X-Git-Url: https://git.dogcows.com/gitweb?p=chaz%2Fyoink;a=blobdiff_plain;f=src%2Fcml%2Fmathlib%2Fvector_ortho.h;fp=src%2Fcml%2Fmathlib%2Fvector_ortho.h;h=3983264d5e8117da20b79e6ad4662b8d72ede711;hp=0000000000000000000000000000000000000000;hb=6b0a0d0efafe34d48ab344fca3b479553bd4e62c;hpb=85783316365181491a3e3c0c63659972477cebba diff --git a/src/cml/mathlib/vector_ortho.h b/src/cml/mathlib/vector_ortho.h new file mode 100644 index 0000000..3983264 --- /dev/null +++ b/src/cml/mathlib/vector_ortho.h @@ -0,0 +1,338 @@ +/* -*- 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 + * + * Functions for orthonormalizing a set of basis vectors in 3D or 2D, and for + * constructing an orthonormal basis given various input parameters. + */ + +#ifndef vector_ortho_h +#define vector_ortho_h + +#include +#include + +namespace cml { + +////////////////////////////////////////////////////////////////////////////// +// Orthonormalization in 3D and 2D +////////////////////////////////////////////////////////////////////////////// + + +/** Orthonormalize 3 basis vectors in R3. + * + * Called with the default values, this function performs a single Gram- + * Schmidt step to orthonormalize the input vectors. By default, the direction + * of the 3rd basis vector is unchanged by this operation, but the unaffected + * axis can be specified via the 'stable_axis' parameter. + * + * The arguments 'num_iter' and 's' can be specified to an iterative Gram- + * Schmidt step. 'num_iter' is the number of iterations applied, and 's' is + * the fraction applied towards orthonormality each step. + * + * In most cases, the default arguments can be ignored, leaving only the three + * input vectors. + */ +template < typename E, class A > void +orthonormalize(vector& v0, vector& v1, vector& v2, + size_t stable_axis = 2, size_t num_iter = 0, E s = E(1)) +{ + /* Checking */ + detail::CheckVec3(v0); + detail::CheckVec3(v1); + detail::CheckVec3(v2); + detail::CheckIndex3(stable_axis); + + typedef vector< E, fixed<3> > vector_type; + typedef typename vector_type::value_type value_type; + + /* Iterative Gram-Schmidt; this step is skipped by default. */ + + for (size_t i = 0; i < num_iter; ++i) { + value_type dot01 = dot(v0,v1); + value_type dot12 = dot(v1,v2); + value_type dot20 = dot(v2,v0); + value_type inv_dot00 = value_type(1) / dot(v0,v0); + value_type inv_dot11 = value_type(1) / dot(v1,v1); + value_type inv_dot22 = value_type(1) / dot(v2,v2); + + vector_type temp0 = v0 - s*dot01*inv_dot11*v1 - s*dot20*inv_dot22*v2; + vector_type temp1 = v1 - s*dot12*inv_dot22*v2 - s*dot01*inv_dot00*v0; + vector_type temp2 = v2 - s*dot20*inv_dot00*v0 - s*dot12*inv_dot11*v1; + + v0 = temp0; + v1 = temp1; + v2 = temp2; + } + + /* Final Gram-Schmidt step to ensure orthonormality. If no iterations + * have been requested (num_iter = 0), this is the only step. The step + * is performed such that the direction of the axis indexed by + * 'stable_axis' is unchanged. + */ + + size_t i, j, k; + cyclic_permutation(stable_axis, i, j, k); + vector_type v[] = { v0, v1, v2 }; + + v[i].normalize(); + v[j] = normalize(project_to_hplane(v[j],v[i])); + v[k] = normalize(project_to_hplane(project_to_hplane(v[k],v[i]),v[j])); + + v0 = v[0]; + v1 = v[1]; + v2 = v[2]; +} + +/** Orthonormalize 2 basis vectors in R2 */ +template < typename E, class A > void +orthonormalize(vector& v0, vector& v1, + size_t stable_axis = 0, size_t num_iter = 0, E s = E(1)) +{ + typedef vector< E, fixed<2> > vector_type; + typedef typename vector_type::value_type value_type; + + /* Checking */ + detail::CheckVec2(v0); + detail::CheckVec2(v1); + detail::CheckIndex2(stable_axis); + + /* Iterative Gram-Schmidt; this step is skipped by default. */ + + for (size_t i = 0; i < num_iter; ++i) { + value_type dot01 = dot(v0,v1); + + vector_type temp0 = v0 - (s * dot01 * v1) / dot(v1,v1); + vector_type temp1 = v1 - (s * dot01 * v0) / dot(v0,v0); + + v0 = temp0; + v1 = temp1; + } + + /* Final Gram-Schmidt step to ensure orthonormality. If no iterations + * have been requested (num_iter = 0), this is the only step. The step + * is performed such that the direction of the axis indexed by + * 'stable_axis' is unchanged. + */ + + size_t i, j; + cyclic_permutation(stable_axis, i, j); + vector_type v[] = { v0, v1 }; + + v[i].normalize(); + v[j] = normalize(project_to_hplane(v[j],v[i])); + + v0 = v[0]; + v1 = v[1]; +} + +////////////////////////////////////////////////////////////////////////////// +// Orthonormal basis construction in 3D and 2D +////////////////////////////////////////////////////////////////////////////// + +/** This version of orthonormal_basis() ultimately does the work for all + * orthonormal_basis_*() functions. Given input vectors 'align' and + * 'reference', and an order 'axis_order_\\\', it constructs an + * orthonormal basis such that the i'th basis vector is aligned with (parallel + * to and pointing in the same direction as) 'align', and the j'th basis + * vector is maximally aligned with 'reference'. The k'th basis vector is + * chosen such that the basis has a determinant of +1. + * + * @note The algorithm fails when 'align' is nearly parallel to + * 'reference'; this should be checked for and handled externally if it's a + * case that may occur. + * + * @internal This is an example of the 