| /* Copyright (C) 2013-2016, The Regents of The University of Michigan. |
| All rights reserved. |
| This software was developed in the APRIL Robotics Lab under the |
| direction of Edwin Olson, ebolson@umich.edu. This software may be |
| available under alternative licensing terms; contact the address above. |
| Redistribution and use in source and binary forms, with or without |
| modification, are permitted provided that the following conditions are met: |
| 1. Redistributions of source code must retain the above copyright notice, this |
| list of conditions and the following disclaimer. |
| 2. Redistributions in binary form must reproduce the above copyright notice, |
| this list of conditions and the following disclaimer in the documentation |
| and/or other materials provided with the distribution. |
| THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND |
| ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED |
| WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
| DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR |
| ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES |
| (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND |
| ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| The views and conclusions contained in the software and documentation are those |
| of the authors and should not be interpreted as representing official policies, |
| either expressed or implied, of the Regents of The University of Michigan. |
| */ |
| |
| #include <stdio.h> |
| #include <math.h> |
| #include <string.h> |
| #include <float.h> |
| |
| #include "matd.h" |
| #include "math_util.h" |
| |
| // XXX Write unit tests for me! |
| // XXX Rewrite matd_coords in terms of this. |
| |
| /* |
| This file provides conversions between the following formats: |
| |
| quaternion (TNAME[4], { w, x, y, z}) |
| |
| xyt (translation in x, y, and rotation in radians.) |
| |
| xytcov (xyt as a TNAME[3] followed by covariance TNAME[9]) |
| |
| xy, xyz (translation in x, y, and z) |
| |
| mat44 (4x4 rigid-body transformation matrix, row-major |
| order. Conventions: We assume points are projected via right |
| multiplication. E.g., p' = Mp.) Note: some functions really do rely |
| on it being a RIGID, scale=1 transform. |
| |
| angleaxis (TNAME[4], { angle-rads, x, y, z } |
| |
| xyzrpy (translation x, y, z, euler angles) |
| |
| Roll Pitch Yaw are evaluated in the order: roll, pitch, then yaw. I.e., |
| rollPitchYawToMatrix(rpy) = rotateZ(rpy[2]) * rotateY(rpy[1]) * Rotatex(rpy[0]) |
| */ |
| |
| #define TRRFN(root, suffix) root ## suffix |
| #define TRFN(root, suffix) TRRFN(root, suffix) |
| #define TFN(suffix) TRFN(TNAME, suffix) |
| |
| // if V is null, returns null. |
| static inline TNAME *TFN(s_dup)(const TNAME *v, int len) |
| { |
| if (!v) |
| return NULL; |
| |
| TNAME *r = (TNAME*)malloc(len * sizeof(TNAME)); |
| memcpy(r, v, len * sizeof(TNAME)); |
| return r; |
| } |
| |
| static inline void TFN(s_print)(const TNAME *a, int len, const char *fmt) |
| { |
| for (int i = 0; i < len; i++) |
| printf(fmt, a[i]); |
| printf("\n"); |
| } |
| |
| static inline void TFN(s_print_mat)(const TNAME *a, int nrows, int ncols, const char *fmt) |
| { |
| for (int i = 0; i < nrows * ncols; i++) { |
| printf(fmt, a[i]); |
| if ((i % ncols) == (ncols - 1)) |
| printf("\n"); |
| } |
| } |
| |
| static inline void TFN(s_print_mat44)(const TNAME *a, const char *fmt) |
| { |
| for (int i = 0; i < 4 * 4; i++) { |
| printf(fmt, a[i]); |
| if ((i % 4) == 3) |
| printf("\n"); |
| } |
| } |
| |
| static inline void TFN(s_add)(const TNAME *a, const TNAME *b, int len, TNAME *r) |
| { |
| for (int i = 0; i < len; i++) |
