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geo_alignedbox.cpp
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Thu, Feb 20, 22:32

geo_alignedbox.cpp
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
#include <Eigen/Geometry>
using namespace std;
// NOTE the following workaround was needed on some 32 bits builds to kill extra precision of x87 registers.
// It seems that it is not needed anymore, but let's keep it here, just in case...
template<typename T> EIGEN_DONT_INLINE
void kill_extra_precision(T& /* x */) {
// This one worked but triggered a warning:
/* eigen_assert((void*)(&x) != (void*)0); */
// An alternative could be:
/* volatile T tmp = x; */
/* x = tmp; */
}
template<typename BoxType> void alignedbox(const BoxType& box)
{
/* this test covers the following files:
AlignedBox.h
*/
typedef typename BoxType::Scalar Scalar;
typedef NumTraits<Scalar> ScalarTraits;
typedef typename ScalarTraits::Real RealScalar;
typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
const Index dim = box.dim();
VectorType p0 = VectorType::Random(dim);
VectorType p1 = VectorType::Random(dim);
while( p1 == p0 ){
p1 = VectorType::Random(dim); }
RealScalar s1 = internal::random<RealScalar>(0,1);
BoxType b0(dim);
BoxType b1(VectorType::Random(dim),VectorType::Random(dim));
BoxType b2;
kill_extra_precision(b1);
kill_extra_precision(p0);
kill_extra_precision(p1);
b0.extend(p0);
b0.extend(p1);
VERIFY(b0.contains(p0*s1+(Scalar(1)-s1)*p1));
VERIFY(b0.contains(b0.center()));
VERIFY_IS_APPROX(b0.center(),(p0+p1)/Scalar(2));
(b2 = b0).extend(b1);
VERIFY(b2.contains(b0));
VERIFY(b2.contains(b1));
VERIFY_IS_APPROX(b2.clamp(b0), b0);
// intersection
BoxType box1(VectorType::Random(dim));
box1.extend(VectorType::Random(dim));
BoxType box2(VectorType::Random(dim));
box2.extend(VectorType::Random(dim));
VERIFY(box1.intersects(box2) == !box1.intersection(box2).isEmpty());
// alignment -- make sure there is no memory alignment assertion
BoxType *bp0 = new BoxType(dim);
BoxType *bp1 = new BoxType(dim);
bp0->extend(*bp1);
delete bp0;
delete bp1;
// sampling
for( int i=0; i<10; ++i )
{
VectorType r = b0.sample();
VERIFY(b0.contains(r));
}
}
template<typename BoxType> void alignedboxTranslatable(const BoxType& box)
{
typedef typename BoxType::Scalar Scalar;
typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
typedef Transform<Scalar, BoxType::AmbientDimAtCompileTime, Isometry> IsometryTransform;
typedef Transform<Scalar, BoxType::AmbientDimAtCompileTime, Affine> AffineTransform;
alignedbox(box);
const VectorType Ones = VectorType::Ones();
const VectorType UnitX = VectorType::UnitX();
const Index dim = box.dim();
// box((-1, -1, -1), (1, 1, 1))
BoxType a(-Ones, Ones);
VERIFY_IS_APPROX(a.sizes(), Ones * Scalar(2));
BoxType b = a;
VectorType translate = Ones;
translate[0] = Scalar(2);
b.translate(translate);
// translate by (2, 1, 1) -> box((1, 0, 0), (3, 2, 2))
VERIFY_IS_APPROX(b.sizes(), Ones * Scalar(2));
VERIFY_IS_APPROX((b.min)(), UnitX);
VERIFY_IS_APPROX((b.max)(), Ones * Scalar(2) + UnitX);
// Test transform
IsometryTransform tf = IsometryTransform::Identity();
tf.translation() = -translate;
BoxType c = b.transformed(tf);
// translate by (-2, -1, -1) -> box((-1, -1, -1), (1, 1, 1))
VERIFY_IS_APPROX(c.sizes(), a.sizes());
VERIFY_IS_APPROX((c.min)(), (a.min)());
VERIFY_IS_APPROX((c.max)(), (a.max)());
c.transform(tf);
// translate by (-2, -1, -1) -> box((-3, -2, -2), (-1, 0, 0))
VERIFY_IS_APPROX(c.sizes(), a.sizes());
VERIFY_IS_APPROX((c.min)(), Ones * Scalar(-2) - UnitX);
VERIFY_IS_APPROX((c.max)(), -UnitX);
// Scaling
AffineTransform atf = AffineTransform::Identity();
atf.scale(Scalar(3));
c.transform(atf);
// scale by 3 -> box((-9, -6, -6), (-3, 0, 0))
VERIFY_IS_APPROX(c.sizes(), Scalar(3) * a.sizes());
VERIFY_IS_APPROX((c.min)(), Ones * Scalar(-6) - UnitX * Scalar(3));
VERIFY_IS_APPROX((c.max)(), UnitX * Scalar(-3));
atf = AffineTransform::Identity();
atf.scale(Scalar(-3));
c.transform(atf);
// scale by -3 -> box((27, 18, 18), (9, 0, 0))
VERIFY_IS_APPROX(c.sizes(), Scalar(9) * a.sizes());
VERIFY_IS_APPROX((c.min)(), UnitX * Scalar(9));
VERIFY_IS_APPROX((c.max)(), Ones * Scalar(18) + UnitX * Scalar(9));
// Check identity transform within numerical precision.