'non-const argument modification + * invalidates expression' gotcha. If x, y or z were to be assigned to before + * we were 'done' with align and reference, and if one of them were the same + * object as align or reference, then the algorithm could fail. As is the + * basis vectors are assigned at the end of the function from a temporary + * array, so all is well. + */ +template < class VecT_1, class VecT_2, typename E, class A > void +orthonormal_basis( + const VecT_1& align, + const VecT_2& reference, + vector& x, + vector& y, + vector& z, + bool normalize_align = true, + AxisOrder order = axis_order_zyx) +{ + typedef vector< E,fixed<3> > vector_type; + typedef typename vector_type::value_type value_type; + + /* Checking handled by cross() and assignment to fixed<3>. */ + + size_t i, j, k; + bool odd; + detail::unpack_axis_order(order, i, j, k, odd); + + vector_type axis[3]; + + axis[i] = normalize_align ? normalize(align) : align; + axis[k] = unit_cross(axis[i],reference); + axis[j] = cross(axis[k],axis[i]); + + if (odd) { + axis[k] = -axis[k]; + } + + x = axis[0]; + y = axis[1]; + z = axis[2]; +} + +/** This version of orthonormal_basis() constructs in arbitrary basis given a + * vector with which to align the i'th basis vector. To avoid the failure + * case, the reference vector is always chosen so as to not be parallel to + * 'align'. This means the algorithm will always generate a valid basis, which + * can be useful in some circumstances; however, it should be noted that the + * basis will likely 'pop' as the alignment vector changes, and so may not be + * suitable for billboarding or other similar applications. + */ +template < class VecT, typename E, class A > +void orthonormal_basis( + const VecT& align, + vector& x, + vector& y, + vector& z, + bool normalize_align = true, + AxisOrder order = axis_order_zyx) +{ + /* Checking (won't be necessary with index_of_min_abs() member function */ + detail::CheckVec3(align); + + /* @todo: vector member function index_of_min_abs() would clean this up */ + + orthonormal_basis( + align, + axis_3D(cml::index_of_min_abs(align[0],align[1],align[2])), + x, y, z, normalize_align, order + ); +} + +/** orthonormal_basis_axial() generates a basis in which the j'th basis vector + * is aligned with 'axis' and the i'th basis vector is maximally aligned (as + * 'aligned as possible') with 'align'. This can be used for e.g. axial + * billboarding for, say, trees or beam effects. + * + * Note that the implementation simply passes off to the 'reference' version + * of orthonormal_basis(), with the parameters adjusted so that the alignment + * is axial. + * + * @note With this algorithm the failure case is when 'align' and 'axis' + * are nearly parallel; if this is likely, it should be checked for and + * handled externally. + */ +template < class VecT_1, class VecT_2, typename E, class A > +void orthonormal_basis_axial( + const VecT_1& align, + const VecT_2& axis, + vector& x, + vector& y, + vector& z, + bool normalize_align = true, + AxisOrder order = axis_order_zyx) +{ + orthonormal_basis( + axis, + align, + x, + y, + z, + normalize_align, + detail::swap_axis_order(order)); +} + +/** orthonormal_basis_viewplane() builds a basis aligned with a viewplane, as + * extracted from the input view matrix. The function takes into account the + * handedness of the input view matrix and orients the basis accordingly. + * + * @note The generated basis will always be valid. + */ +template < class MatT, typename E, class A > +void orthonormal_basis_viewplane( + const MatT& view_matrix, + vector& x, + vector& y, + vector& z, + Handedness handedness, + AxisOrder order = axis_order_zyx) +{ + typedef MatT matrix_type; + typedef typename matrix_type::value_type value_type; + + orthonormal_basis( + -(handedness == left_handed ? value_type(1) : value_type(-1)) * + matrix_get_transposed_z_basis_vector(view_matrix), + matrix_get_transposed_y_basis_vector(view_matrix), + x, y, z, false, order + ); +} + +/** Build a viewplane-oriented basis from a left-handedness view matrix. */ +template < class MatT, typename E, class A > +void orthonormal_basis_viewplane_LH( + const MatT& view_matrix, + vector& x, + vector& y, + vector& z, + AxisOrder order = axis_order_zyx) +{ + orthonormal_basis_viewplane( + view_matrix,x,y,z,left_handed,order); +} + +/** Build a viewplane-oriented basis from a right-handedness view matrix. */ +template < class MatT, typename E, class A > +void orthonormal_basis_viewplane_RH( + const MatT& view_matrix, + vector& x, + vector& y, + vector& z, + AxisOrder order = axis_order_zyx) +{ + orthonormal_basis_viewplane( + view_matrix,x,y,z,right_handed,order); +} + +/** Build a 2D orthonormal basis. */ +template < class VecT, typename E, class A > +void orthonormal_basis_2D( + const VecT& align, + vector& x, + vector& y, + bool normalize_align = true, + AxisOrder2D order = axis_order_xy) +{ + typedef vector< E,fixed<2> > vector_type; + + /* Checking handled by perp() and assignment to fixed<2>. */ + + size_t i, j; + bool odd; + detail::unpack_axis_order_2D(order, i, j, odd); + + vector_type axis[2]; + + axis[i] = normalize_align ? normalize(align) : align; + axis[j] = perp(axis[i]); + + if (odd) { + axis[j] = -axis[j]; + } + + x = axis[0]; + y = axis[1]; +} + +} // namespace cml + +#endif