Math: add AABB and bounding sphere algorithms

src/Magnum/MeshTools/BoundingVolume.cpp

@@ -0,0 +1,80 @@
+/*
+    This file is part of Magnum.
+
+    Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
+                2020, 2021, 2022 Vladimír Vondruš <[email protected]>
+    Copyright © 2022 Pablo Escobar <[email protected]>
+
+    Permission is hereby granted, free of charge, to any person obtaining a
+    copy of this software and associated documentation files (the "Software"),
+    to deal in the Software without restriction, including without limitation
+    the rights to use, copy, modify, merge, publish, distribute, sublicense,
+    and/or sell copies of the Software, and to permit persons to whom the
+    Software is furnished to do so, subject to the following conditions:
+
+    The above copyright notice and this permission notice shall be included
+    in all copies or substantial portions of the Software.
+
+    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+    THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+    DEALINGS IN THE SOFTWARE.
+*/
+
+#include "BoundingVolume.h"
+
+#include <Corrade/Containers/StridedArrayView.h>
+
+#include "Magnum/Math/FunctionsBatch.h"
+
+namespace Magnum { namespace MeshTools {
+
+Range3D boundingBoxAxisAligned(const Containers::StridedArrayView1D<const Vector3>& points) {
+    return Math::minmax(points);
+}
+
+Containers::Pair<Vector3, Float> boundingSphereBouncingBubble(const Containers::StridedArrayView1D<const Vector3>& points) {
+    /* See comment about radius below, this is done for consistency */
+    if(points.isEmpty()) return {{}, Math::TypeTraits<Float>::epsilon()};
+
+    /** @todo Skip NaNs here? To match behaviour of boundingBoxAxisAligned()
+        which uses minmax(). */
+    Vector3 center = points[0];
+    /* Radius ends up in the denominator in the first loop so we can't
+       initialize it to 0. Unfortunately this also means the returned radius is
+       always above or equal to epsilon. */
+    Float radius = Math::TypeTraits<Float>::epsilon();
+    Float radiusSquared = radius*radius;
+
+    for(int i = 0; i < 2; ++i) {
+        for(const Vector3& p : points) {
+            const Float ds = (p - center).dot();
+            if(ds > radiusSquared) {
+                const Float alphaInv = radius/Math::sqrt(ds);
+                /* Not using alphaInv*alphaInv since that may lose precision */
+                const Float alphaSqInv = radiusSquared/ds;
+                radius = (1.0f/alphaInv + alphaInv)*0.5f*radius;
+                center = ((1.0f + alphaSqInv)*center + (1.0f - alphaSqInv)*p)*0.5f;
+                radiusSquared = radius*radius;
+            }
+        }
+    }
+
+    for(const Vector3& p : points) {
+        const Vector3 diff = p - center;
+        const Float ds = diff.dot();
+        if(ds > radiusSquared) {
+            const Float d = Math::sqrt(ds);
+            radius = (radius + d)*0.5f;
+            center = center + ((d - radius)/d*diff);
+            radiusSquared = radius*radius;
+        }
+    }
+
+    return {center, radius};
+}
+
+}}

src/Magnum/MeshTools/BoundingVolume.h

@@ -0,0 +1,72 @@
+#ifndef Magnum_MeshTools_BoundingVolume_h
+#define Magnum_MeshTools_BoundingVolume_h
+/*
+    This file is part of Magnum.
+
+    Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
+                2020, 2021, 2022 Vladimír Vondruš <[email protected]>
+    Copyright © 2022 Pablo Escobar <[email protected]>
+
+    Permission is hereby granted, free of charge, to any person obtaining a
+    copy of this software and associated documentation files (the "Software"),
+    to deal in the Software without restriction, including without limitation
+    the rights to use, copy, modify, merge, publish, distribute, sublicense,
+    and/or sell copies of the Software, and to permit persons to whom the
+    Software is furnished to do so, subject to the following conditions:
+
+    The above copyright notice and this permission notice shall be included
+    in all copies or substantial portions of the Software.
+
+    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+    THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
+    DEALINGS IN THE SOFTWARE.
+*/
+
+/** @file
+ * @brief Function @ref Magnum::MeshTools::boundingBoxAxisAligned(), @ref Magnum::MeshTools::boundingSphereBouncingBubble()
+ * @m_since_latest
+ */
+
+#include <Corrade/Containers/Pair.h>
+
+#include "Magnum/Magnum.h"
+#include "Magnum/Math/Range.h"
+#include "Magnum/Math/Vector3.h"
+#include "Magnum/MeshTools/visibility.h"
+
+namespace Magnum { namespace MeshTools {
+
+/**
+@brief Calculate an axis-aligned bounding box
+@param positions    Vertex positions
+@return Bounding box
+@m_since_latest
+
+Same as @ref Math::minmax(const Corrade::Containers::StridedArrayView1D<const T>&).
+*/
+MAGNUM_MESHTOOLS_EXPORT Range3D boundingBoxAxisAligned(const Containers::StridedArrayView1D<const Vector3>& positions);
+
+/**
+@brief Calculate an approximate bounding sphere using the Bouncing Bubble
+    algorithm
+@param positions    Vertex positions
+@return Sphere center and radius
+@m_since_latest
+
+The resulting bounding sphere is not usually minimal. According to the author,
+a 1% to 2% error can be expected. Due to the nature of the algorithm, the
+radius is never below @ref Math::TypeTraits::epsilon(), even for empty or
+entirely overlapping lists of points. <em>NaN</em>s are ignored, unless the
+first position is <em>NaN</em> in which case it is propagated. Algorithm used:
+* *Bo Tian --- Bouncing Bubble: A fast algorithm for Minimal Enclosing Ball
+problem, 2012, https://www.grin.com/document/204869*
+*/
+MAGNUM_MESHTOOLS_EXPORT Containers::Pair<Vector3, Float> boundingSphereBouncingBubble(const Containers::StridedArrayView1D<const Vector3>& positions);
+
+}}
+
+#endif

src/Magnum/MeshTools/CMakeLists.txt

@@ -33,6 +33,7 @@ set(MagnumMeshTools_SRCS
 
 # Files compiled with different flags for main library and unit test library
 set(MagnumMeshTools_GracefulAssert_SRCS
+    BoundingVolume.cpp
     Combine.cpp
     CompressIndices.cpp
     Concatenate.cpp
@@ -47,6 +48,7 @@ set(MagnumMeshTools_GracefulAssert_SRCS
     Transform.cpp)
 
 set(MagnumMeshTools_HEADERS
+    BoundingVolume.h
     Combine.h
     CompressIndices.h
     Concatenate.h