X-Git-Url: https://git.dogcows.com/gitweb?p=chaz%2Fyoink;a=blobdiff_plain;f=src%2Fcml%2Fmathlib%2Fmatrix_transform.h;fp=src%2Fcml%2Fmathlib%2Fmatrix_transform.h;h=359ab2deeb20ebf687a2bd30dd8fe27ded58e7a4;hp=0000000000000000000000000000000000000000;hb=0fffd0097d7b496454413e57b398c903ecc252e4;hpb=79becf045222f385da5a1b9eb79081f6f5266c86

diff --git a/src/cml/mathlib/matrix_transform.h b/src/cml/mathlib/matrix_transform.h
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+/* -*- 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_transform_h
+#define matrix_transform_h
+
+#include <cml/mathlib/matrix_basis.h>
+#include <cml/mathlib/matrix_rotation.h>
+#include <cml/mathlib/matrix_translation.h>
+
+/* Functions for building matrix transforms other than rotations
+ * (matrix_rotation.h) and viewing projections (matrix_projection.h).
+ */
+
+namespace cml {
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D translation
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 3D translation */
+template < typename E, class A, class B, class L > void
+matrix_translation(matrix<E,A,B,L>& m, E x, E y, E z)
+{
+    identity_transform(m);
+    matrix_set_translation(m,x,y,z);
+}
+
+/** Build a matrix representing a 3D translation with z set to 0 */
+template < typename E, class A, class B, class L > void
+matrix_translation(matrix<E,A,B,L>& m, E x, E y)
+{
+    identity_transform(m);
+    matrix_set_translation(m,x,y);
+}
+
+/** Build a matrix representing a 3D translation */
+template < typename E, class A, class B, class L, class VecT > void
+matrix_translation(matrix<E,A,B,L>& m, const VecT& translation)
+{
+    identity_transform(m);
+    matrix_set_translation(m,translation);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 2D translation
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 2D translation */
+template < typename E, class A, class B, class L > void
+matrix_translation_2D(matrix<E,A,B,L>& m, E x, E y)
+{
+    identity_transform(m);
+    matrix_set_translation_2D(m,x,y);
+}
+
+/** Build a matrix representing a 2D translation */
+template < typename E, class A, class B, class L, class VecT > void
+matrix_translation_2D(matrix<E,A,B,L>& m, const VecT& translation)
+{
+    identity_transform(m);
+    matrix_set_translation_2D(m, translation);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D scale
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a uniform 3D scale */
+template < typename E, class A, class B, class L > void
+matrix_uniform_scale(matrix<E,A,B,L>& m, E scale) {
+    matrix_scale(m,scale,scale,scale);
+}
+
+/** Build a matrix representing a non-uniform 3D scale */
+template < typename E, class A, class B, class L > void
+matrix_scale(matrix<E,A,B,L>& m, E scale_x, E scale_y, E scale_z)
+{
+    /* Checking */
+    detail::CheckMatLinear3D(m);
+    
+    identity_transform(m);
+    
+    m.set_basis_element(0,0,scale_x);
+    m.set_basis_element(1,1,scale_y);
+    m.set_basis_element(2,2,scale_z);
+}
+
+/** Build a matrix representing a non-uniform 3D scale */
+template < typename E, class A, class B, class L, class VecT > void
+matrix_scale(matrix<E,A,B,L>& m, const VecT& scale)
+{
+    /* Checking */
+    detail::CheckVec3(scale);
+    
+    matrix_scale(m, scale[0], scale[1], scale[2]);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 2D scale
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a uniform 2D scale */
+template < typename E, class A, class B, class L > void
+matrix_uniform_scale_2D(matrix<E,A,B,L>& m, E scale) {
+    matrix_scale_2D(m,scale,scale);
+}
+
+/** Build a matrix representing a non-uniform 2D scale */
+template < typename E, class A, class B, class L > void
+matrix_scale_2D(matrix<E,A,B,L>& m, E scale_x, E scale_y)
+{
+    /* Checking */
+    detail::CheckMatLinear2D(m);
