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-rw-r--r--thirdparty/bullet/src/BulletInverseDynamics/IDMath.cpp437
1 files changed, 437 insertions, 0 deletions
diff --git a/thirdparty/bullet/src/BulletInverseDynamics/IDMath.cpp b/thirdparty/bullet/src/BulletInverseDynamics/IDMath.cpp
new file mode 100644
index 0000000000..99fe20e492
--- /dev/null
+++ b/thirdparty/bullet/src/BulletInverseDynamics/IDMath.cpp
@@ -0,0 +1,437 @@
+#include "IDMath.hpp"
+
+#include <cmath>
+#include <limits>
+
+namespace btInverseDynamics {
+static const idScalar kIsZero = 5 * std::numeric_limits<idScalar>::epsilon();
+// requirements for axis length deviation from 1.0
+// experimentally set from random euler angle rotation matrices
+static const idScalar kAxisLengthEpsilon = 10 * kIsZero;
+
+void setZero(vec3 &v) {
+ v(0) = 0;
+ v(1) = 0;
+ v(2) = 0;
+}
+
+void setZero(vecx &v) {
+ for (int i = 0; i < v.size(); i++) {
+ v(i) = 0;
+ }
+}
+
+void setZero(mat33 &m) {
+ m(0, 0) = 0;
+ m(0, 1) = 0;
+ m(0, 2) = 0;
+ m(1, 0) = 0;
+ m(1, 1) = 0;
+ m(1, 2) = 0;
+ m(2, 0) = 0;
+ m(2, 1) = 0;
+ m(2, 2) = 0;
+}
+
+void skew(vec3& v, mat33* result) {
+ (*result)(0, 0) = 0.0;
+ (*result)(0, 1) = -v(2);
+ (*result)(0, 2) = v(1);
+ (*result)(1, 0) = v(2);
+ (*result)(1, 1) = 0.0;
+ (*result)(1, 2) = -v(0);
+ (*result)(2, 0) = -v(1);
+ (*result)(2, 1) = v(0);
+ (*result)(2, 2) = 0.0;
+}
+
+idScalar maxAbs(const vecx &v) {
+ idScalar result = 0.0;
+ for (int i = 0; i < v.size(); i++) {
+ const idScalar tmp = BT_ID_FABS(v(i));
+ if (tmp > result) {
+ result = tmp;
+ }
+ }
+ return result;
+}
+
+idScalar maxAbs(const vec3 &v) {
+ idScalar result = 0.0;
+ for (int i = 0; i < 3; i++) {
+ const idScalar tmp = BT_ID_FABS(v(i));
+ if (tmp > result) {
+ result = tmp;
+ }
+ }
+ return result;
+}
+
+#if (defined BT_ID_HAVE_MAT3X)
+idScalar maxAbsMat3x(const mat3x &m) {
+ // only used for tests -- so just loop here for portability
+ idScalar result = 0.0;
+ for (idArrayIdx col = 0; col < m.cols(); col++) {
+ for (idArrayIdx row = 0; row < 3; row++) {
+ result = BT_ID_MAX(result, std::fabs(m(row, col)));
+ }
+ }
+ return result;
+}
+
+void mul(const mat33 &a, const mat3x &b, mat3x *result) {
+ if (b.cols() != result->cols()) {
+ error_message("size missmatch. b.cols()= %d, result->cols()= %d\n",
+ static_cast<int>(b.cols()), static_cast<int>(result->cols()));
+ abort();
+ }
+
+ for (idArrayIdx col = 0; col < b.cols(); col++) {
+ const idScalar x = a(0,0)*b(0,col)+a(0,1)*b(1,col)+a(0,2)*b(2,col);
+ const idScalar y = a(1,0)*b(0,col)+a(1,1)*b(1,col)+a(1,2)*b(2,col);
+ const idScalar z = a(2,0)*b(0,col)+a(2,1)*b(1,col)+a(2,2)*b(2,col);
+ setMat3xElem(0, col, x, result);
+ setMat3xElem(1, col, y, result);
+ setMat3xElem(2, col, z, result);
+ }
+}
+void add(const mat3x &a, const mat3x &b, mat3x *result) {
+ if (a.cols() != b.cols()) {
+ error_message("size missmatch. a.cols()= %d, b.cols()= %d\n",
