshDict b/tutorials/compressible/rhoSimpleFoam/squareBendLiq/system/blockMeshDict
index 165f4e9b23..366520c4bb 100644
--- a/tutorials/compressible/rhoSimpleFoam/squareBendLiq/system/blockMeshDict
+++ b/tutorials/compressible/rhoSimpleFoam/squareBendLiq/system/blockMeshDict
@@ -16,36 +16,39 @@ FoamFile
 
 scale   0.001;
 
+zmin -25;
+zmax 25;
+
 vertices
 (
-    // front-plane: z = +25mm
+    // front-plane:
     // inlet region
-    (   -50  25   25)           // pt 0
-    (     0  25   25)           // pt 1
-    (   -50  75   25)           // pt 2
-    (     0  75   25)           // pt 3
+    (   -50  25   $zmax)    // pt 0
+    (     0  25   $zmax)    // pt 1
+    (   -50  75   $zmax)    // pt 2
+    (     0  75   $zmax)    // pt 3
     // outlet region
-    (  -500 -75   25)           // pt 4
-    (     0 -75   25)           // pt 5
-    (  -500 -25   25)           // pt 6
-    (     0 -25   25)           // pt 7
+    (  -500 -75   $zmax)    // pt 4
+    (     0 -75   $zmax)    // pt 5
+    (  -500 -25   $zmax)    // pt 6
+    (     0 -25   $zmax)    // pt 7
     // bend mid-points
-    (    25   0   25)           // pt 8
-    (    75   0   25)           // pt 9
-    // back-plane: z = -25mm
+    (    25   0   $zmax)    // pt 8
+    (    75   0   $zmax)    // pt 9
+    // back-plane:
     // inlet region
-    (   -50  25   -25)          // pt 0 + 10
-    (     0  25   -25)          // pt 1 + 10
-    (   -50  75   -25)          // pt 2 + 10
-    (     0  75   -25)          // pt 3 + 10
+    (   -50  25   $zmin)    // pt 0 + 10
+    (     0  25   $zmin)    // pt 1 + 10
+    (   -50  75   $zmin)    // pt 2 + 10
+    (     0  75   $zmin)    // pt 3 + 10
     // outlet region
-    (  -500 -75   -25)          // pt 4 + 10
-    (     0 -75   -25)          // pt 5 + 10
-    (  -500 -25   -25)          // pt 7 + 10
-    (     0 -25   -25)          // pt 8 + 10
+    (  -500 -75   $zmin)    // pt 4 + 10
+    (     0 -75   $zmin)    // pt 5 + 10
+    (  -500 -25   $zmin)    // pt 7 + 10
+    (     0 -25   $zmin)    // pt 8 + 10
     // bend mid-points
-    (    25   0   -25)          // pt 8 + 10
-    (    75   0   -25)          // pt 9 + 10
+    (    25   0   $zmin)    // pt 8 + 10
+    (    75   0   $zmin)    // pt 9 + 10
 );
 
 blocks
@@ -60,15 +63,15 @@ blocks
 edges
 (
     // block 2
-    arc  1  8   (17.678  17.678  25)
-    arc 11 18   (17.678  17.678 -25)
-    arc  3  9   (53.033  53.033  25)
-    arc 13 19   (53.033  53.033 -25)
+    arc  1  8  origin (0 0 $zmax)
+    arc  3  9  origin (0 0 $zmax)
+    arc 11 18  origin (0 0 $zmin)
+    arc 13 19  origin (0 0 $zmin)
     // block 3
-    arc  7  8   (17.678  -17.678  25)
-    arc 17 18   (17.678  -17.678 -25)
-    arc  5  9   (53.033  -53.033  25)
-    arc 15 19   (53.033  -53.033 -25)
+    arc  7  8  origin (0 0 $zmax)
+    arc  5  9  origin (0 0 $zmax)
+    arc 17 18  origin (0 0 $zmin)
+    arc 15 19  origin (0 0 $zmin)
 );
 
 boundary
diff --git a/tutorials/electromagnetics/electrostaticFoam/chargedWire/system/blockMeshDict b/tutorials/electromagnetics/electrostaticFoam/chargedWire/system/blockMeshDict
index 0b40b5bfcf..57c872d8a0 100644
--- a/tutorials/electromagnetics/electrostaticFoam/chargedWire/system/blockMeshDict
+++ b/tutorials/electromagnetics/electrostaticFoam/chargedWire/system/blockMeshDict
@@ -53,14 +53,14 @@ blocks
 
 edges
 (
-    arc 0 5 (0.00092387 0.00038268 0)
-    arc 5 10 (0.00038268 0.00092387 0)
-    arc 1 4 (0.0351074 0.0145419 0)
-    arc 4 9 (0.0145419 0.0351074 0)
-    arc 11 16 (0.00092387 0.00038268 0.5)
-    arc 16 21 (0.00038268 0.00092387 0.5)
-    arc 12 15 (0.0351074 0.0145419 0.5)
-    arc 15 20 (0.0145419 0.0351074 0.5)
+    arc 0 5 origin (0 0 0)
+    arc 5 10 origin (0 0 0)
+    arc 1 4 origin (0 0 0)
+    arc 4 9 origin (0 0 0)
+    arc 11 16 origin (0 0 0.5)
+    arc 16 21 origin (0 0 0.5)
+    arc 12 15 origin (0 0 0.5)
+    arc 15 20 origin (0 0 0.5)
 );
 
 boundary
diff --git a/tutorials/finiteArea/liquidFilmFoam/cylinder/system/blockMeshDict b/tutorials/finiteArea/liquidFilmFoam/cylinder/system/blockMeshDict
index aededbfc0f..6b56721ed0 100644
--- a/tutorials/finiteArea/liquidFilmFoam/cylinder/system/blockMeshDict
+++ b/tutorials/finiteArea/liquidFilmFoam/cylinder/system/blockMeshDict
@@ -14,49 +14,54 @@ FoamFile
 }
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
+// Almost identical to basic/potentialFoam/cylinder
+
 scale   0.016;
 
+// Front/back locations
+zmin 0;
+zmax 0.5;
+
 vertices
 (
-    (0.5 0 0)
-    (1 0 0)
-    (2 0 0)
-    (2 0.707107 0)
-    (0.707107 0.707107 0)
-    (0.353553 0.353553 0)
-    (2 2 0)
-    (0.707107 2 0)
-    (0 2 0)
-    (0 1 0)
-    (0 0.5 0)
-    (-0.5 0 0)
-    (-1 0 0)
-    (-2 0 0)
-    (-2 0.707107 0)
-    (-0.707107 0.707107 0)
-    (-0.353553 0.353553 0)
-    (-2 2 0)
-    (-0.707107 2 0)
-
-    (0.5 0 0.5)
-    (1 0 0.5)
-    (2 0 0.5)
-    (2 0.707107 0.5)
-    (0.707107 0.707107 0.5)
-    (0.353553 0.353553 0.5)
-    (2 2 0.5)
-    (0.707107 2 0.5)
-    (0 2 0.5)
-    (0 1 0.5)
-    (0 0.5 0.5)
-    (-0.5 0 0.5)
-    (-1 0 0.5)
-    (-2 0 0.5)
-    (-2 0.707107 0.5)
-    (-0.707107 0.707107 0.5)
-    (-0.353553 0.353553 0.5)
-    (-2 2 0.5)
-    (-0.707107 2 0.5)
+    (0.5 0 $zmin)
+    (1 0 $zmin)
+    (2 0 $zmin)
+    (2 0.707107 $zmin)
+    (0.707107 0.707107 $zmin)
+    (0.353553 0.353553 $zmin)
+    (2 2 $zmin)
+    (0.707107 2 $zmin)
+    (0 2 $zmin)
+    (0 1 $zmin)
+    (0 0.5 $zmin)
+    (-0.5 0 $zmin)
+    (-1 0 $zmin)
+    (-2 0 $zmin)
+    (-2 0.707107 $zmin)
+    (-0.707107 0.707107 $zmin)
+    (-0.353553 0.353553 $zmin)
+    (-2 2 $zmin)
+    (-0.707107 2 $zmin)
+    (0.5 0 $zmax)
+    (1 0 $zmax)
+    (2 0 $zmax)
+    (2 0.707107 $zmax)
+    (0.707107 0.707107 $zmax)
+    (0.353553 0.353553 $zmax)
+    (2 2 $zmax)
+    (0.707107 2 $zmax)
+    (0 2 $zmax)
+    (0 1 $zmax)
+    (0 0.5 $zmax)
+    (-0.5 0 $zmax)
+    (-1 0 $zmax)
+    (-2 0 $zmax)
+    (-2 0.707107 $zmax)
+    (-0.707107 0.707107 $zmax)
+    (-0.353553 0.353553 $zmax)
+    (-2 2 $zmax)
+    (-0.707107 2 $zmax)
 );
 
