+++ /dev/null
-/* -*- C++ -*- ------------------------------------------------------------
-
-Copyright (c) 2007 Jesse Anders and Demian Nave http://cmldev.net/
-
-The Configurable Math Library (CML) is distributed under the terms of the
-Boost Software License, v1.0 (see cml/LICENSE for details).
-
- *-----------------------------------------------------------------------*/
-/** @file
- * @brief
- */
-
-#ifndef matrix_rotation_h
-#define matrix_rotation_h
-
-#include <cml/mathlib/matrix_misc.h>
-#include <cml/mathlib/vector_ortho.h>
-
-/* Functions related to matrix rotations in 3D and 2D. */
-
-namespace cml {
-
-//////////////////////////////////////////////////////////////////////////////
-// 3D rotation about world axes
-//////////////////////////////////////////////////////////////////////////////
-
-/** Build a matrix representing a 3D rotation about the given world axis */
-template < typename E, class A, class B, class L > void
-matrix_rotation_world_axis( matrix<E,A,B,L>& m, size_t axis, E angle)
-{
- typedef matrix<E,A,B,L> matrix_type;
- typedef typename matrix_type::value_type value_type;
-
- /* Checking */
- detail::CheckMatLinear3D(m);
- detail::CheckIndex3(axis);
-
- size_t i, j, k;
- cyclic_permutation(axis, i, j, k);
-
- value_type s = value_type(std::sin(angle));
- value_type c = value_type(std::cos(angle));
-
- identity_transform(m);
-
- m.set_basis_element(j,j, c);
- m.set_basis_element(j,k, s);
- m.set_basis_element(k,j,-s);
- m.set_basis_element(k,k, c);
-}
-
-/** Build a matrix representing a 3D rotation about the world x axis */
-template < typename E, class A, class B, class L > void
-matrix_rotation_world_x(matrix<E,A,B,L>& m, E angle) {
- matrix_rotation_world_axis(m,0,angle);
-}
-
-/** Build a matrix representing a 3D rotation about the world y axis */
-template < typename E, class A, class B, class L > void
-matrix_rotation_world_y(matrix<E,A,B,L>& m, E angle) {
- matrix_rotation_world_axis(m,1,angle);
-}
-
-/** Build a matrix representing a 3D rotation about the world z axis */
-template < typename E, class A, class B, class L > void
-matrix_rotation_world_z(matrix<E,A,B,L>& m, E angle) {
- matrix_rotation_world_axis(m,2,angle);
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// 3D rotation from an axis-angle pair
-//////////////////////////////////////////////////////////////////////////////
-
-/** Build a rotation matrix from an axis-angle pair */
-template < typename E, class A, class B, class L, class VecT > void
-matrix_rotation_axis_angle(matrix<E,A,B,L>& m, const VecT& axis, E angle)
-{
- typedef matrix<E,A,B,L> matrix_type;
- typedef typename matrix_type::value_type value_type;
-
- /* Checking */
- detail::CheckMatLinear3D(m);
- detail::CheckVec3(axis);
-
- identity_transform(m);
-
- value_type s = std::sin(angle);
- value_type c = std::cos(angle);
- value_type omc = value_type(1) - c;
-
- value_type xomc = axis[0] * omc;
- value_type yomc = axis[1] * omc;
- value_type zomc = axis[2] * omc;
-
- value_type xxomc = axis[0] * xomc;
- value_type yyomc = axis[1] * yomc;
- value_type zzomc = axis[2] * zomc;
- value_type xyomc = axis[0] * yomc;
- value_type yzomc = axis[1] * zomc;
- value_type zxomc = axis[2] * xomc;
-
- value_type xs = axis[0] * s;
- value_type ys = axis[1] * s;
- value_type zs = axis[2] * s;
-
- m.set_basis_element(0,0, xxomc + c );
- m.set_basis_element(0,1, xyomc + zs);
- m.set_basis_element(0,2, zxomc - ys);
- m.set_basis_element(1,0, xyomc - zs);
- m.set_basis_element(1,1, yyomc + c );
- m.set_basis_element(1,2, yzomc + xs);