| r[i] = a[i] + b[i]; |
| } |
| |
| static inline void TFN(s_subtract)(const TNAME *a, const TNAME *b, int len, TNAME *r) |
| { |
| for (int i = 0; i < len; i++) |
| r[i] = a[i] - b[i]; |
| } |
| |
| static inline void TFN(s_scale)(TNAME s, const TNAME *v, int len, TNAME *r) |
| { |
| for (int i = 0; i < len; i++) |
| r[i] = s * v[i]; |
| } |
| |
| static inline TNAME TFN(s_dot)(const TNAME *a, const TNAME *b, int len) |
| { |
| TNAME acc = 0; |
| for (int i = 0; i < len; i++) |
| acc += a[i] * b[i]; |
| return acc; |
| } |
| |
| static inline TNAME TFN(s_distance)(const TNAME *a, const TNAME *b, int len) |
| { |
| TNAME acc = 0; |
| for (int i = 0; i < len; i++) |
| acc += (a[i] - b[i])*(a[i] - b[i]); |
| return (TNAME)sqrt(acc); |
| } |
| |
| static inline TNAME TFN(s_squared_distance)(const TNAME *a, const TNAME *b, int len) |
| { |
| TNAME acc = 0; |
| for (int i = 0; i < len; i++) |
| acc += (a[i] - b[i])*(a[i] - b[i]); |
| return acc; |
| } |
| |
| static inline TNAME TFN(s_squared_magnitude)(const TNAME *v, int len) |
| { |
| TNAME acc = 0; |
| for (int i = 0; i < len; i++) |
| acc += v[i]*v[i]; |
| return acc; |
| } |
| |
| static inline TNAME TFN(s_magnitude)(const TNAME *v, int len) |
| { |
| TNAME acc = 0; |
| for (int i = 0; i < len; i++) |
| acc += v[i]*v[i]; |
| return (TNAME)sqrt(acc); |
| } |
| |
| static inline void TFN(s_normalize)(const TNAME *v, int len, TNAME *r) |
| { |
| TNAME mag = TFN(s_magnitude)(v, len); |
| for (int i = 0; i < len; i++) |
| r[i] = v[i] / mag; |
| } |
| |
| static inline void TFN(s_normalize_self)(TNAME *v, int len) |
| { |
| TNAME mag = TFN(s_magnitude)(v, len); |
| for (int i = 0; i < len; i++) |
| v[i] /= mag; |
| } |
| |
| static inline void TFN(s_scale_self)(TNAME *v, int len, double scale) |
| { |
| for (int i = 0; i < len; i++) |
| v[i] = (TNAME)(v[i] * scale); |
| } |
| |
| static inline void TFN(s_quat_rotate)(const TNAME q[4], const TNAME v[3], TNAME r[3]) |
| { |
| TNAME t2, t3, t4, t5, t6, t7, t8, t9, t10; |
| |
| t2 = q[0]*q[1]; |
| t3 = q[0]*q[2]; |
| t4 = q[0]*q[3]; |
| t5 = -q[1]*q[1]; |
| t6 = q[1]*q[2]; |
| t7 = q[1]*q[3]; |
| t8 = -q[2]*q[2]; |
| t9 = q[2]*q[3]; |
| t10 = -q[3]*q[3]; |
| |
| r[0] = 2*((t8+t10)*v[0] + (t6-t4)*v[1] + (t3+t7)*v[2]) + v[0]; |
| r[1] = 2*((t4+t6)*v[0] + (t5+t10)*v[1] + (t9-t2)*v[2]) + v[1]; |
| r[2] = 2*((t7-t3)*v[0] + (t2+t9)*v[1] + (t5+t8)*v[2]) + v[2]; |
| } |
| |
| static inline void TFN(s_quat_multiply)(const TNAME a[4], const TNAME b[4], TNAME r[4]) |
| { |
| r[0] = a[0]*b[0] - a[1]*b[1] - a[2]*b[2] - a[3]*b[3]; |
| r[1] = a[0]*b[1] + a[1]*b[0] + a[2]*b[3] - a[3]*b[2]; |
| r[2] = a[0]*b[2] - a[1]*b[3] + a[2]*b[0] + a[3]*b[1]; |
| r[3] = a[0]*b[3] + a[1]*b[2] - a[2]*b[1] + a[3]*b[0]; |
| } |
| |
| static inline void TFN(s_quat_inverse)(const TNAME q[4], TNAME r[4]) |
| { |
| TNAME mag = TFN(s_magnitude)(q, 4); |
| r[0] = q[0]/mag; |
| r[1] = -q[1]/mag; |
| r[2] = -q[2]/mag; |
| r[3] = -q[3]/mag; |
| } |
| |
| static inline void TFN(s_copy)(const TNAME *src, TNAME *dst, int n) |
| { |
| memcpy(dst, src, n * sizeof(TNAME)); |
| } |
| |
| static inline void TFN(s_xyt_copy)(const TNAME xyt[3], TNAME r[3]) |
| { |
| TFN(s_copy)(xyt, r, 3); |
| } |
| |
| static inline void TFN(s_xyt_to_mat44)(const TNAME xyt[3], TNAME r[16]) |
| { |
| TNAME s = (TNAME)sin(xyt[2]), c = (TNAME)cos(xyt[2]); |
| memset(r, 0, sizeof(TNAME)*16); |
| r[0] = c; |
| r[1] = -s; |
| r[3] = xyt[0]; |
| r[4] = s; |
| r[5] = c; |
| r[7] = xyt[1]; |
| r[10] = 1; |
| r[15] = 1; |
| } |
| |
| static inline void TFN(s_xyt_transform_xy)(const TNAME xyt[3], const TNAME xy[2], TNAME r[2]) |
| { |
| TNAME s = (TNAME)sin(xyt[2]), c = (TNAME)cos(xyt[2]); |