+    
+    identity_transform(m);
+    
+    m.set_basis_element(0,0,scale_x);
+    m.set_basis_element(1,1,scale_y);
+}
+
+/** Build a matrix representing a non-uniform 2D scale */
+template < typename E, class A, class B, class L, class VecT > void
+matrix_scale_2D(matrix<E,A,B,L>& m, const VecT& scale)
+{
+    /* Checking */
+    detail::CheckVec2(scale);
+    
+    matrix_scale_2D(m, scale[0], scale[1]);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D scale along axis
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 3D scale along an arbitrary axis */
+template < typename E, class A, class B, class L, class VecT > void
+matrix_scale_along_axis(matrix<E,A,B,L>&m, const VecT& axis, E scale)
+{
+    typedef matrix<E,A,B,L> matrix_type;
+    typedef typename matrix_type::value_type value_type;
+
+    /* Checking */
+    detail::CheckVec3(axis);
+
+    matrix<E,fixed<3,3>,B,L> outer_p = outer(axis,axis)*(scale-value_type(1));
+    outer_p(0,0) += value_type(1);
+    outer_p(1,1) += value_type(1);
+    outer_p(2,2) += value_type(1);
+
+    matrix_linear_transform(m, outer_p);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 2D scale along axis
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 2D scale along an arbitrary axis */
+template < typename E, class A, class B, class L, class VecT >
+void matrix_scale_along_axis_2D(matrix<E,A,B,L>&  m, const VecT& axis,
+    E scale)
+{
+    typedef matrix<E,A,B,L> matrix_type;
+    typedef typename matrix_type::value_type value_type;
+
+    /* Checking */
+    detail::CheckVec2(axis);
+
+    matrix<E,fixed<2,2>,B,L> outer_p = outer(axis,axis)*(scale-value_type(1));
+    outer_p(0,0) += value_type(1);
+    outer_p(1,1) += value_type(1);
+
+    matrix_linear_transform_2D(m, outer_p);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D shear
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 3D shear along the specified world axis */
+template < typename E, class A, class B, class L > void
+matrix_shear(matrix<E,A,B,L>& m, size_t axis, E shear_s, E shear_t)
+{
+    /* Checking */
+    detail::CheckMatLinear3D(m);
+    detail::CheckIndex3(axis);
+
+    identity_transform(m);
+    
+    size_t i, j, k;
+    cyclic_permutation(axis, i, j, k);
+    
+    m.set_basis_element(i,j,shear_s);
+    m.set_basis_element(i,k,shear_t);
+}
+
+/** Build a matrix representing a 3D shear along the world x axis */
+template < typename E, class A, class B, class L > void
+matrix_shear_x(matrix<E,A,B,L>& m, E shear_s, E shear_t) {
+    matrix_shear(m,0,shear_s,shear_t);
+}
+
+/** Build a matrix representing a 3D shear along the world y axis */
+template < typename E, class A, class B, class L > void
+matrix_shear_y(matrix<E,A,B,L>& m, E shear_s, E shear_t) {
+    matrix_shear(m,1,shear_s,shear_t);
+}
+
+/** Build a matrix representing a 3D shear along the world z axis */
+template < typename E, class A, class B, class L > void
+matrix_shear_z(matrix<E,A,B,L>& m, E shear_s, E shear_t) {
+    matrix_shear(m,2,shear_s,shear_t);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 2D shear
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 2D shear along the specified world axis */
+template < typename E, class A, class B, class L > void
+matrix_shear_2D(matrix<E,A,B,L>& m, size_t axis, E shear)
+{
+    /* Checking */
+    detail::CheckMatLinear2D(m);
+    detail::CheckIndex2(axis);
+
+    identity_transform(m);
+    
+    size_t i, j;
+    cyclic_permutation(axis, i, j);
+    
+    m.set_basis_element(i,j,shear);
+}
+
+/** Build a matrix representing a 2D shear along the world x axis */
+template < typename E, class A, class B, class L > void
+matrix_shear_x_2D(matrix<E,A,B,L>& m, E shear) {
+    matrix_shear_2D(m,0,shear);
+}
+
+/** Build a matrix representing a 2D shear along the world y axis */