BoxType transformedC = c.transformed(IsometryTransform::Identity());
VERIFY_IS_APPROX(transformedC, c);
for (size_t i = 0; i < 10; ++i)
{
VectorType minCorner;
VectorType maxCorner;
for (Index d = 0; d < dim; ++d)
{
minCorner[d] = internal::random<Scalar>(-10,10);
maxCorner[d] = minCorner[d] + internal::random<Scalar>(0, 10);
}
c = BoxType(minCorner, maxCorner);
translate = VectorType::Random();
c.translate(translate);
VERIFY_IS_APPROX((c.min)(), minCorner + translate);
VERIFY_IS_APPROX((c.max)(), maxCorner + translate);
}
}
template<typename Scalar, typename Rotation>
Rotation rotate2D(Scalar angle) {
return Rotation2D<Scalar>(angle);
}
template<typename Scalar, typename Rotation>
Rotation rotate2DIntegral(typename NumTraits<Scalar>::NonInteger angle) {
typedef typename NumTraits<Scalar>::NonInteger NonInteger;
return Rotation2D<NonInteger>(angle).toRotationMatrix().
template cast<Scalar>();
}
template<typename Scalar, typename Rotation>
Rotation rotate3DZAxis(Scalar angle) {
return AngleAxis<Scalar>(angle, Matrix<Scalar, 3, 1>(0, 0, 1));
}
template<typename Scalar, typename Rotation>
Rotation rotate3DZAxisIntegral(typename NumTraits<Scalar>::NonInteger angle) {
typedef typename NumTraits<Scalar>::NonInteger NonInteger;
return AngleAxis<NonInteger>(angle, Matrix<NonInteger, 3, 1>(0, 0, 1)).
toRotationMatrix().template cast<Scalar>();
}
template<typename Scalar, typename Rotation>
Rotation rotate4DZWAxis(Scalar angle) {
Rotation result = Matrix<Scalar, 4, 4>::Identity();
result.block(0, 0, 3, 3) = rotate3DZAxis<Scalar, AngleAxisd>(angle).toRotationMatrix();
return result;
}
template <typename MatrixType>
MatrixType randomRotationMatrix()
{
// algorithm from
// https://www.isprs-ann-photogramm-remote-sens-spatial-inf-sci.net/III-7/103/2016/isprs-annals-III-7-103-2016.pdf
const MatrixType rand = MatrixType::Random();
const MatrixType q = rand.householderQr().householderQ();
const JacobiSVD<MatrixType> svd = q.jacobiSvd(ComputeFullU | ComputeFullV);
const typename MatrixType::Scalar det = (svd.matrixU() * svd.matrixV().transpose()).determinant();
MatrixType diag = rand.Identity();
diag(MatrixType::RowsAtCompileTime - 1, MatrixType::ColsAtCompileTime - 1) = det;
const MatrixType rotation = svd.matrixU() * diag * svd.matrixV().transpose();
return rotation;
}
template <typename Scalar, int Dim>
Matrix<Scalar, Dim, (1<<Dim)> boxGetCorners(const Matrix<Scalar, Dim, 1>& min_, const Matrix<Scalar, Dim, 1>& max_)
{
Matrix<Scalar, Dim, (1<<Dim) > result;
for(Index i=0; i<(1<<Dim); ++i)
{
for(Index j=0; j<Dim; ++j)
result(j,i) = (i & (1<<j)) ? min_(j) : max_(j);
}
return result;
}
template<typename BoxType, typename Rotation> void alignedboxRotatable(
const BoxType& box,
Rotation (*rotate)(typename NumTraits<typename BoxType::Scalar>::NonInteger /*_angle*/))
{
alignedboxTranslatable(box);
typedef typename BoxType::Scalar Scalar;
typedef typename NumTraits<Scalar>::NonInteger NonInteger;
typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
typedef Transform<Scalar, BoxType::AmbientDimAtCompileTime, Isometry> IsometryTransform;
typedef Transform<Scalar, BoxType::AmbientDimAtCompileTime, Affine> AffineTransform;