| r[0] = c*xy[0] - s*xy[1] + xyt[0]; |
| r[1] = s*xy[0] + c*xy[1] + xyt[1]; |
| } |
| |
| static inline void TFN(s_mat_transform_xyz)(const TNAME M[16], const TNAME xyz[3], TNAME r[3]) |
| { |
| r[0] = M[0]*xyz[0] + M[1]*xyz[1] + M[2]*xyz[2] + M[3]; |
| r[1] = M[4]*xyz[0] + M[5]*xyz[1] + M[6]*xyz[2] + M[7]; |
| r[2] = M[8]*xyz[0] + M[9]*xyz[1] + M[10]*xyz[2] + M[11]; |
| } |
| |
| static inline void TFN(s_quat_to_angleaxis)(const TNAME _q[4], TNAME r[4]) |
| { |
| TNAME q[4]; |
| TFN(s_normalize)(_q, 4, q); |
| |
| // be polite: return an angle from [-pi, pi] |
| // use atan2 to be 4-quadrant safe |
| TNAME mag = TFN(s_magnitude)(&q[1], 3); |
| r[0] = (TNAME)mod2pi(2 * atan2(mag, q[0])); |
| if (mag != 0) { |
| r[1] = q[1] / mag; |
| r[2] = q[2] / mag; |
| r[3] = q[3] / mag; |
| } else { |
| r[1] = 1; |
| r[2] = 0; |
| r[3] = 0; |
| } |
| } |
| |
| static inline void TFN(s_angleaxis_to_quat)(const TNAME aa[4], TNAME q[4]) |
| { |
| TNAME rad = aa[0]; |
| q[0] = (TNAME)cos(rad / 2.0); |
| TNAME s = (TNAME)sin(rad / 2.0); |
| |
| TNAME v[3] = { aa[1], aa[2], aa[3] }; |
| TFN(s_normalize)(v, 3, v); |
| |
| q[1] = s * v[0]; |
| q[2] = s * v[1]; |
| q[3] = s * v[2]; |
| } |
| |
| static inline void TFN(s_quat_to_mat44)(const TNAME q[4], TNAME r[16]) |
| { |
| TNAME w = q[0], x = q[1], y = q[2], z = q[3]; |
| |
| r[0] = w*w + x*x - y*y - z*z; |
| r[1] = 2*x*y - 2*w*z; |
| r[2] = 2*x*z + 2*w*y; |
| r[3] = 0; |
| |
| r[4] = 2*x*y + 2*w*z; |
| r[5] = w*w - x*x + y*y - z*z; |
| r[6] = 2*y*z - 2*w*x; |
| r[7] = 0; |
| |
| r[8] = 2*x*z - 2*w*y; |
| r[9] = 2*y*z + 2*w*x; |
| r[10] = w*w - x*x - y*y + z*z; |
| r[11] = 0; |
| |
| r[12] = 0; |
| r[13] = 0; |
| r[14] = 0; |
| r[15] = 1; |
| } |
| |
| /* Returns the skew-symmetric matrix V such that V*w = v x w (cross product). |
| Sometimes denoted [v]_x or \hat{v}. |
| [ 0 -v3 v2 |
| v3 0 -v1 |
| -v2 v1 0] |
| */ |
| static inline void TFN(s_cross_matrix)(const TNAME v[3], TNAME V[9]) |
| { |
| V[0] = 0; |
| V[1] = -v[2]; |
| V[2] = v[1]; |
| V[3] = v[2]; |
| V[4] = 0; |
| V[5] = -v[0]; |
| V[6] = -v[1]; |
| V[7] = v[0]; |
| V[8] = 0; |
| } |
| |
| static inline void TFN(s_angleaxis_to_mat44)(const TNAME aa[4], TNAME r[16]) |
| { |
| TNAME q[4]; |
| |
| TFN(s_angleaxis_to_quat)(aa, q); |
| TFN(s_quat_to_mat44)(q, r); |
| } |
| |
| static inline void TFN(s_quat_xyz_to_mat44)(const TNAME q[4], const TNAME xyz[3], TNAME r[16]) |
| { |
| TFN(s_quat_to_mat44)(q, r); |
| |
| if (xyz != NULL) { |
| r[3] = xyz[0]; |
| r[7] = xyz[1]; |
| r[11] = xyz[2]; |
| } |
| } |
| |
| static inline void TFN(s_rpy_to_quat)(const TNAME rpy[3], TNAME quat[4]) |
| { |
| TNAME roll = rpy[0], pitch = rpy[1], yaw = rpy[2]; |
| |
| TNAME halfroll = roll / 2; |
| TNAME halfpitch = pitch / 2; |
| TNAME halfyaw = yaw / 2; |
| |
| TNAME sin_r2 = (TNAME)sin(halfroll); |
| TNAME sin_p2 = (TNAME)sin(halfpitch); |
| TNAME sin_y2 = (TNAME)sin(halfyaw); |
| |
| TNAME cos_r2 = (TNAME)cos(halfroll); |
| TNAME cos_p2 = (TNAME)cos(halfpitch); |
| TNAME cos_y2 = (TNAME)cos(halfyaw); |
| |
| quat[0] = cos_r2 * cos_p2 * cos_y2 + sin_r2 * sin_p2 * sin_y2; |
| quat[1] = sin_r2 * cos_p2 * cos_y2 - cos_r2 * sin_p2 * sin_y2; |
| quat[2] = cos_r2 * sin_p2 * cos_y2 + sin_r2 * cos_p2 * sin_y2; |
| quat[3] = cos_r2 * cos_p2 * sin_y2 - sin_r2 * sin_p2 * cos_y2; |
| } |
| |
| // Reference: "A tutorial on SE(3) transformation parameterizations and |
| // on-manifold optimization" by Jose-Luis Blanco |
| static inline void TFN(s_quat_to_rpy)(const TNAME q[4], TNAME rpy[3]) |
| { |
| const TNAME qr = q[0]; |
| const TNAME qx = q[1]; |
| const TNAME qy = q[2]; |
| const TNAME qz = q[3]; |
