[216] | 1 | /************************************************************************* |
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| 2 | * * |
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| 3 | * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. * |
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| 4 | * All rights reserved. Email: russ@q12.org Web: www.q12.org * |
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| 5 | * * |
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| 6 | * This library is free software; you can redistribute it and/or * |
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| 7 | * modify it under the terms of EITHER: * |
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| 8 | * (1) The GNU Lesser General Public License as published by the Free * |
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| 9 | * Software Foundation; either version 2.1 of the License, or (at * |
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| 10 | * your option) any later version. The text of the GNU Lesser * |
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| 11 | * General Public License is included with this library in the * |
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| 12 | * file LICENSE.TXT. * |
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| 13 | * (2) The BSD-style license that is included with this library in * |
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| 14 | * the file LICENSE-BSD.TXT. * |
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| 15 | * * |
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| 16 | * This library is distributed in the hope that it will be useful, * |
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| 17 | * but WITHOUT ANY WARRANTY; without even the implied warranty of * |
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| 18 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files * |
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| 19 | * LICENSE.TXT and LICENSE-BSD.TXT for more details. * |
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| 20 | * * |
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| 21 | *************************************************************************/ |
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| 22 | |
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| 23 | #include "objects.h" |
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| 24 | #include "joint.h" |
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| 25 | #include <ode/config.h> |
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| 26 | #include <ode/odemath.h> |
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| 27 | #include <ode/rotation.h> |
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| 28 | #include <ode/timer.h> |
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| 29 | #include <ode/error.h> |
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| 30 | #include <ode/matrix.h> |
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| 31 | #include "lcp.h" |
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| 32 | |
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| 33 | //**************************************************************************** |
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| 34 | // misc defines |
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| 35 | |
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| 36 | #define FAST_FACTOR |
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| 37 | //#define TIMING |
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| 38 | |
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| 39 | #define ALLOCA dALLOCA16 |
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| 40 | |
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| 41 | //**************************************************************************** |
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| 42 | // debugging - comparison of various vectors and matrices produced by the |
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| 43 | // slow and fast versions of the stepper. |
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| 44 | |
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| 45 | //#define COMPARE_METHODS |
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| 46 | |
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| 47 | #ifdef COMPARE_METHODS |
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| 48 | #include "testing.h" |
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| 49 | dMatrixComparison comparator; |
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| 50 | #endif |
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| 51 | |
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| 52 | //**************************************************************************** |
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| 53 | // special matrix multipliers |
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| 54 | |
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| 55 | // this assumes the 4th and 8th rows of B and C are zero. |
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| 56 | |
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| 57 | static void Multiply2_p8r (dReal *A, dReal *B, dReal *C, |
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| 58 | int p, int r, int Askip) |
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| 59 | { |
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| 60 | int i,j; |
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| 61 | dReal sum,*bb,*cc; |
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| 62 | dIASSERT (p>0 && r>0 && A && B && C); |
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| 63 | bb = B; |
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| 64 | for (i=p; i; i--) { |
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| 65 | cc = C; |
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| 66 | for (j=r; j; j--) { |
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| 67 | sum = bb[0]*cc[0]; |
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| 68 | sum += bb[1]*cc[1]; |
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| 69 | sum += bb[2]*cc[2]; |
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| 70 | sum += bb[4]*cc[4]; |
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| 71 | sum += bb[5]*cc[5]; |
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| 72 | sum += bb[6]*cc[6]; |
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| 73 | *(A++) = sum; |
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| 74 | cc += 8; |
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| 75 | } |
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| 76 | A += Askip - r; |
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| 77 | bb += 8; |
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| 78 | } |
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| 79 | } |
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| 80 | |
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| 81 | |
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| 82 | // this assumes the 4th and 8th rows of B and C are zero. |
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| 83 | |
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| 84 | static void MultiplyAdd2_p8r (dReal *A, dReal *B, dReal *C, |
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| 85 | int p, int r, int Askip) |
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| 86 | { |
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| 87 | int i,j; |
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| 88 | dReal sum,*bb,*cc; |
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| 89 | dIASSERT (p>0 && r>0 && A && B && C); |
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| 90 | bb = B; |
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| 91 | for (i=p; i; i--) { |
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| 92 | cc = C; |
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| 93 | for (j=r; j; j--) { |
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| 94 | sum = bb[0]*cc[0]; |
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| 95 | sum += bb[1]*cc[1]; |
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| 96 | sum += bb[2]*cc[2]; |
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| 97 | sum += bb[4]*cc[4]; |
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| 98 | sum += bb[5]*cc[5]; |
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| 99 | sum += bb[6]*cc[6]; |
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| 100 | *(A++) += sum; |
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| 101 | cc += 8; |
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| 102 | } |
