diff --git a/applications/test/minMax1/Test-minMax1.C b/applications/test/minMax1/Test-minMax1.C
index 664a3a7f22..586b6f0384 100644
--- a/applications/test/minMax1/Test-minMax1.C
+++ b/applications/test/minMax1/Test-minMax1.C
@@ -44,7 +44,7 @@ using namespace Foam;
 template<class T>
 Ostream& printInfo(const MinMax<T>& range)
 {
-    Info<< range << " valid=" << range.valid() << " span=" << range.span();
+    Info<< range << " good=" << range.good() << " span=" << range.span();
 
     return Info;
 }
diff --git a/applications/test/minMax2/Test-minMax2.C b/applications/test/minMax2/Test-minMax2.C
index 0a225ff893..95a3ced198 100644
--- a/applications/test/minMax2/Test-minMax2.C
+++ b/applications/test/minMax2/Test-minMax2.C
@@ -44,7 +44,7 @@ using namespace Foam;
 template<class T>
 Ostream& printInfo(const MinMax<T>& range)
 {
-    Info<< range << " valid=" << range.valid();
+    Info<< range << " good=" << range.good();
 
     return Info;
 }
diff --git a/src/OpenFOAM/meshes/boundBox/boundBox.C b/src/OpenFOAM/meshes/boundBox/boundBox.C
index 949dc4e40a..7c45b2ad23 100644
--- a/src/OpenFOAM/meshes/boundBox/boundBox.C
+++ b/src/OpenFOAM/meshes/boundBox/boundBox.C
@@ -197,15 +197,6 @@ Foam::boundBox Foam::boundBox::returnReduce(const boundBox& bb)
 }
 
 
-bool Foam::boundBox::intersect(const boundBox& bb)
-{
-    min_ = ::Foam::max(min_, bb.min_);
-    max_ = ::Foam::min(max_, bb.max_);
-
-    return valid();
-}
-
-
 bool Foam::boundBox::intersects(const plane& pln) const
 {
     // Require a full 3D box
@@ -290,6 +281,15 @@ Foam::point Foam::boundBox::nearest(const point& p) const
 }
 
 
+// * * * * * * * * * * * * * * * Member Operators  * * * * * * * * * * * * * //
+
+void Foam::boundBox::operator&=(const boundBox& bb)
+{
+    min_ = ::Foam::max(min_, bb.min_);
+    max_ = ::Foam::min(max_, bb.max_);
+}
+
+
 // * * * * * * * * * * * * * * * Ostream Operator  * * * * * * * * * * * * * //
 
 Foam::Ostream& Foam::operator<<(Ostream& os, const boundBox& bb)
diff --git a/src/OpenFOAM/meshes/boundBox/boundBox.H b/src/OpenFOAM/meshes/boundBox/boundBox.H
index c2218325e3..189e6ab2f5 100644
--- a/src/OpenFOAM/meshes/boundBox/boundBox.H
+++ b/src/OpenFOAM/meshes/boundBox/boundBox.H
@@ -35,6 +35,9 @@ Note
     bounding box. Points can be added later and the bounding box will grow to
     include them.
 
+SeeAlso
+    Foam::treeBoundBox
+
 \*---------------------------------------------------------------------------*/
 
 #ifndef Foam_boundBox_H
@@ -164,7 +167,10 @@ public:
             inline bool empty() const;
 
             //- Bounding box is non-inverted.
-            inline bool valid() const;
+            inline bool good() const;
+
+            //- Bounding box is non-inverted - same as good().
+            bool valid() const { return good(); }
 
             //- Minimum describing the bounding box
             inline const point& min() const noexcept;
@@ -227,6 +233,12 @@ public:
             //- Reset to an inverted box
             inline void reset();
 
+            //- Reset min/max to be identical to the specified point
+            inline void reset(const point& pt);
+
+            //- Reset min/max to specified values
+            inline void reset(const point& min, const point& max);
+
             //- Same as reset() - reset to an inverted box
             void clear() { reset(); }
 
@@ -288,10 +300,6 @@ public:
 
         // Query
 
-            //- Intersection (union) with the second box.
-            //  The return value is true if the intersection is non-empty.
-            bool intersect(const boundBox& bb);
-
             //- Does plane intersect this bounding box.
             //  There is an intersection if the plane segments the corner points
             //  \note the results are unreliable when plane coincides almost
@@ -372,7 +380,11 @@ public:
 
     // Member Operators
 
+        //- Restrict min/max to union with other box.
+        void operator&=(const boundBox& bb);
+
         //- Extend box to include the second box, as per the add() method.
+        //  Can be used in a reduction operation.
         void operator+=(const boundBox& bb) { add(bb); }
 
 
@@ -384,6 +396,12 @@ public:
 