 blocks
@@ -75,22 +80,24 @@ blocks
 
 edges
 (
-    arc 0 5 (0.469846 0.17101 0)
-    arc 5 10 (0.17101 0.469846 0)
-    arc 1 4 (0.939693 0.34202 0)
-    arc 4 9 (0.34202 0.939693 0)
-    arc 19 24 (0.469846 0.17101 0.5)
-    arc 24 29 (0.17101 0.469846 0.5)
-    arc 20 23 (0.939693 0.34202 0.5)
-    arc 23 28 (0.34202 0.939693 0.5)
-    arc 11 16 (-0.469846 0.17101 0)
-    arc 16 10 (-0.17101 0.469846 0)
-    arc 12 15 (-0.939693 0.34202 0)
-    arc 15 9 (-0.34202 0.939693 0)
-    arc 30 35 (-0.469846 0.17101 0.5)
-    arc 35 29 (-0.17101 0.469846 0.5)
-    arc 31 34 (-0.939693 0.34202 0.5)
-    arc 34 28 (-0.34202 0.939693 0.5)
+    // Inner cylinder
+    arc  0  5 origin (0 0 $zmin)
+    arc  5 10 origin (0 0 $zmin)
+    arc  1  4 origin (0 0 $zmin)
+    arc  4  9 origin (0 0 $zmin)
+    arc 19 24 origin (0 0 $zmax)
+    arc 24 29 origin (0 0 $zmax)
+    arc 20 23 origin (0 0 $zmax)
+    arc 23 28 origin (0 0 $zmax)
+    // Intermediate cylinder
+    arc 11 16 origin (0 0 $zmin)
+    arc 16 10 origin (0 0 $zmin)
+    arc 12 15 origin (0 0 $zmin)
+    arc 15  9 origin (0 0 $zmin)
+    arc 30 35 origin (0 0 $zmax)
+    arc 35 29 origin (0 0 $zmax)
+    arc 31 34 origin (0 0 $zmax)
+    arc 34 28 origin (0 0 $zmax)
 );
 
 patches
diff --git a/tutorials/incompressible/SRFSimpleFoam/mixer/system/blockMeshDict b/tutorials/incompressible/SRFSimpleFoam/mixer/system/blockMeshDict
index 56729cdf23..578ecbf576 100644
--- a/tutorials/incompressible/SRFSimpleFoam/mixer/system/blockMeshDict
+++ b/tutorials/incompressible/SRFSimpleFoam/mixer/system/blockMeshDict
@@ -17,57 +17,60 @@ FoamFile
 
 scale   0.1;
 
+zmin 0;
+zmax 2;
+
 vertices
 (
-      (       0.500        0.000        0.000)
-      (       0.369        0.338        0.000)
-      (       0.338        0.369        0.000)
-      (       0.000        0.500        0.000)
-      (       0.737        0.676        0.000)
-      (       0.074        0.068        0.000)
-      (       0.676        0.737        0.000)
-      (       0.068        0.074        0.000)
-      (       0.000        1.000        0.000)
-      (       1.000        0.000        0.000)
-      (       0.100        0.000        0.000)
-      (       0.000        0.100        0.000)
-      (       0.500        0.000        2.000)
-      (       0.369        0.338        2.000)
-      (       0.338        0.369        2.000)
-      (       0.000        0.500        2.000)
-      (       0.737        0.676        2.000)
-      (       0.074        0.068        2.000)
-      (       0.676        0.737        2.000)
-      (       0.068        0.074        2.000)
-      (       0.000        1.000        2.000)
-      (       1.000        0.000        2.000)
-      (       0.100        0.000        2.000)
-      (       0.000        0.100        2.000)
+    (0.500        0.000    $zmin)
+    (0.369        0.338    $zmin)
+    (0.338        0.369    $zmin)
+    (0.000        0.500    $zmin)
+    (0.737        0.676    $zmin)
+    (0.074        0.068    $zmin)
+    (0.676        0.737    $zmin)
+    (0.068        0.074    $zmin)
+    (0.000        1.000    $zmin)
+    (1.000        0.000    $zmin)
+    (0.100        0.000    $zmin)
+    (0.000        0.100    $zmin)
+    (0.500        0.000    $zmax)
+    (0.369        0.338    $zmax)
+    (0.338        0.369    $zmax)
+    (0.000        0.500    $zmax)
+    (0.737        0.676    $zmax)
+    (0.074        0.068    $zmax)
+    (0.676        0.737    $zmax)
+    (0.068        0.074    $zmax)
+    (0.000        1.000    $zmax)
+    (1.000        0.000    $zmax)
+    (0.100        0.000    $zmax)
+    (0.000        0.100    $zmax)
 );
 
 blocks
 (
-      hex (1 0 9 4 13 12 21 16) (10 20 40) simpleGrading (1 1 1)
-      hex (2 1 4 6 14 13 16 18) (2 20 40) simpleGrading (1 1 1)
-      hex (3 2 6 8 15 14 18 20) (10 20 40) simpleGrading (1 1 1)
-      hex (5 10 0 1 17 22 12 13) (10 20 40) simpleGrading (1 1 1)
-      hex (11 7 2 3 23 19 14 15) (10 20 40) simpleGrading (1 1 1)
+    hex (1 0 9 4 13 12 21 16) (10 20 40) simpleGrading (1 1 1)
+    hex (2 1 4 6 14 13 16 18) (2 20 40) simpleGrading (1 1 1)
+    hex (3 2 6 8 15 14 18 20) (10 20 40) simpleGrading (1 1 1)
+    hex (5 10 0 1 17 22 12 13) (10 20 40) simpleGrading (1 1 1)
+    hex (11 7 2 3 23 19 14 15) (10 20 40) simpleGrading (1 1 1)
 );
 
 edges
 (
-      arc  0 1 (       0.470        0.171        0.000 )
-      arc  12 13 (       0.470        0.171        2.000 )
-      arc  2 3 (       0.171        0.470        0.000 )
-      arc  14 15 (       0.171        0.470        2.000 )
-      arc  9 4 (       0.940        0.342        0.000 )
-      arc  21 16 (       0.940        0.342        2.000 )
-      arc  5 10 (       0.094        0.034        0.000 )
-      arc  17 22 (       0.094        0.034        2.000 )
-      arc  6 8 (       0.342        0.940        0.000 )
-      arc  18 20 (       0.342        0.940        2.000 )
-      arc  11 7 (       0.034        0.094        0.000 )
-      arc  23 19 (       0.034        0.094        2.000 )
+    arc   0  1 origin (0 0 $zmin)
+    arc  12 13 origin (0 0 $zmax)
+    arc   2  3 origin (0 0 $zmin)
+    arc  14 15 origin (0 0 $zmax)
+    arc   9  4 origin (0 0 $zmin)
+    arc  21 16 origin (0 0 $zmax)
+    arc   5 10 origin (0 0 $zmin)
+    arc  17 22 origin (0 0 $zmax)
+    arc   6  8 origin (0 0 $zmin)
+    arc  18 20 origin (0 0 $zmax)
+    arc  11  7 origin (0 0 $zmin)
+    arc  23 19 origin (0 0 $zmax)
 );
 
 boundary
diff --git a/tutorials/incompressible/nonNewtonianIcoFoam/offsetCylinder/system/blockMeshDict b/tutorials/incompressible/nonNewtonianIcoFoam/offsetCylinder/system/blockMeshDict
index 2ec0e7a55a..5ec15e9252 100644
--- a/tutorials/incompressible/nonNewtonianIcoFoam/offsetCylinder/system/blockMeshDict
+++ b/tutorials/incompressible/nonNewtonianIcoFoam/offsetCylinder/system/blockMeshDict
@@ -16,72 +16,75 @@ FoamFile
 
 scale   1;
 