const VectorType Zero = VectorType::Zero();
const VectorType Ones = VectorType::Ones();
const VectorType UnitX = VectorType::UnitX();
const VectorType UnitY = VectorType::UnitY();
// this is vector (0, 0, -1, -1, -1, ...), i.e. with zeros at first and second dimensions
const VectorType UnitZ = Ones - UnitX - UnitY;
// in this kind of comments the 3D case values will be illustrated
// box((-1, -1, -1), (1, 1, 1))
BoxType a(-Ones, Ones);
// to allow templating this test for both 2D and 3D cases, we always set all
// but the first coordinate to the same value; so basically 3D case works as
// if you were looking at the scene from top
VectorType minPoint = -2 * Ones;
minPoint[0] = -3;
VectorType maxPoint = Zero;
maxPoint[0] = -1;
BoxType c(minPoint, maxPoint);
// box((-3, -2, -2), (-1, 0, 0))
IsometryTransform tf2 = IsometryTransform::Identity();
// for some weird reason the following statement has to be put separate from
// the following rotate call, otherwise precision problems arise...
Rotation rot = rotate(NonInteger(EIGEN_PI));
tf2.rotate(rot);
c.transform(tf2);
// rotate by 180 deg around origin -> box((1, 0, -2), (3, 2, 0))
VERIFY_IS_APPROX(c.sizes(), a.sizes());
VERIFY_IS_APPROX((c.min)(), UnitX - UnitZ * Scalar(2));
VERIFY_IS_APPROX((c.max)(), UnitX * Scalar(3) + UnitY * Scalar(2));
rot = rotate(NonInteger(EIGEN_PI / 2));
tf2.setIdentity();
tf2.rotate(rot);
c.transform(tf2);
// rotate by 90 deg around origin -> box((-2, 1, -2), (0, 3, 0))
VERIFY_IS_APPROX(c.sizes(), a.sizes());
VERIFY_IS_APPROX((c.min)(), Ones * Scalar(-2) + UnitY * Scalar(3));
VERIFY_IS_APPROX((c.max)(), UnitY * Scalar(3));
// box((-1, -1, -1), (1, 1, 1))
AffineTransform atf = AffineTransform::Identity();
atf.linearExt()(0, 1) = Scalar(1);
c = BoxType(-Ones, Ones);
c.transform(atf);
// 45 deg shear in x direction -> box((-2, -1, -1), (2, 1, 1))
VERIFY_IS_APPROX(c.sizes(), Ones * Scalar(2) + UnitX * Scalar(2));
VERIFY_IS_APPROX((c.min)(), -Ones - UnitX);
VERIFY_IS_APPROX((c.max)(), Ones + UnitX);
}
template<typename BoxType, typename Rotation> void alignedboxNonIntegralRotatable(
const BoxType& box,
Rotation (*rotate)(typename NumTraits<typename BoxType::Scalar>::NonInteger /*_angle*/))
{
alignedboxRotatable(box, rotate);
typedef typename BoxType::Scalar Scalar;
typedef typename NumTraits<Scalar>::NonInteger NonInteger;
enum { Dim = BoxType::AmbientDimAtCompileTime };
typedef Matrix<Scalar, Dim, 1> VectorType;
typedef Matrix<Scalar, Dim, (1 << Dim)> CornersType;
typedef Transform<Scalar, Dim, Isometry> IsometryTransform;
typedef Transform<Scalar, Dim, Affine> AffineTransform;
const Index dim = box.dim();
const VectorType Zero = VectorType::Zero();
const VectorType Ones = VectorType::Ones();
VectorType minPoint = -2 * Ones;
minPoint[1] = 1;
VectorType maxPoint = Zero;
maxPoint[1] = 3;
BoxType c(minPoint, maxPoint);
// ((-2, 1, -2), (0, 3, 0))
VectorType cornerBL = (c.min)();
VectorType cornerTR = (c.max)();
VectorType cornerBR = (c.min)(); cornerBR[0] = cornerTR[0];
VectorType cornerTL = (c.max)(); cornerTL[0] = cornerBL[0];
NonInteger angle = NonInteger(EIGEN_PI/3);
Rotation rot = rotate(angle);
IsometryTransform tf2;
tf2.setIdentity();