- m.set_basis_element(2,0, zxomc + ys);
- m.set_basis_element(2,1, yzomc - xs);
- m.set_basis_element(2,2, zzomc + c );
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// 3D rotation from a quaternion
-//////////////////////////////////////////////////////////////////////////////
-
-/** Build a rotation matrix from a quaternion */
-template < typename E, class A, class B, class L, class QuatT > void
-matrix_rotation_quaternion(matrix<E,A,B,L>& m, const QuatT& q)
-{
- typedef matrix<E,A,B,L> matrix_type;
- typedef QuatT quaternion_type;
- typedef typename quaternion_type::order_type order_type;
- typedef typename matrix_type::value_type value_type;
-
- enum {
- W = order_type::W,
- X = order_type::X,
- Y = order_type::Y,
- Z = order_type::Z
- };
-
- /* Checking */
- detail::CheckMatLinear3D(m);
- detail::CheckQuat(q);
-
- identity_transform(m);
-
- value_type x2 = q[X] + q[X];
- value_type y2 = q[Y] + q[Y];
- value_type z2 = q[Z] + q[Z];
-
- value_type xx2 = q[X] * x2;
- value_type yy2 = q[Y] * y2;
- value_type zz2 = q[Z] * z2;
- value_type xy2 = q[X] * y2;
- value_type yz2 = q[Y] * z2;
- value_type zx2 = q[Z] * x2;
- value_type xw2 = q[W] * x2;
- value_type yw2 = q[W] * y2;
- value_type zw2 = q[W] * z2;
-
- m.set_basis_element(0,0, value_type(1) - yy2 - zz2);
- m.set_basis_element(0,1, xy2 + zw2);
- m.set_basis_element(0,2, zx2 - yw2);
- m.set_basis_element(1,0, xy2 - zw2);
- m.set_basis_element(1,1, value_type(1) - zz2 - xx2);
- m.set_basis_element(1,2, yz2 + xw2);
- m.set_basis_element(2,0, zx2 + yw2);
- m.set_basis_element(2,1, yz2 - xw2);
- m.set_basis_element(2,2, value_type(1) - xx2 - yy2);
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// 3D rotation from Euler angles
-//////////////////////////////////////////////////////////////////////////////
-
-/** Build a rotation matrix from an Euler-angle triple
- *
- * The rotations are applied about the cardinal axes in the order specified by
- * the 'order' argument, where 'order' is one of the following enumerants:
- *
- * euler_order_xyz
- * euler_order_xzy
- * euler_order_xyx
- * euler_order_xzx
- * euler_order_yzx
- * euler_order_yxz
- * euler_order_yzy
- * euler_order_yxy
- * euler_order_zxy
- * euler_order_zyx
- * euler_order_zxz
- * euler_order_zyz
- */
-
-template < typename E, class A, class B, class L > void
-matrix_rotation_euler(matrix<E,A,B,L>& m, E angle_0, E angle_1, E angle_2,
- EulerOrder order)
-{
- typedef matrix<E,A,B,L> matrix_type;
- typedef typename matrix_type::value_type value_type;
-
- /* Checking */
- detail::CheckMatLinear3D(m);
-
- identity_transform(m);
-
- size_t i, j, k;
- bool odd, repeat;
- detail::unpack_euler_order(order, i, j, k, odd, repeat);
-
- if (odd) {
- angle_0 = -angle_0;
- angle_1 = -angle_1;
- angle_2 = -angle_2;
- }
-
- value_type s0 = std::sin(angle_0);
- value_type c0 = std::cos(angle_0);
- value_type s1 = std::sin(angle_1);
- value_type c1 = std::cos(angle_1);
- value_type s2 = std::sin(angle_2);
- value_type c2 = std::cos(angle_2);
-
- value_type s0s2 = s0 * s2;
- value_type s0c2 = s0 * c2;
- value_type c0s2 = c0 * s2;
- value_type c0c2 = c0 * c2;
-
- if (repeat) {
- m.set_basis_element(i,i, c1 );
- m.set_basis_element(i,j, s1 * s2 );
- m.set_basis_element(i,k,-s1 * c2 );
- m.set_basis_element(j,i, s0 * s1 );
- m.set_basis_element(j,j,-c1 * s0s2 + c0c2);
- m.set_basis_element(j,k, c1 * s0c2 + c0s2);
- m.set_basis_element(k,i, c0 * s1 );
- m.set_basis_element(k,j,-c1 * c0s2 - s0c2);
- m.set_basis_element(k,k, c1 * c0c2 - s0s2);
- } else {
- m.set_basis_element(i,i, c1 * c2 );