+zmin -1;
+zmax 1;
+
 vertices
 (
-    (1 0 -1)
-    (1.4 0 -1)
-    (5 0 -1)
-    (5 0.989949 -1)
-    (0.989949 0.989949 -1)
-    (0.707107 0.707107 -1)
-    (5 2.5 -1)
-    (0.989949 2.5 -1)
-    (0 2.5 -1)
-    (0 1.4 -1)
-    (0 1 -1)
-    (-1 0 -1)
-    (-1.4 0 -1)
-    (-5 0 -1)
-    (-5 0.989949 -1)
-    (-0.989949 0.989949 -1)
-    (-0.707107 0.707107 -1)
-    (-5 2.5 -1)
-    (-0.989949 2.5 -1)
-    (5 -0.989949 -1)
-    (0.989949 -0.989949 -1)
-    (0.707107 -0.707107 -1)
-    (5 -1.5 -1)
-    (0.989949 -1.5 -1)
-    (0 -1.5 -1)
-    (0 -1.4 -1)
-    (0 -1 -1)
-    (-5 -0.989949 -1)
-    (-0.989949 -0.989949 -1)
-    (-0.707107 -0.707107 -1)
-    (-5 -1.5 -1)
-    (-0.989949 -1.5 -1)
-    (1 0 1)
-    (1.4 0 1)
-    (5 0 1)
-    (5 0.989949 1)
-    (0.989949 0.989949 1)
-    (0.707107 0.707107 1)
-    (5 2.5 1)
-    (0.989949 2.5 1)
-    (0 2.5 1)
-    (0 1.4 1)
-    (0 1 1)
-    (-1 0 1)
-    (-1.4 0 1)
-    (-5 0 1)
-    (-5 0.989949 1)
-    (-0.989949 0.989949 1)
-    (-0.707107 0.707107 1)
-    (-5 2.5 1)
-    (-0.989949 2.5 1)
-    (5 -0.989949 1)
-    (0.989949 -0.989949 1)
-    (0.707107 -0.707107 1)
-    (5 -1.5 1)
-    (0.989949 -1.5 1)
-    (0 -1.5 1)
-    (0 -1.4 1)
-    (0 -1 1)
-    (-5 -0.989949 1)
-    (-0.989949 -0.989949 1)
-    (-0.707107 -0.707107 1)
-    (-5 -1.5 1)
-    (-0.989949 -1.5 1)
+    (1 0 $zmin)
+    (1.4 0 $zmin)
+    (5 0 $zmin)
+    (5 0.989949 $zmin)
+    (0.989949 0.989949 $zmin)
+    (0.707107 0.707107 $zmin)
+    (5 2.5 $zmin)
+    (0.989949 2.5 $zmin)
+    (0 2.5 $zmin)
+    (0 1.4 $zmin)
+    (0 1 $zmin)
+    (-1 0 $zmin)
+    (-1.4 0 $zmin)
+    (-5 0 $zmin)
+    (-5 0.989949 $zmin)
+    (-0.989949 0.989949 $zmin)
+    (-0.707107 0.707107 $zmin)
+    (-5 2.5 $zmin)
+    (-0.989949 2.5 $zmin)
+    (5 -0.989949 $zmin)
+    (0.989949 -0.989949 $zmin)
+    (0.707107 -0.707107 $zmin)
+    (5 -1.5 $zmin)
+    (0.989949 -1.5 $zmin)
+    (0 -1.5 $zmin)
+    (0 -1.4 $zmin)
+    (0 -1 $zmin)
+    (-5 -0.989949 $zmin)
+    (-0.989949 -0.989949 $zmin)
+    (-0.707107 -0.707107 $zmin)
+    (-5 -1.5 $zmin)
+    (-0.989949 -1.5 $zmin)
+    (1 0 $zmax)
+    (1.4 0 $zmax)
+    (5 0 $zmax)
+    (5 0.989949 $zmax)
+    (0.989949 0.989949 $zmax)
+    (0.707107 0.707107 $zmax)
+    (5 2.5 $zmax)
+    (0.989949 2.5 $zmax)
+    (0 2.5 $zmax)
+    (0 1.4 $zmax)
+    (0 1 $zmax)
+    (-1 0 $zmax)
+    (-1.4 0 $zmax)
+    (-5 0 $zmax)
+    (-5 0.989949 $zmax)
+    (-0.989949 0.989949 $zmax)
+    (-0.707107 0.707107 $zmax)
+    (-5 2.5 $zmax)
+    (-0.989949 2.5 $zmax)
+    (5 -0.989949 $zmax)
+    (0.989949 -0.989949 $zmax)
+    (0.707107 -0.707107 $zmax)
+    (5 -1.5 $zmax)
+    (0.989949 -1.5 $zmax)
+    (0 -1.5 $zmax)
+    (0 -1.4 $zmax)
+    (0 -1 $zmax)
+    (-5 -0.989949 $zmax)
+    (-0.989949 -0.989949 $zmax)
+    (-0.707107 -0.707107 $zmax)
+    (-5 -1.5 $zmax)
+    (-0.989949 -1.5 $zmax)
 );
 
 blocks
@@ -110,38 +113,38 @@ blocks
 
 edges
 (
-    arc 5 0 (0.92388 0.382683 -1)
-    arc 5 10 (0.382683 0.923879 -1)
-    arc 1 4 (1.29343 0.535757 -1)
-    arc 4 9 (0.535757 1.29343 -1)
-    arc 32 37 (0.92388 0.382683 1)
-    arc 37 42 (0.382683 0.923879 1)
-    arc 33 36 (1.29343 0.535757 1)
-    arc 36 41 (0.535757 1.29343 1)
-    arc 11 16 (-0.923879 0.382683 -1)
-    arc 16 10 (-0.382683 0.923879 -1)
-    arc 12 15 (-1.29343 0.535757 -1)
-    arc 15 9 (-0.535757 1.29343 -1)
-    arc 43 48 (-0.923879 0.382683 1)
-    arc 48 42 (-0.382683 0.923879 1)
-    arc 44 47 (-1.29343 0.535757 1)
-    arc 47 41 (-0.535757 1.29343 1)
-    arc 0 21 (0.923879 -0.382683 -1)
-    arc 21 26 (0.382683 -0.923879 -1)
-    arc 1 20 (1.29343 -0.535757 -1)
-    arc 20 25 (0.535757 -1.29343 -1)
-    arc 32 53 (0.923879 -0.382683 1)
-    arc 53 58 (0.382683 -0.923879 1)
-    arc 33 52 (1.29343 -0.535757 1)
-    arc 52 57 (0.535757 -1.29343 1)
-    arc 11 29 (-0.923879 -0.382683 -1)
-    arc 29 26 (-0.382683 -0.923879 -1)
-    arc 12 28 (-1.29343 -0.535757 -1)
-    arc 28 25 (-0.535757 -1.29343 -1)
-    arc 43 61 (-0.923879 -0.382683 1)
-    arc 61 58 (-0.382683 -0.923879 1)
-    arc 44 60 (-1.29343 -0.535757 1)
-    arc 60 57 (-0.535757 -1.29343 1)
+    arc 5 0 origin (0 0 $zmin)
+    arc 5 10 origin (0 0 $zmin)
+    arc 1 4 origin (0 0 $zmin)
+    arc 4 9 origin (0 0 $zmin)
+    arc 32 37 origin (0 0 $zmax)
+    arc 37 42 origin (0 0 $zmax)
+    arc 33 36 origin (0 0 $zmax)
+    arc 36 41 origin (0 0 $zmax)
+    arc 11 16 origin (0 0 $zmin)
+    arc 16 10 origin (0 0 $zmin)
+    arc 12 15 origin (0 0 $zmin)
+    arc 15 9 origin (0 0 $zmin)
+    arc 43 48 origin (0 0 $zmax)
+    arc 48 42 origin (0 0 $zmax)
+    arc 44 47 origin (0 0 $zmax)
+    arc 47 41 origin (0 0 $zmax)
+    arc 0 21 origin (0 0 $zmin)
+    arc 21 26 origin (0 0 $zmin)
+    arc 1 20 origin (0 0 $zmin)
+    arc 20 25 origin (0 0 $zmin)
+    arc 32 53 origin (0 0 $zmax)
+    arc 53 58 origin (0 0 $zmax)
+    arc 33 52 origin (0 0 $zmax)
+    arc 52 57 origin (0 0 $zmax)
+    arc 11 29 origin (0 0 $zmin)
+    arc 29 26 origin (0 0 $zmin)
+    arc 12 28 origin (0 0 $zmin)
+    arc 28 25 origin (0 0 $zmin)
+    arc 43 61 origin (0 0 $zmax)
+    arc 61 58 origin (0 0 $zmax)
+    arc 44 60 origin (0 0 $zmax)
+    arc 60 57 origin (0 0 $zmax)
 );
 
 boundary
diff --git a/tutorials/incompressible/pimpleFoam/laminar/cylinder2D/system/blockMeshDict.main b/tutorials/incompressible/pimpleFoam/laminar/cylinder2D/system/blockMeshDict.main
index f6c2adc8f7..223dc50e5a 100644
--- a/tutorials/incompressible/pimpleFoam/laminar/cylinder2D/system/blockMeshDict.main
+++ b/tutorials/incompressible/pimpleFoam/laminar/cylinder2D/system/blockMeshDict.main
@@ -23,18 +23,6 @@ x3        #eval{ 10.0*$R };
 xOutlet   #eval{ 18.6667*$R };
 xInlet    #eval{ -10.125*$R };
 