+template < typename E, class A, class B, class L > void
+matrix_shear_y_2D(matrix<E,A,B,L>& m, E shear) {
+    matrix_shear_2D(m,1,shear);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D reflection
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 3D reflection along the given world axis */
+template < typename E, class A, class B, class L > void
+matrix_reflect(matrix<E,A,B,L>& m, size_t axis)
+{
+    typedef matrix<E,A,B,L> matrix_type;
+    typedef typename matrix_type::value_type value_type;
+
+    /* Checking */
+    detail::CheckMatLinear3D(m);
+    detail::CheckIndex3(axis);
+
+    identity_transform(m);
+    
+    m(axis,axis) = value_type(-1);
+}
+
+/** Build a matrix representing a 3D reflection along the world x axis */
+template < typename E, class A, class B, class L > void
+matrix_reflect_x(matrix<E,A,B,L>& m) {
+    matrix_reflect(m,0);
+}
+
+/** Build a matrix representing a 3D reflection along the world y axis */
+template < typename E, class A, class B, class L > void
+matrix_reflect_y(matrix<E,A,B,L>& m) {
+    matrix_reflect(m,1);
+}
+
+/** Build a matrix representing a 3D reflection along the world z axis */
+template < typename E, class A, class B, class L > void
+matrix_reflect_z(matrix<E,A,B,L>& m) {
+    matrix_reflect(m,2);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 2D reflection
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 2D reflection along the given world axis */
+template < typename E, class A, class B, class L > void
+matrix_reflect_2D(matrix<E,A,B,L>& m, size_t axis)
+{
+    typedef matrix<E,A,B,L> matrix_type;
+    typedef typename matrix_type::value_type value_type;
+
+    /* Checking */
+    detail::CheckMatLinear2D(m);
+    detail::CheckIndex2(axis);
+
+    identity_transform(m);
+    
+    m(axis,axis) = value_type(-1);
+}
+
+/** Build a matrix representing a 2D reflection along the world x axis */
+template < typename E, class A, class B, class L > void
+matrix_reflect_x_2D(matrix<E,A,B,L>& m) {
+    matrix_reflect_2D(m,0);
+}
+
+/** Build a matrix representing a 2D reflection along the world y axis */
+template < typename E, class A, class B, class L > void
+matrix_reflect_y_2D(matrix<E,A,B,L>& m) {
+    matrix_reflect_2D(m,1);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D reflection about hyperplane
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 3D reflection about the given hyperplane */
+template < typename E, class A, class B, class L, class VecT > void
+matrix_reflect_about_hplane(matrix<E,A,B,L>& m, const VecT& normal)
+{
+    typedef matrix<E,A,B,L> matrix_type;
+    typedef typename matrix_type::value_type value_type;
+
+    matrix_scale_along_axis(m, normal, value_type(-1));
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 2D reflection about hyperplane
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 2D reflection about the given hyperplane */
+template < typename E, class A, class B, class L, class VecT > void
+matrix_reflect_about_hplane_2D(matrix<E,A,B,L>&m, const VecT& normal)
+{
+    typedef matrix<E,A,B,L> matrix_type;
+    typedef typename matrix_type::value_type value_type;
+
+    matrix_scale_along_axis_2D(m, normal, value_type(-1));
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D orthographic projection to cardinal hyperplane
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing an orthographic projection onto a plane */
+template < typename E, class A, class B, class L > void
+matrix_ortho_project(matrix<E,A,B,L>& m, size_t axis)
+{
+    typedef matrix<E,A,B,L> matrix_type;
+    typedef typename matrix_type::value_type value_type;
+
+    /* Checking */
+    detail::CheckMatLinear3D(m);
+    detail::CheckIndex3(axis);
+
+    identity_transform(m);
+    
+    m(axis,axis) = value_type(0);
+}
+