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| 103 | A += Askip - r; |
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| 104 | bb += 8; |
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| 105 | } |
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| 106 | } |
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| 107 | |
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| 108 | |
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| 109 | // this assumes the 4th and 8th rows of B are zero. |
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| 110 | |
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| 111 | static void Multiply0_p81 (dReal *A, dReal *B, dReal *C, int p) |
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| 112 | { |
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| 113 | int i; |
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| 114 | dIASSERT (p>0 && A && B && C); |
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| 115 | dReal sum; |
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| 116 | for (i=p; i; i--) { |
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| 117 | sum = B[0]*C[0]; |
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| 118 | sum += B[1]*C[1]; |
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| 119 | sum += B[2]*C[2]; |
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| 120 | sum += B[4]*C[4]; |
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| 121 | sum += B[5]*C[5]; |
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| 122 | sum += B[6]*C[6]; |
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| 123 | *(A++) = sum; |
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| 124 | B += 8; |
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| 125 | } |
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| 126 | } |
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| 127 | |
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| 128 | |
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| 129 | // this assumes the 4th and 8th rows of B are zero. |
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| 130 | |
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| 131 | static void MultiplyAdd0_p81 (dReal *A, dReal *B, dReal *C, int p) |
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| 132 | { |
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| 133 | int i; |
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| 134 | dIASSERT (p>0 && A && B && C); |
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| 135 | dReal sum; |
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| 136 | for (i=p; i; i--) { |
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| 137 | sum = B[0]*C[0]; |
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| 138 | sum += B[1]*C[1]; |
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| 139 | sum += B[2]*C[2]; |
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| 140 | sum += B[4]*C[4]; |
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| 141 | sum += B[5]*C[5]; |
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| 142 | sum += B[6]*C[6]; |
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| 143 | *(A++) += sum; |
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| 144 | B += 8; |
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| 145 | } |
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| 146 | } |
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| 147 | |
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| 148 | |
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| 149 | // this assumes the 4th and 8th rows of B are zero. |
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| 150 | |
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| 151 | static void MultiplyAdd1_8q1 (dReal *A, dReal *B, dReal *C, int q) |
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| 152 | { |
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| 153 | int k; |
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| 154 | dReal sum; |
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| 155 | dIASSERT (q>0 && A && B && C); |
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| 156 | sum = 0; |
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| 157 | for (k=0; k<q; k++) sum += B[k*8] * C[k]; |
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| 158 | A[0] += sum; |
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| 159 | sum = 0; |
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| 160 | for (k=0; k<q; k++) sum += B[1+k*8] * C[k]; |
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| 161 | A[1] += sum; |
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| 162 | sum = 0; |
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| 163 | for (k=0; k<q; k++) sum += B[2+k*8] * C[k]; |
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| 164 | A[2] += sum; |
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| 165 | sum = 0; |
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| 166 | for (k=0; k<q; k++) sum += B[4+k*8] * C[k]; |
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| 167 | A[4] += sum; |
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| 168 | sum = 0; |
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| 169 | for (k=0; k<q; k++) sum += B[5+k*8] * C[k]; |
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| 170 | A[5] += sum; |
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| 171 | sum = 0; |
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| 172 | for (k=0; k<q; k++) sum += B[6+k*8] * C[k]; |
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| 173 | A[6] += sum; |
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| 174 | } |
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| 175 | |
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| 176 | |
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| 177 | // this assumes the 4th and 8th rows of B are zero. |
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| 178 | |
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| 179 | static void Multiply1_8q1 (dReal *A, dReal *B, dReal *C, int q) |
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| 180 | { |
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| 181 | int k; |
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| 182 | dReal sum; |
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| 183 | dIASSERT (q>0 && A && B && C); |
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| 184 | sum = 0; |
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| 185 | for (k=0; k<q; k++) sum += B[k*8] * C[k]; |
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| 186 | A[0] = sum; |
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| 187 | sum = 0; |
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| 188 | for (k=0; k<q; k++) sum += B[1+k*8] * C[k]; |
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| 189 | A[1] = sum; |
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| 190 | sum = 0; |
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| 191 | for (k=0; k<q; k++) sum += B[2+k*8] * C[k]; |
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| 192 | A[2] = sum; |
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| 193 | sum = 0; |
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| 194 | for (k=0; k<q; k++) sum += B[4+k*8] * C[k]; |
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| 195 | A[4] = sum; |
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| 196 | sum = 0; |
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| 197 | for (k=0; k<q; k++) sum += B[5+k*8] * C[k]; |
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| 198 | A[5] = sum; |
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| 199 | sum = 0; |
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| 200 | for (k=0; k<q; k++) sum += B[6+k*8] * C[k]; |
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| 201 | A[6] = sum; |
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| 202 | } |
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| 203 | |
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| 204 | //**************************************************************************** |
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| 205 | // body rotation |
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| 206 | |
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| 207 | // return sin(x)/x. this has a singularity at 0 so special handling is needed |
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| 208 | // for small arguments. |
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| 209 | |
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| 210 | static inline dReal sinc (dReal x) |
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| 211 | { |