| |
| TNAME disc = qr*qy - qx*qz; |
| |
| if (fabs(disc+0.5) < DBL_EPSILON) { // near -1/2 |
| rpy[0] = 0; |
| rpy[1] = (TNAME)(-M_PI/2); |
| rpy[2] = (TNAME)(2 * atan2(qx, qr)); |
| } |
| else if (fabs(disc-0.5) < DBL_EPSILON) { // near 1/2 |
| rpy[0] = 0; |
| rpy[1] = (TNAME)(M_PI/2); |
| rpy[2] = (TNAME)(-2 * atan2(qx, qr)); |
| } |
| else { |
| // roll |
| TNAME roll_a = 2 * (qr*qx + qy*qz); |
| TNAME roll_b = 1 - 2 * (qx*qx + qy*qy); |
| rpy[0] = (TNAME)atan2(roll_a, roll_b); |
| |
| // pitch |
| rpy[1] = (TNAME)asin(2*disc); |
| |
| // yaw |
| TNAME yaw_a = 2 * (qr*qz + qx*qy); |
| TNAME yaw_b = 1 - 2 * (qy*qy + qz*qz); |
| rpy[2] = (TNAME)atan2(yaw_a, yaw_b); |
| } |
| } |
| |
| static inline void TFN(s_rpy_to_mat44)(const TNAME rpy[3], TNAME M[16]) |
| { |
| TNAME q[4]; |
| TFN(s_rpy_to_quat)(rpy, q); |
| TFN(s_quat_to_mat44)(q, M); |
| } |
| |
| |
| static inline void TFN(s_xyzrpy_to_mat44)(const TNAME xyzrpy[6], TNAME M[16]) |
| { |
| TFN(s_rpy_to_mat44)(&xyzrpy[3], M); |
| M[3] = xyzrpy[0]; |
| M[7] = xyzrpy[1]; |
| M[11] = xyzrpy[2]; |
| } |
| |
| static inline void TFN(s_mat44_transform_xyz)(const TNAME M[16], const TNAME in[3], TNAME out[3]) |
| { |
| for (int i = 0; i < 3; i++) |
| out[i] = M[4*i + 0]*in[0] + M[4*i + 1]*in[1] + M[4*i + 2]*in[2] + M[4*i + 3]; |
| } |
| |
| // out = (upper 3x3 of M) * in |
| static inline void TFN(s_mat44_rotate_vector)(const TNAME M[16], const TNAME in[3], TNAME out[3]) |
| { |
| for (int i = 0; i < 3; i++) |
| out[i] = M[4*i + 0]*in[0] + M[4*i + 1]*in[1] + M[4*i + 2]*in[2]; |
| } |
| |
| static inline void TFN(s_mat44_to_xyt)(const TNAME M[16], TNAME xyt[3]) |
| { |
| // c -s |
| // s c |
| xyt[0] = M[3]; |
| xyt[1] = M[7]; |
| xyt[2] = (TNAME)atan2(M[4], M[0]); |
| } |
| |
| static inline void TFN(s_mat_to_xyz)(const TNAME M[16], TNAME xyz[3]) |
| { |
| xyz[0] = M[3]; |
| xyz[1] = M[7]; |
| xyz[2] = M[11]; |
| } |
| |
| static inline void TFN(s_mat_to_quat)(const TNAME M[16], TNAME q[4]) |
| { |
| double T = M[0] + M[5] + M[10] + 1.0; |
| double S; |
| |
| if (T > 0.0000001) { |
| S = sqrt(T) * 2; |
| q[0] = (TNAME)(0.25 * S); |
| q[1] = (TNAME)((M[9] - M[6]) / S); |
| q[2] = (TNAME)((M[2] - M[8]) / S); |
| q[3] = (TNAME)((M[4] - M[1]) / S); |
| } else if (M[0] > M[5] && M[0] > M[10]) { // Column 0: |
| S = sqrt(1.0 + M[0] - M[5] - M[10]) * 2; |
| q[0] = (TNAME)((M[9] - M[6]) / S); |
| q[1] = (TNAME)(0.25 * S); |
| q[2] = (TNAME)((M[4] + M[1]) / S); |
| q[3] = (TNAME)((M[2] + M[8]) / S); |
| } else if (M[5] > M[10]) { // Column 1: |
| S = sqrt(1.0 + M[5] - M[0] - M[10]) * 2; |
| q[0] = (TNAME)((M[2] - M[8]) / S); |
| q[1] = (TNAME)((M[4] + M[1]) / S); |
| q[2] = (TNAME)(0.25 * S); |
| q[3] = (TNAME)((M[9] + M[6]) / S); |
| } else { // Column 2: |
| S = sqrt(1.0 + M[10] - M[0] - M[5]); |
| q[0] = (TNAME)((M[4] - M[1]) / S); |
| q[1] = (TNAME)((M[2] + M[8]) / S); |
| q[2] = (TNAME)((M[9] + M[6]) / S); |
| q[3] = (TNAME)(0.25 * S); |
| } |
| |
| TFN(s_normalize)(q, 4, q); |
| } |
| |
| static inline void TFN(s_quat_xyz_to_xyt)(const TNAME q[4], const TNAME xyz[3], TNAME xyt[3]) |
| { |
| TNAME M[16]; |
| TFN(s_quat_xyz_to_mat44)(q, xyz, M); |
| TFN(s_mat44_to_xyt)(M, xyt); |
| } |
| |
| // xytr = xyta * xytb; |
| static inline void TFN(s_xyt_mul)(const TNAME xyta[3], const TNAME xytb[3], TNAME xytr[3]) |
| { |
| TNAME xa = xyta[0], ya = xyta[1], ta = xyta[2]; |
| TNAME s = (TNAME)sin(ta), c = (TNAME)cos(ta); |
| |
| xytr[0] = c*xytb[0] - s*xytb[1] + xa; |
| xytr[1] = s*xytb[0] + c*xytb[1] + ya; |
| xytr[2] = ta + xytb[2]; |
| } |
| |
| static inline void TFN(s_xytcov_copy)(const TNAME xyta[3], const TNAME Ca[9], |
| TNAME xytr[3], TNAME Cr[9]) |