+/** Build a matrix representing an orthographic projection onto the yz plane*/
+template < typename E, class A, class B, class L > void
+matrix_ortho_project_yz(matrix<E,A,B,L>& m) {
+    matrix_ortho_project(m,0);
+}
+
+/** Build a matrix representing an orthographic projection onto the zx plane*/
+template < typename E, class A, class B, class L > void
+matrix_ortho_project_zx(matrix<E,A,B,L>& m) {
+    matrix_ortho_project(m,1);
+}
+
+/** Build a matrix representing an orthographic projection onto the zy plane*/
+template < typename E, class A, class B, class L > void
+matrix_ortho_project_xy(matrix<E,A,B,L>& m) {
+    matrix_ortho_project(m,2);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 2D orthographic projection to cardinal hyperplane
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 2D orthographic projection */
+template < typename E, class A, class B, class L > void
+matrix_ortho_project_2D(matrix<E,A,B,L>& m, size_t axis)
+{
+    typedef matrix<E,A,B,L> matrix_type;
+    typedef typename matrix_type::value_type value_type;
+
+    /* Checking */
+    detail::CheckMatLinear2D(m);
+    detail::CheckIndex2(axis);
+
+    identity_transform(m);
+    
+    m(axis,axis) = value_type(0);
+}
+
+/** Build a matrix representing an orthographic projection onto the y axis */
+template < typename E, class A, class B, class L > void
+matrix_ortho_project_y_2D(matrix<E,A,B,L>& m) {
+    matrix_ortho_project_2D(m,0);
+}
+
+/** Build a matrix representing an orthographic projection onto the x axis */
+template < typename E, class A, class B, class L > void
+matrix_ortho_project_x_2D(matrix<E,A,B,L>& m) {
+    matrix_ortho_project_2D(m,1);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D orthographic projection to hyperplane
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 3D orthographic projection about the given
+ * hyperplane passing through the origin.
+ */
+template < typename E, class A, class B, class L, class VecT > void
+matrix_ortho_project_to_hplane(matrix<E,A,B,L>& m, const VecT& normal)
+{
+    typedef matrix<E,A,B,L> matrix_type;
+    typedef typename matrix_type::value_type value_type;
+
+    matrix_scale_along_axis(m, normal, value_type(0));
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 2D orthographic projection to hyperplane
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 2D orthographic projection about the given
+ * hyperplane passing through the origin.
+ */
+template < typename E, class A, class B, class L, class VecT > void
+matrix_ortho_project_to_hplane_2D(matrix<E,A,B,L>& m, const VecT& normal)
+{
+    typedef matrix<E,A,B,L> matrix_type;
+    typedef typename matrix_type::value_type value_type;
+
+    matrix_scale_along_axis_2D(m, normal, value_type(0));
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D 'aim at'
+//////////////////////////////////////////////////////////////////////////////
+
+/** 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_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_aim_at(m, pos, target, reference, order);
+    matrix_set_translation(m, pos);
+}
+
+/** See vector_ortho.h for details */
+template < typename E, class A, class B, class L,
+    class VecT_1, class VecT_2 > void
+matrix_aim_at(matrix<E,A,B,L>& m, const VecT_1& pos, const VecT_2& target,
+    AxisOrder order = axis_order_zyx)
+{
+    matrix_rotation_aim_at(m, pos, target, order);
+    matrix_set_translation(m, pos);
+}
+
+/** 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_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_aim_at_axial(m, pos, target, axis, order);
+    matrix_set_translation(m, pos);
+}
+
+/** See vector_ortho.h for details */
+template < typename E,class A,class B,class L,class VecT,class MatT > void
+matrix_aim_at_viewplane(
+    matrix<E,A,B,L>& m,