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| 212 | // if |x| < 1e-4 then use a taylor series expansion. this two term expansion |
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| 213 | // is actually accurate to one LS bit within this range if double precision |
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| 214 | // is being used - so don't worry! |
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| 215 | if (dFabs(x) < 1.0e-4) return REAL(1.0) - x*x*REAL(0.166666666666666666667); |
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| 216 | else return dSin(x)/x; |
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| 217 | } |
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| 218 | |
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| 219 | |
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| 220 | // given a body b, apply its linear and angular rotation over the time |
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| 221 | // interval h, thereby adjusting its position and orientation. |
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| 222 | |
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| 223 | static inline void moveAndRotateBody (dxBody *b, dReal h) |
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| 224 | { |
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| 225 | int j; |
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| 226 | |
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| 227 | // handle linear velocity |
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| 228 | for (j=0; j<3; j++) b->pos[j] += h * b->lvel[j]; |
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| 229 | |
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| 230 | if (b->flags & dxBodyFlagFiniteRotation) { |
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| 231 | dVector3 irv; // infitesimal rotation vector |
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| 232 | dQuaternion q; // quaternion for finite rotation |
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| 233 | |
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| 234 | if (b->flags & dxBodyFlagFiniteRotationAxis) { |
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| 235 | // split the angular velocity vector into a component along the finite |
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| 236 | // rotation axis, and a component orthogonal to it. |
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| 237 | dVector3 frv,irv; // finite rotation vector |
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| 238 | dReal k = dDOT (b->finite_rot_axis,b->avel); |
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| 239 | frv[0] = b->finite_rot_axis[0] * k; |
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| 240 | frv[1] = b->finite_rot_axis[1] * k; |
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| 241 | frv[2] = b->finite_rot_axis[2] * k; |
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| 242 | irv[0] = b->avel[0] - frv[0]; |
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| 243 | irv[1] = b->avel[1] - frv[1]; |
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| 244 | irv[2] = b->avel[2] - frv[2]; |
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| 245 | |
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| 246 | // make a rotation quaternion q that corresponds to frv * h. |
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| 247 | // compare this with the full-finite-rotation case below. |
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| 248 | h *= REAL(0.5); |
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| 249 | dReal theta = k * h; |
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| 250 | q[0] = dCos(theta); |
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| 251 | dReal s = sinc(theta) * h; |
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| 252 | q[1] = frv[0] * s; |
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| 253 | q[2] = frv[1] * s; |
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| 254 | q[3] = frv[2] * s; |
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| 255 | } |
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| 256 | else { |
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| 257 | // make a rotation quaternion q that corresponds to w * h |
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| 258 | dReal wlen = dSqrt (b->avel[0]*b->avel[0] + b->avel[1]*b->avel[1] + |
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| 259 | b->avel[2]*b->avel[2]); |
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| 260 | h *= REAL(0.5); |
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| 261 | dReal theta = wlen * h; |
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| 262 | q[0] = dCos(theta); |
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| 263 | dReal s = sinc(theta) * h; |
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| 264 | q[1] = b->avel[0] * s; |
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| 265 | q[2] = b->avel[1] * s; |
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| 266 | q[3] = b->avel[2] * s; |
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| 267 | } |
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| 268 | |
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| 269 | // do the finite rotation |
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| 270 | dQuaternion q2; |
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| 271 | dQMultiply0 (q2,q,b->q); |
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| 272 | for (j=0; j<4; j++) b->q[j] = q2[j]; |
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| 273 | |
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| 274 | // do the infitesimal rotation if required |
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| 275 | if (b->flags & dxBodyFlagFiniteRotationAxis) { |
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| 276 | dReal dq[4]; |
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| 277 | dWtoDQ (irv,b->q,dq); |
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| 278 | for (j=0; j<4; j++) b->q[j] += h * dq[j]; |
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| 279 | } |
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| 280 | } |
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| 281 | else { |
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| 282 | // the normal way - do an infitesimal rotation |
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| 283 | dReal dq[4]; |
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| 284 | dWtoDQ (b->avel,b->q,dq); |
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| 285 | for (j=0; j<4; j++) b->q[j] += h * dq[j]; |
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| 286 | } |
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| 287 | |
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| 288 | // normalize the quaternion and convert it to a rotation matrix |
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| 289 | dNormalize4 (b->q); |
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| 290 | dQtoR (b->q,b->R); |
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| 291 | |
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| 292 | // notify all attached geoms that this body has moved |
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| 293 | for (dxGeom *geom = b->geom; geom; geom = dGeomGetBodyNext (geom)) |
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| 294 | dGeomMoved (geom); |
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| 295 | } |
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| 296 | |
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| 297 | //**************************************************************************** |
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| 298 | // the slow, but sure way |
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| 299 | // note that this does not do any joint feedback! |
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| 300 | |
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| 301 | // given lists of bodies and joints that form an island, perform a first |
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| 302 | // order timestep. |
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| 303 | // |
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| 304 | // `body' is the body array, `nb' is the size of the array. |
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| 305 | // `_joint' is the body array, `nj' is the size of the array. |
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| 306 | |
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| 307 | void dInternalStepIsland_x1 (dxWorld *world, dxBody * const *body, int nb, |
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| 308 | dxJoint * const *_joint, int nj, dReal stepsize) |