| { |
| memcpy(xytr, xyta, 3 * sizeof(TNAME)); |
| memcpy(Cr, Ca, 9 * sizeof(TNAME)); |
| } |
| |
| static inline void TFN(s_xytcov_mul)(const TNAME xyta[3], const TNAME Ca[9], |
| const TNAME xytb[3], const TNAME Cb[9], |
| TNAME xytr[3], TNAME Cr[9]) |
| { |
| TNAME xa = xyta[0], ya = xyta[1], ta = xyta[2]; |
| TNAME xb = xytb[0], yb = xytb[1]; |
| |
| TNAME sa = (TNAME)sin(ta), ca = (TNAME)cos(ta); |
| |
| TNAME P11 = Ca[0], P12 = Ca[1], P13 = Ca[2]; |
| TNAME P22 = Ca[4], P23 = Ca[5]; |
| TNAME P33 = Ca[8]; |
| |
| TNAME Q11 = Cb[0], Q12 = Cb[1], Q13 = Cb[2]; |
| TNAME Q22 = Cb[4], Q23 = Cb[5]; |
| TNAME Q33 = Cb[8]; |
| |
| TNAME JA13 = -sa*xb - ca*yb; |
| TNAME JA23 = ca*xb - sa*yb; |
| TNAME JB11 = ca; |
| TNAME JB12 = -sa; |
| TNAME JB21 = sa; |
| TNAME JB22 = ca; |
| |
| Cr[0] = P33*JA13*JA13 + 2*P13*JA13 + Q11*JB11*JB11 + 2*Q12*JB11*JB12 + Q22*JB12*JB12 + P11; |
| Cr[1] = P12 + JA23*(P13 + JA13*P33) + JA13*P23 + JB21*(JB11*Q11 + JB12*Q12) + JB22*(JB11*Q12 + JB12*Q22); |
| Cr[2] = P13 + JA13*P33 + JB11*Q13 + JB12*Q23; |
| Cr[3] = Cr[1]; |
| Cr[4] = P33*JA23*JA23 + 2*P23*JA23 + Q11*JB21*JB21 + 2*Q12*JB21*JB22 + Q22*JB22*JB22 + P22; |
| Cr[5] = P23 + JA23*P33 + JB21*Q13 + JB22*Q23; |
| Cr[6] = Cr[2]; |
| Cr[7] = Cr[5]; |
| Cr[8] = P33 + Q33; |
| |
| xytr[0] = ca*xb - sa*yb + xa; |
| xytr[1] = sa*xb + ca*yb + ya; |
| xytr[2] = xyta[2] + xytb[2]; |
| |
| /* |
| // the code above is just an unrolling of the following: |
| |
| TNAME JA[][] = new TNAME[][] { { 1, 0, -sa*xb - ca*yb }, |
| { 0, 1, ca*xb - sa*yb }, |
| { 0, 0, 1 } }; |
| TNAME JB[][] = new TNAME[][] { { ca, -sa, 0 }, |
| { sa, ca, 0 }, |
| { 0, 0, 1 } }; |
| |
| newge.P = LinAlg.add(LinAlg.matrixABCt(JA, P, JA), |
| LinAlg.matrixABCt(JB, ge.P, JB)); |
| */ |
| } |
| |
| |
| static inline void TFN(s_xyt_inv)(const TNAME xyta[3], TNAME xytr[3]) |
| { |
| TNAME s = (TNAME)sin(xyta[2]), c = (TNAME)cos(xyta[2]); |
| xytr[0] = -s*xyta[1] - c*xyta[0]; |
| xytr[1] = -c*xyta[1] + s*xyta[0]; |
| xytr[2] = -xyta[2]; |
| } |
| |
| static inline void TFN(s_xytcov_inv)(const TNAME xyta[3], const TNAME Ca[9], |
| TNAME xytr[3], TNAME Cr[9]) |
| { |
| TNAME x = xyta[0], y = xyta[1], theta = xyta[2]; |
| TNAME s = (TNAME)sin(theta), c = (TNAME)cos(theta); |
| |
| TNAME J11 = -c, J12 = -s, J13 = -c*y + s*x; |
| TNAME J21 = s, J22 = -c, J23 = s*y + c*x; |
| |
| TNAME P11 = Ca[0], P12 = Ca[1], P13 = Ca[2]; |
| TNAME P22 = Ca[4], P23 = Ca[5]; |
| TNAME P33 = Ca[8]; |
| |
| Cr[0] = P11*J11*J11 + 2*P12*J11*J12 + 2*P13*J11*J13 + |
| P22*J12*J12 + 2*P23*J12*J13 + P33*J13*J13; |
| Cr[1] = J21*(J11*P11 + J12*P12 + J13*P13) + |
| J22*(J11*P12 + J12*P22 + J13*P23) + |
| J23*(J11*P13 + J12*P23 + J13*P33); |
| Cr[2] = - J11*P13 - J12*P23 - J13*P33; |
| Cr[3] = Cr[1]; |
| Cr[4] = P11*J21*J21 + 2*P12*J21*J22 + 2*P13*J21*J23 + |
| P22*J22*J22 + 2*P23*J22*J23 + P33*J23*J23; |
| Cr[5] = - J21*P13 - J22*P23 - J23*P33; |
| Cr[6] = Cr[2]; |
| Cr[7] = Cr[5]; |
| Cr[8] = P33; |
| |
| /* |
| // the code above is just an unrolling of the following: |
| |
| TNAME J[][] = new TNAME[][] { { -c, -s, -c*y + s*x }, |
| { s, -c, s*y + c*x }, |
| { 0, 0, -1 } }; |
| ge.P = LinAlg.matrixABCt(J, P, J); |
| */ |
| |
| xytr[0] = -s*y - c*x; |
| xytr[1] = -c*y + s*x; |
| xytr[2] = -xyta[2]; |
| } |
| |
| // xytr = inv(xyta) * xytb |
| static inline void TFN(s_xyt_inv_mul)(const TNAME xyta[3], const TNAME xytb[3], TNAME xytr[3]) |
| { |
| TNAME theta = xyta[2]; |
| TNAME ca = (TNAME)cos(theta); |
| TNAME sa = (TNAME)sin(theta); |
| TNAME dx = xytb[0] - xyta[0]; |
| TNAME dy = xytb[1] - xyta[1]; |
| |
| xytr[0] = ca*dx + sa*dy; |
| xytr[1] = -sa*dx + ca*dy; |
| xytr[2]= xytb[2] - xyta[2]; |