tf2.rotate(rot);
c.transform(tf2);
// rotate by 60 deg -> box((-3.59, -1.23, -2), (-0.86, 1.5, 0))
cornerBL = tf2 * cornerBL;
cornerBR = tf2 * cornerBR;
cornerTL = tf2 * cornerTL;
cornerTR = tf2 * cornerTR;
VectorType minCorner = Ones * Scalar(-2);
VectorType maxCorner = Zero;
minCorner[0] = (min)((min)(cornerBL[0], cornerBR[0]), (min)(cornerTL[0], cornerTR[0]));
maxCorner[0] = (max)((max)(cornerBL[0], cornerBR[0]), (max)(cornerTL[0], cornerTR[0]));
minCorner[1] = (min)((min)(cornerBL[1], cornerBR[1]), (min)(cornerTL[1], cornerTR[1]));
maxCorner[1] = (max)((max)(cornerBL[1], cornerBR[1]), (max)(cornerTL[1], cornerTR[1]));
for (Index d = 2; d < dim; ++d)
VERIFY_IS_APPROX(c.sizes()[d], Scalar(2));
VERIFY_IS_APPROX((c.min)(), minCorner);
VERIFY_IS_APPROX((c.max)(), maxCorner);
VectorType minCornerValue = Ones * Scalar(-2);
VectorType maxCornerValue = Zero;
minCornerValue[0] = Scalar(Scalar(-sqrt(2*2 + 3*3)) * Scalar(cos(Scalar(atan(2.0/3.0)) - angle/2)));
minCornerValue[1] = Scalar(Scalar(-sqrt(1*1 + 2*2)) * Scalar(sin(Scalar(atan(2.0/1.0)) - angle/2)));
maxCornerValue[0] = Scalar(-sin(angle));
maxCornerValue[1] = Scalar(3 * cos(angle));
VERIFY_IS_APPROX((c.min)(), minCornerValue);
VERIFY_IS_APPROX((c.max)(), maxCornerValue);
// randomized test - translate and rotate the box and compare to a box made of transformed vertices
for (size_t i = 0; i < 10; ++i)
{
for (Index d = 0; d < dim; ++d)
{
minCorner[d] = internal::random<Scalar>(-10,10);
maxCorner[d] = minCorner[d] + internal::random<Scalar>(0, 10);
}
c = BoxType(minCorner, maxCorner);
CornersType corners = boxGetCorners(minCorner, maxCorner);
typename AffineTransform::LinearMatrixType rotation =
randomRotationMatrix<typename AffineTransform::LinearMatrixType>();
tf2.setIdentity();
tf2.rotate(rotation);
tf2.translate(VectorType::Random());
c.transform(tf2);
corners = tf2 * corners;
minCorner = corners.rowwise().minCoeff();
maxCorner = corners.rowwise().maxCoeff();
VERIFY_IS_APPROX((c.min)(), minCorner);
VERIFY_IS_APPROX((c.max)(), maxCorner);
}
// randomized test - transform the box with a random affine matrix and compare to a box made of transformed vertices
for (size_t i = 0; i < 10; ++i)
{
for (Index d = 0; d < dim; ++d)
{
minCorner[d] = internal::random<Scalar>(-10,10);
maxCorner[d] = minCorner[d] + internal::random<Scalar>(0, 10);
}
c = BoxType(minCorner, maxCorner);
CornersType corners = boxGetCorners(minCorner, maxCorner);
AffineTransform atf = AffineTransform::Identity();
atf.linearExt() = AffineTransform::LinearPart::Random();
atf.translate(VectorType::Random());
c.transform(atf);
corners = atf * corners;
minCorner = corners.rowwise().minCoeff();
maxCorner = corners.rowwise().maxCoeff();
VERIFY_IS_APPROX((c.min)(), minCorner);
VERIFY_IS_APPROX((c.max)(), maxCorner);
}
}
template<typename BoxType>
void alignedboxCastTests(const BoxType& box)
{
// casting
typedef typename BoxType::Scalar Scalar;
typedef Matrix<Scalar, BoxType::AmbientDimAtCompileTime, 1> VectorType;
const Index dim = box.dim();
VectorType p0 = VectorType::Random(dim);
VectorType p1 = VectorType::Random(dim);
BoxType b0(dim);
b0.extend(p0);
b0.extend(p1);
const int Dim = BoxType::AmbientDimAtCompileTime;