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| 309 | { |
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| 310 | int i,j,k; |
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| 311 | int n6 = 6*nb; |
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| 312 | |
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| 313 | # ifdef TIMING |
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| 314 | dTimerStart("preprocessing"); |
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| 315 | # endif |
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| 316 | |
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| 317 | // number all bodies in the body list - set their tag values |
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| 318 | for (i=0; i<nb; i++) body[i]->tag = i; |
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| 319 | |
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| 320 | // make a local copy of the joint array, because we might want to modify it. |
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| 321 | // (the "dxJoint *const*" declaration says we're allowed to modify the joints |
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| 322 | // but not the joint array, because the caller might need it unchanged). |
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| 323 | dxJoint **joint = (dxJoint**) ALLOCA (nj * sizeof(dxJoint*)); |
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| 324 | memcpy (joint,_joint,nj * sizeof(dxJoint*)); |
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| 325 | |
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| 326 | // for all bodies, compute the inertia tensor and its inverse in the global |
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| 327 | // frame, and compute the rotational force and add it to the torque |
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| 328 | // accumulator. |
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| 329 | // @@@ check computation of rotational force. |
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| 330 | dReal *I = (dReal*) ALLOCA (3*nb*4 * sizeof(dReal)); |
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| 331 | dReal *invI = (dReal*) ALLOCA (3*nb*4 * sizeof(dReal)); |
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| 332 | |
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| 333 | //dSetZero (I,3*nb*4); |
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| 334 | //dSetZero (invI,3*nb*4); |
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| 335 | for (i=0; i<nb; i++) { |
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| 336 | dReal tmp[12]; |
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| 337 | // compute inertia tensor in global frame |
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| 338 | dMULTIPLY2_333 (tmp,body[i]->mass.I,body[i]->R); |
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| 339 | dMULTIPLY0_333 (I+i*12,body[i]->R,tmp); |
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| 340 | // compute inverse inertia tensor in global frame |
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| 341 | dMULTIPLY2_333 (tmp,body[i]->invI,body[i]->R); |
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| 342 | dMULTIPLY0_333 (invI+i*12,body[i]->R,tmp); |
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| 343 | // compute rotational force |
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| 344 | dMULTIPLY0_331 (tmp,I+i*12,body[i]->avel); |
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| 345 | dCROSS (body[i]->tacc,-=,body[i]->avel,tmp); |
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| 346 | } |
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| 347 | |
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| 348 | // add the gravity force to all bodies |
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| 349 | for (i=0; i<nb; i++) { |
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| 350 | if ((body[i]->flags & dxBodyNoGravity)==0) { |
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| 351 | body[i]->facc[0] += body[i]->mass.mass * world->gravity[0]; |
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| 352 | body[i]->facc[1] += body[i]->mass.mass * world->gravity[1]; |
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| 353 | body[i]->facc[2] += body[i]->mass.mass * world->gravity[2]; |
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| 354 | } |
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| 355 | } |
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| 356 | |
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| 357 | // get m = total constraint dimension, nub = number of unbounded variables. |
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| 358 | // create constraint offset array and number-of-rows array for all joints. |
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| 359 | // the constraints are re-ordered as follows: the purely unbounded |
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| 360 | // constraints, the mixed unbounded + LCP constraints, and last the purely |
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| 361 | // LCP constraints. |
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| 362 | // |
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| 363 | // joints with m=0 are inactive and are removed from the joints array |
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| 364 | // entirely, so that the code that follows does not consider them. |
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| 365 | int m = 0; |
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| 366 | dxJoint::Info1 *info = (dxJoint::Info1*) ALLOCA (nj*sizeof(dxJoint::Info1)); |
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| 367 | int *ofs = (int*) ALLOCA (nj*sizeof(int)); |
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| 368 | for (i=0, j=0; j<nj; j++) { // i=dest, j=src |
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| 369 | joint[j]->vtable->getInfo1 (joint[j],info+i); |
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| 370 | dIASSERT (info[i].m >= 0 && info[i].m <= 6 && |
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| 371 | info[i].nub >= 0 && info[i].nub <= info[i].m); |
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| 372 | if (info[i].m > 0) { |
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| 373 | joint[i] = joint[j]; |
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| 374 | i++; |
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| 375 | } |
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| 376 | } |
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| 377 | nj = i; |
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| 378 | |
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| 379 | // the purely unbounded constraints |
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| 380 | for (i=0; i<nj; i++) if (info[i].nub == info[i].m) { |
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| 381 | ofs[i] = m; |
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| 382 | m += info[i].m; |
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| 383 | } |
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| 384 | int nub = m; |
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| 385 | // the mixed unbounded + LCP constraints |
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| 386 | for (i=0; i<nj; i++) if (info[i].nub > 0 && info[i].nub < info[i].m) { |
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| 387 | ofs[i] = m; |
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| 388 | m += info[i].m; |
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| 389 | } |
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| 390 | // the purely LCP constraints |
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| 391 | for (i=0; i<nj; i++) if (info[i].nub == 0) { |
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| 392 | ofs[i] = m; |
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| 393 | m += info[i].m; |
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| 394 | } |
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| 395 | |
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| 396 | // create (6*nb,6*nb) inverse mass matrix `invM', and fill it with mass |
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| 397 | // parameters |
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| 398 | # ifdef TIMING |
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| 399 | dTimerNow ("create mass matrix"); |
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| 400 | # endif |
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| 401 | int nskip = dPAD (n6); |