-RsinPi8   #eval{ $R*sin(0.125*pi()) };
-RsinPi8n  #eval{ -$RsinPi8 };
-RcosPi8   #eval{ $R*cos(0.125*pi()) };
-RcosPi8n  #eval{ -$RcosPi8 };
-RsinPi4   #eval{ $R*sin(0.25*pi()) };
-
-x2sinPi8  #eval{ $x2*sin(0.125*pi()) };
-x2sinPi8n #eval{ -$x2sinPi8 };
-x2cosPi8  #eval{ $x2*cos(0.125*pi()) };
-x2cosPi8n #eval{ -$x2cosPi8 };
-x2sinPi4  #eval{ $x2*sin(0.25*pi()) };
-
 z0        -0.0075;
 z1        0.0075;
 nz        1;
@@ -49,15 +37,18 @@ vertices #codeStream
 
     code
     #{
+        // sin(45), cos(45)
+        const scalar sqrt05 = sqrt(0.5);
+
         pointField points(19);
         points[0] = point($R, 0, $z0);
         points[1] = point($x2, 0, $z0);
         points[2] = point($x3, 0, $z0);
-        points[3] = point($x3, $x2sinPi4, $z0);
-        points[4] = point($x2sinPi4, $x2sinPi4, $z0);
-        points[5] = point($RsinPi4, $RsinPi4, $z0);
+        points[3] = point($x3, $x2*sqrt05, $z0);
+        points[4] = point($x2*sqrt05, $x2*sqrt05, $z0);
+        points[5] = point($R*sqrt05, $R*sqrt05, $z0);
         points[6] = point($x3, $x3, $z0);
-        points[7] = point($x2sinPi4, $x3, $z0);
+        points[7] = point($x2*sqrt05, $x3, $z0);
 
         // Mirror +x points to -x side
         points[11] = point(-points[0].x(), points[0].y(), points[0].z());
@@ -76,7 +67,7 @@ vertices #codeStream
 
         // Mirror -z points to +z side
         label sz = points.size();
-        points.setSize(2*sz);
+        points.resize(2*sz);
         for (label i = 0; i < sz; ++i)
         {
             const point& pt = points[i];
@@ -86,7 +77,7 @@ vertices #codeStream
         // Add an inner cylinder
         sz = points.size();
         label nAdd = 6;
-        points.setSize(sz + nAdd);
+        points.resize(sz + nAdd);
 
         // Points within the inner cylinder
         points[sz] = point(0, 0, $z0);
@@ -102,7 +93,7 @@ vertices #codeStream
 
         // Mirror -z points to +z side
         sz = points.size();
-        points.setSize(sz + nAdd);
+        points.resize(sz + nAdd);
         for (label i = 0; i < nAdd; ++i)
         {
             const point& pt = points[i+sz-nAdd];
@@ -112,21 +103,21 @@ vertices #codeStream
         // Add downstream and upstream blocks
         sz = points.size();
         nAdd = 6;
-        points.setSize(sz + nAdd);
+        points.resize(sz + nAdd);
 
         // Points on outlet
         points[sz] = point($xOutlet, 0, $z0);
         points[sz + 1] = point($xOutlet, $x3, $z0);
-        points[sz + 4] = point($xOutlet, $x2sinPi4, $z0);
+        points[sz + 4] = point($xOutlet, $x2*sqrt05, $z0);
 
         // Points on inlet
         points[sz + 2] = point($xInlet, 0, $z0);
         points[sz + 3] = point($xInlet, $x3, $z0);
-        points[sz + 5] = point($xInlet, $x2sinPi4, $z0);
+        points[sz + 5] = point($xInlet, $x2*sqrt05, $z0);
 
         // Mirror -z points to +z side
         sz = points.size();
-        points.setSize(sz + nAdd);
+        points.resize(sz + nAdd);
         for (label i = 0; i < nAdd; ++i)
         {
             const point& pt = points[i + sz - nAdd];
@@ -158,22 +149,22 @@ blocks
 
 edges
 (
-    arc  0  5 ($RcosPi8   $RsinPi8  $z0)
-    arc  5 10 ($RsinPi8   $RcosPi8  $z0)
-    arc  1  4 ($x2cosPi8  $x2sinPi8 $z0)
-    arc  4  9 ($x2sinPi8  $x2cosPi8 $z0)
-    arc 19 24 ($RcosPi8   $RsinPi8  $z1)
-    arc 24 29 ($RsinPi8   $RcosPi8  $z1)
-    arc 20 23 ($x2cosPi8  $x2sinPi8 $z1)
-    arc 23 28 ($x2sinPi8  $x2cosPi8 $z1)
-    arc 11 16 ($RcosPi8n  $RsinPi8  $z0)
-    arc 16 10 ($RsinPi8n  $RcosPi8  $z0)
-    arc 12 15 ($x2cosPi8n $x2sinPi8 $z0)
-    arc 15  9 ($x2sinPi8n $x2cosPi8 $z0)
-    arc 30 35 ($RcosPi8n  $RsinPi8  $z1)
-    arc 35 29 ($RsinPi8n  $RcosPi8  $z1)
-    arc 31 34 ($x2cosPi8n $x2sinPi8 $z1)
-    arc 34 28 ($x2sinPi8n $x2cosPi8 $z1)
+    arc  0  5 origin (0 0 $z0)
+    arc  5 10 origin (0 0 $z0)
+    arc  1  4 origin (0 0 $z0)
+    arc  4  9 origin (0 0 $z0)
+    arc 19 24 origin (0 0 $z1)
+    arc 24 29 origin (0 0 $z1)
+    arc 20 23 origin (0 0 $z1)
+    arc 23 28 origin (0 0 $z1)
+    arc 11 16 origin (0 0 $z0)
+    arc 16 10 origin (0 0 $z0)
+    arc 12 15 origin (0 0 $z0)
+    arc 15  9 origin (0 0 $z0)
+    arc 30 35 origin (0 0 $z1)
+    arc 35 29 origin (0 0 $z1)
+    arc 31 34 origin (0 0 $z1)
+    arc 34 28 origin (0 0 $z1)
 );
 
 boundary
diff --git a/tutorials/incompressible/simpleFoam/bump2D/system/blockMeshDict b/tutorials/incompressible/simpleFoam/bump2D/system/blockMeshDict
index 890fc02425..5d2a59b5cd 100644
--- a/tutorials/incompressible/simpleFoam/bump2D/system/blockMeshDict
+++ b/tutorials/incompressible/simpleFoam/bump2D/system/blockMeshDict
@@ -74,14 +74,14 @@ edges #codeStream
 
     code
     #{
-        const scalar xMin = 0.3;
-        const scalar xMax = 1.2;
-        const label nPoints = 100;
-        const scalar dx = (xMax - xMin)/scalar(nPoints - 1);
+        constexpr scalar xMin = 0.3;
+        constexpr scalar xMax = 1.2;
+        constexpr label nPoints = 100;
+        constexpr scalar dx = (xMax - xMin)/scalar(nPoints - 1);
+        constexpr scalar pi = constant::mathematical::pi;
 
         os  << "(" << nl << "spline 2 3" << nl;
         pointField profile(nPoints);
-        const scalar pi = constant::mathematical::pi;
 
         for (label i = 0; i < nPoints; ++i)
         {
diff --git a/tutorials/incompressible/simpleFoam/pipeCyclic/system/blockMeshDict b/tutorials/incompressible/simpleFoam/pipeCyclic/system/blockMeshDict
index bdbbf798dd..b97babdd44 100644
--- a/tutorials/incompressible/simpleFoam/pipeCyclic/system/blockMeshDict
+++ b/tutorials/incompressible/simpleFoam/pipeCyclic/system/blockMeshDict
@@ -25,34 +25,33 @@ halfAngle 45.0;
 radius  0.5;
 
 y               #eval{ $radius*sin(degToRad($halfAngle)) };
-minY            #eval{ -1*$y };
 z               #eval{ $radius*cos(degToRad($halfAngle)) };
+minY            #eval{ -1*$y };
 minZ            #eval{ -1*$z };
 
 vertices
 (
-    (0.0    0.0 0)      //0
-    (10     0.0 0)
-    (10     0.0 0)      //2
-    (0.0    0.0 0)
+    (0  0 0)        //0
+    (10 0 0)        //1
+    (10 0 0)        //2
+    (0  0 0)        //3
 