typedef typename GetDifferentType<Scalar>::type OtherScalar;
AlignedBox<OtherScalar,Dim> hp1f = b0.template cast<OtherScalar>();
VERIFY_IS_APPROX(hp1f.template cast<Scalar>(),b0);
AlignedBox<Scalar,Dim> hp1d = b0.template cast<Scalar>();
VERIFY_IS_APPROX(hp1d.template cast<Scalar>(),b0);
}
void specificTest1()
{
Vector2f m; m << -1.0f, -2.0f;
Vector2f M; M << 1.0f, 5.0f;
typedef AlignedBox2f BoxType;
BoxType box( m, M );
Vector2f sides = M-m;
VERIFY_IS_APPROX(sides, box.sizes() );
VERIFY_IS_APPROX(sides[1], box.sizes()[1] );
VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() );
VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() );
VERIFY_IS_APPROX( 14.0f, box.volume() );
VERIFY_IS_APPROX( 53.0f, box.diagonal().squaredNorm() );
VERIFY_IS_APPROX( std::sqrt( 53.0f ), box.diagonal().norm() );
VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeft ) );
VERIFY_IS_APPROX( M, box.corner( BoxType::TopRight ) );
Vector2f bottomRight; bottomRight << M[0], m[1];
Vector2f topLeft; topLeft << m[0], M[1];
VERIFY_IS_APPROX( bottomRight, box.corner( BoxType::BottomRight ) );
VERIFY_IS_APPROX( topLeft, box.corner( BoxType::TopLeft ) );
}
void specificTest2()
{
Vector3i m; m << -1, -2, 0;
Vector3i M; M << 1, 5, 3;
typedef AlignedBox3i BoxType;
BoxType box( m, M );
Vector3i sides = M-m;
VERIFY_IS_APPROX(sides, box.sizes() );
VERIFY_IS_APPROX(sides[1], box.sizes()[1] );
VERIFY_IS_APPROX(sides[1], box.sizes().maxCoeff() );
VERIFY_IS_APPROX(sides[0], box.sizes().minCoeff() );
VERIFY_IS_APPROX( 42, box.volume() );
VERIFY_IS_APPROX( 62, box.diagonal().squaredNorm() );
VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeftFloor ) );
VERIFY_IS_APPROX( M, box.corner( BoxType::TopRightCeil ) );
Vector3i bottomRightFloor; bottomRightFloor << M[0], m[1], m[2];
Vector3i topLeftFloor; topLeftFloor << m[0], M[1], m[2];
VERIFY_IS_APPROX( bottomRightFloor, box.corner( BoxType::BottomRightFloor ) );
VERIFY_IS_APPROX( topLeftFloor, box.corner( BoxType::TopLeftFloor ) );
}
EIGEN_DECLARE_TEST(geo_alignedbox)
{
for(int i = 0; i < g_repeat; i++)
{
CALL_SUBTEST_1( (alignedboxNonIntegralRotatable<AlignedBox2f, Rotation2Df>(AlignedBox2f(), &rotate2D)) );
CALL_SUBTEST_2( alignedboxCastTests(AlignedBox2f()) );
CALL_SUBTEST_3( (alignedboxNonIntegralRotatable<AlignedBox3f, AngleAxisf>(AlignedBox3f(), &rotate3DZAxis)) );
CALL_SUBTEST_4( alignedboxCastTests(AlignedBox3f()) );
CALL_SUBTEST_5( (alignedboxNonIntegralRotatable<AlignedBox4d, Matrix4d>(AlignedBox4d(), &rotate4DZWAxis)) );
CALL_SUBTEST_6( alignedboxCastTests(AlignedBox4d()) );
CALL_SUBTEST_7( alignedboxTranslatable(AlignedBox1d()) );
CALL_SUBTEST_8( alignedboxCastTests(AlignedBox1d()) );
CALL_SUBTEST_9( alignedboxTranslatable(AlignedBox1i()) );
CALL_SUBTEST_10( (alignedboxRotatable<AlignedBox2i, Matrix2i>(AlignedBox2i(), &rotate2DIntegral<int, Matrix2i>)) );
CALL_SUBTEST_11( (alignedboxRotatable<AlignedBox3i, Matrix3i>(AlignedBox3i(), &rotate3DZAxisIntegral<int, Matrix3i>)) );
CALL_SUBTEST_14( alignedbox(AlignedBox<double,Dynamic>(4)) );
}
CALL_SUBTEST_12( specificTest1() );
CALL_SUBTEST_13( specificTest2() );
}

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