+    const VecT& pos,
+    const MatT& view_matrix,
+    Handedness handedness,
+    AxisOrder order = axis_order_zyx)
+{
+    matrix_rotation_align_viewplane(m, view_matrix, handedness, order);
+    matrix_set_translation(m, pos);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 2D 'aim at'
+//////////////////////////////////////////////////////////////////////////////
+
+/** See vector_ortho.h for details */
+template < typename E,class A,class B,class L,class VecT_1,class VecT_2 > void
+matrix_aim_at_2D(
+    matrix<E,A,B,L>& m,
+    const VecT_1& pos,
+    const VecT_2& target,
+    AxisOrder2D order = axis_order_xy)
+{
+    matrix_rotation_align_2D(m, target - pos, true, order);
+    matrix_set_translation_2D(m, pos);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D 'look at' view matrix
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix representing a 'look at' view transform */
+template < typename E, class A, class B, class L,
+    class VecT_1, class VecT_2, class VecT_3 > void
+matrix_look_at(
+    matrix<E,A,B,L>& m,
+    const VecT_1& eye,
+    const VecT_2& target,
+    const VecT_3& up,
+    Handedness handedness)
+{
+    typedef matrix<E,A,B,L> matrix_type;
+    typedef vector< E,fixed<3> > vector_type;
+    typedef typename matrix_type::value_type value_type;
+
+    /* Checking */
+    detail::CheckMatAffine3D(m);
+
+    identity_transform(m);
+
+    value_type s = handedness == left_handed ? 1 : -1;
+    vector_type z = s * normalize(target - eye);
+    vector_type x = unit_cross(up,z);
+    vector_type y = cross(z,x);
+
+    matrix_set_transposed_basis_vectors(m,x,y,z);
+    matrix_set_translation(m,-dot(eye,x),-dot(eye,y),-dot(eye,z));
+}
+
+/** Build a matrix representing a left-handedness 'look at' view transform */
+template < typename E, class A, class B, class L,
+    class VecT_1, class VecT_2, class VecT_3 > void
+matrix_look_at_LH(matrix<E,A,B,L>& m, const VecT_1& eye,
+    const VecT_2& target, const VecT_3& up)
+{
+    matrix_look_at(m, eye, target, up, left_handed);
+}
+
+/** Build a matrix representing a right-handedness 'look at' view transform */
+template < typename E, class A, class B, class L,
+    class VecT_1, class VecT_2, class VecT_3 > void
+matrix_look_at_RH(matrix<E,A,B,L>& m, const VecT_1& eye,
+    const VecT_2& target, const VecT_3& up)
+{
+    matrix_look_at(m, eye, target, up, right_handed);
+}
+
+/** Build a matrix representing a 'look at' view transform */
+template < typename E, class A, class B, class L > void
+matrix_look_at(matrix<E,A,B,L>& m, E eye_x, E eye_y, E eye_z, E target_x,
+    E target_y, E target_z, E up_x, E up_y, E up_z,
+    Handedness handedness)
+{
+    typedef vector< E, fixed<3> > vector_type;
+    
+    matrix_look_at(m,
+        vector_type(eye_x,eye_y,eye_z),
+        vector_type(target_x,target_y,target_z),
+        vector_type(up_x,up_y,up_z),
+        handedness
+    );
+}
+
+/** Build a matrix representing a left-handed'look at' view transform */
+template < typename E, class A, class B, class L > void
+matrix_look_at_LH(matrix<E,A,B,L>& m, E eye_x, E eye_y, E eye_z,
+    E target_x, E target_y, E target_z, E up_x, E up_y, E up_z)
+{
+    matrix_look_at(m,eye_x,eye_y,eye_z,target_x,target_y,target_z,up_x,up_y,
+        up_z,left_handed);
+}
+
+/** Build a matrix representing a right-handed'look at' view transform */
+template < typename E, class A, class B, class L > void
+matrix_look_at_RH(matrix<E,A,B,L>& m, E eye_x, E eye_y, E eye_z,
+    E target_x, E target_y, E target_z, E up_x, E up_y, E up_z)
+{
+    matrix_look_at(m,eye_x,eye_y,eye_z,target_x,target_y,target_z,up_x,up_y,
+        up_z,right_handed);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D linear transform
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix from the 3x3 linear transform part of another matrix */
