--- /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 vector_misc_h
+#define vector_misc_h
+
+#include <cml/mathlib/coord_conversion.h>
+
+/* Miscellaneous vector functions. */
+
+namespace cml {
+
+/* Function to project a vector v onto a hyperplane specified by a unit-length
+ * normal n.
+ *
+ * @todo: Clean up promotion code.
+ */
+
+template < class VecT_1, class VecT_2 >
+typename detail::CrossPromote<VecT_1,VecT_2>::promoted_vector
+project_to_hplane(const VecT_1& v, const VecT_2& n)
+{
+ typedef typename detail::CrossPromote<VecT_1,VecT_2>::promoted_vector
+ result_type;
+
+ result_type result;
+ et::detail::Resize(result, v.size());
+
+ result = v - dot(v,n) * n;
+ return result;
+}
+
+/* Return a vector perpendicular (CCW) to a 2D vector. */
+template < class VecT > vector< typename VecT::value_type, fixed<2> >
+perp(const VecT& v)
+{
+ typedef vector< typename VecT::value_type, fixed<2> > temporary_type;
+
+ /* Checking */
+ detail::CheckVec2(v);
+
+ return temporary_type(-v[1],v[0]);
+}
+
+/* @todo: unit_cross() and cross_cardinal() should probably go in
+ * vector_products.h, but I'm trying to avoid modifying the existing codebase
+ * for now.
+ */
+
+/** Return normalized cross product of two vectors */
+template< class LeftT, class RightT >
+typename detail::CrossPromote<LeftT,RightT>::promoted_vector
+unit_cross(const LeftT& left, const RightT& right) {
+ /* @todo: This will probably break with dynamic<> vectors */
+ return normalize(cross(left,right));
+}
+
+/** Return the cross product of v and the i'th cardinal basis vector */
+template < class VecT > vector< typename VecT::value_type, fixed<3> >
+cross_cardinal(const VecT& v, size_t i)
+{
+ typedef vector< typename VecT::value_type, fixed<3> > vector_type;
+ typedef typename vector_type::value_type value_type;
+
+ /* Checking */
+ detail::CheckVec3(v);
+ detail::CheckIndex3(i);
+
+ size_t j, k;
+ cyclic_permutation(i, i, j, k);
+ vector_type result;
+ result[i] = value_type(0);
+ result[j] = v[k];
+ result[k] = -v[j];
+ return result;
+}
+
+/** Return the cross product of the i'th cardinal basis vector and v */
+template < class VecT > vector< typename VecT::value_type, fixed<3> >
+cross_cardinal(size_t i, const VecT& v)
+{
+ typedef vector< typename VecT::value_type, fixed<3> > vector_type;
+ typedef typename vector_type::value_type value_type;
+
+ /* Checking */
+ detail::CheckVec3(v);
+ detail::CheckIndex3(i);
+
+ size_t j, k;
+ cyclic_permutation(i, i, j, k);
+ vector_type result;
+ result[i] = value_type(0);
+ result[j] = -v[k];
+ result[k] = v[j];
+ return result;
+}
+
+/** Rotate a 3D vector v about a unit-length vector n. */
+template< class VecT_1, class VecT_2, typename Real >
+vector<
+ typename et::ScalarPromote<
+ typename VecT_1::value_type,
+ typename VecT_2::value_type
+ >::type,
+ fixed<3>
+>
+rotate_vector(const VecT_1& v, const VecT_2& n, Real angle)
+{
+ typedef vector<
+ typename et::ScalarPromote<
+ typename VecT_1::value_type,
+ typename VecT_2::value_type
+ >::type,
+ fixed<3>
+ > result_type;
+
+ /* Checking */
+ detail::CheckVec3(v);
+ detail::CheckVec3(n);
+
+ result_type parallel = dot(v,n)*n;
+ return (
+ std::cos(angle)*(v-parallel) + std::sin(angle)*cross(n,v) + parallel
+ );
+}
+
+/** Rotate a 2D vector v about a unit-length vector n. */
+template< class VecT, typename Real >
+vector< typename VecT::value_type, fixed<2> >
+rotate_vector_2D(const VecT& v, Real angle)
+{
+ typedef vector< typename VecT::value_type, fixed<2> > result_type;
+ typedef typename result_type::value_type value_type;
+
+ /* Checking */
+ detail::CheckVec2(v);
+
+ value_type s = std::sin(angle);
+ value_type c = std::cos(angle);
+
+ return result_type(c * v[0] - s * v[1], s * v[0] + c * v[1]);
+}
+
+/** Random unit 3D or 2D vector
+ *
+ * @todo: This is just placeholder code for what will be a more thorough
+ * 'random unit' implementation:
+ *
+ * - All dimensions will be handled uniformly if practical, perhaps through
+ * a normal distrubution PRNG.
