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