+template < typename E, class A, class B, class L, class MatT > void
+matrix_linear_transform(matrix<E,A,B,L>& m, const MatT& linear)
+{
+    /* Checking */
+    detail::CheckMatLinear3D(m);
+    detail::CheckMatLinear3D(linear);
+    
+    identity_transform(m);
+    
+    for(size_t i = 0; i < 3; ++i) {
+        for(size_t j = 0; j < 3; ++j) {
+            m.set_basis_element(i,j,linear.basis_element(i,j));
+        }
+    }
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 2D linear transform
+//////////////////////////////////////////////////////////////////////////////
+
+/** Build a matrix from the 2x2 linear transform part of another matrix */
+template < typename E, class A, class B, class L, class MatT > void
+matrix_linear_transform_2D(matrix<E,A,B,L>& m, const MatT& linear)
+{
+    /* Checking */
+    detail::CheckMatLinear2D(m);
+    detail::CheckMatLinear2D(linear);
+    
+    identity_transform(m);
+    
+    for(size_t i = 0; i < 2; ++i) {
+        for(size_t j = 0; j < 2; ++j) {
+            m.set_basis_element(i,j,linear.basis_element(i,j));
+        }
+    }
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D affine transform
+//////////////////////////////////////////////////////////////////////////////
+
+/** 3D affine transform from three basis vectors and a translation */
+template <typename E, class A, class B, class L,
+    class VecT_1, class VecT_2, class VecT_3, class VecT_4 > void
+matrix_affine_transform(matrix<E,A,B,L>& m, const VecT_1& x, const VecT_2& y,
+    const VecT_3& z, const VecT_4& translation)
+{
+    identity_transform(m);
+    matrix_set_basis_vectors(m,x,y,z);
+    matrix_set_translation(m,translation);
+}
+
+/** 3D affine transform from a quaternion and a translation */
+template <
+    typename E, class A, class B, class L,
+    typename QE, class QA, class O, class C, class VecT > void
+matrix_affine_transform(
+    matrix<E,A,B,L>& m, const quaternion<QE,QA,O,C>& q,
+    const VecT& translation)
+{
+    matrix_rotation_quaternion(m,q);
+    matrix_set_translation(m,translation);
+}
+
+/** 3D affine transform from a quaternion expression and a translation */
+template < typename E,class A,class B,class L,class XprT,class VecT > void
+matrix_affine_transform(
+    matrix<E,A,B,L>& m, const et::QuaternionXpr<XprT>& q,
+    const VecT& translation)
+{
+    matrix_rotation_quaternion(m,q);
+    matrix_set_translation(m,translation);
+}
+
+/** 3D affine transform from an axis-angle pair and a translation */
+template <
+    typename E, class A, class B, class L, class VecT_1, class VecT_2 > void
+matrix_affine_transform(
+    matrix<E,A,B,L>& m,const VecT_1& axis,E angle,const VecT_2& translation)
+{
+    matrix_rotation_axis_angle(m,axis,angle);
+    matrix_set_translation(m,translation);
+}
+
+/** 3D affine transform from an Euler-angle triple and a translation */
+template < typename E, class A, class B, class L, class VecT > void
+matrix_affine_transform(matrix<E,A,B,L>& m, E angle_0, E angle_1,
+    E angle_2, EulerOrder order, const VecT& translation)
+{
+    matrix_rotation_euler(m,angle_0,angle_1,angle_2,order);
+    matrix_set_translation(m,translation);
+}
+
+/** 3D affine transform from a matrix and a translation */
+template <
+    typename E, class A, class B, class L,
+    typename ME, class MA, class MB, class ML, class VecT > void
+matrix_affine_transform(matrix<E,A,B,L>& m,
+    const matrix<ME,MA,MB,ML>& linear, const VecT& translation)
+{
+    matrix_linear_transform(m,linear);
+    matrix_set_translation(m,translation);
+}
+
+/** 3D affine transform from a matrix expression and a translation */
+template < typename E,class A,class B,class L,class XprT,class VecT > void
+matrix_affine_transform(
