/* * ***** BEGIN GPL LICENSE BLOCK ***** * * This program is free software; you can redistribute it and/or * modify it under the terms of the GNU General Public License * as published by the Free Software Foundation; either version 2 * of the License, or (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with this program; if not, write to the Free Software Foundation, * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. * * The Original Code is Copyright (C) 2001-2002 by NaN Holding BV. * All rights reserved. * * The Original Code is: some of this file. * * ***** END GPL LICENSE BLOCK ***** * */ /** \file blender/blenlib/intern/math_vector.c * \ingroup bli */ #include "BLI_math.h" //******************************* Interpolation *******************************/ void interp_v2_v2v2(float target[2], const float a[2], const float b[2], const float t) { float s = 1.0f - t; target[0] = s * a[0] + t * b[0]; target[1] = s * a[1] + t * b[1]; } /* weight 3 2D vectors, * 'w' must be unit length but is not a vector, just 3 weights */ void interp_v2_v2v2v2(float p[2], const float v1[2], const float v2[2], const float v3[2], const float w[3]) { p[0] = v1[0] * w[0] + v2[0] * w[1] + v3[0] * w[2]; p[1] = v1[1] * w[0] + v2[1] * w[1] + v3[1] * w[2]; } void interp_v3_v3v3(float target[3], const float a[3], const float b[3], const float t) { float s = 1.0f - t; target[0] = s * a[0] + t * b[0]; target[1] = s * a[1] + t * b[1]; target[2] = s * a[2] + t * b[2]; } void interp_v4_v4v4(float target[4], const float a[4], const float b[4], const float t) { float s = 1.0f - t; target[0] = s * a[0] + t * b[0]; target[1] = s * a[1] + t * b[1]; target[2] = s * a[2] + t * b[2]; target[3] = s * a[3] + t * b[3]; } /* weight 3 vectors, * 'w' must be unit length but is not a vector, just 3 weights */ void interp_v3_v3v3v3(float p[3], const float v1[3], const float v2[3], const float v3[3], const float w[3]) { p[0] = v1[0] * w[0] + v2[0] * w[1] + v3[0] * w[2]; p[1] = v1[1] * w[0] + v2[1] * w[1] + v3[1] * w[2]; p[2] = v1[2] * w[0] + v2[2] * w[1] + v3[2] * w[2]; } /* weight 3 vectors, * 'w' must be unit length but is not a vector, just 4 weights */ void interp_v3_v3v3v3v3(float p[3], const float v1[3], const float v2[3], const float v3[3], const float v4[3], const float w[4]) { p[0] = v1[0] * w[0] + v2[0] * w[1] + v3[0] * w[2] + v4[0] * w[3]; p[1] = v1[1] * w[0] + v2[1] * w[1] + v3[1] * w[2] + v4[1] * w[3]; p[2] = v1[2] * w[0] + v2[2] * w[1] + v3[2] * w[2] + v4[2] * w[3]; } void interp_v4_v4v4v4(float p[4], const float v1[4], const float v2[4], const float v3[4], const float w[3]) { p[0] = v1[0] * w[0] + v2[0] * w[1] + v3[0] * w[2]; p[1] = v1[1] * w[0] + v2[1] * w[1] + v3[1] * w[2]; p[2] = v1[2] * w[0] + v2[2] * w[1] + v3[2] * w[2]; p[3] = v1[3] * w[0] + v2[3] * w[1] + v3[3] * w[2]; } void interp_v4_v4v4v4v4(float p[4], const float v1[4], const float v2[4], const float v3[4], const float v4[4], const float w[4]) { p[0] = v1[0] * w[0] + v2[0] * w[1] + v3[0] * w[2] + v4[0] * w[3]; p[1] = v1[1] * w[0] + v2[1] * w[1] + v3[1] * w[2] + v4[1] * w[3]; p[2] = v1[2] * w[0] + v2[2] * w[1] + v3[2] * w[2] + v4[2] * w[3]; p[3] = v1[3] * w[0] + v2[3] * w[1] + v3[3] * w[2] + v4[3] * w[3]; } void