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MeshTools: add initial AABB and sphere bounding volume algorithms

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Pablo Escobar 4 years ago committed by Vladimír Vondruš
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  1. 79
      src/Magnum/MeshTools/BoundingVolume.cpp
  2. 72
      src/Magnum/MeshTools/BoundingVolume.h
  3. 2
      src/Magnum/MeshTools/CMakeLists.txt
  4. 264
      src/Magnum/MeshTools/Test/BoundingVolumeTest.cpp
  5. 1
      src/Magnum/MeshTools/Test/CMakeLists.txt

79
src/Magnum/MeshTools/BoundingVolume.cpp
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@ -0,0 +1,79 @@
/*
This file is part of Magnum.
Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
2020, 2021, 2022 Vladimír Vondruš <mosra@centrum.cz>
Copyright © 2022 Pablo Escobar <mail@rvrs.in>
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);
const Float alphaSqInv = alphaInv*alphaInv;
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};
}
}}

72
src/Magnum/MeshTools/BoundingVolume.h
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#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 <mosra@centrum.cz>
Copyright © 2022 Pablo Escobar <mail@rvrs.in>
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

2
src/Magnum/MeshTools/CMakeLists.txt
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@ -33,6 +33,7 @@ set(MagnumMeshTools_SRCS
# Files compiled with different flags for main library and unit test library # Files compiled with different flags for main library and unit test library
set(MagnumMeshTools_GracefulAssert_SRCS set(MagnumMeshTools_GracefulAssert_SRCS
BoundingVolume.cpp
Combine.cpp Combine.cpp
CompressIndices.cpp CompressIndices.cpp
Concatenate.cpp Concatenate.cpp
@ -47,6 +48,7 @@ set(MagnumMeshTools_GracefulAssert_SRCS
Transform.cpp) Transform.cpp)
set(MagnumMeshTools_HEADERS set(MagnumMeshTools_HEADERS
BoundingVolume.h
Combine.h Combine.h
CompressIndices.h CompressIndices.h
Concatenate.h Concatenate.h