- m.set_basis_element(i,j, c1 * s2 );
- m.set_basis_element(i,k,-s1 );
- m.set_basis_element(j,i, s1 * s0c2 - c0s2);
- m.set_basis_element(j,j, s1 * s0s2 + c0c2);
- m.set_basis_element(j,k, s0 * c1 );
- m.set_basis_element(k,i, s1 * c0c2 + s0s2);
- m.set_basis_element(k,j, s1 * c0s2 - s0c2);
- m.set_basis_element(k,k, c0 * c1 );
- }
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// 3D rotation to align with a vector, multiple vectors, or the view plane
-//////////////////////////////////////////////////////////////////////////////
-
-/** See vector_ortho.h for details */
-template < typename E,class A,class B,class L,class VecT_1,class VecT_2 > void
-matrix_rotation_align(
- matrix<E,A,B,L>& m,
- const VecT_1& align,
- const VecT_2& reference,
- bool normalize = true,
- AxisOrder order = axis_order_zyx)
-{
- typedef vector< E,fixed<3> > vector_type;
-
- identity_transform(m);
-
- vector_type x, y, z;
-
- orthonormal_basis(align, reference, x, y, z, normalize, order);
- matrix_set_basis_vectors(m, x, y, z);
-}
-
-/** See vector_ortho.h for details */
-template < typename E, class A, class B, class L, class VecT > void
-matrix_rotation_align(matrix<E,A,B,L>& m, const VecT& align,
- bool normalize = true, AxisOrder order = axis_order_zyx)
-{
- typedef vector< E,fixed<3> > vector_type;
-
- identity_transform(m);
-
- vector_type x, y, z;
-
- orthonormal_basis(align, x, y, z, normalize, order);
- matrix_set_basis_vectors(m, x, y, z);
-}
-
-/** See vector_ortho.h for details */
-template < typename E,class A,class B,class L,class VecT_1,class VecT_2 > void
-matrix_rotation_align_axial(matrix<E,A,B,L>& m, const VecT_1& align,
- const VecT_2& axis, bool normalize = true,
- AxisOrder order = axis_order_zyx)
-{
- typedef vector< E,fixed<3> > vector_type;
-
- identity_transform(m);
-
- vector_type x, y, z;
-
- orthonormal_basis_axial(align, axis, x, y, z, normalize, order);
- matrix_set_basis_vectors(m, x, y, z);
-}
-
-/** See vector_ortho.h for details */
-template < typename E, class A, class B, class L, class MatT > void
-matrix_rotation_align_viewplane(
- matrix<E,A,B,L>& m,
- const MatT& view_matrix,
- Handedness handedness,
- AxisOrder order = axis_order_zyx)
-{
- typedef vector< E, fixed<3> > vector_type;
-
- identity_transform(m);
-
- vector_type x, y, z;
-
- orthonormal_basis_viewplane(view_matrix, x, y, z, handedness, order);
- matrix_set_basis_vectors(m, x, y, z);
-}
-
-/** See vector_ortho.h for details */
-template < typename E, class A, class B, class L, class MatT > void
-matrix_rotation_align_viewplane_LH(
- matrix<E,A,B,L>& m,
- const MatT& view_matrix,
- AxisOrder order = axis_order_zyx)
-{
- matrix_rotation_align_viewplane(
- m,view_matrix,left_handed,order);
-}
-
-/** See vector_ortho.h for details */
-template < typename E, class A, class B, class L, class MatT > void
-matrix_rotation_align_viewplane_RH(
- matrix<E,A,B,L>& m,
- const MatT& view_matrix,
- AxisOrder order = axis_order_zyx)
-{
- matrix_rotation_align_viewplane(
- m,view_matrix,right_handed,order);
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// 3D rotation to aim at a target
-//////////////////////////////////////////////////////////////////////////////
-
-/** See vector_ortho.h for details */
-template < typename E, class A, class B, class L,
- class VecT_1, class VecT_2, class VecT_3 > void
-matrix_rotation_aim_at(
- matrix<E,A,B,L>& m,
- const VecT_1& pos,
- const VecT_2& target,
- const VecT_3& reference,
- AxisOrder order = axis_order_zyx)
-{