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| 402 | dReal *invM = (dReal*) ALLOCA (n6*nskip*sizeof(dReal)); |
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| 403 | dSetZero (invM,n6*nskip); |
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| 404 | for (i=0; i<nb; i++) { |
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| 405 | dReal *MM = invM+(i*6)*nskip+(i*6); |
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| 406 | MM[0] = body[i]->invMass; |
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| 407 | MM[nskip+1] = body[i]->invMass; |
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| 408 | MM[2*nskip+2] = body[i]->invMass; |
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| 409 | MM += 3*nskip+3; |
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| 410 | for (j=0; j<3; j++) for (k=0; k<3; k++) { |
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| 411 | MM[j*nskip+k] = invI[i*12+j*4+k]; |
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| 412 | } |
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| 413 | } |
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| 414 | |
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| 415 | // assemble some body vectors: fe = external forces, v = velocities |
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| 416 | dReal *fe = (dReal*) ALLOCA (n6 * sizeof(dReal)); |
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| 417 | dReal *v = (dReal*) ALLOCA (n6 * sizeof(dReal)); |
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| 418 | //dSetZero (fe,n6); |
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| 419 | //dSetZero (v,n6); |
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| 420 | for (i=0; i<nb; i++) { |
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| 421 | for (j=0; j<3; j++) fe[i*6+j] = body[i]->facc[j]; |
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| 422 | for (j=0; j<3; j++) fe[i*6+3+j] = body[i]->tacc[j]; |
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| 423 | for (j=0; j<3; j++) v[i*6+j] = body[i]->lvel[j]; |
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| 424 | for (j=0; j<3; j++) v[i*6+3+j] = body[i]->avel[j]; |
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| 425 | } |
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| 426 | |
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| 427 | // this will be set to the velocity update |
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| 428 | dReal *vnew = (dReal*) ALLOCA (n6 * sizeof(dReal)); |
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| 429 | dSetZero (vnew,n6); |
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| 430 | |
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| 431 | // if there are constraints, compute cforce |
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| 432 | if (m > 0) { |
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| 433 | // create a constraint equation right hand side vector `c', a constraint |
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| 434 | // force mixing vector `cfm', and LCP low and high bound vectors, and an |
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| 435 | // 'findex' vector. |
---|
| 436 | dReal *c = (dReal*) ALLOCA (m*sizeof(dReal)); |
---|
| 437 | dReal *cfm = (dReal*) ALLOCA (m*sizeof(dReal)); |
---|
| 438 | dReal *lo = (dReal*) ALLOCA (m*sizeof(dReal)); |
---|
| 439 | dReal *hi = (dReal*) ALLOCA (m*sizeof(dReal)); |
---|
| 440 | int *findex = (int*) alloca (m*sizeof(int)); |
---|
| 441 | dSetZero (c,m); |
---|
| 442 | dSetValue (cfm,m,world->global_cfm); |
---|
| 443 | dSetValue (lo,m,-dInfinity); |
---|
| 444 | dSetValue (hi,m, dInfinity); |
---|
| 445 | for (i=0; i<m; i++) findex[i] = -1; |
---|
| 446 | |
---|
| 447 | // create (m,6*nb) jacobian mass matrix `J', and fill it with constraint |
---|
| 448 | // data. also fill the c vector. |
---|
| 449 | # ifdef TIMING |
---|
| 450 | dTimerNow ("create J"); |
---|
| 451 | # endif |
---|
| 452 | dReal *J = (dReal*) ALLOCA (m*nskip*sizeof(dReal)); |
---|
| 453 | dSetZero (J,m*nskip); |
---|
| 454 | dxJoint::Info2 Jinfo; |
---|
| 455 | Jinfo.rowskip = nskip; |
---|
| 456 | Jinfo.fps = dRecip(stepsize); |
---|
| 457 | Jinfo.erp = world->global_erp; |
---|
| 458 | for (i=0; i<nj; i++) { |
---|
| 459 | Jinfo.J1l = J + nskip*ofs[i] + 6*joint[i]->node[0].body->tag; |
---|
| 460 | Jinfo.J1a = Jinfo.J1l + 3; |
---|
| 461 | if (joint[i]->node[1].body) { |
---|
| 462 | Jinfo.J2l = J + nskip*ofs[i] + 6*joint[i]->node[1].body->tag; |
---|
| 463 | Jinfo.J2a = Jinfo.J2l + 3; |
---|
| 464 | } |
---|
| 465 | else { |
---|
| 466 | Jinfo.J2l = 0; |
---|
| 467 | Jinfo.J2a = 0; |
---|
| 468 | } |
---|
| 469 | Jinfo.c = c + ofs[i]; |
---|
| 470 | Jinfo.cfm = cfm + ofs[i]; |
---|
| 471 | Jinfo.lo = lo + ofs[i]; |
---|
| 472 | Jinfo.hi = hi + ofs[i]; |
---|
| 473 | Jinfo.findex = findex + ofs[i]; |
---|
| 474 | joint[i]->vtable->getInfo2 (joint[i],&Jinfo); |
---|
| 475 | // adjust returned findex values for global index numbering |
---|
| 476 | for (j=0; j<info[i].m; j++) { |
---|
| 477 | if (findex[ofs[i] + j] >= 0) findex[ofs[i] + j] += ofs[i]; |
---|
| 478 | } |
---|
| 479 | } |
---|
| 480 | |
---|
| 481 | // compute A = J*invM*J' |
---|
| 482 | # ifdef TIMING |
---|
| 483 | dTimerNow ("compute A"); |
---|
| 484 | # endif |
---|
| 485 | dReal *JinvM = (dReal*) ALLOCA (m*nskip*sizeof(dReal)); |
---|
| 486 | //dSetZero (JinvM,m*nskip); |
---|
| 487 | dMultiply0 (JinvM,J,invM,m,n6,n6); |
---|
| 488 | int mskip = dPAD(m); |
---|
| 489 | dReal *A = (dReal*) ALLOCA (m*mskip*sizeof(dReal)); |
---|
| 490 | //dSetZero (A,m*mskip); |
---|
| 491 | dMultiply2 (A,JinvM,J,m,n6,m); |
---|
| 492 | |
---|
| 493 | // add cfm to the diagonal of A |
---|
| 494 | for (i=0; i<m; i++) A[i*mskip+i] += cfm[i] * Jinfo.fps; |
---|
| 495 | |
---|
| 496 | # ifdef COMPARE_METHODS |
---|
| 497 | comparator.nextMatrix (A,m,m,1,"A"); |
---|
| 498 | # endif |
---|
| 499 | |
---|
| 500 | // compute `rhs', the right hand side of the equation J*a=c |
---|
| 501 | # ifdef TIMING |
---|
| 502 | dTimerNow ("compute rhs"); |
---|
| 503 | # endif |
---|
| 504 | dReal *tmp1 = (dReal*) ALLOCA (n6 * sizeof(dReal)); |
---|
| 505 | //dSetZero (tmp1,n6); |
---|
| 506 | dMultiply0 (tmp1,invM,fe,n6,n6,1); |
---|
| 507 | for (i=0; i<n6; i++) tmp1[i] += v[i]/stepsize; |
---|
| 508 | dReal *rhs = (dReal*) ALLOCA (m * sizeof(dReal)); |
---|
| 509 | //dSetZero (rhs,m); |
---|
| 510 | dMultiply0 (rhs,J,tmp1,m,n6,1); |
---|
| 511 | for (i=0; i<m; i++) rhs[i] = c[i]/stepsize - rhs[i]; |
---|
| 512 | |
---|
| 513 | # ifdef COMPARE_METHODS |
---|
| 514 | comparator.nextMatrix (c,m,1,0,"c"); |
---|
| 515 | comparator.nextMatrix (rhs,m,1,0,"rhs"); |
---|
| 516 | # endif |
---|
| 517 | |
---|
| 518 | // solve the LCP problem and get lambda. |
---|
| 519 | // this will destroy A but that's okay |
---|
| 520 | # ifdef TIMING |
---|
| 521 | dTimerNow ("solving LCP problem"); |
---|
| 522 | # endif |
---|
| 523 | dReal *lambda = (dReal*) ALLOCA (m * sizeof(dReal)); |
---|
| 524 | dReal *residual = (dReal*) ALLOCA (m * sizeof(dReal)); |
---|
| 525 | dSolveLCP (m,A,lambda,rhs,residual,nub,lo,hi,findex); |
---|
| 526 | |
---|
| 527 | // OLD WAY - direct factor and solve |
---|
| 528 | // |
---|
| 529 | // // factorize A (L*L'=A) |
---|
| 530 | //# ifdef TIMING |
---|
| 531 | // dTimerNow ("factorize A"); |
---|
| 532 | //# endif |
---|
| 533 | // dReal *L = (dReal*) ALLOCA (m*mskip*sizeof(dReal)); |
---|
| 534 | // memcpy (L,A,m*mskip*sizeof(dReal)); |
---|
| 535 | // if (dFactorCholesky (L,m)==0) dDebug (0,"A is not positive definite"); |
---|
| 536 | // |
---|
| 537 | // // compute lambda |
---|
| 538 | //# ifdef TIMING |
---|
| 539 | // dTimerNow ("compute lambda"); |
---|
| 540 | //# endif |
---|
| 541 | // dReal *lambda = (dReal*) ALLOCA (m * sizeof(dReal)); |
---|
| 542 | // memcpy (lambda,rhs,m * sizeof(dReal)); |
---|
| 543 | // dSolveCholesky (L,lambda,m); |
---|
| 544 | |
---|
| 545 | # ifdef COMPARE_METHODS |
---|
| 546 | comparator.nextMatrix (lambda,m,1,0,"lambda"); |
---|
| 547 | # endif |
---|
| 548 | |
---|
| 549 | // compute the velocity update `vnew' |
---|
| 550 | # ifdef TIMING |
---|
| 551 | dTimerNow ("compute velocity update"); |
---|
| 552 | # endif |
---|
| 553 | dMultiply1 (tmp1,J,lambda,n6,m,1); |
---|
| 554 | for (i=0; i<n6; i++) tmp1[i] += fe[i]; |
---|
| 555 | dMultiply0 (vnew,invM,tmp1,n6,n6,1); |
---|
| 556 | for (i=0; i<n6; i++) vnew[i] = v[i] + stepsize*vnew[i]; |
---|
| 557 | |
---|
| 558 | // see if the constraint has worked: compute J*vnew and make sure it equals |
---|
| 559 | // `c' (to within a certain tolerance). |
---|
| 560 | # ifdef TIMING |
---|
| 561 | dTimerNow ("verify constraint equation"); |
---|
| 562 | # endif |
---|
| 563 | dMultiply0 (tmp1,J,vnew,m,n6,1); |
---|
| 564 | dReal err = 0; |
---|
| 565 | for (i=0; i<m; i++) err += dFabs(tmp1[i]-c[i]); |
---|
| 566 | printf ("%.6e\n",err); |