-    (0.0    $minY $z)   //4
-    (10     $minY $z)
-    (10     $y $z)      //6
-    (0.0    $y $z)
+    (0  $minY $z)   //4
+    (10 $minY $z)   //5
+    (10 $y $z)      //6
+    (0  $y $z)      //7
 
 );
 
 blocks
 (
-    // inlet block
-    hex (0 1 2 3  4 5 6 7) (50 5 5) simpleGrading (1 1 1)
+    hex (0 1 2 3 4 5 6 7) (50 5 5) simpleGrading (1 1 1)
 );
 
 edges
 (
-    arc 4 7 (0 0 $radius)
-    arc 5 6 (10 0 $radius)
+    arc 4 7 origin (0 0 0)
+    arc 5 6 origin (10 0 0)
 );
 
 boundary
diff --git a/tutorials/incompressible/simpleFoam/squareBend/system/blockMeshDict b/tutorials/incompressible/simpleFoam/squareBend/system/blockMeshDict
index 165f4e9b23..366520c4bb 100644
--- a/tutorials/incompressible/simpleFoam/squareBend/system/blockMeshDict
+++ b/tutorials/incompressible/simpleFoam/squareBend/system/blockMeshDict
@@ -16,36 +16,39 @@ FoamFile
 
 scale   0.001;
 
+zmin -25;
+zmax 25;
+
 vertices
 (
-    // front-plane: z = +25mm
+    // front-plane:
     // inlet region
-    (   -50  25   25)           // pt 0
-    (     0  25   25)           // pt 1
-    (   -50  75   25)           // pt 2
-    (     0  75   25)           // pt 3
+    (   -50  25   $zmax)    // pt 0
+    (     0  25   $zmax)    // pt 1
+    (   -50  75   $zmax)    // pt 2
+    (     0  75   $zmax)    // pt 3
     // outlet region
-    (  -500 -75   25)           // pt 4
-    (     0 -75   25)           // pt 5
-    (  -500 -25   25)           // pt 6
-    (     0 -25   25)           // pt 7
+    (  -500 -75   $zmax)    // pt 4
+    (     0 -75   $zmax)    // pt 5
+    (  -500 -25   $zmax)    // pt 6
+    (     0 -25   $zmax)    // pt 7
     // bend mid-points
-    (    25   0   25)           // pt 8
-    (    75   0   25)           // pt 9
-    // back-plane: z = -25mm
+    (    25   0   $zmax)    // pt 8
+    (    75   0   $zmax)    // pt 9
+    // back-plane:
     // inlet region
-    (   -50  25   -25)          // pt 0 + 10
-    (     0  25   -25)          // pt 1 + 10
-    (   -50  75   -25)          // pt 2 + 10
-    (     0  75   -25)          // pt 3 + 10
+    (   -50  25   $zmin)    // pt 0 + 10
+    (     0  25   $zmin)    // pt 1 + 10
+    (   -50  75   $zmin)    // pt 2 + 10
+    (     0  75   $zmin)    // pt 3 + 10
     // outlet region
-    (  -500 -75   -25)          // pt 4 + 10
-    (     0 -75   -25)          // pt 5 + 10
-    (  -500 -25   -25)          // pt 7 + 10
-    (     0 -25   -25)          // pt 8 + 10
+    (  -500 -75   $zmin)    // pt 4 + 10
+    (     0 -75   $zmin)    // pt 5 + 10
+    (  -500 -25   $zmin)    // pt 7 + 10
+    (     0 -25   $zmin)    // pt 8 + 10
     // bend mid-points
-    (    25   0   -25)          // pt 8 + 10
-    (    75   0   -25)          // pt 9 + 10
+    (    25   0   $zmin)    // pt 8 + 10
+    (    75   0   $zmin)    // pt 9 + 10
 );
 
 blocks
@@ -60,15 +63,15 @@ blocks
 edges
 (
     // block 2
-    arc  1  8   (17.678  17.678  25)
-    arc 11 18   (17.678  17.678 -25)
-    arc  3  9   (53.033  53.033  25)
-    arc 13 19   (53.033  53.033 -25)
+    arc  1  8  origin (0 0 $zmax)
+    arc  3  9  origin (0 0 $zmax)
+    arc 11 18  origin (0 0 $zmin)
+    arc 13 19  origin (0 0 $zmin)
     // block 3
-    arc  7  8   (17.678  -17.678  25)
-    arc 17 18   (17.678  -17.678 -25)
-    arc  5  9   (53.033  -53.033  25)
-    arc 15 19   (53.033  -53.033 -25)
+    arc  7  8  origin (0 0 $zmax)
+    arc  5  9  origin (0 0 $zmax)
+    arc 17 18  origin (0 0 $zmin)
+    arc 15 19  origin (0 0 $zmin)
 );
 
 boundary
diff --git a/tutorials/lagrangian/reactingParcelFoam/cylinder/system/blockMeshDict b/tutorials/lagrangian/reactingParcelFoam/cylinder/system/blockMeshDict
index 7445c24428..2161b74b1c 100644
--- a/tutorials/lagrangian/reactingParcelFoam/cylinder/system/blockMeshDict
+++ b/tutorials/lagrangian/reactingParcelFoam/cylinder/system/blockMeshDict
@@ -14,48 +14,54 @@ FoamFile
 }
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
+// Almost identical to basic/potentialFoam/cylinder
+
 scale   1;
 
+// Front/back locations
+zmin -0.5;
+zmax 0.5;
+
 vertices
 (
-    (0.5 0 -0.5)
-    (1 0 -0.5)
-    (2 0 -0.5)
-    (2 0.707107 -0.5)
-    (0.707107 0.707107 -0.5)
-    (0.353553 0.353553 -0.5)
-    (2 2 -0.5)
-    (0.707107 2 -0.5)
-    (0 2 -0.5)
-    (0 1 -0.5)
-    (0 0.5 -0.5)
-    (-0.5 0 -0.5)
-    (-1 0 -0.5)
-    (-2 0 -0.5)
-    (-2 0.707107 -0.5)
-    (-0.707107 0.707107 -0.5)
-    (-0.353553 0.353553 -0.5)
-    (-2 2 -0.5)
-    (-0.707107 2 -0.5)
-    (0.5 0 0.5)
-    (1 0 0.5)
-    (2 0 0.5)
-    (2 0.707107 0.5)
-    (0.707107 0.707107 0.5)
-    (0.353553 0.353553 0.5)
-    (2 2 0.5)
-    (0.707107 2 0.5)
-    (0 2 0.5)
-    (0 1 0.5)
-    (0 0.5 0.5)
-    (-0.5 0 0.5)
-    (-1 0 0.5)
-    (-2 0 0.5)
-    (-2 0.707107 0.5)
-    (-0.707107 0.707107 0.5)
-    (-0.353553 0.353553 0.5)
-    (-2 2 0.5)
-    (-0.707107 2 0.5)
+    (0.5 0 $zmin)
+    (1 0 $zmin)
+    (2 0 $zmin)
+    (2 0.707107 $zmin)
+    (0.707107 0.707107 $zmin)
+    (0.353553 0.353553 $zmin)
+    (2 2 $zmin)
+    (0.707107 2 $zmin)
+    (0 2 $zmin)
+    (0 1 $zmin)
+    (0 0.5 $zmin)
+    (-0.5 0 $zmin)
+    (-1 0 $zmin)
+    (-2 0 $zmin)
+    (-2 0.707107 $zmin)
+    (-0.707107 0.707107 $zmin)
+    (-0.353553 0.353553 $zmin)
+    (-2 2 $zmin)
+    (-0.707107 2 $zmin)
+    (0.5 0 $zmax)
+    (1 0 $zmax)
+    (2 0 $zmax)
+    (2 0.707107 $zmax)
+    (0.707107 0.707107 $zmax)
+    (0.353553 0.353553 $zmax)
+    (2 2 $zmax)
+    (0.707107 2 $zmax)
+    (0 2 $zmax)
+    (0 1 $zmax)
+    (0 0.5 $zmax)
+    (-0.5 0 $zmax)
+    (-1 0 $zmax)
+    (-2 0 $zmax)
+    (-2 0.707107 $zmax)
+    (-0.707107 0.707107 $zmax)
+    (-0.353553 0.353553 $zmax)
+    (-2 2 $zmax)
+    (-0.707107 2 $zmax)
 );
 