     // Housekeeping
 
+        //- Deprecated(2022-10) - use 'operator&=' to avoid confusion with
+        //- other intersects() methods.
+        //  \deprecated(2022-10) - use 'operator&='
+        FOAM_DEPRECATED_FOR(2022-10, "boundBox::operator&=(const boundBox&)")
+        bool intersect(const boundBox& bb) { *this &= bb; return good(); }
+
         //- Identical to centre()
         point midpoint() const { return centre(); }
 };
diff --git a/src/OpenFOAM/meshes/boundBox/boundBoxI.H b/src/OpenFOAM/meshes/boundBox/boundBoxI.H
index c028a61762..9acad5a6ba 100644
--- a/src/OpenFOAM/meshes/boundBox/boundBoxI.H
+++ b/src/OpenFOAM/meshes/boundBox/boundBoxI.H
@@ -135,30 +135,19 @@ inline Foam::boundBox::boundBox(Istream& is)
 
 inline bool Foam::boundBox::empty() const
 {
-    // Check each component for max < min
-    for (direction dir = 0; dir < vector::nComponents; ++dir)
-    {
-        if (max_[dir] < min_[dir])
-        {
-            return true;
-        }
-    }
-    return false;
+    // Is empty/invalid if any component has (max < min), ie, !(min <= max)
+    return
+    (
+        (max_.x() < min_.x())
+     || (max_.y() < min_.y())
+     || (max_.z() < min_.z())
+    );
 }
 
 
-inline bool Foam::boundBox::valid() const
+inline bool Foam::boundBox::good() const
 {
-    // Check each component for max < min
-    for (direction dir = 0; dir < vector::nComponents; ++dir)
-    {
-        if (max_[dir] < min_[dir])
-        {
-            return false;
-        }
-    }
-
-    return true;
+    return !empty();
 }
 
 
@@ -256,6 +245,20 @@ inline void Foam::boundBox::reset()
 }
 
 
+inline void Foam::boundBox::reset(const point& pt)
+{
+    min_ = pt;
+    max_ = pt;
+}
+
+
+inline void Foam::boundBox::reset(const point& min, const point& max)
+{
+    min_ = min;
+    max_ = max;
+}
+
+
 inline void Foam::boundBox::add(const boundBox& bb)
 {
     min_ = ::Foam::min(min_, bb.min_);
@@ -310,9 +313,9 @@ inline bool Foam::boundBox::overlaps(const boundBox& bb) const
 {
     return
     (
-        bb.max_.x() >= min_.x() && bb.min_.x() <= max_.x()
-     && bb.max_.y() >= min_.y() && bb.min_.y() <= max_.y()
-     && bb.max_.z() >= min_.z() && bb.min_.z() <= max_.z()
+        min_.x() <= bb.max_.x() && bb.min_.x() <= max_.x()
+     && min_.y() <= bb.max_.y() && bb.min_.y() <= max_.y()
+     && min_.z() <= bb.max_.z() && bb.min_.z() <= max_.z()
     );
 }
 
diff --git a/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.H b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.H
index 5bdd6979be..4a05407d63 100644
--- a/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.H
+++ b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangle.H
@@ -40,8 +40,8 @@ SourceFiles
 #ifndef Foam_triangle_H
 #define Foam_triangle_H
 
+#include "triangleFwd.H"
 #include "intersection.H"
-#include "point.H"
 #include "vector.H"
 #include "tensor.H"
 #include "pointHit.H"
@@ -62,8 +62,6 @@ namespace Foam
 // Forward Declarations
 class plane;
 
-template<class Point, class PointRef> class triangle;
-
 template<class Point, class PointRef>
 inline Istream& operator>>(Istream&, triangle<Point, PointRef>&);
 
@@ -71,12 +69,6 @@ template<class Point, class PointRef>
 inline Ostream& operator<<(Ostream&, const triangle<Point, PointRef>&);
 
 
-// Common Typedefs
-
-//- A triangle using referred points
-typedef triangle<point, const point&> triPointRef;
-
-
 /*---------------------------------------------------------------------------*\
                           Class triPoints Declaration
 \*---------------------------------------------------------------------------*/
diff --git a/src/OpenFOAM/meshes/primitiveShapes/triangle/triangleFwd.H b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangleFwd.H
new file mode 100644
index 0000000000..c3474e37e8
--- /dev/null
+++ b/src/OpenFOAM/meshes/primitiveShapes/triangle/triangleFwd.H
@@ -0,0 +1,61 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | www.openfoam.com
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+    Copyright (C) 2022 OpenCFD Ltd.
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Typedef
+    Foam::triPointRef
+
+Description
+    A triangle using referred points
+
+\*---------------------------------------------------------------------------*/
+
+#ifndef Foam_triangleFwd_H
+#define Foam_triangleFwd_H
+
+#include "point.H"
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+namespace Foam
+{
+
+// Forward Declarations
+template<class Point, class PointRef> class triangle;
+
+// Common Typedefs
+
+//- A triangle using referred points
+typedef triangle<point, const point&> triPointRef;
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+} // End namespace Foam
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+
+#endif
+
+// ************************************************************************* //
diff --git a/src/OpenFOAM/primitives/ranges/MinMax/MinMax.H b/src/OpenFOAM/primitives/ranges/MinMax/MinMax.H
index ee2e6c479c..403a5b22da 100644
--- a/src/OpenFOAM/primitives/ranges/MinMax/MinMax.H
+++ b/src/OpenFOAM/primitives/ranges/MinMax/MinMax.H
@@ -202,23 +202,31 @@ public:
         //- Range is empty if it is inverted
         inline bool empty() const;
 