---|
| 567 | } |
---|
| 568 | else { |
---|
| 569 | // no constraints |
---|
| 570 | dMultiply0 (vnew,invM,fe,n6,n6,1); |
---|
| 571 | for (i=0; i<n6; i++) vnew[i] = v[i] + stepsize*vnew[i]; |
---|
| 572 | } |
---|
| 573 | |
---|
| 574 | # ifdef COMPARE_METHODS |
---|
| 575 | comparator.nextMatrix (vnew,n6,1,0,"vnew"); |
---|
| 576 | # endif |
---|
| 577 | |
---|
| 578 | // apply the velocity update to the bodies |
---|
| 579 | # ifdef TIMING |
---|
| 580 | dTimerNow ("update velocity"); |
---|
| 581 | # endif |
---|
| 582 | for (i=0; i<nb; i++) { |
---|
| 583 | for (j=0; j<3; j++) body[i]->lvel[j] = vnew[i*6+j]; |
---|
| 584 | for (j=0; j<3; j++) body[i]->avel[j] = vnew[i*6+3+j]; |
---|
| 585 | } |
---|
| 586 | |
---|
| 587 | // update the position and orientation from the new linear/angular velocity |
---|
| 588 | // (over the given timestep) |
---|
| 589 | # ifdef TIMING |
---|
| 590 | dTimerNow ("update position"); |
---|
| 591 | # endif |
---|
| 592 | for (i=0; i<nb; i++) moveAndRotateBody (body[i],stepsize); |
---|
| 593 | |
---|
| 594 | # ifdef TIMING |
---|
| 595 | dTimerNow ("tidy up"); |
---|
| 596 | # endif |
---|
| 597 | |
---|
| 598 | // zero all force accumulators |
---|
| 599 | for (i=0; i<nb; i++) { |
---|
| 600 | body[i]->facc[0] = 0; |
---|
| 601 | body[i]->facc[1] = 0; |
---|
| 602 | body[i]->facc[2] = 0; |
---|
| 603 | body[i]->facc[3] = 0; |
---|
| 604 | body[i]->tacc[0] = 0; |
---|
| 605 | body[i]->tacc[1] = 0; |
---|
| 606 | body[i]->tacc[2] = 0; |
---|
| 607 | body[i]->tacc[3] = 0; |
---|
| 608 | } |
---|
| 609 | |
---|
| 610 | # ifdef TIMING |
---|
| 611 | dTimerEnd(); |
---|
| 612 | if (m > 0) dTimerReport (stdout,1); |
---|
| 613 | # endif |
---|
| 614 | } |
---|
| 615 | |
---|
| 616 | //**************************************************************************** |
---|
| 617 | // an optimized version of dInternalStepIsland1() |
---|
| 618 | |
---|
| 619 | void dInternalStepIsland_x2 (dxWorld *world, dxBody * const *body, int nb, |
---|
| 620 | dxJoint * const *_joint, int nj, dReal stepsize) |
---|
| 621 | { |
---|
| 622 | int i,j,k; |
---|
| 623 | # ifdef TIMING |
---|
| 624 | dTimerStart("preprocessing"); |
---|
| 625 | # endif |
---|
| 626 | |
---|
| 627 | dReal stepsize1 = dRecip(stepsize); |
---|
| 628 | |
---|
| 629 | // number all bodies in the body list - set their tag values |
---|
| 630 | for (i=0; i<nb; i++) body[i]->tag = i; |
---|
| 631 | |
---|
| 632 | // make a local copy of the joint array, because we might want to modify it. |
---|
| 633 | // (the "dxJoint *const*" declaration says we're allowed to modify the joints |
---|
| 634 | // but not the joint array, because the caller might need it unchanged). |
---|
| 635 | dxJoint **joint = (dxJoint**) ALLOCA (nj * sizeof(dxJoint*)); |
---|
| 636 | memcpy (joint,_joint,nj * sizeof(dxJoint*)); |
---|
| 637 | |
---|
| 638 | // for all bodies, compute the inertia tensor and its inverse in the global |
---|
| 639 | // frame, and compute the rotational force and add it to the torque |
---|
| 640 | // accumulator. I and invI are vertically stacked 3x4 matrices, one per body. |
---|
| 641 | // @@@ check computation of rotational force. |
---|
| 642 | dReal *I = (dReal*) ALLOCA (3*nb*4 * sizeof(dReal)); |
---|
| 643 | dReal *invI = (dReal*) ALLOCA (3*nb*4 * sizeof(dReal)); |
---|
| 644 | |
---|
| 645 | //dSetZero (I,3*nb*4); |
---|
| 646 | //dSetZero (invI,3*nb*4); |
---|
| 647 | for (i=0; i<nb; i++) { |
---|
| 648 | dReal tmp[12]; |
---|
| 649 | // compute inertia tensor in global frame |
---|
| 650 | dMULTIPLY2_333 (tmp,body[i]->mass.I,body[i]->R); |
---|
| 651 | dMULTIPLY0_333 (I+i*12,body[i]->R,tmp); |
---|
| 652 | // compute inverse inertia tensor in global frame |
---|
| 653 | dMULTIPLY2_333 (tmp,body[i]->invI,body[i]->R); |
---|
| 654 | dMULTIPLY0_333 (invI+i*12,body[i]->R,tmp); |
---|
| 655 | // compute rotational force |
---|
| 656 | dMULTIPLY0_331 (tmp,I+i*12,body[i]->avel); |
---|
| 657 | dCROSS (body[i]->tacc,-=,body[i]->avel,tmp); |
---|
| 658 | } |
---|
| 659 | |
---|
| 660 | // add the gravity force to all bodies |
---|
| 661 | for (i=0; i<nb; i++) { |
---|
| 662 | if ((body[i]->flags & dxBodyNoGravity)==0) { |
---|
| 663 | body[i]->facc[0] += body[i]->mass.mass * world->gravity[0]; |
---|
| 664 | body[i]->facc[1] += body[i]->mass.mass * world->gravity[1]; |
---|
| 665 | body[i]->facc[2] += body[i]->mass.mass * world->gravity[2]; |
---|
| 666 | } |
---|
| 667 | } |
---|
| 668 | |
---|
| 669 | // get m = total constraint dimension, nub = number of unbounded variables. |
---|
| 670 | // create constraint offset array and number-of-rows array for all joints. |
---|
| 671 | // the constraints are re-ordered as follows: the purely unbounded |
---|
| 672 | // constraints, the mixed unbounded + LCP constraints, and last the purely |
---|
| 673 | // LCP constraints. this assists the LCP solver to put all unbounded |
---|
| 674 | // variables at the start for a quick factorization. |
---|
| 675 | // |
---|
| 676 | // joints with m=0 are inactive and are removed from the joints array |
---|
| 677 | // entirely, so that the code that follows does not consider them. |
---|
| 678 | // also number all active joints in the joint list (set their tag values). |
---|
| 679 | // inactive joints receive a tag value of -1. |
---|
| 680 | |
---|
| 681 | int m = 0; |
---|
| 682 | dxJoint::Info1 *info = (dxJoint::Info1*) ALLOCA (nj*sizeof(dxJoint::Info1)); |
---|
| 683 | int *ofs = (int*) ALLOCA (nj*sizeof(int)); |
---|
| 684 | for (i=0, j=0; j<nj; j++) { // i=dest, j=src |
---|
| 685 | joint[j]->vtable->getInfo1 (joint[j],info+i); |
---|
| 686 | dIASSERT (info[i].m >= 0 && info[i].m <= 6 && |
---|
| 687 | info[i].nub >= 0 && info[i].nub <= info[i].m); |
---|
| 688 | if (info[i].m > 0) { |
---|
| 689 | joint[i] = joint[j]; |
---|
| 690 | joint[i]->tag = i; |
---|
| 691 | i++; |
---|
| 692 | } |
---|
| 693 | else { |
---|
| 694 | joint[j]->tag = -1; |
---|
| 695 | } |
---|
| 696 | } |
---|
| 697 | nj = i; |
---|
| 698 | |
---|
| 699 | // the purely unbounded constraints |
---|
| 700 | for (i=0; i<nj; i++) if (info[i].nub == info[i].m) { |
---|
| 701 | ofs[i] = m; |
---|
| 702 | m += info[i].m; |
---|
| 703 | } |
---|
| 704 | int nub = m; |
---|
| 705 | // the mixed unbounded + LCP constraints |
---|
| 706 | for (i=0; i<nj; i++) if (info[i].nub > 0 && info[i].nub < info[i].m) { |
---|
| 707 | ofs[i] = m; |
---|
| 708 | m += info[i].m; |
---|
| 709 | } |
---|
| 710 | // the purely LCP constraints |
---|
| 711 | for (i=0; i<nj; i++) if (info[i].nub == 0) { |
---|
| 712 | ofs[i] = m; |
---|
| 713 | m += info[i].m; |
---|
| 714 | } |
---|
| 715 | |
---|
| 716 | // this will be set to the force due to the constraints |
---|
| 717 | dReal *cforce = (dReal*) ALLOCA (nb*8 * sizeof(dReal)); |
---|
| 718 | dSetZero (cforce,nb*8); |
---|
| 719 | |
---|
| 720 | // if there are constraints, compute cforce |
---|
| 721 | if (m > 0) { |
---|
| 722 | // create a constraint equation right hand side vector `c', a constraint |
---|
| 723 | // force mixing vector `cfm', and LCP low and high bound vectors, and an |
---|
| 724 | // 'findex' vector. |
---|
| 725 | dReal *c = (dReal*) ALLOCA (m*sizeof(dReal)); |
---|
| 726 | dReal *cfm = (dReal*) ALLOCA (m*sizeof(dReal)); |
---|
| 727 | dReal *lo = (dReal*) ALLOCA (m*sizeof(dReal)); |
---|
| 728 | dReal *hi = (dReal*) ALLOCA (m*sizeof(dReal)); |
---|
| 729 | int *findex = (int*) alloca (m*sizeof(int)); |
---|
| 730 | dSetZero (c,m); |
---|
| 731 | dSetValue (cfm,m,world->global_cfm); |
---|
| 732 | dSetValue (lo,m,-dInfinity); |
---|
| 733 | dSetValue (hi,m, dInfinity); |
---|
| 734 | for (i=0; i<m; i++) findex[i] = -1; |
---|
| 735 | |
---|
| 736 | // get jacobian data from constraints. a (2*m)x8 matrix will be created |
---|
| 737 | // to store the two jacobian blocks from each constraint. it has this |
---|
| 738 | // format: |
---|
| 739 | // |
---|
| 740 | // l l l 0 a a a 0 \ . |
---|
| 741 | // l l l 0 a a a 0 }-- jacobian body 1 block for joint 0 (3 rows) |
---|
| 742 | // l l l 0 a a a 0 / |
---|
| 743 | // l l l 0 a a a 0 \ . |
---|
| 744 | // l l l 0 a a a 0 }-- jacobian body 2 block for joint 0 (3 rows) |
---|
| 745 | // l l l 0 a a a 0 / |
---|
| 746 | // l l l 0 a a a 0 }--- jacobian body 1 block for joint 1 (1 row) |
---|
| 747 | // l l l 0 a a a 0 }--- jacobian body 2 block for joint 1 (1 row) |
---|
| 748 | // etc... |
---|
| 749 | // |
---|
| 750 | // (lll) = linear jacobian data |
---|
| 751 | // (aaa) = angular jacobian data |
---|
| 752 | // |
---|
| 753 | # ifdef TIMING |
---|
| 754 | dTimerNow ("create J"); |
---|
| 755 | # endif |
---|
| 756 | dReal *J = (dReal*) ALLOCA (2*m*8*sizeof(dReal)); |
---|
| 757 | dSetZero (J,2*m*8); |
---|
| 758 | dxJoint::Info2 Jinfo; |
---|
| 759 | Jinfo.rowskip = 8; |
---|
| 760 | Jinfo.fps = stepsize1; |
---|
| 761 | Jinfo.erp = world->global_erp; |
---|
| 762 | for (i=0; i<nj; i++) { |