+ *
+ * - Failing that (or perhaps even in this case), dimensions 2 and 3 will be
+ * dispatched to special-case code, most likely implementing the algorithms
+ * below.
+ *
+ * - Like the utility random functions, the option of using one's own PRGN
+ * will be made available.
+ *
+ * @todo: Once N-d random vectors are supported, add a 'random unit
+ * quaternion' function that wraps a call to random_unit() with a 4D vector as
+ * the argument.
+ */
+template < typename E, class A > void
+random_unit(vector<E,A>& v)
+{
+ typedef vector<E,A> vector_type;
+ typedef typename vector_type::value_type value_type;
+
+ switch (v.size()) {
+ case 3:
+ {
+ vector< E, fixed<3> > temp;
+ spherical_to_cartesian(
+ value_type(1),
+ value_type(random_unit() * constants<value_type>::two_pi()),
+ acos_safe(random_real(value_type(-1),value_type(1))),
+ 2,
+ colatitude,
+ temp
+ );
+ v[0] = temp[0];
+ v[1] = temp[1];
+ v[2] = temp[2];
+ break;
+ }
+ case 2:
+ {
+ vector< E, fixed<2> > temp;
+ polar_to_cartesian(
+ value_type(1),
+ value_type(random_unit() * constants<value_type>::two_pi()),
+ temp
+ );
+ v[0] = temp[0];
+ v[1] = temp[1];
+ break;
+ }
+ default:
+ throw std::invalid_argument(
+ "random_unit() for N-d vectors not implemented yet");
+ break;
+ }
+}
+
+/* Random vector within a given angle of a unit-length axis, i.e. in a cone
+ * (3D) or wedge (2D).
+ *
+ * The same notes the appear above apply here too, more or less. One
+ * difference is that this is really only useful in 2D and 3D (presumably), so
+ * we'll probably just do a compile- or run-time dispatch as appropriate.
+ *
+ * Also, there may be a better algorithm for generating a random unit vector
+ * in a cone; need to look into that.
+ *
+ * All of this 'temp' stuff is because there's no compile-time dispatch for
+ * 3D and 2D vectors, but that'll be fixed soon.
+ */
+
+template < typename E, class A, class VecT > void
+random_unit(vector<E,A>& v, const VecT& axis, E theta)
+{
+ typedef vector<E,A> vector_type;
+ typedef typename vector_type::value_type value_type;
+
+ switch (v.size()) {
+ case 3:
+ {
+ vector< E, fixed<3> > temp, n, temp_axis;
+ temp_axis[0] = axis[0];
+ temp_axis[1] = axis[1];
+ temp_axis[2] = axis[2];
+
+ /* @todo: Function for finding 'any perpendicular vector'? */
+ n = axis_3D(cml::index_of_min_abs(axis[0],axis[1],axis[2]));
+ n = cross(n,temp_axis);
+
+ /* Rotate v 'away from' the axis by a random angle in the range
+ * [-theta,theta]
+ */
+ temp = rotate_vector(temp_axis,n,random_real(-theta,theta));
+
+ /* Rotate v about the axis by a random angle in the range [-pi,pi]
+ */
+ temp = rotate_vector(
+ temp,
+ temp_axis,
+ random_real(
+ -constants<value_type>::pi(),
+ constants<value_type>::pi()
+ )
+ );
+
+ v[0] = temp[0];
+ v[1] = temp[1];
+ v[2] = temp[2];
+ break;
+ }
+ case 2:
+ {
+ vector< E, fixed<2> > temp, temp_axis;
+ temp_axis[0] = axis[0];
+ temp_axis[1] = axis[1];
+ temp = rotate_vector_2D(temp_axis, random_real(-theta,theta));
+ v[0] = temp[0];
+ v[1] = temp[1];
+ break;
+ }
+ default:
+ throw std::invalid_argument(
+ "random_unit(v,axis,theta) only implemented for 2D and 3D");
+ break;
+ }
+}
+
+/* NEW: Manhattan distance */
+
+template< class VecT_1, class VecT_2 >
+typename detail::DotPromote< VecT_1, VecT_2 >::promoted_scalar
+manhattan_distance(const VecT_1& v1, const VecT_2& v2) {
+ /* Check that a promotion exists */
+ typedef typename et::VectorPromote<
+ VecT_1,VecT_2>::temporary_type promoted_vector;
+
+ typedef typename detail::DotPromote< VecT_1, VecT_2 >::promoted_scalar scalar_type;
+
+ scalar_type sum = scalar_type(0);
+ for (size_t i = 0; i < v1.size(); ++i) {
+ sum += std::fabs(v2[i]-v1[i]);
+ }
+ return sum;
+}
+
+} // namespace cml
+
+#endif
projects / chaz / yoink / blobdiff