264
src/Magnum/MeshTools/Test/BoundingVolumeTest.cpp
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/*
This file is part of Magnum.
Copyright © 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019,
2020, 2021, 2022 Vladimír Vondruš <mosra@centrum.cz>
Copyright © 2022 Pablo Escobar <mail@rvrs.in>
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 <Corrade/Containers/Array.h>
#include <Corrade/Containers/StridedArrayView.h>
#include <Corrade/TestSuite/Tester.h>
#include <Corrade/TestSuite/Compare/Numeric.h>
#include "Magnum/Math/FunctionsBatch.h"
#include "Magnum/Math/TypeTraits.h"
#include "Magnum/Math/Angle.h"
#include "Magnum/Math/Vector3.h"
#include "Magnum/MeshTools/BoundingVolume.h"
#include "Magnum/MeshTools/Reference.h"
#include "Magnum/MeshTools/Transform.h"
#include "Magnum/Primitives/Capsule.h"
#include "Magnum/Primitives/Cube.h"
#include "Magnum/Primitives/Icosphere.h"
#include "Magnum/Trade/MeshData.h"
namespace Magnum { namespace MeshTools { namespace Test { namespace {
struct BoundingVolumeTest: TestSuite::Tester {
explicit BoundingVolumeTest();
void boxAxisAligned();
void boxAxisAlignedNaN();
void sphereBouncingBubble();
void sphereBouncingBubbleNaN();
void benchmarkBoxAxisAligned();
void benchmarkSphereBouncingBubble();
};
BoundingVolumeTest::BoundingVolumeTest() {
addTests({&BoundingVolumeTest::boxAxisAligned,
&BoundingVolumeTest::boxAxisAlignedNaN,
&BoundingVolumeTest::sphereBouncingBubble,
&BoundingVolumeTest::sphereBouncingBubbleNaN});
addBenchmarks({&BoundingVolumeTest::benchmarkBoxAxisAligned,
&BoundingVolumeTest::benchmarkSphereBouncingBubble}, 150);
}
void BoundingVolumeTest::boxAxisAligned() {
/* boundingboxAxisAligned() is just a wrapper around minmax() so only test
that the input and output are forwarded correctly */
constexpr Float cylinderLength = 7.0f;
const Trade::MeshData cylinderMesh = Primitives::capsule3DSolid(3, 1, 12, cylinderLength*0.5f);
const Range3D box = MeshTools::boundingBoxAxisAligned(
cylinderMesh.attribute<Vector3>(Trade::MeshAttribute::Position));
CORRADE_COMPARE(box.center(), (Vector3{}));
CORRADE_COMPARE(box.size(), (Vector3{2.0f, cylinderLength + 2.0f, 2.0f}));
}
void BoundingVolumeTest::boxAxisAlignedNaN() {
/* NaNs are skipped (unless it's all NaNs), matching minmax() behaviour */
{
const Range3D box = MeshTools::boundingBoxAxisAligned(Containers::stridedArrayView({
Vector3{Constants::nan()},
Vector3{1.0f, 1.0f, 1.0f},
Vector3{Constants::nan()},
Vector3{2.0f, 2.0f, 2.0f},
Vector3{Constants::nan()}
}));
CORRADE_COMPARE(box.min(), (Vector3{1.0f, 1.0f, 1.0f}));
CORRADE_COMPARE(box.max(), (Vector3{2.0f, 2.0f, 2.0f}));
} {
const Range3D box = MeshTools::boundingBoxAxisAligned(Containers::stridedArrayView({
Vector3{Constants::nan()},
Vector3{Constants::nan()}
}));
CORRADE_VERIFY(Math::isNan(box.min()));
CORRADE_VERIFY(Math::isNan(box.max()));
}
}
void BoundingVolumeTest::sphereBouncingBubble() {
/* Empty positions -- produces radius epsilon for consistency with all
all identical positions */
{
const Containers::Pair<Vector3, Float> sphere =
MeshTools::boundingSphereBouncingBubble(Containers::StridedArrayView1D<const Vector3>{});
CORRADE_COMPARE(sphere.first(), (Vector3{}));
CORRADE_COMPARE(sphere.second(), Math::TypeTraits<Float>::epsilon());
/* Identical positions -- radius is always >= epsilon due to specifics of
the algorithm */
} {
const Containers::Pair<Vector3, Float> sphere =
MeshTools::boundingSphereBouncingBubble(Containers::stridedArrayView({
Vector3{1.0f, 2.0f, 3.0f}
}));
CORRADE_COMPARE(sphere.first(), (Vector3{1.0f, 2.0f, 3.0f}));
CORRADE_COMPARE(sphere.second(), Math::TypeTraits<Float>::epsilon());
} {
const Containers::Pair<Vector3, Float> sphere =
MeshTools::boundingSphereBouncingBubble(Containers::stridedArrayView({
Vector3{3.0f, 1.0f, 2.0f},
Vector3{3.0f, 1.0f, 2.0f},
Vector3{3.0f, 1.0f, 2.0f}
}));
CORRADE_COMPARE(sphere.first(), (Vector3{3.0f, 1.0f, 2.0f}));
CORRADE_COMPARE(sphere.second(), Math::TypeTraits<Float>::epsilon());
/* Simple cases */
} {
const Containers::Pair<Vector3, Float> sphere =
MeshTools::boundingSphereBouncingBubble(Containers::stridedArrayView({
Vector3{1.0f, 1.0f, 1.0f},
Vector3{2.0f, 2.0f, 2.0f}
}));
CORRADE_COMPARE(sphere.first(), (Vector3{1.5f}));
CORRADE_COMPARE(sphere.second(), Vector3{0.5f}.length());
} {
const Containers::Pair<Vector3, Float> sphere =
MeshTools::boundingSphereBouncingBubble(Containers::stridedArrayView({
Vector3{2.0f, 0.0f, 0.0f},
Vector3{-2.0f, 0.0f, 0.0f},
Vector3{0.0f, 2.0f, 0.0f},
Vector3{0.0f, -2.0f, 0.0f}
}));
CORRADE_COMPARE(sphere.first(), (Vector3{0.0f, 0.0f, 0.0f}));
CORRADE_COMPARE(sphere.second(), 2.0f);
/* Icosphere -- original/translated and scaled */
} {
const Trade::MeshData sphereMesh = Primitives::icosphereSolid(1);
const Containers::Pair<Vector3, Float> sphere =
MeshTools::boundingSphereBouncingBubble(sphereMesh.attribute<Vector3>(Trade::MeshAttribute::Position));
/* No error */
CORRADE_COMPARE(sphere.first(), (Vector3{0.0f, 0.0f, 0.0f}));
CORRADE_COMPARE(sphere.second(), 1.0f);
} {
Trade::MeshData sphereMesh = Primitives::icosphereSolid(1);
constexpr Vector3 translation{1.0f, 2.0f, 3.0f};
constexpr Vector3 scale{0.5f, 1.2f, 2.8f};
MeshTools::transform3DInPlace(sphereMesh, Matrix4::translation(translation)*Matrix4::scaling(scale));
const Containers::Pair<Vector3, Float> sphere =
MeshTools::boundingSphereBouncingBubble(sphereMesh.attribute<Vector3>(Trade::MeshAttribute::Position));
/* Noticeable error */
constexpr Float Delta = 0.04f;
CORRADE_COMPARE_WITH(sphere.first(), translation, TestSuite::Compare::around(Vector3{Delta}));
/* Radius should never be smaller than the ground truth */
CORRADE_COMPARE_WITH(sphere.second(), scale.max() + Delta, TestSuite::Compare::around(Delta));
/* Cube -- translated and scaled */
} {
Trade::MeshData cubeMesh = MeshTools::owned(Primitives::cubeSolid());
constexpr Vector3 translation{1.0f, 2.0f, 3.0f};
constexpr Float scale = 13.2f;
MeshTools::transform3DInPlace(cubeMesh, Matrix4::translation(translation)*Matrix4::scaling(Vector3{scale}));
const Containers::Pair<Vector3, Float> sphere =
MeshTools::boundingSphereBouncingBubble(cubeMesh.attribute<Vector3>(Trade::MeshAttribute::Position));
/* Noticeable error */
constexpr Float Delta = 0.04f;
CORRADE_COMPARE_WITH(sphere.first(), translation, TestSuite::Compare::around(Vector3{Delta}));
CORRADE_COMPARE_WITH(sphere.second(), Constants::sqrt3()*scale + Delta,
TestSuite::Compare::around(Delta));
}
/* Radius is rotationally invariant */
using namespace Math::Literals;
for(Deg degrees = 0.0_degf; degrees < 360.0_degf; degrees += 60.0_degf) {
CORRADE_ITERATION(degrees);
Trade::MeshData cubeMesh = MeshTools::owned(Primitives::cubeSolid());
constexpr Vector3 translation{1.0f, 2.0f, 3.0f};
MeshTools::transform3DInPlace(cubeMesh, Matrix4::rotationY(degrees)*Matrix4::translation(translation));
const Containers::Pair<Vector3, Float> sphere =
MeshTools::boundingSphereBouncingBubble(cubeMesh.attribute<Vector3>(Trade::MeshAttribute::Position));
CORRADE_COMPARE(sphere.second(), Constants::sqrt3());
}
}
void BoundingVolumeTest::sphereBouncingBubbleNaN() {
/* NaN is ignored except for the first position element */
{
const Containers::Pair<Vector3, Float> sphere =
MeshTools::boundingSphereBouncingBubble(Containers::stridedArrayView({
Vector3{1.0f, 1.0f, 1.0f},
Vector3{Constants::nan()},
Vector3{2.0f, 2.0f, 2.0f},
Vector3{Constants::nan()}
}));
CORRADE_COMPARE(sphere.first(), (Vector3{1.5f}));
CORRADE_COMPARE(sphere.second(), Vector3{0.5f}.length());
} {
const Containers::Pair<Vector3, Float> sphere =
MeshTools::boundingSphereBouncingBubble(Containers::stridedArrayView({
Vector3{Constants::nan()},
Vector3{1.0f, 1.0f, 1.0f},
Vector3{2.0f, 2.0f, 2.0f}
}));
{
CORRADE_EXPECT_FAIL("NaN in the first position is not ignored.");
CORRADE_COMPARE(sphere.first(), (Vector3{1.5f}));
CORRADE_COMPARE(sphere.second(), Vector3{0.5f}.length());
}
CORRADE_VERIFY(Math::isNan(sphere.first()));
CORRADE_COMPARE(sphere.second(), Math::TypeTraits<Float>::epsilon());
}
}
void BoundingVolumeTest::benchmarkBoxAxisAligned() {
Containers::Array<Vector3> points{NoInit, 500};
for(size_t i = 0; i < points.size(); ++i) {
points[i] = Vector3{Float(i)*0.01f};
}
Float r = 0.0f;
CORRADE_BENCHMARK(50) {
const Range3D box = MeshTools::boundingBoxAxisAligned(points);
r += box.size().x();
}
CORRADE_COMPARE_AS(r, 1.0f, TestSuite::Compare::Greater);
}
void BoundingVolumeTest::benchmarkSphereBouncingBubble() {
Containers::Array<Vector3> points{NoInit, 500};
for(size_t i = 0; i < points.size(); ++i) {
points[i] = Vector3{Float(i)*0.01f};
}
Float r = 0.0f;
CORRADE_BENCHMARK(50) {
const Containers::Pair<Vector3, Float> sphere =
MeshTools::boundingSphereBouncingBubble(points);
r += sphere.second();
}
CORRADE_COMPARE_AS(r, 1.0f, TestSuite::Compare::Greater);
}
}}}}
CORRADE_TEST_MAIN(Magnum::MeshTools::Test::BoundingVolumeTest)