-        //- Range is valid if it is not inverted
-        inline bool valid() const;
+        //- Range is non-inverted
+        inline bool good() const;
+
+        //- Range is non-inverted
+        bool valid() const { return good(); }
 
         //- Reset to an inverted (invalid) range
         inline void reset();
 
+        //- Reset min/max to be identical to the specified value
+        inline void reset(const T& val);
+
+        //- Reset min/max to specified values
+        inline void reset(const T& minVal, const T& maxVal);
+
         //- Same as reset() - reset to an inverted (invalid) range
         void clear() { reset(); }
 
 
     // Testing / Query
 
-        //- Intersect (union) with the second range.
-        //  \return True if the resulting intersection is non-empty.
-        inline bool intersect(const MinMax<T>& b);
+        //- Test if the ranges intersect (exclusive check)
+        inline bool intersects(const MinMax<T>& b) const;
 
-        //- Test if the ranges overlap
+        //- Test if ranges overlap/touch (inclusive check)
         inline bool overlaps(const MinMax<T>& b) const;
 
         //- Compares the min/max range with the specified value.
@@ -228,7 +236,7 @@ public:
         //  - +1: range (min) is greater than value
         inline int compare(const T& val) const;
 
-        //- True if the value is within the range
+        //- True if the value is within the range (inclusive check)
         inline bool contains(const T& val) const;
 
         //- If out of range, return the respective min/max limits, otherwise
@@ -258,6 +266,9 @@ public:
         //- Identical to contains(), for use as a predicate.
         inline bool operator()(const T& val) const;
 
+        //- Restrict min/max range to union with other range
+        inline MinMax<T>& operator&=(const MinMax<T>& b);
+
         //- Extend min/max range to include other range
         //  Can be used in a reduction operation.
         inline MinMax<T>& operator+=(const MinMax<T>& b);
diff --git a/src/OpenFOAM/primitives/ranges/MinMax/MinMaxI.H b/src/OpenFOAM/primitives/ranges/MinMax/MinMaxI.H
index c656b0328e..6f9e965a7c 100644
--- a/src/OpenFOAM/primitives/ranges/MinMax/MinMaxI.H
+++ b/src/OpenFOAM/primitives/ranges/MinMax/MinMaxI.H
@@ -5,7 +5,7 @@
     \\  /    A nd           | www.openfoam.com
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
-    Copyright (C) 2019-2020 OpenCFD Ltd.
+    Copyright (C) 2019-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -156,14 +156,15 @@ inline Foam::scalar Foam::MinMax<T>::mag() const
 template<class T>
 inline bool Foam::MinMax<T>::empty() const
 {
+    // Is empty/invalid if (max < min), ie, !(min <= max)
     return (max() < min());
 }
 
 
 template<class T>
-inline bool Foam::MinMax<T>::valid() const
+inline bool Foam::MinMax<T>::good() const
 {
-    return !(max() < min());
+    return !empty();
 }
 
 
@@ -176,12 +177,26 @@ inline void Foam::MinMax<T>::reset()
 
 
 template<class T>
-inline bool Foam::MinMax<T>::intersect(const MinMax<T>& b)
+inline void Foam::MinMax<T>::reset(const T& val)
 {
-    min() = ::Foam::max(min(), b.min());
-    max() = ::Foam::min(max(), b.max());
+    min() = val;
+    max() = val;
+}
 
-    return valid();
+
+template<class T>
+inline void Foam::MinMax<T>::reset(const T& minVal, const T& maxVal)
+{
+    min() = minVal;
+    max() = maxVal;
+}
+
+
+template<class T>
+inline bool Foam::MinMax<T>::intersects(const MinMax<T>& b) const
+{
+    const MinMax<T>& a = *this;
+    return (a.min() < b.max() && b.min() < a.max());
 }
 