| } |
| |
| static inline void TFN(s_mat_add)(const TNAME *A, int Arows, int Acols, |
| const TNAME *B, int Brows, int Bcols, |
| TNAME *R, int Rrows, int Rcols) |
| { |
| assert(Arows == Brows); |
| assert(Arows == Rrows); |
| assert(Bcols == Bcols); |
| assert(Bcols == Rcols); |
| |
| for (int i = 0; i < Arows; i++) |
| for (int j = 0; j < Bcols; j++) |
| R[i*Acols + j] = A[i*Acols + j] + B[i*Acols + j]; |
| } |
| |
| // matrix should be in row-major order, allocated in a single packed |
| // array. (This is compatible with matd.) |
| static inline void TFN(s_mat_AB)(const TNAME *A, int Arows, int Acols, |
| const TNAME *B, int Brows, int Bcols, |
| TNAME *R, int Rrows, int Rcols) |
| { |
| assert(Acols == Brows); |
| assert(Rrows == Arows); |
| assert(Bcols == Rcols); |
| |
| for (int Rrow = 0; Rrow < Rrows; Rrow++) { |
| for (int Rcol = 0; Rcol < Rcols; Rcol++) { |
| TNAME acc = 0; |
| for (int i = 0; i < Acols; i++) |
| acc += A[Rrow*Acols + i] * B[i*Bcols + Rcol]; |
| R[Rrow*Rcols + Rcol] = acc; |
| } |
| } |
| } |
| |
| // matrix should be in row-major order, allocated in a single packed |
| // array. (This is compatible with matd.) |
| static inline void TFN(s_mat_ABt)(const TNAME *A, int Arows, int Acols, |
| const TNAME *B, int Brows, int Bcols, |
| TNAME *R, int Rrows, int Rcols) |
| { |
| assert(Acols == Bcols); |
| assert(Rrows == Arows); |
| assert(Brows == Rcols); |
| |
| for (int Rrow = 0; Rrow < Rrows; Rrow++) { |
| for (int Rcol = 0; Rcol < Rcols; Rcol++) { |
| TNAME acc = 0; |
| for (int i = 0; i < Acols; i++) |
| acc += A[Rrow*Acols + i] * B[Rcol*Bcols + i]; |
| R[Rrow*Rcols + Rcol] = acc; |
| } |
| } |
| } |
| |
| static inline void TFN(s_mat_ABC)(const TNAME *A, int Arows, int Acols, |
| const TNAME *B, int Brows, int Bcols, |
| const TNAME *C, int Crows, int Ccols, |
| TNAME *R, int Rrows, int Rcols) |
| { |
| TNAME *tmp = malloc(sizeof(TNAME)*Arows*Bcols); |
| |
| TFN(s_mat_AB)(A, Arows, Acols, B, Brows, Bcols, tmp, Arows, Bcols); |
| TFN(s_mat_AB)(tmp, Arows, Bcols, C, Crows, Ccols, R, Rrows, Rcols); |
| free(tmp); |
| } |
| |
| static inline void TFN(s_mat_Ab)(const TNAME *A, int Arows, int Acols, |
| const TNAME *B, int Blength, |
| TNAME *R, int Rlength) |
| { |
| assert(Acols == Blength); |
| assert(Arows == Rlength); |
| |
| for (int Ridx = 0; Ridx < Rlength; Ridx++) { |
| TNAME acc = 0; |
| for (int i = 0; i < Blength; i++) |
| acc += A[Ridx*Acols + i] * B[i]; |
| R[Ridx] = acc; |
| } |
| } |
| |
| static inline void TFN(s_mat_AtB)(const TNAME *A, int Arows, int Acols, |
| const TNAME *B, int Brows, int Bcols, |
| TNAME *R, int Rrows, int Rcols) |
| { |
| assert(Arows == Brows); |
| assert(Rrows == Acols); |
| assert(Bcols == Rcols); |
| |
| for (int Rrow = 0; Rrow < Rrows; Rrow++) { |
| for (int Rcol = 0; Rcol < Rcols; Rcol++) { |
| TNAME acc = 0; |
| for (int i = 0; i < Acols; i++) |
| acc += A[i*Acols + Rrow] * B[i*Bcols + Rcol]; |
| R[Rrow*Rcols + Rcol] = acc; |
| } |
| } |
| } |
| |
| static inline void TFN(s_quat_slerp)(const TNAME q0[4], const TNAME _q1[4], TNAME r[4], TNAME w) |
| { |
| TNAME dot = TFN(s_dot)(q0, _q1, 4); |
| |
| TNAME q1[4]; |
| memcpy(q1, _q1, sizeof(TNAME) * 4); |
| |
| if (dot < 0) { |
| // flip sign on one of them so we don't spin the "wrong |
| // way" around. This doesn't change the rotation that the |
| // quaternion represents. |
| dot = -dot; |
| for (int i = 0; i < 4; i++) |
| q1[i] *= -1; |
| } |
| |
| // if large dot product (1), slerp will scale both q0 and q1 |
| // by 0, and normalization will blow up. |
| if (dot > 0.95) { |
| |
| for (int i = 0; i < 4; i++) |
| r[i] = q0[i]*(1-w) + q1[i]*w; |
| |
| } else { |