- matrix_rotation_align(m, target - pos, reference, true, order);
-}
-
-/** See vector_ortho.h for details */
-template < typename E, class A, class B, class L,
- class VecT_1, class VecT_2 > void
-matrix_rotation_aim_at(
- matrix<E,A,B,L>& m,
- const VecT_1& pos,
- const VecT_2& target,
- AxisOrder order = axis_order_zyx)
-{
- matrix_rotation_align(m, target - pos, true, order);
-}
-
-/** See vector_ortho.h for details */
-template < typename E, class A, class B, class L,
- class VecT_1, class VecT_2, class VecT_3 > void
-matrix_rotation_aim_at_axial(
- matrix<E,A,B,L>& m,
- const VecT_1& pos,
- const VecT_2& target,
- const VecT_3& axis,
- AxisOrder order = axis_order_zyx)
-{
- matrix_rotation_align_axial(m, target - pos, axis, true, order);
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// 2D rotation
-//////////////////////////////////////////////////////////////////////////////
-
-/** Build a matrix representing a 2D rotation */
-template < typename E, class A, class B, class L > void
-matrix_rotation_2D( matrix<E,A,B,L>& m, E angle)
-{
- typedef matrix<E,A,B,L> matrix_type;
- typedef typename matrix_type::value_type value_type;
-
- /* Checking */
- detail::CheckMatLinear2D(m);
-
- value_type s = value_type(std::sin(angle));
- value_type c = value_type(std::cos(angle));
-
- identity_transform(m);
-
- m.set_basis_element(0,0, c);
- m.set_basis_element(0,1, s);
- m.set_basis_element(1,0,-s);
- m.set_basis_element(1,1, c);
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// 2D rotation to align with a vector
-//////////////////////////////////////////////////////////////////////////////
-
-/** See vector_ortho.h for details */
-template < typename E, class A, class B, class L, class VecT > void
-matrix_rotation_align_2D(matrix<E,A,B,L>& m, const VecT& align,
- bool normalize = true, AxisOrder2D order = axis_order_xy)
-{
- typedef vector< E, fixed<2> > vector_type;
-
- identity_transform(m);
-
- vector_type x, y;
-
- orthonormal_basis_2D(align, x, y, normalize, order);
- matrix_set_basis_vectors_2D(m, x, y);
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// 3D relative rotation about world axes
-//////////////////////////////////////////////////////////////////////////////
-
-/** Rotate a rotation matrix about the given world axis */
-template < typename E, class A, class B, class L > void
-matrix_rotate_about_world_axis(matrix<E,A,B,L>& m, size_t axis, E angle)
-{
- typedef matrix<E,A,B,L> matrix_type;
- typedef typename matrix_type::value_type value_type;
-
- /* Checking */
- detail::CheckMatLinear3D(m);
- detail::CheckIndex3(axis);
-
- size_t i, j, k;
- cyclic_permutation(axis, i, j, k);
-
- value_type s = value_type(std::sin(angle));
- value_type c = value_type(std::cos(angle));
-
- value_type ij = c * m.basis_element(i,j) - s * m.basis_element(i,k);
- value_type jj = c * m.basis_element(j,j) - s * m.basis_element(j,k);
- value_type kj = c * m.basis_element(k,j) - s * m.basis_element(k,k);
-
- m.set_basis_element(i,k, s*m.basis_element(i,j) + c*m.basis_element(i,k));
- m.set_basis_element(j,k, s*m.basis_element(j,j) + c*m.basis_element(j,k));
- m.set_basis_element(k,k, s*m.basis_element(k,j) + c*m.basis_element(k,k));
-
- m.set_basis_element(i,j,ij);
- m.set_basis_element(j,j,jj);
- m.set_basis_element(k,j,kj);
-}
-
-/** Rotate a rotation matrix about the world x axis */
-template < typename E, class A, class B, class L > void
-matrix_rotate_about_world_x(matrix<E,A,B,L>& m, E angle) {
- matrix_rotate_about_world_axis(m,0,angle);
-}
-
-/** Rotate a rotation matrix about the world y axis */