1
src/Magnum/MeshTools/Test/CMakeLists.txt
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@ -27,6 +27,7 @@
# property that would have to be set on each target separately. # property that would have to be set on each target separately.
set(CMAKE_FOLDER "Magnum/MeshTools/Test") set(CMAKE_FOLDER "Magnum/MeshTools/Test")
corrade_add_test(MeshToolsBoundingVolumeTest BoundingVolumeTest.cpp LIBRARIES MagnumMeshToolsTestLib MagnumPrimitives)
corrade_add_test(MeshToolsCombineTest CombineTest.cpp LIBRARIES MagnumMeshToolsTestLib) corrade_add_test(MeshToolsCombineTest CombineTest.cpp LIBRARIES MagnumMeshToolsTestLib)
corrade_add_test(MeshToolsCompressIndicesTest CompressIndicesTest.cpp LIBRARIES MagnumMeshToolsTestLib) corrade_add_test(MeshToolsCompressIndicesTest CompressIndicesTest.cpp LIBRARIES MagnumMeshToolsTestLib)
corrade_add_test(MeshToolsConcatenateTest ConcatenateTest.cpp LIBRARIES MagnumMeshToolsTestLib) corrade_add_test(MeshToolsConcatenateTest ConcatenateTest.cpp LIBRARIES MagnumMeshToolsTestLib)

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