 blocks
@@ -74,22 +80,24 @@ blocks
 
 edges
 (
-    arc 0 5 (0.469846 0.17101 -0.5)
-    arc 5 10 (0.17101 0.469846 -0.5)
-    arc 1 4 (0.939693 0.34202 -0.5)
-    arc 4 9 (0.34202 0.939693 -0.5)
-    arc 19 24 (0.469846 0.17101 0.5)
-    arc 24 29 (0.17101 0.469846 0.5)
-    arc 20 23 (0.939693 0.34202 0.5)
-    arc 23 28 (0.34202 0.939693 0.5)
-    arc 11 16 (-0.469846 0.17101 -0.5)
-    arc 16 10 (-0.17101 0.469846 -0.5)
-    arc 12 15 (-0.939693 0.34202 -0.5)
-    arc 15 9 (-0.34202 0.939693 -0.5)
-    arc 30 35 (-0.469846 0.17101 0.5)
-    arc 35 29 (-0.17101 0.469846 0.5)
-    arc 31 34 (-0.939693 0.34202 0.5)
-    arc 34 28 (-0.34202 0.939693 0.5)
+    // Inner cylinder
+    arc  0  5 origin (0 0 $zmin)
+    arc  5 10 origin (0 0 $zmin)
+    arc  1  4 origin (0 0 $zmin)
+    arc  4  9 origin (0 0 $zmin)
+    arc 19 24 origin (0 0 $zmax)
+    arc 24 29 origin (0 0 $zmax)
+    arc 20 23 origin (0 0 $zmax)
+    arc 23 28 origin (0 0 $zmax)
+    // Intermediate cylinder
+    arc 11 16 origin (0 0 $zmin)
+    arc 16 10 origin (0 0 $zmin)
+    arc 12 15 origin (0 0 $zmin)
+    arc 15  9 origin (0 0 $zmin)
+    arc 30 35 origin (0 0 $zmax)
+    arc 35 29 origin (0 0 $zmax)
+    arc 31 34 origin (0 0 $zmax)
+    arc 34 28 origin (0 0 $zmax)
 );
 
 defaultPatch
diff --git a/tutorials/mesh/blockMesh/sphere/system/blockMeshDict b/tutorials/mesh/blockMesh/sphere/system/blockMeshDict
index 59d5a948f8..191c1f6a49 100644
--- a/tutorials/mesh/blockMesh/sphere/system/blockMeshDict
+++ b/tutorials/mesh/blockMesh/sphere/system/blockMeshDict
@@ -16,65 +16,71 @@ FoamFile
 
 scale   1;
 
+// Geometric parameters
+outerRadius 1;
+
+// Divisions in x/y/z directions. Can be unequal.
+nx   10;
+ny   $nx;
+nz   $nx;
+
 geometry
 {
     sphere
     {
         type   sphere;
         origin (0 0 0);
-        radius 1;
+        radius $outerRadius;
     }
 }
 
-v 0.5773502;
-mv -0.5773502;
-
-a 0.7071067;
-ma -0.7071067;
+// Box sizes
+vo   #eval{ sqrt($outerRadius/3) };
+mvo  #eval{ -$vo };
 
 vertices
 (
-    ($mv $mv $mv)
-    ( $v $mv $mv)
-    ( $v  $v $mv)
-    ($mv  $v $mv)
-    ($mv $mv  $v)
-    ( $v $mv  $v)
-    ( $v  $v  $v)
-    ($mv  $v  $v)
+    ($mvo $mvo $mvo)
+    ( $vo $mvo $mvo)
+    ( $vo  $vo $mvo)
+    ($mvo  $vo $mvo)
+    ($mvo $mvo  $vo)
+    ( $vo $mvo  $vo)
+    ( $vo  $vo  $vo)
+    ($mvo  $vo  $vo)
 );
 
 blocks
 (
-    hex (0 1 2 3 4 5 6 7) (10 10 10) simpleGrading (1 1 1)
+    hex (0 1 2 3 4 5 6 7) ($nx $ny $nz) grading (1 1 1)
 );
 
 edges
 (
-    arc 0 1 (0 $ma $ma)
-    arc 2 3 (0 $a $ma)
-    arc 6 7 (0 $a $a)
-    arc 4 5 (0 $ma $a)
+    arc 0 1 origin (0 0 0)
+    arc 2 3 origin (0 0 0)
+    arc 6 7 origin (0 0 0)
+    arc 4 5 origin (0 0 0)
 
-    arc 0 3 ($ma 0 $ma)
-    arc 1 2 ($a 0 $ma)
-    arc 5 6 ($a 0 $a)
-    arc 4 7 ($ma 0 $a)
+    arc 0 3 origin (0 0 0)
+    arc 1 2 origin (0 0 0)
+    arc 5 6 origin (0 0 0)
+    arc 4 7 origin (0 0 0)
 
-    arc 0 4 ($ma $ma 0)
-    arc 1 5 ($a $ma 0)
-    arc 2 6 ($a $a 0)
-    arc 3 7 ($ma $a 0)
+    arc 0 4 origin (0 0 0)
+    arc 1 5 origin (0 0 0)
+    arc 2 6 origin (0 0 0)
+    arc 3 7 origin (0 0 0)
 );
 
 faces
 (
-    project (0 4 7 3) sphere
-    project (2 6 5 1) sphere
-    project (1 5 4 0) sphere
-    project (3 7 6 2) sphere
-    project (0 3 2 1) sphere
-    project (4 5 6 7) sphere
+    project (0 4 7 3) sphere  // x-min
+    project (1 2 6 5) sphere  // x-max
+    project (0 1 5 4) sphere  // y-min
+    project (3 7 6 2) sphere  // y-max
+    project (0 3 2 1) sphere  // z-min
+    project (4 5 6 7) sphere  // z-max
 );
 
 boundary
@@ -84,12 +90,12 @@ boundary
         type wall;
         faces
         (
-            (0 4 7 3)
-            (2 6 5 1)
-            (1 5 4 0)
-            (3 7 6 2)
-            (0 3 2 1)
-            (4 5 6 7)
+            (0 4 7 3)  // x-min
+            (1 2 6 5)  // x-max
+            (0 1 5 4)  // y-min
+            (3 7 6 2)  // y-max
+            (0 3 2 1)  // z-min
+            (4 5 6 7)  // z-max
         );
     }
 );
diff --git a/tutorials/mesh/blockMesh/sphere7/system/blockMeshDict b/tutorials/mesh/blockMesh/sphere7/system/blockMeshDict
index 3e7c71adee..6d19d4a536 100644
--- a/tutorials/mesh/blockMesh/sphere7/system/blockMeshDict
+++ b/tutorials/mesh/blockMesh/sphere7/system/blockMeshDict
@@ -17,103 +17,115 @@ FoamFile
 scale   1;
 verbose no;
 
+// Geometric parameters
+outerRadius 1;
+innerRatio  0.7;
+
+// Divisions in x/y/z and radial directions. Can be unequal.
+nx   10;
+ny   $nx;
+nz   $nx;
+nr   6;
+
 geometry
 {
     sphere
     {
         type   sphere;
         origin (0 0 0);
-        radius 1;
+        radius $outerRadius;
     }
 }
 
+// Outer box sizes
+vo   #eval{ sqrt($outerRadius/3) };
+mvo  #eval{ -$vo };
 
-n    10;
-
-v    0.5773502;
-mv  -0.5773502;
-vh   0.2886751;
-mvh -0.2886751;
-
-a    0.7071067;
-ma  -0.7071067;
-ah   0.3464101;
-mah -0.3464101;
+// Inner box sizes - % of overall dimension
+vi   #eval{ $innerRatio*$vo };
+mvi  #eval{ $innerRatio*$mvo };
 
 vertices
 (
-    ($mvh $mvh $mvh)
-    ( $vh $mvh $mvh)
-    ( $vh  $vh $mvh)
-    ($mvh  $vh $mvh)
-    ($mvh $mvh  $vh)
-    ( $vh $mvh  $vh)
-    ( $vh  $vh  $vh)
-    ($mvh  $vh  $vh)
+    // Inner block
+    ($mvi $mvi $mvi)
+    ( $vi $mvi $mvi)
+    ( $vi  $vi $mvi)
+    ($mvi  $vi $mvi)
+    ($mvi $mvi  $vi)
+    ( $vi $mvi  $vi)
+    ( $vi  $vi  $vi)
+    ($mvi  $vi  $vi)
 