-template < typename E, class A, class B, class L > void
-matrix_rotate_about_world_y(matrix<E,A,B,L>& m, E angle) {
- matrix_rotate_about_world_axis(m,1,angle);
-}
-
-/** Rotate a rotation matrix about the world z axis */
-template < typename E, class A, class B, class L > void
-matrix_rotate_about_world_z(matrix<E,A,B,L>& m, E angle) {
- matrix_rotate_about_world_axis(m,2,angle);
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// 3D relative rotation about local axes
-//////////////////////////////////////////////////////////////////////////////
-
-/** Rotate a rotation matrix about the given local axis */
-template < typename E, class A, class B, class L > void
-matrix_rotate_about_local_axis(matrix<E,A,B,L>& m, size_t axis, E angle)
-{
- typedef matrix<E,A,B,L> matrix_type;
- typedef typename matrix_type::value_type value_type;
-
- /* Checking */
- detail::CheckMatLinear3D(m);
- detail::CheckIndex3(axis);
-
- size_t i, j, k;
- cyclic_permutation(axis, i, j, k);
-
- value_type s = value_type(std::sin(angle));
- value_type c = value_type(std::cos(angle));
-
- value_type j0 = c * m.basis_element(j,0) + s * m.basis_element(k,0);
- value_type j1 = c * m.basis_element(j,1) + s * m.basis_element(k,1);
- value_type j2 = c * m.basis_element(j,2) + s * m.basis_element(k,2);
-
- m.set_basis_element(k,0, c*m.basis_element(k,0) - s*m.basis_element(j,0));
- m.set_basis_element(k,1, c*m.basis_element(k,1) - s*m.basis_element(j,1));
- m.set_basis_element(k,2, c*m.basis_element(k,2) - s*m.basis_element(j,2));
-
- m.set_basis_element(j,0,j0);
- m.set_basis_element(j,1,j1);
- m.set_basis_element(j,2,j2);
-}
-
-/** Rotate a rotation matrix about its local x axis */
-template < typename E, class A, class B, class L > void
-matrix_rotate_about_local_x(matrix<E,A,B,L>& m, E angle) {
- matrix_rotate_about_local_axis(m,0,angle);
-}
-
-/** Rotate a rotation matrix about its local y axis */
-template < typename E, class A, class B, class L > void
-matrix_rotate_about_local_y(matrix<E,A,B,L>& m, E angle) {
- matrix_rotate_about_local_axis(m,1,angle);
-}
-
-/** Rotate a rotation matrix about its local z axis */
-template < typename E, class A, class B, class L > void
-matrix_rotate_about_local_z(matrix<E,A,B,L>& m, E angle) {
- matrix_rotate_about_local_axis(m,2,angle);
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// 2D relative rotation
-//////////////////////////////////////////////////////////////////////////////
-
-template < typename E, class A, class B, class L > void
-matrix_rotate_2D(matrix<E,A,B,L>& m, E angle)
-{
- typedef matrix<E,A,B,L> matrix_type;
- typedef typename matrix_type::value_type value_type;
-
- /* Checking */
- detail::CheckMatLinear2D(m);
-
- value_type s = value_type(std::sin(angle));
- value_type c = value_type(std::cos(angle));
-
- value_type m00 = c * m.basis_element(0,0) - s * m.basis_element(0,1);
- value_type m10 = c * m.basis_element(1,0) - s * m.basis_element(1,1);
-
- m.set_basis_element(0,1, s*m.basis_element(0,0) + c*m.basis_element(0,1));
- m.set_basis_element(1,1, s*m.basis_element(1,0) + c*m.basis_element(1,1));
-
- m.set_basis_element(0,0,m00);
- m.set_basis_element(1,0,m10);
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// Rotation from vector to vector
-//////////////////////////////////////////////////////////////////////////////
-
-/** Build a rotation matrix to rotate from one vector to another
- *
- * Note: The quaternion algorithm is more stable than the matrix algorithm, so
- * we simply pass off to the quaternion function here.