+    matrix<E,A,B,L>& m, const et::MatrixXpr<XprT>& linear,
+    const VecT& translation)
+{
+    matrix_linear_transform(m,linear);
+    matrix_set_translation(m,translation);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 2D affine transform
+//////////////////////////////////////////////////////////////////////////////
+
+/** 2D affine transform from two basis vectors and a translation */
+template <typename E, class A, class B, class L,
+    class VecT_1, class VecT_2, class VecT_3 > void
+matrix_affine_transform_2D(matrix<E,A,B,L>& m, const VecT_1& x,
+    const VecT_2& y, const VecT_3& translation)
+{
+    identity_transform(m);
+    matrix_set_basis_vectors_2D(m,x,y);
+    matrix_set_translation_2D(m,translation);
+}
+
+/** 2D affine transform from a rotation angle and a translation */
+template <typename E, class A, class B, class L, class VecT >
+void matrix_affine_transform_2D(matrix<E,A,B,L>& m, E angle,
+    const VecT& translation)
+{
+    matrix_rotation_2D(m,angle);
+    matrix_set_translation_2D(m,translation);
+}
+
+/** 2D affine transform from a matrix and a translation */
+template < typename E,class A,class B,class L,class MatT,class VecT > void
+matrix_affine_transform_2D(
+    matrix<E,A,B,L>& m, const MatT& linear, const VecT& translation)
+{
+    matrix_linear_transform_2D(m, linear);
+    matrix_set_translation_2D(m,translation);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D affine from 2D affine
+//////////////////////////////////////////////////////////////////////////////
+
+/** Construct a 3D affine transform from a 2D affine transform */
+template < typename E, class A, class B, class L, class MatT > void
+matrix_3D_affine_from_2D_affine(matrix<E,A,B,L>& m, const MatT& affine_2D)
+{
+    typedef vector< E, fixed<2> > vector_type;
+
+    vector_type x = matrix_get_x_basis_vector_2D(affine_2D);
+    vector_type y = matrix_get_y_basis_vector_2D(affine_2D);
+    vector_type p = matrix_get_translation_2D(affine_2D);
+    
+    identity_transform(m);
+    
+    matrix_set_basis_vectors_2D(m,x,y);
+    matrix_set_translation(m,p);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// 3D affine from 3D affine
+//////////////////////////////////////////////////////////////////////////////
+
+/** Construct a 3D affine transform from another 3D affine transform */
+template < typename E, class A, class B, class L, class MatT > void
+matrix_3D_affine_from_3D_affine(matrix<E,A,B,L>& m, const MatT& affine_3D)
+{
+    typedef vector< E, fixed<3> > vector_type;
+
+    vector_type x = matrix_get_x_basis_vector(affine_3D);
+    vector_type y = matrix_get_y_basis_vector(affine_3D);
+    vector_type z = matrix_get_z_basis_vector(affine_3D);
+    vector_type p = matrix_get_translation(affine_3D);
+    
+    identity_transform(m);
+    
+    matrix_set_basis_vectors(m,x,y,z);
+    matrix_set_translation(m,p);
+}
+
+//////////////////////////////////////////////////////////////////////////////
+// Matrix decomposition (scale->rotate->translate)
+//////////////////////////////////////////////////////////////////////////////
+
+/* 3x3 matrix version */
+template <
+    class MatT,
+    typename Real,
+    typename ME,
+    class MA,
+    class B,
+    class L,
+    typename VE,
+    class VA
+>
+void matrix_decompose_SRT(
+    const MatT& m,
+    Real& scale_x,
+    Real& scale_y,
+    Real& scale_z,
+    matrix<ME,MA,B,L>& rotation,
+    vector<VE,VA>& translation)
+{
+    typedef MatT matrix_type;
+    typedef typename matrix_type::value_type value_type;
+    typedef vector<value_type, fixed<3> > vector_type;
+
+    /* Checking */
+    detail::CheckMatAffine3D(m);
+    detail::CheckMatLinear3D(rotation);
+    
+    vector_type x, y, z;
+    matrix_get_basis_vectors(m, x, y, z);
+    
+    scale_x = x.length();
+    scale_y = y.length();