-    ($mv $mv $mv)
-    ( $v $mv $mv)
-    ( $v  $v $mv)
-    ($mv  $v $mv)
-    ($mv $mv  $v)
-    ( $v $mv  $v)
-    ( $v  $v  $v)
-    ($mv  $v  $v)
+    // Outer blocks
+    ($mvo $mvo $mvo)
+    ( $vo $mvo $mvo)
+    ( $vo  $vo $mvo)
+    ($mvo  $vo $mvo)
+    ($mvo $mvo  $vo)
+    ( $vo $mvo  $vo)
+    ( $vo  $vo  $vo)
+    ($mvo  $vo  $vo)
 );
 
 blocks
 (
-    hex ( 0  1  2  3  4  5  6  7) ($n $n $n) simpleGrading (1 1 1)
-    hex ( 9  8 12 13  1  0  4  5) ($n $n $n) simpleGrading (1 1 1)
-    hex (10  9 13 14  2  1  5  6) ($n $n $n) simpleGrading (1 1 1)
-    hex (11 10 14 15  3  2  6  7) ($n $n $n) simpleGrading (1 1 1)
-    hex ( 8 11 15 12  0  3  7  4) ($n $n $n) simpleGrading (1 1 1)
-    hex ( 8  9 10 11  0  1  2  3) ($n $n $n) simpleGrading (1 1 1)
-    hex (13 12 15 14  5  4  7  6) ($n $n $n) simpleGrading (1 1 1)
+    hex (0 1 2 3 4 5 6 7) ($nx $ny $nz) grading (1 1 1)  // Inner block
+
+    // Outer blocks
+    hex ( 8  0  3 11 12  4  7 15) ($nr $ny $nz) grading (1 1 1)  // x-min
+    hex ( 1  9 10  2  5 13 14  6) ($nr $ny $nz) grading (1 1 1)  // x-max
+    hex ( 8  9  1  0 12 13  5  4) ($nx $nr $nz) grading (1 1 1)  // y-min
+    hex ( 3  2 10 11  7  6 14 15) ($nx $nr $nz) grading (1 1 1)  // y-max
+    hex ( 8  9 10 11  0  1  2  3) ($nx $ny $nr) grading (1 1 1)  // z-min
+    hex ( 4  5  6  7 12 13 14 15) ($nx $ny $nr) grading (1 1 1)  // z-max
 );
 
+
 edges
 (
-    arc  8  9 (0 $ma $ma)
-    arc 10 11 (0 $a $ma)
-    arc 14 15 (0 $a $a)
-    arc 12 13 (0 $ma $a)
+    // Outer blocks
+    arc  8  9 origin (0 0 0)
+    arc 10 11 origin (0 0 0)
+    arc 14 15 origin (0 0 0)
+    arc 12 13 origin (0 0 0)
 
-    arc  8 11 ($ma 0 $ma)
-    arc  9 10 ($a 0 $ma)
-    arc 13 14 ($a 0 $a)
-    arc 12 15 ($ma 0 $a)
+    arc  8 11 origin (0 0 0)
+    arc  9 10 origin (0 0 0)
+    arc 13 14 origin (0 0 0)
+    arc 12 15 origin (0 0 0)
 
-    arc  8 12 ($ma $ma 0)
-    arc  9 13 ($a $ma 0)
-    arc 10 14 ($a $a 0)
-    arc 11 15 ($ma $a 0)
+    arc  8 12 origin (0 0 0)
+    arc  9 13 origin (0 0 0)
+    arc 10 14 origin (0 0 0)
+    arc 11 15 origin (0 0 0)
 
+    // Inner block - flattened by factor 1.1
+    arc 0 1 origin 1.1 (0 0 0)
+    arc 2 3 origin 1.1 (0 0 0)
+    arc 6 7 origin 1.1 (0 0 0)
+    arc 4 5 origin 1.1 (0 0 0)
 
-    arc  0  1 (0 $mah $mah)
-    arc  2  3 (0 $ah $mah)
-    arc  6  7 (0 $ah $ah)
-    arc  4  5 (0 $mah $ah)
+    arc 0 3 origin 1.1 (0 0 0)
+    arc 1 2 origin 1.1 (0 0 0)
+    arc 5 6 origin 1.1 (0 0 0)
+    arc 4 7 origin 1.1 (0 0 0)
 
-    arc  0  3 ($mah 0 $mah)
-    arc  1  2 ($ah 0 $mah)
-    arc  5  6 ($ah 0 $ah)
-    arc  4  7 ($mah 0 $ah)
-
-    arc  0  4 ($mah $mah 0)
-    arc  1  5 ($ah $mah 0)
-    arc  2  6 ($ah $ah 0)
-    arc  3  7 ($mah $ah 0)
+    arc 0 4 origin 1.1 (0 0 0)
+    arc 1 5 origin 1.1 (0 0 0)
+    arc 2 6 origin 1.1 (0 0 0)
+    arc 3 7 origin 1.1 (0 0 0)
 );
 
 faces
 (
-    project ( 8 12 15 11) sphere
-    project (10 14 13  9) sphere
-    project ( 9 13 12  8) sphere
-    project (11 15 14 10) sphere
-    project ( 8 11 10  9) sphere
-    project (12 13 14 15) sphere
+    // Outer blocks
+    project ( 8 12 15 11) sphere  // x-min
+    project ( 9 10 14 13) sphere  // x-max
+    project ( 8  9 13 12) sphere  // y-min
+    project (11 15 14 10) sphere  // y-max
+    project ( 8 11 10  9) sphere  // z-min
+    project (12 13 14 15) sphere  // z-max
 );
 
 boundary
@@ -123,12 +135,12 @@ boundary
         type wall;
         faces
         (
-            ( 8 12 15 11)
-            (10 14 13  9)
-            ( 9 13 12  8)
-            (11 15 14 10)
-            ( 8 11 10  9)
-            (12 13 14 15)
+            ( 8 12 15 11)  // x-min
+            ( 9 10 14 13)  // x-max
+            ( 8  9 13 12)  // y-min
+            (11 15 14 10)  // y-max
+            ( 8 11 10  9)  // z-min
+            (12 13 14 15)  // z-max
         );
     }
 );
diff --git a/tutorials/mesh/blockMesh/sphere7ProjectedEdges/system/blockMeshDict b/tutorials/mesh/blockMesh/sphere7ProjectedEdges/system/blockMeshDict
index 27624af930..6f7108118f 100644
--- a/tutorials/mesh/blockMesh/sphere7ProjectedEdges/system/blockMeshDict
+++ b/tutorials/mesh/blockMesh/sphere7ProjectedEdges/system/blockMeshDict
@@ -17,68 +17,81 @@ FoamFile
 scale   1;
 verbose no;
 
+// Geometric parameters
+outerRadius 1;
+innerRatio  0.5;
+
+// Divisions in x/y/z and radial directions. Can be unequal.
+nx   10;
+ny   $nx;
+nz   $nx;
+nr   6;
+
 geometry
 {
     sphere
     {
         type   sphere;
         origin (0 0 0);
-        radius 1;
+        radius $outerRadius;
     }
 
     innerSphere
     {
         type   sphere;
         origin (0 0 0);
-        radius 0.5;
+        radius #eval{ $innerRatio * $outerRadius };
     }
 }
 
-n    10;
 
-// Rough approximation of corner points
-v    0.5773502;
-mv  -0.5773502;
-vh   0.2886751;
-mvh -0.2886751;
+// Outer box sizes (approximate)
+vo   #eval{ sqrt($outerRadius/3) };
+mvo  #eval{ -$vo };
+
+// Inner box sizes - % of overall dimension
+vi   #eval{ $innerRatio*$vo };
+mvi  #eval{ $innerRatio*$mvo };
 
 vertices
 (
     // Inner block points
-    project ($mvh $mvh $mvh) (innerSphere)
-    project ( $vh $mvh $mvh) (innerSphere)
-    project ( $vh  $vh $mvh) (innerSphere)
-    project ($mvh  $vh $mvh) (innerSphere)
-    project ($mvh $mvh  $vh) (innerSphere)
-    project ( $vh $mvh  $vh) (innerSphere)
-    project ( $vh  $vh  $vh) (innerSphere)
-    project ($mvh  $vh  $vh) (innerSphere)
+    project ($mvi $mvi $mvi) (innerSphere)
+    project ( $vi $mvi $mvi) (innerSphere)
+    project ( $vi  $vi $mvi) (innerSphere)
+    project ($mvi  $vi $mvi) (innerSphere)
+    project ($mvi $mvi  $vi) (innerSphere)
+    project ( $vi $mvi  $vi) (innerSphere)
+    project ( $vi  $vi  $vi) (innerSphere)
+    project ($mvi  $vi  $vi) (innerSphere)
 
