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James Russell
2026-04-03 00:22:39 -05:00
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Lib/Include/CML/mathlib/vector_misc.h Normal file
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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 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