+    scale_z = z.length();
+    
+    x /= scale_x;
+    y /= scale_y;
+    z /= scale_z;
+    
+    matrix_set_basis_vectors(rotation, x, y, z);
+    translation = matrix_get_translation(m);
+}
+
+/* Quaternion version */
+template <
+    class MatT,
+    typename Real,
+    typename QE,
+    class QA,
+    class O,
+    class C,
+    typename VE,
+    class VA
+>
+void matrix_decompose_SRT(
+    const MatT& m,
+    Real& scale_x,
+    Real& scale_y,
+    Real& scale_z,
+    quaternion<QE,QA,O,C>& rotation,
+    vector<VE,VA>& translation)
+{
+    typedef MatT matrix_type;
+    typedef typename matrix_type::value_type value_type;
+    typedef matrix< value_type, fixed<3,3> > rotation_type;
+
+    rotation_type rotation_matrix;
+    matrix_decompose_SRT(
+        m, scale_x, scale_y, scale_z, rotation_matrix, translation);
+    quaternion_rotation_matrix(rotation, rotation_matrix);
+}
+
+/* Euler angle version */
+template < class MatT, typename Real, typename E, class A >
+void matrix_decompose_SRT(
+    const MatT& m,
+    Real& scale_x,
+    Real& scale_y,
+    Real& scale_z,
+    Real& angle_0,
+    Real& angle_1,
+    Real& angle_2,
+    EulerOrder order,
+    vector<E,A>& translation,
+    Real tolerance = epsilon<Real>::placeholder())
+{
+    typedef MatT matrix_type;
+    typedef typename matrix_type::value_type value_type;
+    typedef matrix< value_type, fixed<3,3> > rotation_type;
+
+    rotation_type rotation_matrix;
+    matrix_decompose_SRT(
+        m, scale_x, scale_y, scale_z, rotation_matrix, translation);
+    matrix_to_euler(
+        rotation_matrix, angle_0, angle_1, angle_2, order, tolerance);
+}
+
+/* Axis-angle version */
+template < class MatT, typename Real, typename E, class A >
+void matrix_decompose_SRT(
+    const MatT& m,
+    Real& scale_x,
+    Real& scale_y,
+    Real& scale_z,
+    vector<E,A>& axis,
+    Real& angle,
+    vector<E,A>& translation,
+    Real tolerance = epsilon<Real>::placeholder())
+{
+    typedef MatT matrix_type;
+    typedef typename matrix_type::value_type value_type;
+    typedef matrix< value_type, fixed<3,3> > rotation_type;
+
+    rotation_type rotation_matrix;
+    matrix_decompose_SRT(
+        m, scale_x, scale_y, scale_z, rotation_matrix, translation);
+    matrix_to_axis_angle(rotation_matrix, axis, angle, tolerance);
+}
+
+/* 2x2 matrix version, 2-d */
+template <
+    class MatT,
+    typename Real,
+    typename ME,
+    class MA,
+    class B,
+    class L,
+    typename VE,
+    class VA
+>
+void matrix_decompose_SRT_2D(
+    const MatT& m,
+    Real& scale_x,
+    Real& scale_y,
+    matrix<ME,MA,B,L>& rotation,
+    vector<VE,VA>& translation)
+{
+    typedef MatT matrix_type;
+    typedef typename matrix_type::value_type value_type;
+    typedef vector<value_type, fixed<2> > vector_type;
+
+    /* Checking */
+    detail::CheckMatAffine2D(m);
+    detail::CheckMatLinear2D(rotation);
+    
+    vector_type x, y;
+    matrix_get_basis_vectors_2D(m, x, y);
+    
+    scale_x = x.length();
+    scale_y = y.length();
+    
+    x /= scale_x;
+    y /= scale_y;
+    
+    matrix_set_basis_vectors_2D(rotation, x, y);
+    translation = matrix_get_translation_2D(m);
+}
+
+/* Angle version, 2-d */
+template < class MatT, typename Real, typename E, class A >
+void matrix_decompose_SRT_2D(
+    const MatT& m,
+    Real& scale_x,
+    Real& scale_y,
+    Real& angle,
+    vector<E,A>& translation)
+{
+    typedef MatT matrix_type;
+    typedef typename matrix_type::value_type value_type;
+    typedef matrix< value_type, fixed<2,2> > rotation_type;
+
+    rotation_type rotation_matrix;
+    matrix_decompose_SRT_2D(
+        m, scale_x, scale_y, rotation_matrix, translation);
+    angle = matrix_to_rotation_2D(rotation_matrix);
+}
+
+} // namespace cml
+
+#endif