---|
| 763 | Jinfo.J1l = J + 2*8*ofs[i]; |
---|
| 764 | Jinfo.J1a = Jinfo.J1l + 4; |
---|
| 765 | Jinfo.J2l = Jinfo.J1l + 8*info[i].m; |
---|
| 766 | Jinfo.J2a = Jinfo.J2l + 4; |
---|
| 767 | Jinfo.c = c + ofs[i]; |
---|
| 768 | Jinfo.cfm = cfm + ofs[i]; |
---|
| 769 | Jinfo.lo = lo + ofs[i]; |
---|
| 770 | Jinfo.hi = hi + ofs[i]; |
---|
| 771 | Jinfo.findex = findex + ofs[i]; |
---|
| 772 | joint[i]->vtable->getInfo2 (joint[i],&Jinfo); |
---|
| 773 | // adjust returned findex values for global index numbering |
---|
| 774 | for (j=0; j<info[i].m; j++) { |
---|
| 775 | if (findex[ofs[i] + j] >= 0) findex[ofs[i] + j] += ofs[i]; |
---|
| 776 | } |
---|
| 777 | } |
---|
| 778 | |
---|
| 779 | // compute A = J*invM*J'. first compute JinvM = J*invM. this has the same |
---|
| 780 | // format as J so we just go through the constraints in J multiplying by |
---|
| 781 | // the appropriate scalars and matrices. |
---|
| 782 | # ifdef TIMING |
---|
| 783 | dTimerNow ("compute A"); |
---|
| 784 | # endif |
---|
| 785 | dReal *JinvM = (dReal*) ALLOCA (2*m*8*sizeof(dReal)); |
---|
| 786 | dSetZero (JinvM,2*m*8); |
---|
| 787 | for (i=0; i<nj; i++) { |
---|
| 788 | int b = joint[i]->node[0].body->tag; |
---|
| 789 | dReal body_invMass = body[b]->invMass; |
---|
| 790 | dReal *body_invI = invI + b*12; |
---|
| 791 | dReal *Jsrc = J + 2*8*ofs[i]; |
---|
| 792 | dReal *Jdst = JinvM + 2*8*ofs[i]; |
---|
| 793 | for (j=info[i].m-1; j>=0; j--) { |
---|
| 794 | for (k=0; k<3; k++) Jdst[k] = Jsrc[k] * body_invMass; |
---|
| 795 | dMULTIPLY0_133 (Jdst+4,Jsrc+4,body_invI); |
---|
| 796 | Jsrc += 8; |
---|
| 797 | Jdst += 8; |
---|
| 798 | } |
---|
| 799 | if (joint[i]->node[1].body) { |
---|
| 800 | b = joint[i]->node[1].body->tag; |
---|
| 801 | body_invMass = body[b]->invMass; |
---|
| 802 | body_invI = invI + b*12; |
---|
| 803 | for (j=info[i].m-1; j>=0; j--) { |
---|
| 804 | for (k=0; k<3; k++) Jdst[k] = Jsrc[k] * body_invMass; |
---|
| 805 | dMULTIPLY0_133 (Jdst+4,Jsrc+4,body_invI); |
---|
| 806 | Jsrc += 8; |
---|
| 807 | Jdst += 8; |
---|
| 808 | } |
---|
| 809 | } |
---|
| 810 | } |
---|
| 811 | |
---|
| 812 | // now compute A = JinvM * J'. A's rows and columns are grouped by joint, |
---|
| 813 | // i.e. in the same way as the rows of J. block (i,j) of A is only nonzero |
---|
| 814 | // if joints i and j have at least one body in common. this fact suggests |
---|
| 815 | // the algorithm used to fill A: |
---|
| 816 | // |
---|
| 817 | // for b = all bodies |
---|
| 818 | // n = number of joints attached to body b |
---|
| 819 | // for i = 1..n |
---|
| 820 | // for j = i+1..n |
---|
| 821 | // ii = actual joint number for i |
---|
| 822 | // jj = actual joint number for j |
---|
| 823 | // // (ii,jj) will be set to all pairs of joints around body b |
---|
| 824 | // compute blockwise: A(ii,jj) += JinvM(ii) * J(jj)' |
---|
| 825 | // |
---|
| 826 | // this algorithm catches all pairs of joints that have at least one body |
---|
| 827 | // in common. it does not compute the diagonal blocks of A however - |
---|
| 828 | // another similar algorithm does that. |
---|
| 829 | |
---|
| 830 | int mskip = dPAD(m); |
---|
| 831 | dReal *A = (dReal*) ALLOCA (m*mskip*sizeof(dReal)); |
---|
| 832 | dSetZero (A,m*mskip); |
---|
| 833 | for (i=0; i<nb; i++) { |
---|
| 834 | for (dxJointNode *n1=body[i]->firstjoint; n1; n1=n1->next) { |
---|
| 835 | for (dxJointNode *n2=n1->next; n2; n2=n2->next) { |
---|
| 836 | // get joint numbers and ensure ofs[j1] >= ofs[j2] |
---|
| 837 | int j1 = n1->joint->tag; |
---|
| 838 | int j2 = n2->joint->tag; |
---|
| 839 | if (ofs[j1] < ofs[j2]) { |
---|
| 840 | int tmp = j1; |
---|
| 841 | j1 = j2; |
---|
| 842 | j2 = tmp; |
---|
| 843 | } |
---|
| 844 | |
---|
| 845 | // if either joint was tagged as -1 then it is an inactive (m=0) |
---|
| 846 | // joint that should not be considered |
---|
| 847 | if (j1==-1 || j2==-1) continue; |
---|
| 848 | |
---|
| 849 | // determine if body i is the 1st or 2nd body of joints j1 and j2 |
---|
| 850 | int jb1 = (joint[j1]->node[1].body == body[i]); |
---|
| 851 | int jb2 = (joint[j2]->node[1].body == body[i]); |
---|
| 852 | // jb1/jb2 must be 0 for joints with only one body |
---|
| 853 | dIASSERT(joint[j1]->node[1].body || jb1==0); |
---|
| 854 | dIASSERT(joint[j2]->node[1].body || jb2==0); |
---|
| 855 | |
---|
| 856 | // set block of A |
---|
| 857 | MultiplyAdd2_p8r (A + ofs[j1]*mskip + ofs[j2], |
---|
| 858 | JinvM + 2*8*ofs[j1] + jb1*8*info[j1].m, |
---|
| 859 | J + 2*8*ofs[j2] + jb2*8*info[j2].m, |
---|
| 860 | info[j1].m,info[j2].m, mskip); |
---|
| 861 | } |
---|
| 862 | } |
---|
| 863 | } |
---|
| 864 | // compute diagonal blocks of A |
---|
| 865 | for (i=0; i<nj; i++) { |
---|
| 866 | Multiply2_p8r (A + ofs[i]*(mskip+1), |
---|
| 867 | JinvM + 2*8*ofs[i], |
---|
| 868 | J + 2*8*ofs[i], |
---|
| 869 | info[i].m,info[i].m, mskip); |
---|
| 870 | if (joint[i]->node[1].body) { |
---|
| 871 | MultiplyAdd2_p8r (A + ofs[i]*(mskip+1), |
---|
| 872 | JinvM + 2*8*ofs[i] + 8*info[i].m, |
---|
| 873 | J + 2*8*ofs[i] + 8*info[i].m, |
---|
| 874 | info[i].m,info[i].m, mskip); |
---|
| 875 | } |
---|
| 876 | } |
---|
| 877 | |
---|
| 878 | // add cfm to the diagonal of A |
---|
| 879 | for (i=0; i<m; i++) A[i*mskip+i] += cfm[i] * stepsize1; |
---|
| 880 | |
---|
| 881 | # ifdef COMPARE_METHODS |
---|
| 882 | comparator.nextMatrix (A,m,m,1,"A"); |
---|
| 883 | # endif |
---|
| 884 | |
---|
| 885 | // compute the right hand side `rhs' |
---|
| 886 | # ifdef TIMING |
---|
| 887 | dTimerNow ("compute rhs"); |
---|
| 888 | # endif |
---|
| 889 | dReal *tmp1 = (dReal*) ALLOCA (nb*8 * sizeof(dReal)); |
---|
| 890 | //dSetZero (tmp1,nb*8); |
---|
| 891 | // put v/h + invM*fe into tmp1 |
---|
| 892 | for (i=0; i<nb; i++) { |
---|
| 893 | dReal body_invMass = body[i]->invMass; |
---|
| 894 | dReal *body_invI = invI + i*12; |
---|
| 895 | for (j=0; j<3; j++) tmp1[i*8+j] = body[i]->facc[j] * body_invMass + |
---|
| 896 | body[i]->lvel[j] * stepsize1; |
---|
| 897 | dMULTIPLY0_331 (tmp1 + i*8 + 4,body_invI,body[i]->tacc); |
---|
| 898 | for (j=0; j<3; j++) tmp1[i*8+4+j] += body[i]->avel[j] * stepsize1; |
---|
| 899 | } |
---|
| 900 | // put J*tmp1 into rhs |
---|
| 901 | dReal *rhs = (dReal*) ALLOCA (m * sizeof(dReal)); |
---|
| 902 | //dSetZero (rhs,m); |
---|
| 903 | for (i=0; i<nj; i++) { |
---|
| 904 | dReal *JJ = J + 2*8*ofs[i]; |
---|
| 905 | Multiply0_p81 (rhs+ofs[i],JJ, |
---|
| 906 | tmp1 + 8*joint[i]->node[0].body->tag, info[i].m); |
---|
| 907 | if (joint[i]->node[1].body) { |
---|
| 908 | MultiplyAdd0_p81 (rhs+ofs[i],JJ + 8*info[i].m, |
---|
| 909 | tmp1 + 8*joint[i]->node[1].body->tag, info[i].m); |
---|
| 910 | } |
---|
| 911 | } |
---|
| 912 | // complete rhs |
---|
| 913 | for (i=0; i<m; i++) rhs[i] = c[i]*stepsize1 - rhs[i]; |
---|
| 914 | |
---|
| 915 | # ifdef COMPARE_METHODS |
---|
| 916 | comparator.nextMatrix (c,m,1,0,"c"); |
---|
| 917 | comparator.nextMatrix (rhs,m,1,0,"rhs"); |
---|
| 918 | # endif |
---|
| 919 | |
---|
| 920 | // solve the LCP problem and get lambda. |
---|
| 921 | // this will destroy A but that's okay |
---|
| 922 | # ifdef TIMING |
---|
| 923 | dTimerNow ("solving LCP problem"); |
---|
| 924 | # endif |
---|
| 925 | dReal *lambda = (dReal*) ALLOCA (m * sizeof(dReal)); |
---|
| 926 | dReal *residual = (dReal*) ALLOCA (m * sizeof(dReal)); |
---|
| 927 | dSolveLCP (m,A,lambda,rhs,residual,nub,lo,hi,findex); |
---|
| 928 | |
---|
| 929 | // OLD WAY - direct factor and solve |
---|
| 930 | // |
---|
| 931 | // // factorize A (L*L'=A) |
---|
| 932 | //# ifdef TIMING |
---|
| 933 | // dTimerNow ("factorize A"); |
---|
| 934 | //# endif |
---|
| 935 | // dReal *L = (dReal*) ALLOCA (m*mskip*sizeof(dReal)); |
---|
| 936 | // memcpy (L,A,m*mskip*sizeof(dReal)); |
---|
| 937 | //# ifdef FAST_FACTOR |
---|
| 938 | // dFastFactorCholesky (L,m); // does not report non positive definiteness |
---|
| 939 | //# else |
---|
| 940 | // if (dFactorCholesky (L,m)==0) dDebug (0,"A is not positive definite"); |
---|
| 941 | //# endif |
---|
| 942 | // |
---|
| 943 | // // compute lambda |
---|
| 944 | //# ifdef TIMING |
---|
| 945 | // dTimerNow ("compute lambda"); |
---|
| 946 | //# endif |
---|
| 947 | // dReal *lambda = (dReal*) ALLOCA (m * sizeof(dReal)); |
---|
| 948 | // memcpy (lambda,rhs,m * sizeof(dReal)); |
---|
| 949 | // dSolveCholesky (L,lambda,m); |
---|
| 950 | |
---|
| 951 | # ifdef COMPARE_METHODS |
---|
| 952 | comparator.nextMatrix (lambda,m,1,0,"lambda"); |
---|
| 953 | # endif |
---|
| 954 | |
---|
| 955 | // compute the constraint force `cforce' |
---|
| 956 | # ifdef TIMING |
---|
| 957 | dTimerNow ("compute constraint force"); |
---|
| 958 | # endif |
---|
| 959 | // compute cforce = J'*lambda |
---|
| 960 | for (i=0; i<nj; i++) { |
---|
| 961 | dReal *JJ = J + 2*8*ofs[i]; |
---|
| 962 | dxBody* b1 = joint[i]->node[0].body; |
---|
| 963 | dxBody* b2 = joint[i]->node[1].body; |