mid_v3_v3v3(float v[3], const float v1[3], const float v2[3]) { v[0] = 0.5f * (v1[0] + v2[0]); v[1] = 0.5f * (v1[1] + v2[1]); v[2] = 0.5f * (v1[2] + v2[2]); } void mid_v2_v2v2(float v[2], const float v1[2], const float v2[2]) { v[0] = 0.5f * (v1[0] + v2[0]); v[1] = 0.5f * (v1[1] + v2[1]); } void mid_v3_v3v3v3(float v[3], const float v1[3], const float v2[3], const float v3[3]) { v[0] = (v1[0] + v2[0] + v3[0]) / 3.0f; v[1] = (v1[1] + v2[1] + v3[1]) / 3.0f; v[2] = (v1[2] + v2[2] + v3[2]) / 3.0f; } /** * Equivalent to: * interp_v3_v3v3(v, v1, v2, -1.0f); */ void flip_v4_v4v4(float v[4], const float v1[4], const float v2[4]) { v[0] = v1[0] + (v1[0] - v2[0]); v[1] = v1[1] + (v1[1] - v2[1]); v[2] = v1[2] + (v1[2] - v2[2]); v[3] = v1[3] + (v1[3] - v2[3]); } void flip_v3_v3v3(float v[3], const float v1[3], const float v2[3]) { v[0] = v1[0] + (v1[0] - v2[0]); v[1] = v1[1] + (v1[1] - v2[1]); v[2] = v1[2] + (v1[2] - v2[2]); } void flip_v2_v2v2(float v[2], const float v1[2], const float v2[2]) { v[0] = v1[0] + (v1[0] - v2[0]); v[1] = v1[1] + (v1[1] - v2[1]); } /********************************** Angles ***********************************/ /* Return the angle in radians between vecs 1-2 and 2-3 in radians * If v1 is a shoulder, v2 is the elbow and v3 is the hand, * this would return the angle at the elbow. * * note that when v1/v2/v3 represent 3 points along a straight line * that the angle returned will be pi (180deg), rather then 0.0 */ float angle_v3v3v3(const float v1[3], const float v2[3], const float v3[3]) { float vec1[3], vec2[3]; sub_v3_v3v3(vec1, v2, v1); sub_v3_v3v3(vec2, v2, v3); normalize_v3(vec1); normalize_v3(vec2); return angle_normalized_v3v3(vec1, vec2); } /* Quicker than full angle computation */ float cos_v3v3v3(const float p1[3], const float p2[3], const float p3[3]) { float vec1[3], vec2[3]; sub_v3_v3v3(vec1, p2, p1); sub_v3_v3v3(vec2, p2, p3); normalize_v3(vec1); normalize_v3(vec2); return dot_v3v3(vec1, vec2); } /* Return the shortest angle in radians between the 2 vectors */ float angle_v3v3(const float v1[3], const float v2[3]) { float vec1[3], vec2[3]; normalize_v3_v3(vec1, v1); normalize_v3_v3(vec2, v2); return angle_normalized_v3v3(vec1, vec2); } float angle_v2v2v2(const float v1[2], const float v2[2], const float v3[2]) { float vec1[2], vec2[2]; vec1[0] = v2[0] - v1[0]; vec1[1] = v2[1] - v1[1]; vec2[0] = v2[0] - v3[0]; vec2[1] = v2[1] - v3[1]; normalize_v2(vec1); normalize_v2(vec2); return angle_normalized_v2v2(vec1, vec2); } /* Return the shortest angle in radians between the 2 vectors */ float angle_v2v2(const float v1[2], const float v2[2]) { float vec1[2], vec2[2]; vec1[0] = v1[0]; vec1[1] = v1[1]; vec2[0] = v2[0]; vec2[1] = v2[1]; normalize_v2(vec1); normalize_v2(vec2); return angle_normalized_v2v2(vec1, vec2); } float angle_signed_v2v2(const float v1[2], const float v2[2]) { const float perp_dot = (v1[1] * v2[0]) - (v1[0] * v2[1]); return