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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, ComputeFullU | ComputeFullV> svd(q);
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());
}