- */
-template < class E,class A,class B,class L,class VecT_1,class VecT_2 > void
-matrix_rotation_vec_to_vec(
- matrix<E,A,B,L>& m,
- const VecT_1& v1,
- const VecT_2& v2,
- bool unit_length_vectors = false)
-{
- typedef quaternion< E,fixed<>,vector_first,positive_cross >
- quaternion_type;
-
- quaternion_type q;
- quaternion_rotation_vec_to_vec(q,v1,v2,unit_length_vectors);
- matrix_rotation_quaternion(m,q);
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// Scale the angle of a rotation matrix
-//////////////////////////////////////////////////////////////////////////////
-
-/** Scale the angle of a 3D rotation matrix */
-template < typename E, class A, class B, class L > void
-matrix_scale_rotation_angle(matrix<E,A,B,L>& m, E t,
- E tolerance = epsilon<E>::placeholder())
-{
- typedef vector< E,fixed<3> > vector_type;
- typedef typename vector_type::value_type value_type;
-
- vector_type axis;
- value_type angle;
- matrix_to_axis_angle(m, axis, angle, tolerance);
- matrix_rotation_axis_angle(m, axis, angle * t);
-}
-
-/** Scale the angle of a 2D rotation matrix */
-template < typename E, class A, class B, class L > void
-matrix_scale_rotation_angle_2D(
- matrix<E,A,B,L>& m, E t, E tolerance = epsilon<E>::placeholder())
-{
- typedef vector< E,fixed<2> > vector_type;
- typedef typename vector_type::value_type value_type;
-
- value_type angle = matrix_to_rotation_2D(m);
- matrix_rotation_2D(m, angle * t);
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// Support functions for uniform handling of row- and column-basis matrices
-//////////////////////////////////////////////////////////////////////////////
-
-/* Note: The matrix rotation slerp, difference and concatenation functions do
- * not use et::MatrixPromote<M1,M2>::temporary_type as the return type, even
- * though that is the return type of the underlying matrix multiplication.
- * This is because the sizes of these matrices are known at compile time (3x3
- * and 2x2), and using fixed<> obviates the need for resizing of intermediate
- * temporaries.
- *
- * Also, no size- or type-checking is done on the arguments to these
- * functions, as any such errors will be caught by the matrix multiplication
- * and assignment to the 3x3 temporary.
- */
-
-/** A fixed-size temporary 3x3 matrix */
-#define MAT_TEMP_3X3 matrix< \
- typename et::ScalarPromote< \
- typename MatT_1::value_type, \
- typename MatT_2::value_type \
- >::type, \
- fixed<3,3>, \
- typename MatT_1::basis_orient, \
- row_major \
->
-
-/** A fixed-size temporary 2x2 matrix */
-#define MAT_TEMP_2X2 matrix< \
- typename et::ScalarPromote< \
- typename MatT_1::value_type, \
- typename MatT_2::value_type \
- >::type, \
- fixed<2,2>, \
- typename MatT_1::basis_orient, \
- row_major \
->
-
-namespace detail {
-
-/** Concatenate two 3D row-basis rotation matrices in the order m1->m2 */
-template < class MatT_1, class MatT_2 > MAT_TEMP_3X3
-matrix_concat_rotations(const MatT_1& m1, const MatT_2& m2, row_basis) {
- return m1*m2;
-}
-
-/** Concatenate two 3D col-basis rotation matrices in the order m1->m2 */
-template < class MatT_1, class MatT_2 > MAT_TEMP_3X3
-matrix_concat_rotations(const MatT_1& m1, const MatT_2& m2, col_basis) {
- return m2*m1;
-}
-
-/** Concatenate two 3D rotation matrices in the order m1->m2 */