atan2f(perp_dot, dot_v2v2(v1, v2)); } float angle_normalized_v3v3(const float v1[3], const float v2[3]) { /* double check they are normalized */ BLI_ASSERT_UNIT_V3(v1); BLI_ASSERT_UNIT_V3(v2); /* this is the same as acos(dot_v3v3(v1, v2)), but more accurate */ if (dot_v3v3(v1, v2) < 0.0f) { float vec[3]; vec[0] = -v2[0]; vec[1] = -v2[1]; vec[2] = -v2[2]; return (float)M_PI - 2.0f * (float)saasin(len_v3v3(vec, v1) / 2.0f); } else return 2.0f * (float)saasin(len_v3v3(v2, v1) / 2.0f); } float angle_normalized_v2v2(const float v1[2], const float v2[2]) { /* double check they are normalized */ BLI_ASSERT_UNIT_V2(v1); BLI_ASSERT_UNIT_V2(v2); /* this is the same as acos(dot_v3v3(v1, v2)), but more accurate */ if (dot_v2v2(v1, v2) < 0.0f) { float vec[2]; vec[0] = -v2[0]; vec[1] = -v2[1]; return (float)M_PI - 2.0f * saasin(len_v2v2(vec, v1) / 2.0f); } else return 2.0f * (float)saasin(len_v2v2(v2, v1) / 2.0f); } /** * angle between 2 vectors defined by 3 coords, about an axis. */ float angle_on_axis_v3v3v3_v3(const float v1[3], const float v2[3], const float v3[3], const float axis[3]) { float v1_proj[3], v2_proj[3], tproj[3]; sub_v3_v3v3(v1_proj, v1, v2); sub_v3_v3v3(v2_proj, v3, v2); /* project the vectors onto the axis */ project_v3_v3v3(tproj, v1_proj, axis); sub_v3_v3(v1_proj, tproj); project_v3_v3v3(tproj, v2_proj, axis); sub_v3_v3(v2_proj, tproj); return angle_v3v3(v1_proj, v2_proj); } void angle_tri_v3(float angles[3], const float v1[3], const float v2[3], const float v3[3]) { float ed1[3], ed2[3], ed3[3]; sub_v3_v3v3(ed1, v3, v1); sub_v3_v3v3(ed2, v1, v2); sub_v3_v3v3(ed3, v2, v3); normalize_v3(ed1); normalize_v3(ed2); normalize_v3(ed3); angles[0] = (float)M_PI - angle_normalized_v3v3(ed1, ed2); angles[1] = (float)M_PI - angle_normalized_v3v3(ed2, ed3); // face_angles[2] = M_PI - angle_normalized_v3v3(ed3, ed1); angles[2] = (float)M_PI - (angles[0] + angles[1]); } void angle_quad_v3(float angles[4], const float v1[3], const float v2[3], const float v3[3], const float v4[3]) { float ed1[3], ed2[3], ed3[3], ed4[3]; sub_v3_v3v3(ed1, v4, v1); sub_v3_v3v3(ed2, v1, v2); sub_v3_v3v3(ed3, v2, v3); sub_v3_v3v3(ed4, v3, v4); normalize_v3(ed1); normalize_v3(ed2); normalize_v3(ed3); normalize_v3(ed4); angles[0] = (float)M_PI - angle_normalized_v3v3(ed1, ed2); angles[1] = (float)M_PI - angle_normalized_v3v3(ed2, ed3); angles[2] = (float)M_PI - angle_normalized_v3v3(ed3, ed4); angles[3] = (float)M_PI - angle_normalized_v3v3(ed4, ed1); } void angle_poly_v3(float *angles, const float *verts[3], int len) { int i; float vec[3][3]; sub_v3_v3v3(vec[2], verts[len - 1], verts[0]); normalize_v3(vec[2]); for (i = 0; i < len; i++) { sub_v3_v3v3(vec[i % 3], verts[i % len], verts[(i + 1) % len]); normalize_v3(vec[i % 3]); angles[i] = (float)M_PI - angle_normalized_v3v3(vec[(i + 2) % 3], vec[i % 3]); } } /********************************* Geometry **********************************/ /* Project v1 on v2 */ void project_v2_v2v2(float c[2], const float v1[2], const float v2[2]) { float mul; mul = dot_v2v2(v1, v2) / dot_v2v2(v2, v2); c[0] = mul * v2[0]; c[1] = mul * v2[1]; } /* Project v1 on v2 */ void project_v3_v3v3(float c[3], const float v1[3], const float v2[3]) { float mul; mul = dot_v3v3(v1, v2) / dot_v3v3(v2, v2); c[0] = mul * v2[0]; c[1] = mul * v2[1]; c[2] = mul * v2[2]; } /* project a vector on a plane defined by normal and a plane point p */ void project_v3_plane(float v[3], const float n[3], const float p[3]) { float vector[3]; float mul; sub_v3_v3v3(vector, v, p); mul = dot_v3v3(vector, n) / len_squared_v3(n); mul_v3_v3fl(vector, n, mul); sub_v3_v3(v, vector); } /* Returns a vector bisecting the angle at v2 formed by v1, v2 and v3 */ void bisect_v3_v3v3v3(float out[3], const float v1[3], const float v2[3], const float v3[3]) { float d_12[3], d_23[3]; sub_v3_v3v3(d_12, v2, v1); sub_v3_v3v3(d_23, v3, v2); normalize_v3(d_12); normalize_v3(d_23); add_v3_v3v3(out, d_12, d_23); normalize_v3(out); } /* Returns a reflection vector from a vector and a normal vector * reflect = vec - ((2 * DotVecs(vec, mirror)) * mirror) */ void reflect_v3_v3v3(float out[3], const float v1[3], const float v2[3]) { float vec[3], normal[3]; float reflect[3] = {0.0f, 0.0f, 0.0f}; float dot2; copy_v3_v3(vec, v1); copy_v3_v3(normal, v2); dot2 = 2 * dot_v3v3(vec, normal); reflect[0] = vec[0] - (dot2 * normal[0]); reflect[1] = vec[1] - (dot2 * normal[1]); reflect[2] = vec[2] - (dot2 * normal[2]); copy_v3_v3(out, reflect); } void ortho_basis_v3v3_v3(float v1[3], float v2[3], const float v[3]) { const float f = (float)sqrt(v[0] * v[0] + v[1] * v[1]); if (f < 1e-35f) { // degenerate case v1[0] = (v[2] < 0.0f) ? -1.0f : 1.0f; v1[1] = v1[2] = v2[0] = v2[2] = 0.0f; v2[1] = 1.0f; } else { const float d = 1.0f / f; v1[0] = v[1] * d; v1[1] = -v[0] * d; v1[2] = 0.0f; v2[0] = -v[2] * v1[1]; v2[1] = v[2] * v1[0]; v2[2] = v[0] * v1[1] - v[1] * v1[0]; } } /* Rotate a point p by angle theta around an arbitrary axis r * http://local.wasp.uwa.edu.au/~pbourke/geometry/ */ void rotate_normalized_v3_v3v3fl(float r[3], const float p[3], const float axis[3], const float angle) { const float costheta = cos(angle); const float sintheta = sin(angle); /* double check they are normalized */ BLI_ASSERT_UNIT_V3(axis); r[0] = ((costheta + (1 - costheta) * axis[0] * axis[0]) * p[0]) + (((1 - costheta) * axis[0] * axis[1] - axis[2] * sintheta) * p[1]) + (((1 - costheta) * axis[0] * axis[2] + axis[1] * sintheta) * p[2]); r[1] = (((1 - costheta) * axis[0] * axis[1] + axis[2] * sintheta) * p[0]) + ((costheta + (1 - costheta) * axis[1] * axis[1]) * p[1]) + (((1 - costheta) * axis[1] * axis[2] - axis[0] * sintheta) * p[2]); r[2] = (((1 - costheta) * axis[0] * axis[2] - axis[1] * sintheta) * p[0]) + (((1 - costheta) * axis[1] * axis[2] + axis[0] * sintheta) * p[1]) + ((costheta + (1 - costheta) * axis[2] * axis[2]) * p[2]); } void rotate_v3_v3v3fl(float r[3], const float p[3], const float axis[3], const float angle) { float axis_n[3]; normalize_v3_v3(axis_n, axis); rotate_normalized_v3_v3v3fl(r, p, axis_n, angle); } /*********************************** Other ***********************************/ void print_v2(const char *str, const float v[2]) { printf("%s: %.3f %.3f\n", str, v[0], v[1]); } void print_v3(const char *str, const float v[3]) { printf("%s: %.3f %.3f %.3f\n", str, v[0], v[1], v[2]); } void print_v4(const char *str, const float v[4]) { printf("%s: %.3f %.3f %.3f %.3f\n", str, v[0], v[1], v[2], v[3]); } void minmax_v3v3_v3(float min[3], float max[3], const float vec[3]) { if (min[0] > vec[0]) min[0] = vec[0]; if (min[1] > vec[1]) min[1] = vec[1]; if (min[2] > vec[2]) min[2] = vec[2]; if (max[0] < vec[0]) max[0] = vec[0]; if (max[1] < vec[1]) max[1] = vec[1]; if (max[2] < vec[2]) max[2] = vec[2]; } void minmax_v2v2_v2(float min[2], float max[2], const float vec[2]) { if (min[0] > vec[0]) min[0] = vec[0]; if (min[1] > vec[1]) min[1] = vec[1]; if (max[0] < vec[0]) max[0] = vec[0]; if (max[1] < vec[1]) max[1] = vec[1]; } /** ensure \a v1 is \a dist from \a v2 */ void dist_ensure_v3_v3fl(float v1[3], const float v2[3], const float dist) { if (!equals_v3v3(v2, v1)) { float nor[3]; sub_v3_v3v3(nor, v1, v2); normalize_v3(nor); madd_v3_v3v3fl(v1, v2, nor, dist); } } void dist_ensure_v2_v2fl(float v1[2], const float v2[2], const float dist) { if (!equals_v2v2(v2, v1)) { float nor[2]; sub_v2_v2v2(nor, v1, v2); normalize_v2(nor); madd_v2_v2v2fl(v1, v2, nor, dist); } } /***************************** Array Functions *******************************/ double dot_vn_vn(const float *array_src_a, const float *array_src_b, const int size) { double d = 0.0f; const float *array_pt_a = array_src_a + (size - 1); const float *array_pt_b = array_src_b + (size - 1); int i = size; while (i--) { d += (double)(*(array_pt_a--) * *(array_pt_b--)); } return d; } float normalize_vn_vn(float *array_tar, const float *array_src, const int size) { double d = dot_vn_vn(array_tar, array_src, size); float d_sqrt; if (d > 1.0e-35) { d_sqrt = (float)sqrt(d); mul_vn_vn_fl(array_tar, array_src, size, 1.0f / d_sqrt); } else { fill_vn_fl(array_tar, size, 0.0f); d_sqrt = 0.0f; } return d_sqrt; } float normalize_vn(float *array_tar, const int size) { return normalize_vn_vn(array_tar, array_tar, size); } void range_vn_i(int *array_tar, const int size, const int start) { int *array_pt = array_tar + (size - 1); int j = start + (size - 1); int i = size; while (i--) { *(array_pt--) = j--; } } void range_vn_fl(float *array_tar, const int size, const float start, const float step) { float *array_pt = array_tar + (size - 1); int i = size; while (i--) { *(array_pt--) = start + step * (float)(i); } } void negate_vn(float *array_tar, const int size) { float *array_pt = array_tar + (size - 1); int i = size; while (i--) { *(array_pt--) *= -1.0f; } } void negate_vn_vn(float *array_tar, const float *array_src, const int size) { float *tar = array_tar + (size - 1); const float *src = array_src + (size - 1); int i = size; while (i--) { *(tar--) = -*(src--); } } void mul_vn_fl(float *array_tar, const int size, const float f) { float *array_pt = array_tar + (size - 1); int i = size; while (i--) { *(array_pt--) *= f; } } void mul_vn_vn_fl(float *array_tar, const float *array_src, const