     // Outer block points
-    project ($mv $mv $mv) (sphere)
-    project ( $v $mv $mv) (sphere)
-    project ( $v  $v $mv) (sphere)
-    project ($mv  $v $mv) (sphere)
-    project ($mv $mv  $v) (sphere)
-    project ( $v $mv  $v) (sphere)
-    project ( $v  $v  $v) (sphere)
-    project ($mv  $v  $v) (sphere)
+    project ($mvo $mvo $mvo) (sphere)
+    project ( $vo $mvo $mvo) (sphere)
+    project ( $vo  $vo $mvo) (sphere)
+    project ($mvo  $vo $mvo) (sphere)
+    project ($mvo $mvo  $vo) (sphere)
+    project ( $vo $mvo  $vo) (sphere)
+    project ( $vo  $vo  $vo) (sphere)
+    project ($mvo  $vo  $vo) (sphere)
 );
 
 blocks
 (
-    hex ( 0  1  2  3  4  5  6  7) ($n $n $n) simpleGrading (1 1 1)
-    hex ( 9  8 12 13  1  0  4  5) ($n $n $n) simpleGrading (1 1 1)
-    hex (10  9 13 14  2  1  5  6) ($n $n $n) simpleGrading (1 1 1)
-    hex (11 10 14 15  3  2  6  7) ($n $n $n) simpleGrading (1 1 1)
-    hex ( 8 11 15 12  0  3  7  4) ($n $n $n) simpleGrading (1 1 1)
-    hex ( 8  9 10 11  0  1  2  3) ($n $n $n) simpleGrading (1 1 1)
-    hex (13 12 15 14  5  4  7  6) ($n $n $n) simpleGrading (1 1 1)
+    hex (0 1 2 3 4 5 6 7) ($nx $ny $nz) grading (1 1 1)  // Inner block
+
+    // Outer blocks
+    hex ( 8  0  3 11 12  4  7 15) ($nr $ny $nz) grading (1 1 1)  // x-min
+    hex ( 1  9 10  2  5 13 14  6) ($nr $ny $nz) grading (1 1 1)  // x-max
+    hex ( 8  9  1  0 12 13  5  4) ($nx $nr $nz) grading (1 1 1)  // y-min
+    hex ( 3  2 10 11  7  6 14 15) ($nx $nr $nz) grading (1 1 1)  // y-max
+    hex ( 8  9 10 11  0  1  2  3) ($nx $ny $nr) grading (1 1 1)  // z-min
+    hex ( 4  5  6  7 12 13 14 15) ($nx $ny $nr) grading (1 1 1)  // z-max
 );
 
 edges
 (
-    // Outer edges
+    // Outer blocks
     project  8  9 (sphere)
     project 10 11 (sphere)
     project 14 15 (sphere)
@@ -94,32 +107,32 @@ edges
     project 10 14 (sphere)
     project 11 15 (sphere)
 
+    // Inner block
+    project 0 1 (innerSphere)
+    project 2 3 (innerSphere)
+    project 6 7 (innerSphere)
+    project 4 5 (innerSphere)
 
-    // Inner edges
-    project  0  1 (innerSphere)
-    project  2  3 (innerSphere)
-    project  6  7 (innerSphere)
-    project  4  5 (innerSphere)
+    project 0 3 (innerSphere)
+    project 1 2 (innerSphere)
+    project 5 6 (innerSphere)
+    project 4 7 (innerSphere)
 
-    project  0  3 (innerSphere)
-    project  1  2 (innerSphere)
-    project  5  6 (innerSphere)
-    project  4  7 (innerSphere)
-
-    project  0  4 (innerSphere)
-    project  1  5 (innerSphere)
-    project  2  6 (innerSphere)
-    project  3  7 (innerSphere)
+    project 0 4 (innerSphere)
+    project 1 5 (innerSphere)
+    project 2 6 (innerSphere)
+    project 3 7 (innerSphere)
 );
 
 faces
 (
-    project ( 8 12 15 11) sphere
-    project (10 14 13  9) sphere
-    project ( 9 13 12  8) sphere
-    project (11 15 14 10) sphere
-    project ( 8 11 10  9) sphere
-    project (12 13 14 15) sphere
+    // Outer blocks
+    project ( 8 12 15 11) sphere  // x-min
+    project ( 9 10 14 13) sphere  // x-max
+    project ( 8  9 13 12) sphere  // y-min
+    project (11 15 14 10) sphere  // y-max
+    project ( 8 11 10  9) sphere  // z-min
+    project (12 13 14 15) sphere  // z-max
 );
 
 boundary
@@ -129,12 +142,12 @@ boundary
         type wall;
         faces
         (
-            ( 8 12 15 11)
-            (10 14 13  9)
-            ( 9 13 12  8)
-            (11 15 14 10)
-            ( 8 11 10  9)
-            (12 13 14 15)
+            ( 8 12 15 11)  // x-min
+            ( 9 10 14 13)  // x-max
+            ( 8  9 13 12)  // y-min
+            (11 15 14 10)  // y-max
+            ( 8 11 10  9)  // z-min
+            (12 13 14 15)  // z-max
         );
     }
 );
diff --git a/tutorials/mesh/refineMesh/refineFieldDirs/system/blockMeshDict b/tutorials/mesh/refineMesh/refineFieldDirs/system/blockMeshDict
index a7266f14e1..f97a1d3387 100644
--- a/tutorials/mesh/refineMesh/refineFieldDirs/system/blockMeshDict
+++ b/tutorials/mesh/refineMesh/refineFieldDirs/system/blockMeshDict
@@ -1,9 +1,15 @@
+/*--------------------------------*- C++ -*----------------------------------*\
+| =========                 |                                                 |
+| \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox           |
+|  \\    /   O peration     | Version:  v2006                                 |
+|   \\  /    A nd           | Website:  www.openfoam.com                      |
+|    \\/     M anipulation  |                                                 |
+\*---------------------------------------------------------------------------*/
 FoamFile
 {
     version     2.0;
     format      ascii;
     class       dictionary;
-    location    "system";
     object      blockMeshDict;
 }
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -25,13 +31,10 @@ scale   1;
                          D
 */
 
-Ax  0.438912;    Ay  0.000000;
-Bx  18.28800;    By  0.000000;
-Cx  0.310358;    Cy  -0.310358;
-Dx  12.931569;   Dy  -12.931569;
-
-Hx  0.405502;    Hy  -0.167964;
-Gx  16.895909;   Gy  -6.998515;
+Ax  0.438912;    Ay  0;
+Bx  18.28800;    By  0;
+Cx  0.310358;    Cy  #eval{-$Cx};
+Dx  12.931569;   Dy  #eval{-$Dx};
 
 Z_DB_low  -0.88706;
 Z_AC_low  -1.07;
@@ -51,16 +54,15 @@ vertices
 
 blocks
 (
-   hex (0 1 2 3 4 5 6 7)    (47 10 4) simpleGrading (41.6669 1 1)
+    hex (0 1 2 3 4 5 6 7) (47 10 4) simpleGrading (41.6669 1 1)
 );
 
 edges
 (
-  arc 0 3 ($Hx $Hy $Z_AC_low)
-  arc 4 7 ($Hx $Hy $Z_high)
-
-  arc 1 2 ($Gx $Gy $Z_DB_low)
-  arc 5 6 ($Gx $Gy $Z_high)
+    arc 0 3 origin (0 0 $Z_AC_low)
+    arc 4 7 origin (0 0 $Z_high)
+    arc 1 2 origin (0 0 $Z_DB_low)
+    arc 5 6 origin (0 0 $Z_high)
 );
 
 patches
diff --git a/tutorials/stressAnalysis/solidDisplacementFoam/plateHole/system/blockMeshDict b/tutorials/stressAnalysis/solidDisplacementFoam/plateHole/system/blockMeshDict
index bce421f9a9..b194cb8d50 100644
--- a/tutorials/stressAnalysis/solidDisplacementFoam/plateHole/system/blockMeshDict
+++ b/tutorials/stressAnalysis/solidDisplacementFoam/plateHole/system/blockMeshDict
@@ -53,14 +53,14 @@ blocks
 
 edges
 (
-    arc 0 5 (0.469846 0.17101 0)
-    arc 5 10 (0.17101 0.469846 0)
-    arc 1 4 (0.939693 0.34202 0)
-    arc 4 9 (0.34202 0.939693 0)
-    arc 11 16 (0.469846 0.17101 0.5)
-    arc 16 21 (0.17101 0.469846 0.5)
-    arc 12 15 (0.939693 0.34202 0.5)
-    arc 15 20 (0.34202 0.939693 0.5)
+    arc  0  5 origin (0 0 0)
+    arc  5 10 origin (0 0 0)
+    arc  1  4 origin (0 0 0)
+    arc  4  9 origin (0 0 0)
+    arc 11 16 origin (0 0 0.5)
+    arc 16 21 origin (0 0 0.5)
+    arc 12 15 origin (0 0 0.5)
+    arc 15 20 origin (0 0 0.5)
 );
 
 boundary