-template < class MatT_1, class MatT_2 > MAT_TEMP_3X3
-matrix_concat_rotations(const MatT_1& m1, const MatT_2& m2) {
- return matrix_concat_rotations(m1,m2,typename MatT_1::basis_orient());
-}
-
-/** Concatenate two 2D row-basis rotation matrices in the order m1->m2 */
-template < class MatT_1, class MatT_2 > MAT_TEMP_2X2
-matrix_concat_rotations_2D(const MatT_1& m1, const MatT_2& m2, row_basis) {
- return m1*m2;
-}
-
-/** Concatenate two 2D col-basis rotation matrices in the order m1->m2 */
-template < class MatT_1, class MatT_2 > MAT_TEMP_2X2
-matrix_concat_rotations_2D(const MatT_1& m1, const MatT_2& m2, col_basis) {
- return m2*m1;
-}
-
-/** Concatenate two 2D rotation matrices in the order m1->m2 */
-template < class MatT_1, class MatT_2 > MAT_TEMP_2X2
-matrix_concat_rotations_2D(const MatT_1& m1, const MatT_2& m2) {
- return matrix_concat_rotations_2D(m1,m2,typename MatT_1::basis_orient());
-}
-
-} // namespace detail
-
-//////////////////////////////////////////////////////////////////////////////
-// Matrix rotation difference
-//////////////////////////////////////////////////////////////////////////////
-
-/** Return the rotational 'difference' between two 3D rotation matrices */
-template < class MatT_1, class MatT_2 > MAT_TEMP_3X3
-matrix_rotation_difference(const MatT_1& m1, const MatT_2& m2) {
- return detail::matrix_concat_rotations(transpose(m1),m2);
-}
-
-/** Return the rotational 'difference' between two 2D rotation matrices */
-template < class MatT_1, class MatT_2 > MAT_TEMP_2X2
-matrix_rotation_difference_2D(const MatT_1& m1, const MatT_2& m2) {
- return detail::matrix_concat_rotations_2D(transpose(m1),m2);
-}
-
-//////////////////////////////////////////////////////////////////////////////
-// Spherical linear interpolation of rotation matrices
-//////////////////////////////////////////////////////////////////////////////
-
-/* @todo: It might be as fast or faster to simply convert the matrices to
- * quaternions, interpolate, and convert back.
- *
- * @todo: The behavior of matrix slerp is currently a little different than
- * for quaternions: in the matrix function, when the two matrices are close
- * to identical the first is returned, while in the quaternion function the
- * quaternions are nlerp()'d in this case.
- *
- * I still need to do the equivalent of nlerp() for matrices, in which case
- * these functions could be revised to pass off to nlerp() when the matrices
- * are nearly aligned.
-*/
-
-/** Spherical linear interpolation of two 3D rotation matrices */
-template < class MatT_1, class MatT_2, typename E > MAT_TEMP_3X3
-matrix_slerp(const MatT_1& m1, const MatT_2& m2, E t,
- E tolerance = epsilon<E>::placeholder())
-{
- typedef MAT_TEMP_3X3 temporary_type;
-
- temporary_type m = matrix_rotation_difference(m1,m2);
- matrix_scale_rotation_angle(m,t,tolerance);
- return detail::matrix_concat_rotations(m1,m);
-}
-
-/** Spherical linear interpolation of two 2D rotation matrices */
-template < class MatT_1, class MatT_2, typename E > MAT_TEMP_2X2
-matrix_slerp_2D(const MatT_1& m1, const MatT_2& m2, E t,
- E tolerance = epsilon<E>::placeholder())
-{
- typedef MAT_TEMP_2X2 temporary_type;
-
- temporary_type m = matrix_rotation_difference_2D(m1,m2);
- matrix_scale_rotation_angle_2D(m,t,tolerance);
- return detail::matrix_concat_rotations_2D(m1,m);
-}
-