| TNAME angle = (TNAME)acos(dot); |
| |
| TNAME w0 = (TNAME)sin(angle*(1-w)), w1 = (TNAME)sin(angle*w); |
| |
| for (int i = 0; i < 4; i++) |
| r[i] = q0[i]*w0 + q1[i]*w1; |
| |
| TFN(s_normalize)(r, 4, r); |
| } |
| } |
| |
| static inline void TFN(s_cross_product)(const TNAME v1[3], const TNAME v2[3], TNAME r[3]) |
| { |
| r[0] = v1[1]*v2[2] - v1[2]*v2[1]; |
| r[1] = v1[2]*v2[0] - v1[0]*v2[2]; |
| r[2] = v1[0]*v2[1] - v1[1]*v2[0]; |
| } |
| |
| //////////////////// |
| static inline void TFN(s_mat44_identity)(TNAME out[16]) |
| { |
| memset(out, 0, 16 * sizeof(TNAME)); |
| out[0] = 1; |
| out[5] = 1; |
| out[10] = 1; |
| out[15] = 1; |
| } |
| |
| static inline void TFN(s_mat44_translate)(const TNAME txyz[3], TNAME out[16]) |
| { |
| TFN(s_mat44_identity)(out); |
| |
| for (int i = 0; i < 3; i++) |
| out[4*i + 3] += txyz[i]; |
| } |
| |
| static inline void TFN(s_mat44_scale)(const TNAME sxyz[3], TNAME out[16]) |
| { |
| TFN(s_mat44_identity)(out); |
| |
| for (int i = 0; i < 3; i++) |
| out[4*i + i] = sxyz[i]; |
| } |
| |
| static inline void TFN(s_mat44_rotate_z)(TNAME rad, TNAME out[16]) |
| { |
| TFN(s_mat44_identity)(out); |
| TNAME s = (TNAME)sin(rad), c = (TNAME)cos(rad); |
| out[0*4 + 0] = c; |
| out[0*4 + 1] = -s; |
| out[1*4 + 0] = s; |
| out[1*4 + 1] = c; |
| } |
| |
| static inline void TFN(s_mat44_rotate_y)(TNAME rad, TNAME out[16]) |
| { |
| TFN(s_mat44_identity)(out); |
| TNAME s = (TNAME)sin(rad), c = (TNAME)cos(rad); |
| out[0*4 + 0] = c; |
| out[0*4 + 2] = s; |
| out[2*4 + 0] = -s; |
| out[2*4 + 2] = c; |
| } |
| |
| static inline void TFN(s_mat44_rotate_x)(TNAME rad, TNAME out[16]) |
| { |
| TFN(s_mat44_identity)(out); |
| TNAME s = (TNAME)sin(rad), c = (TNAME)cos(rad); |
| out[1*4 + 1] = c; |
| out[1*4 + 2] = -s; |
| out[2*4 + 1] = s; |
| out[2*4 + 2] = c; |
| } |
| |
| // out = out * translate(txyz) |
| static inline void TFN(s_mat44_translate_self)(const TNAME txyz[3], TNAME out[16]) |
| { |
| TNAME tmp[16], prod[16]; |
| TFN(s_mat44_translate(txyz, tmp)); |
| TFN(s_mat_AB)(out, 4, 4, tmp, 4, 4, prod, 4, 4); |
| memcpy(out, prod, sizeof(TNAME)*16); |
| } |
| |
| static inline void TFN(s_mat44_scale_self)(const TNAME sxyz[3], TNAME out[16]) |
| { |
| TNAME tmp[16], prod[16]; |
| TFN(s_mat44_scale(sxyz, tmp)); |
| TFN(s_mat_AB)(out, 4, 4, tmp, 4, 4, prod, 4, 4); |
| memcpy(out, prod, sizeof(TNAME)*16); |
| } |
| |
| static inline void TFN(s_mat44_rotate_z_self)(TNAME rad, TNAME out[16]) |
| { |
| TNAME tmp[16], prod[16]; |
| TFN(s_mat44_rotate_z(rad, tmp)); |
| TFN(s_mat_AB)(out, 4, 4, tmp, 4, 4, prod, 4, 4); |
| memcpy(out, prod, sizeof(TNAME)*16); |
| } |
| |
| // out = inv(M)*in. Note: this assumes that mat44 is a rigid-body transformation. |
| static inline void TFN(s_mat44_inv)(const TNAME M[16], TNAME out[16]) |
| { |
| // NB: M = T*R, inv(M) = inv(R) * inv(T) |
| |
| // transpose of upper-left corner |
| for (int i = 0; i < 3; i++) |
| for (int j = 0; j < 3; j++) |
| out[4*i + j] = M[4*j + i]; |
| |
| out[4*0 + 3] = 0; |
| out[4*1 + 3] = 0; |
| out[4*2 + 3] = 0; |
| |
| for (int i = 0; i < 3; i++) |
| for (int j = 0; j < 3; j++) |
| out[4*i + 3] -= out[4*i + j] * M[4*j + 3]; |
| |
| out[4*3 + 0] = 0; |
| out[4*3 + 1] = 0; |
| out[4*3 + 2] = 0; |
| out[4*3 + 3] = 1; |
| |
| /* TNAME tmp[16]; |
| TFN(s_mat_AB)(M, 4, 4, out, 4, 4, tmp, 4, 4); |
| printf("identity: "); |
| TFN(s_print_mat)(tmp, 4, 4, "%15f"); */ |
| } |
| |
| // out = inv(M)*in |
| static inline void TFN(s_mat44_inv_transform_xyz)(const TNAME M[16], const TNAME in[3], TNAME out[3]) |
| { |
| TNAME T[16]; |
| TFN(s_mat44_inv)(M, T); |
| |
| TFN(s_mat44_transform_xyz)(T, in, out); |
| } |
| |