 
@@ -196,7 +211,7 @@ inline bool Foam::MinMax<T>::overlaps(const MinMax<T>& b) const
 template<class T>
 inline int Foam::MinMax<T>::compare(const T& val) const
 {
-    if (valid())
+    if (good())
     {
         if (max() < val)
         {
@@ -215,14 +230,14 @@ inline int Foam::MinMax<T>::compare(const T& val) const
 template<class T>
 inline bool Foam::MinMax<T>::contains(const T& val) const
 {
-    return (valid() && !compare(val));
+    return good() && !(val < min() || max() < val);
 }
 
 
 template<class T>
 inline const T& Foam::MinMax<T>::clip(const T& val) const
 {
-    if (valid())
+    if (good())
     {
         if (val < min())
         {
@@ -241,7 +256,7 @@ inline const T& Foam::MinMax<T>::clip(const T& val) const
 template<class T>
 inline bool Foam::MinMax<T>::inplaceClip(T& val) const
 {
-    if (valid())
+    if (good())
     {
         if (val < min())
         {
@@ -309,7 +324,7 @@ inline bool Foam::MinMax<T>::operator()(const T& val) const
 //
 //     // Remove overlapping portion, but cannot create a 'hole' in the middle
 //
-//     if (!a.valid() || !b.valid())
+//     if (a.empty() || b.empty())
 //     {
 //         // Invalid range(s): no-op
 //     }
@@ -328,6 +343,16 @@ inline bool Foam::MinMax<T>::operator()(const T& val) const
 // }
 
 
+template<class T>
+inline Foam::MinMax<T>& Foam::MinMax<T>::operator&=(const MinMax<T>& b)
+{
+    min() = ::Foam::max(min(), b.min());
+    max() = ::Foam::min(max(), b.max());
+
+    return *this;
+}
+
+
 template<class T>
 inline Foam::MinMax<T>& Foam::MinMax<T>::operator+=(const MinMax<T>& b)
 {
diff --git a/src/OpenFOAM/primitives/ranges/MinMax/MinMaxOps.H b/src/OpenFOAM/primitives/ranges/MinMax/MinMaxOps.H
index 10e7a723d4..f174787309 100644
--- a/src/OpenFOAM/primitives/ranges/MinMax/MinMaxOps.H
+++ b/src/OpenFOAM/primitives/ranges/MinMax/MinMaxOps.H
@@ -32,8 +32,8 @@ Description
 
 \*---------------------------------------------------------------------------*/
 
-#ifndef MinMaxOps_H
-#define MinMaxOps_H
+#ifndef Foam_MinMaxOps_H
+#define Foam_MinMaxOps_H
 
 #include "MinMax.H"
 #include "VectorSpace.H"
diff --git a/src/sampling/sampledSurface/sampledMeshedSurface/sampledMeshedSurface.C b/src/sampling/sampledSurface/sampledMeshedSurface/sampledMeshedSurface.C
index 8151e09754..24b0180a92 100644
--- a/src/sampling/sampledSurface/sampledMeshedSurface/sampledMeshedSurface.C
+++ b/src/sampling/sampledSurface/sampledMeshedSurface/sampledMeshedSurface.C
@@ -6,7 +6,7 @@
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
     Copyright (C) 2011-2016 OpenFOAM Foundation
-    Copyright (C) 2016-2021 OpenCFD Ltd.
+    Copyright (C) 2016-2022 OpenCFD Ltd.
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -632,10 +632,16 @@ bool Foam::sampledMeshedSurface::update()
     // Calculate surface and mesh overlap bounding box
     treeBoundBox bb(surface_.points(), surface_.meshPoints());
 
-    // Check for overlap with (global!) mesh bb
-    const bool intersect = bb.intersect(mesh().bounds());
+    // Restrict surface to (global!) mesh bound box
+    bb &= mesh().bounds();
 
-    if (!intersect)
+    if (bb.good())
+    {
+        // Extend a bit
+        bb.grow(0.5*bb.span());
+        bb.inflate(1e-6);
+    }
+    else
     {
         // Surface and mesh do not overlap at all. Guarantee a valid
         // bounding box so we don't get any 'invalid bounding box' errors.
@@ -645,20 +651,8 @@ bool Foam::sampledMeshedSurface::update()
             << " does not overlap bounding box of mesh " << mesh().bounds()
             << endl;
 
-        bb = treeBoundBox(mesh().bounds());
-        const vector span(bb.span());
-
-        bb.min() += (0.5-1e-6)*span;
-        bb.max() -= (0.5-1e-6)*span;
-    }
-    else
-    {
-        // Extend a bit
-        const vector span(bb.span());
-        bb.min() -= 0.5*span;
-        bb.max() += 0.5*span;
-
-        bb.inflate(1e-6);
+        bb.reset(mesh().bounds().centre());
+        bb.grow(1e-6*mesh().bounds().span());
     }
 
     // Mesh search engine, no triangulation of faces.