geo_alignedbox.cpp File Reference

#include "main.h"
#include <Eigen/Geometry>

Functions
template<typename T >
EIGEN_DONT_INLINE void	kill_extra_precision (T &)
template<typename BoxType >
void	alignedbox (const BoxType &box)
template<typename BoxType >
void	alignedboxTranslatable (const BoxType &box)
template<typename Scalar , typename Rotation >
Rotation	rotate2D (Scalar angle)
template<typename Scalar , typename Rotation >
Rotation	rotate2DIntegral (typename NumTraits< Scalar >::NonInteger angle)
template<typename Scalar , typename Rotation >
Rotation	rotate3DZAxis (Scalar angle)
template<typename Scalar , typename Rotation >
Rotation	rotate3DZAxisIntegral (typename NumTraits< Scalar >::NonInteger angle)
template<typename Scalar , typename Rotation >
Rotation	rotate4DZWAxis (Scalar angle)
template<typename MatrixType >
MatrixType	randomRotationMatrix ()
template<typename Scalar , int Dim>
Matrix< Scalar, Dim,(1<< Dim)>	boxGetCorners (const Matrix< Scalar, Dim, 1 > &min_, const Matrix< Scalar, Dim, 1 > &max_)
template<typename BoxType , typename Rotation >
void	alignedboxRotatable (const BoxType &box, Rotation(*rotate)(typename NumTraits< typename BoxType::Scalar >::NonInteger))
template<typename BoxType , typename Rotation >
void	alignedboxNonIntegralRotatable (const BoxType &box, Rotation(*rotate)(typename NumTraits< typename BoxType::Scalar >::NonInteger))
template<typename BoxType >
void	alignedboxCastTests (const BoxType &box)
void	specificTest1 ()
void	specificTest2 ()
	EIGEN_DECLARE_TEST (geo_alignedbox)

Function Documentation

alignedbox()

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) / Scalar(2);
  VectorType p1 = VectorType::Random(dim) / Scalar(2);
  while (p1 == p0) {
    p1 = VectorType::Random(dim) / Scalar(2);
  }
  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);
 
  VERIFY(numext::equal_strict(b0.volume(), Scalar(0)));
 
  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));
  }
}

References Eigen::numext::equal_strict(), i, kill_extra_precision(), p0, p1, UniformPSDSelfTest::r, VERIFY, and VERIFY_IS_APPROX.

Referenced by alignedboxTranslatable(), and EIGEN_DECLARE_TEST().

alignedboxCastTests()

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);
 
  VERIFY(numext::equal_strict(b0.volume(), Scalar(0)));
 
  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);
}

References Global_Variables::Dim, Eigen::numext::equal_strict(), p0, p1, VERIFY, and VERIFY_IS_APPROX.

Referenced by EIGEN_DECLARE_TEST().

alignedboxNonIntegralRotatable()

template<typename BoxType , typename Rotation >

void alignedboxNonIntegralRotatable	(	const BoxType &	box,
		Rotation(*)(typename NumTraits< typename BoxType::Scalar >::NonInteger)	rotate
	)

                                                                                                    {
  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);
  }
}

References alignedboxRotatable(), Jeffery_Solution::angle(), Eigen::bfloat16_impl::atan(), boxGetCorners(), calibrate::c, corners(), cos(), Global_Variables::Dim, EIGEN_PI, i, max, min, rot(), sin(), sqrt(), VERIFY_IS_APPROX, and oomph::PseudoSolidHelper::Zero.

alignedboxRotatable()

template<typename BoxType , typename Rotation >

void alignedboxRotatable	(	const BoxType &	box,
		Rotation(*)(typename NumTraits< typename BoxType::Scalar >::NonInteger)	rotate
	)

                                                                                                     {
  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);
}

References a, alignedboxTranslatable(), calibrate::c, EIGEN_PI, rot(), VERIFY_IS_APPROX, and oomph::PseudoSolidHelper::Zero.

Referenced by alignedboxNonIntegralRotatable().

alignedboxTranslatable()

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);
  }
}

References a, alignedbox(), b, calibrate::c, i, and VERIFY_IS_APPROX.

Referenced by alignedboxRotatable(), and EIGEN_DECLARE_TEST().

boxGetCorners()

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 & (Index(1) << j)) ? min_(j) : max_(j);
  }
  return result;
}

References Global_Variables::Dim, i, and j.

Referenced by alignedboxNonIntegralRotatable().

EIGEN_DECLARE_TEST()

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());
}

References alignedbox(), alignedboxCastTests(), alignedboxTranslatable(), CALL_SUBTEST_1, CALL_SUBTEST_10, CALL_SUBTEST_11, CALL_SUBTEST_12, CALL_SUBTEST_13, CALL_SUBTEST_14, CALL_SUBTEST_2, CALL_SUBTEST_3, CALL_SUBTEST_4, CALL_SUBTEST_5, CALL_SUBTEST_6, CALL_SUBTEST_7, CALL_SUBTEST_8, CALL_SUBTEST_9, Eigen::g_repeat, i, rotate2D(), rotate3DZAxis(), rotate4DZWAxis(), specificTest1(), and specificTest2().

kill_extra_precision()

template<typename T >

EIGEN_DONT_INLINE void kill_extra_precision

(

T &

)

                                                  {
  // This one worked but triggered a warning:
  /* eigen_assert((void*)(&x) != (void*)0); */
  // An alternative could be:
  /* volatile T tmp = x; */
  /* x = tmp; */
}

Referenced by alignedbox().

randomRotationMatrix()

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;
}

References determinant(), diag, Eigen::numext::q, and svd().

rotate2D()

template<typename Scalar , typename Rotation >

Rotation rotate2D

(

Scalar

angle

)

                                {
  return Rotation2D<Scalar>(angle);
}

References Jeffery_Solution::angle().

Referenced by EIGEN_DECLARE_TEST().

rotate2DIntegral()

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>();
}

References Jeffery_Solution::angle(), and Eigen::Rotation2D< Scalar_ >::toRotationMatrix().

rotate3DZAxis()

template<typename Scalar , typename Rotation >

Rotation rotate3DZAxis

(

Scalar

angle

)

                                     {
  return AngleAxis<Scalar>(angle, Matrix<Scalar, 3, 1>(0, 0, 1));
}

References Jeffery_Solution::angle().

Referenced by EIGEN_DECLARE_TEST().

rotate3DZAxisIntegral()

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>();
}

References Jeffery_Solution::angle(), and Eigen::AngleAxis< Scalar_ >::toRotationMatrix().

rotate4DZWAxis()

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;
}

References Jeffery_Solution::angle().

Referenced by EIGEN_DECLARE_TEST().

specificTest1()

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));
}

References m, sqrt(), and VERIFY_IS_APPROX.

Referenced by EIGEN_DECLARE_TEST().

specificTest2()

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));
}

References m, and VERIFY_IS_APPROX.

Referenced by EIGEN_DECLARE_TEST().