| // out = (upper 3x3 of inv(M)) * in |
| static inline void TFN(s_mat44_inv_rotate_vector)(const TNAME M[16], const TNAME in[3], TNAME out[3]) |
| { |
| TNAME T[16]; |
| TFN(s_mat44_inv)(M, T); |
| |
| TFN(s_mat44_rotate_vector)(T, in, out); |
| } |
| |
| static inline void TFN(s_elu_to_mat44)(const TNAME eye[3], const TNAME lookat[3], const TNAME _up[3], |
| TNAME M[16]) |
| { |
| TNAME f[3]; |
| TFN(s_subtract)(lookat, eye, 3, f); |
| TFN(s_normalize)(f, 3, f); |
| |
| TNAME up[3]; |
| |
| // remove any component of 'up' that isn't perpendicular to the look direction. |
| TFN(s_normalize)(_up, 3, up); |
| |
| TNAME up_dot = TFN(s_dot)(f, up, 3); |
| for (int i = 0; i < 3; i++) |
| up[i] -= up_dot*f[i]; |
| |
| TFN(s_normalize_self)(up, 3); |
| |
| TNAME s[3], u[3]; |
| TFN(s_cross_product)(f, up, s); |
| TFN(s_cross_product)(s, f, u); |
| |
| TNAME R[16] = { s[0], s[1], s[2], 0, |
| u[0], u[1], u[2], 0, |
| -f[0], -f[1], -f[2], 0, |
| 0, 0, 0, 1}; |
| |
| TNAME T[16] = {1, 0, 0, -eye[0], |
| 0, 1, 0, -eye[1], |
| 0, 0, 1, -eye[2], |
| 0, 0, 0, 1}; |
| |
| // M is the extrinsics matrix [R | t] where t = -R*c |
| TNAME tmp[16]; |
| TFN(s_mat_AB)(R, 4, 4, T, 4, 4, tmp, 4, 4); |
| TFN(s_mat44_inv)(tmp, M); |
| } |
| |
| // Computes the cholesky factorization of A, putting the lower |
| // triangular matrix into R. |
| static inline void TFN(s_mat33_chol)(const TNAME *A, int Arows, int Acols, |
| TNAME *R, int Brows, int Bcols) |
| { |
| assert(Arows == Brows); |
| assert(Bcols == Bcols); |
| |
| // A[0] = R[0]*R[0] |
| R[0] = (TNAME)sqrt(A[0]); |
| |
| // A[1] = R[0]*R[3]; |
| R[3] = A[1] / R[0]; |
| |
| // A[2] = R[0]*R[6]; |
| R[6] = A[2] / R[0]; |
| |
| // A[4] = R[3]*R[3] + R[4]*R[4] |
| R[4] = (TNAME)sqrt(A[4] - R[3]*R[3]); |
| |
| // A[5] = R[3]*R[6] + R[4]*R[7] |
| R[7] = (A[5] - R[3]*R[6]) / R[4]; |
| |
| // A[8] = R[6]*R[6] + R[7]*R[7] + R[8]*R[8] |
| R[8] = (TNAME)sqrt(A[8] - R[6]*R[6] - R[7]*R[7]); |
| |
| R[1] = 0; |
| R[2] = 0; |
| R[5] = 0; |
| } |
| |
| static inline void TFN(s_mat33_lower_tri_inv)(const TNAME *A, int Arows, int Acols, |
| TNAME *R, int Rrows, int Rcols) |
| { |
| // A[0]*R[0] = 1 |
| R[0] = 1 / A[0]; |
| |
| // A[3]*R[0] + A[4]*R[3] = 0 |
| R[3] = -A[3]*R[0] / A[4]; |
| |
| // A[4]*R[4] = 1 |
| R[4] = 1 / A[4]; |
| |
| // A[6]*R[0] + A[7]*R[3] + A[8]*R[6] = 0 |
| R[6] = (-A[6]*R[0] - A[7]*R[3]) / A[8]; |
| |
| // A[7]*R[4] + A[8]*R[7] = 0 |
| R[7] = -A[7]*R[4] / A[8]; |
| |
| // A[8]*R[8] = 1 |
| R[8] = 1 / A[8]; |
| } |
| |
| |
| static inline void TFN(s_mat33_sym_solve)(const TNAME *A, int Arows, int Acols, |
| const TNAME *B, int Brows, int Bcols, |
| TNAME *R, int Rrows, int Rcols) |
| { |
| assert(Arows == Acols); |
| assert(Acols == 3); |
| assert(Brows == 3); |
| assert(Bcols == 1); |
| assert(Rrows == 3); |
| assert(Rcols == 1); |
| |
| TNAME L[9]; |
| TFN(s_mat33_chol)(A, 3, 3, L, 3, 3); |
| |
| TNAME M[9]; |
| TFN(s_mat33_lower_tri_inv)(L, 3, 3, M, 3, 3); |
| |
| double tmp[3]; |
| tmp[0] = M[0]*B[0]; |
| tmp[1] = M[3]*B[0] + M[4]*B[1]; |
| tmp[2] = M[6]*B[0] + M[7]*B[1] + M[8]*B[2]; |
| |
| R[0] = (TNAME)(M[0]*tmp[0] + M[3]*tmp[1] + M[6]*tmp[2]); |
| R[1] = (TNAME)(M[4]*tmp[1] + M[7]*tmp[2]); |
| R[2] = (TNAME)(M[8]*tmp[2]); |
| } |
| |
| /* |
| // solve Ax = B. Assumes A is symmetric; uses cholesky factorization |
| static inline void TFN(s_mat_solve_chol)(const TNAME *A, int Arows, int Acols, |
| const TNAME *B, int Brows, int Bcols, |
| TNAME *R, int Rrows, int Rcols) |
| { |
| assert(Arows == Acols); |
| assert(Arows == Brows); |
| assert(Acols == Rrows); |
| assert(Bcols == Rcols); |
| |
| // |
| } |
| */ |
| #undef TRRFN |
| #undef TRFN |
| #undef TFN |