int size, const float f) { float *tar = array_tar + (size - 1); const float *src = array_src + (size - 1); int i = size; while (i--) { *(tar--) = *(src--) * f; } } void add_vn_vn(float *array_tar, const float *array_src, const int size) { float *tar = array_tar + (size - 1); const float *src = array_src + (size - 1); int i = size; while (i--) { *(tar--) += *(src--); } } void add_vn_vnvn(float *array_tar, const float *array_src_a, const float *array_src_b, const int size) { float *tar = array_tar + (size - 1); const float *src_a = array_src_a + (size - 1); const float *src_b = array_src_b + (size - 1); int i = size; while (i--) { *(tar--) = *(src_a--) + *(src_b--); } } void madd_vn_vn(float *array_tar, const float *array_src, const float f, const int size) { float *tar = array_tar + (size - 1); const float *src = array_src + (size - 1); int i = size; while (i--) { *(tar--) += *(src--) * f; } } void madd_vn_vnvn(float *array_tar, const float *array_src_a, const float *array_src_b, const float f, const int size) { float *tar = array_tar + (size - 1); const float *src_a = array_src_a + (size - 1); const float *src_b = array_src_b + (size - 1); int i = size; while (i--) { *(tar--) = *(src_a--) + (*(src_b--) * f); } } void sub_vn_vn(float *array_tar, const float *array_src, const int size) { float *tar = array_tar + (size - 1); const float *src = array_src + (size - 1); int i = size; while (i--) { *(tar--) -= *(src--); } } void sub_vn_vnvn(float *array_tar, const float *array_src_a, const float *array_src_b, const int size) { float *tar = array_tar + (size - 1); const float *src_a = array_src_a + (size - 1); const float *src_b = array_src_b + (size - 1); int i = size; while (i--) { *(tar--) = *(src_a--) - *(src_b--); } } void msub_vn_vn(float *array_tar, const float *array_src, const float f, const int size) { float *tar = array_tar + (size - 1); const float *src = array_src + (size - 1); int i = size; while (i--) { *(tar--) -= *(src--) * f; } } void msub_vn_vnvn(float *array_tar, const float *array_src_a, const float *array_src_b, const float f, const int size) { float *tar = array_tar + (size - 1); const float *src_a = array_src_a + (size - 1); const float *src_b = array_src_b + (size - 1); int i = size; while (i--) { *(tar--) = *(src_a--) - (*(src_b--) * f); } } void interp_vn_vn(float *array_tar, const float *array_src, const float t, const int size) { const float s = 1.0f - t; float *tar = array_tar + (size - 1); const float *src = array_src + (size - 1); int i = size; while (i--) { *(tar) = (s * *(tar)) + (t * *(src)); tar--; src--; } } void fill_vn_i(int *array_tar, const int size, const int val) { int *tar = array_tar + (size - 1); int i = size; while (i--) { *(tar--) = val; } } void fill_vn_ushort(unsigned short *array_tar, const int size, const unsigned short val) { unsigned short *tar = array_tar + (size - 1); int i = size; while (i--) { *(tar--) = val; } } void fill_vn_fl(float *array_tar, const int size, const float val) { float *tar = array_tar + (size - 1); int i = size; while (i--) { *(tar--) = val; } }