---|
| 964 | dJointFeedback *fb = joint[i]->feedback; |
---|
| 965 | |
---|
| 966 | /******************** breakable joint contribution ***********************/ |
---|
| 967 | // this saves us a few dereferences |
---|
| 968 | dxJointBreakInfo *jBI = joint[i]->breakInfo; |
---|
| 969 | // we need joint feedback if the joint is breakable or if the user |
---|
| 970 | // requested feedback. |
---|
| 971 | if (jBI||fb) { |
---|
| 972 | // we need feedback on the amount of force that this joint is |
---|
| 973 | // applying to the bodies. we use a slightly slower computation |
---|
| 974 | // that splits out the force components and puts them in the |
---|
| 975 | // feedback structure. |
---|
| 976 | dJointFeedback temp_fb; // temporary storage for joint feedback |
---|
| 977 | dReal data1[8],data2[8]; |
---|
| 978 | Multiply1_8q1 (data1, JJ, lambda+ofs[i], info[i].m); |
---|
| 979 | dReal *cf1 = cforce + 8*b1->tag; |
---|
| 980 | cf1[0] += (temp_fb.f1[0] = data1[0]); |
---|
| 981 | cf1[1] += (temp_fb.f1[1] = data1[1]); |
---|
| 982 | cf1[2] += (temp_fb.f1[2] = data1[2]); |
---|
| 983 | cf1[4] += (temp_fb.t1[0] = data1[4]); |
---|
| 984 | cf1[5] += (temp_fb.t1[1] = data1[5]); |
---|
| 985 | cf1[6] += (temp_fb.t1[2] = data1[6]); |
---|
| 986 | if (b2) { |
---|
| 987 | Multiply1_8q1 (data2, JJ + 8*info[i].m, lambda+ofs[i], info[i].m); |
---|
| 988 | dReal *cf2 = cforce + 8*b2->tag; |
---|
| 989 | cf2[0] += (temp_fb.f2[0] = data2[0]); |
---|
| 990 | cf2[1] += (temp_fb.f2[1] = data2[1]); |
---|
| 991 | cf2[2] += (temp_fb.f2[2] = data2[2]); |
---|
| 992 | cf2[4] += (temp_fb.t2[0] = data2[4]); |
---|
| 993 | cf2[5] += (temp_fb.t2[1] = data2[5]); |
---|
| 994 | cf2[6] += (temp_fb.t2[2] = data2[6]); |
---|
| 995 | } |
---|
| 996 | // if the user requested so we must copy the feedback information to |
---|
| 997 | // the feedback struct that the user suplied. |
---|
| 998 | if (fb) { |
---|
| 999 | // copy temp_fb to fb |
---|
| 1000 | fb->f1[0] = temp_fb.f1[0]; |
---|
| 1001 | fb->f1[1] = temp_fb.f1[1]; |
---|
| 1002 | fb->f1[2] = temp_fb.f1[2]; |
---|
| 1003 | fb->t1[0] = temp_fb.t1[0]; |
---|
| 1004 | fb->t1[1] = temp_fb.t1[1]; |
---|
| 1005 | fb->t1[2] = temp_fb.t1[2]; |
---|
| 1006 | if (b2) { |
---|
| 1007 | fb->f2[0] = temp_fb.f2[0]; |
---|
| 1008 | fb->f2[1] = temp_fb.f2[1]; |
---|
| 1009 | fb->f2[2] = temp_fb.f2[2]; |
---|
| 1010 | fb->t2[0] = temp_fb.t2[0]; |
---|
| 1011 | fb->t2[1] = temp_fb.t2[1]; |
---|
| 1012 | fb->t2[2] = temp_fb.t2[2]; |
---|
| 1013 | } |
---|
| 1014 | } |
---|
| 1015 | // if the joint is breakable we need to check the breaking conditions |
---|
| 1016 | if (jBI) { |
---|
| 1017 | dReal relCF1[3]; |
---|
| 1018 | dReal relCT1[3]; |
---|
| 1019 | // multiply the force and torque vectors by the rotation matrix of body 1 |
---|
| 1020 | dMULTIPLY1_331 (&relCF1[0],b1->R,&temp_fb.f1[0]); |
---|
| 1021 | dMULTIPLY1_331 (&relCT1[0],b1->R,&temp_fb.t1[0]); |
---|
| 1022 | if (jBI->flags & dJOINT_BREAK_AT_B1_FORCE) { |
---|
| 1023 | // check if the force is to high |
---|
| 1024 | for (int i = 0; i < 3; i++) { |
---|
| 1025 | if (relCF1[i] > jBI->b1MaxF[i]) { |
---|
| 1026 | jBI->flags |= dJOINT_BROKEN; |
---|
| 1027 | goto doneCheckingBreaks; |
---|
| 1028 | } |
---|
| 1029 | } |
---|
| 1030 | } |
---|
| 1031 | if (jBI->flags & dJOINT_BREAK_AT_B1_TORQUE) { |
---|
| 1032 | // check if the torque is to high |
---|
| 1033 | for (int i = 0; i < 3; i++) { |
---|
| 1034 | if (relCT1[i] > jBI->b1MaxT[i]) { |
---|
| 1035 | jBI->flags |= dJOINT_BROKEN; |
---|
| 1036 | goto doneCheckingBreaks; |
---|
| 1037 | } |
---|
| 1038 | } |
---|
| 1039 | } |
---|
| 1040 | if (b2) { |
---|
| 1041 | dReal relCF2[3]; |
---|
| 1042 | dReal relCT2[3]; |
---|
| 1043 | // multiply the force and torque vectors by the rotation matrix of body 2 |
---|
| 1044 | dMULTIPLY1_331 (&relCF2[0],b2->R,&temp_fb.f2[0]); |
---|
| 1045 | dMULTIPLY1_331 (&relCT2[0],b2->R,&temp_fb.t2[0]); |
---|
| 1046 | if (jBI->flags & dJOINT_BREAK_AT_B2_FORCE) { |
---|
| 1047 | // check if the force is to high |
---|
| 1048 | for (int i = 0; i < 3; i++) { |
---|
| 1049 | if (relCF2[i] > jBI->b2MaxF[i]) { |
---|
| 1050 | jBI->flags |= dJOINT_BROKEN; |
---|
| 1051 | goto doneCheckingBreaks; |
---|
| 1052 | } |
---|
| 1053 | } |
---|
| 1054 | } |
---|
| 1055 | if (jBI->flags & dJOINT_BREAK_AT_B2_TORQUE) { |
---|
| 1056 | // check if the torque is to high |
---|
| 1057 | for (int i = 0; i < 3; i++) { |
---|
| 1058 | if (relCT2[i] > jBI->b2MaxT[i]) { |
---|
| 1059 | jBI->flags |= dJOINT_BROKEN; |
---|
| 1060 | goto doneCheckingBreaks; |
---|
| 1061 | } |
---|
| 1062 | } |
---|
| 1063 | } |
---|
| 1064 | } |
---|
| 1065 | doneCheckingBreaks: |
---|
| 1066 | ; |
---|
| 1067 | } |
---|
| 1068 | } |
---|
| 1069 | /*************************************************************************/ |
---|
| 1070 | else { |
---|
| 1071 | // no feedback is required, let's compute cforce the faster way |
---|
| 1072 | MultiplyAdd1_8q1 (cforce + 8*b1->tag,JJ, lambda+ofs[i], info[i].m); |
---|
| 1073 | if (b2) { |
---|
| 1074 | MultiplyAdd1_8q1 (cforce + 8*b2->tag, |
---|
| 1075 | JJ + 8*info[i].m, lambda+ofs[i], info[i].m); |
---|
| 1076 | } |
---|
| 1077 | } |
---|
| 1078 | } |
---|
| 1079 | } |
---|
| 1080 | |
---|
| 1081 | // compute the velocity update |
---|
| 1082 | # ifdef TIMING |
---|
| 1083 | dTimerNow ("compute velocity update"); |
---|
| 1084 | # endif |
---|
| 1085 | |
---|
| 1086 | // add fe to cforce |
---|
| 1087 | for (i=0; i<nb; i++) { |
---|
| 1088 | for (j=0; j<3; j++) cforce[i*8+j] += body[i]->facc[j]; |
---|
| 1089 | for (j=0; j<3; j++) cforce[i*8+4+j] += body[i]->tacc[j]; |
---|
| 1090 | } |
---|
| 1091 | // multiply cforce by stepsize |
---|
| 1092 | for (i=0; i < nb*8; i++) cforce[i] *= stepsize; |
---|
| 1093 | // add invM * cforce to the body velocity |
---|
| 1094 | for (i=0; i<nb; i++) { |
---|
| 1095 | dReal body_invMass = body[i]->invMass; |
---|
| 1096 | dReal *body_invI = invI + i*12; |
---|
| 1097 | for (j=0; j<3; j++) body[i]->lvel[j] += body_invMass * cforce[i*8+j]; |
---|
| 1098 | dMULTIPLYADD0_331 (body[i]->avel,body_invI,cforce+i*8+4); |
---|
| 1099 | } |
---|
| 1100 | |
---|
| 1101 | // update the position and orientation from the new linear/angular velocity |
---|
| 1102 | // (over the given timestep) |
---|
| 1103 | # ifdef TIMING |
---|
| 1104 | dTimerNow ("update position"); |
---|
| 1105 | # endif |
---|
| 1106 | for (i=0; i<nb; i++) moveAndRotateBody (body[i],stepsize); |
---|
| 1107 | |
---|
| 1108 | # ifdef COMPARE_METHODS |
---|
| 1109 | dReal *tmp_vnew = (dReal*) ALLOCA (nb*6*sizeof(dReal)); |
---|
| 1110 | for (i=0; i<nb; i++) { |
---|
| 1111 | for (j=0; j<3; j++) tmp_vnew[i*6+j] = body[i]->lvel[j]; |
---|
| 1112 | for (j=0; j<3; j++) tmp_vnew[i*6+3+j] = body[i]->avel[j]; |
---|
| 1113 | } |
---|
| 1114 | comparator.nextMatrix (tmp_vnew,nb*6,1,0,"vnew"); |
---|
| 1115 | # endif |
---|
| 1116 | |
---|
| 1117 | # ifdef TIMING |
---|
| 1118 | dTimerNow ("tidy up"); |
---|
| 1119 | # endif |
---|
| 1120 | |
---|
| 1121 | // zero all force accumulators |
---|
| 1122 | for (i=0; i<nb; i++) { |
---|
| 1123 | body[i]->facc[0] = 0; |
---|
| 1124 | body[i]->facc[1] = 0; |
---|
| 1125 | body[i]->facc[2] = 0; |
---|
| 1126 | body[i]->facc[3] = 0; |
---|
| 1127 | body[i]->tacc[0] = 0; |
---|
| 1128 | body[i]->tacc[1] = 0; |
---|
| 1129 | body[i]->tacc[2] = 0; |
---|
| 1130 | body[i]->tacc[3] = 0; |
---|
| 1131 | } |
---|
| 1132 | |
---|
| 1133 | # ifdef TIMING |
---|
| 1134 | dTimerEnd(); |
---|
| 1135 | if (m > 0) dTimerReport (stdout,1); |
---|
| 1136 | # endif |
---|
| 1137 | } |
---|
| 1138 | |
---|
| 1139 | //**************************************************************************** |
---|
| 1140 | |
---|
| 1141 | void dInternalStepIsland (dxWorld *world, dxBody * const *body, int nb, |
---|
| 1142 | dxJoint * const *joint, int nj, dReal stepsize) |
---|
| 1143 | { |
---|
| 1144 | # ifndef COMPARE_METHODS |
---|
| 1145 | dInternalStepIsland_x2 (world,body,nb,joint,nj,stepsize); |
---|
| 1146 | # endif |
---|
| 1147 | |
---|
| 1148 | # ifdef COMPARE_METHODS |
---|
| 1149 | int i; |
---|
| 1150 | |
---|
| 1151 | // save body state |
---|
| 1152 | dxBody *state = (dxBody*) ALLOCA (nb*sizeof(dxBody)); |
---|
| 1153 | for (i=0; i<nb; i++) memcpy (state+i,body[i],sizeof(dxBody)); |
---|
| 1154 | |
---|
| 1155 | // take slow step |
---|
| 1156 | comparator.reset(); |
---|
| 1157 | dInternalStepIsland_x1 (world,body,nb,joint,nj,stepsize); |
---|
| 1158 | comparator.end(); |
---|
| 1159 | |
---|
| 1160 | // restore state |
---|
| 1161 | for (i=0; i<nb; i++) memcpy (body[i],state+i,sizeof(dxBody)); |
---|
| 1162 | |
---|
| 1163 | // take fast step |
---|
| 1164 | dInternalStepIsland_x2 (world,body,nb,joint,nj,stepsize); |
---|
| 1165 | comparator.end(); |
---|
| 1166 | |
---|
| 1167 | //comparator.dump(); |
---|
| 1168 | //_exit (1); |
---|
| 1169 | # endif |
---|
| 1170 | } |
---|