-#undef MAT_TEMP_3X3
-#undef MAT_TEMP_2X2
-
-//////////////////////////////////////////////////////////////////////////////
-// Conversions
-//////////////////////////////////////////////////////////////////////////////
-
-/** Convert a 3D rotation matrix to an axis-angle pair */
-template < class MatT, typename E, class A > void
-matrix_to_axis_angle(
- const MatT& m,
- vector<E,A >& axis,
- E& angle,
- E tolerance = epsilon<E>::placeholder())
-{
- typedef MatT matrix_type;
- typedef typename matrix_type::value_type value_type;
-
- /* Checking */
- detail::CheckMatLinear3D(m);
-
- axis.set(
- m.basis_element(1,2) - m.basis_element(2,1),
- m.basis_element(2,0) - m.basis_element(0,2),
- m.basis_element(0,1) - m.basis_element(1,0)
- );
- value_type l = length(axis);
- value_type tmo = trace_3x3(m) - value_type(1);
-
- if (l > tolerance) {
- axis /= l;
- angle = std::atan2(l, tmo); // l=2sin(theta),tmo=2cos(theta)
- } else if (tmo > value_type(0)) {
- axis.zero();
- angle = value_type(0);
- } else {
- size_t largest_diagonal_element =
- index_of_max(
- m.basis_element(0,0),
- m.basis_element(1,1),
- m.basis_element(2,2)
- );
- size_t i, j, k;
- cyclic_permutation(largest_diagonal_element, i, j, k);
- axis[i] =
- std::sqrt(
- m.basis_element(i,i) -
- m.basis_element(j,j) -
- m.basis_element(k,k) +
- value_type(1)
- ) * value_type(.5);
- value_type s = value_type(.5) / axis[i];
- axis[j] = m.basis_element(i,j) * s;
- axis[k] = m.basis_element(i,k) * s;
- angle = constants<value_type>::pi();
- }
-}
-
-/** Convert a 3D rotation matrix to an Euler-angle triple */
-template < class MatT, typename Real >
-void matrix_to_euler(
- const MatT& m,
- Real& angle_0,
- Real& angle_1,
- Real& angle_2,
- EulerOrder order,
- Real tolerance = epsilon<Real>::placeholder())
-{
- typedef MatT matrix_type;
- typedef typename matrix_type::value_type value_type;
-
- /* Checking */
- detail::CheckMatLinear3D(m);
-
- size_t i, j, k;
- bool odd, repeat;
- detail::unpack_euler_order(order, i, j, k, odd, repeat);
-
- if (repeat) {
- value_type s1 = length(m.basis_element(j,i),m.basis_element(k,i));
- value_type c1 = m.basis_element(i,i);
-
- angle_1 = std::atan2(s1, c1);
- if (s1 > tolerance) {
- angle_0 = std::atan2(m.basis_element(j,i),m.basis_element(k,i));
- angle_2 = std::atan2(m.basis_element(i,j),-m.basis_element(i,k));
- } else {
- angle_0 = value_type(0);
- angle_2 = sign(c1) *
- std::atan2(-m.basis_element(k,j),m.basis_element(j,j));
- }
- } else {
- value_type s1 = -m.basis_element(i,k);
- value_type c1 = length(m.basis_element(i,i),m.basis_element(i,j));
-
- angle_1 = std::atan2(s1, c1);
- if (c1 > tolerance) {
- angle_0 = std::atan2(m.basis_element(j,k),m.basis_element(k,k));
- angle_2 = std::atan2(m.basis_element(i,j),m.basis_element(i,i));
- } else {
- angle_0 = value_type(0);
- angle_2 = -sign(s1) *
- std::atan2(-m.basis_element(k,j),m.basis_element(j,j));
- }
- }
-
- if (odd) {
- angle_0 = -angle_0;
- angle_1 = -angle_1;
- angle_2 = -angle_2;
- }
-}
-
-/** Convert a 2D rotation matrix to a rotation angle */
-template < class MatT > typename MatT::value_type
-matrix_to_rotation_2D(const MatT& m)
-{
- /* Checking */
- detail::CheckMatLinear2D(m);
-
- return std::atan2(m.basis_element(0,1),m.basis_element(0,0));
-}
-
-} // namespace cml
-
-#endif
projects / chaz / yoink / blobdiff