+ static_cast<int>(a.cols()), static_cast<int>(b.cols()));
+ abort();
+ }
+ for (idArrayIdx col = 0; col < b.cols(); col++) {
+ for (idArrayIdx row = 0; row < 3; row++) {
+ setMat3xElem(row, col, a(row, col) + b(row, col), result);
+ }
+ }
+}
+void sub(const mat3x &a, const mat3x &b, mat3x *result) {
+ if (a.cols() != b.cols()) {
+ error_message("size missmatch. a.cols()= %d, b.cols()= %d\n",
+ static_cast<int>(a.cols()), static_cast<int>(b.cols()));
+ abort();
+ }
+ for (idArrayIdx col = 0; col < b.cols(); col++) {
+ for (idArrayIdx row = 0; row < 3; row++) {
+ setMat3xElem(row, col, a(row, col) - b(row, col), result);
+ }
+ }
+}
+#endif
+
+mat33 transformX(const idScalar &alpha) {
+ mat33 T;
+ const idScalar cos_alpha = BT_ID_COS(alpha);
+ const idScalar sin_alpha = BT_ID_SIN(alpha);
+ // [1 0 0]
+ // [0 c s]
+ // [0 -s c]
+ T(0, 0) = 1.0;
+ T(0, 1) = 0.0;
+ T(0, 2) = 0.0;
+
+ T(1, 0) = 0.0;
+ T(1, 1) = cos_alpha;
+ T(1, 2) = sin_alpha;
+
+ T(2, 0) = 0.0;
+ T(2, 1) = -sin_alpha;
+ T(2, 2) = cos_alpha;
+
+ return T;
+}
+
+mat33 transformY(const idScalar &beta) {
+ mat33 T;
+ const idScalar cos_beta = BT_ID_COS(beta);
+ const idScalar sin_beta = BT_ID_SIN(beta);
+ // [c 0 -s]
+ // [0 1 0]
+ // [s 0 c]
+ T(0, 0) = cos_beta;
+ T(0, 1) = 0.0;
+ T(0, 2) = -sin_beta;
+
+ T(1, 0) = 0.0;
+ T(1, 1) = 1.0;
+ T(1, 2) = 0.0;
+
+ T(2, 0) = sin_beta;
+ T(2, 1) = 0.0;
+ T(2, 2) = cos_beta;
+
+ return T;
+}
+
+mat33 transformZ(const idScalar &gamma) {
+ mat33 T;
+ const idScalar cos_gamma = BT_ID_COS(gamma);
+ const idScalar sin_gamma = BT_ID_SIN(gamma);
+ // [ c s 0]
+ // [-s c 0]
+ // [ 0 0 1]
+ T(0, 0) = cos_gamma;
+ T(0, 1) = sin_gamma;
+ T(0, 2) = 0.0;
+
+ T(1, 0) = -sin_gamma;
+ T(1, 1) = cos_gamma;
+ T(1, 2) = 0.0;
+
+ T(2, 0) = 0.0;
+ T(2, 1) = 0.0;
+ T(2, 2) = 1.0;
+
+ return T;
+}
+
+mat33 tildeOperator(const vec3 &v) {
+ mat33 m;
+ m(0, 0) = 0.0;
+ m(0, 1) = -v(2);
+ m(0, 2) = v(1);
+ m(1, 0) = v(2);
+ m(1, 1) = 0.0;
+ m(1, 2) = -v(0);
+ m(2, 0) = -v(1);
+ m(2, 1) = v(0);
+ m(2, 2) = 0.0;
+ return m;
+}
+
+void getVecMatFromDH(idScalar theta, idScalar d, idScalar a, idScalar alpha, vec3 *r, mat33 *T) {
+ const idScalar sa = BT_ID_SIN(alpha);
+ const idScalar ca = BT_ID_COS(alpha);
+ const idScalar st = BT_ID_SIN(theta);
+ const idScalar ct = BT_ID_COS(theta);
+
+ (*r)(0) = a;
+ (*r)(1) = -sa * d;
+ (*r)(2) = ca * d;
+
+ (*T)(0, 0) = ct;
+ (*T)(0, 1) = -st;
+ (*T)(0, 2) = 0.0;
+
+ (*T)(1, 0) = st * ca;
+ (*T)(1, 1) = ct * ca;
+ (*T)(1, 2) = -sa;
+
+ (*T)(2, 0) = st * sa;
+ (*T)(2, 1) = ct * sa;
+ (*T)(2, 2) = ca;
+}
+
+void bodyTParentFromAxisAngle(const vec3 &axis, const idScalar &angle, mat33 *T) {
+ const idScalar c = BT_ID_COS(angle);
+ const idScalar s = -BT_ID_SIN(angle);
+ const idScalar one_m_c = 1.0 - c;
+
+ const idScalar &x = axis(0);
+ const idScalar &y = axis(1);
+ const idScalar &z = axis(2);
+
+ (*T)(0, 0) = x * x * one_m_c + c;
+ (*T)(0, 1) = x * y * one_m_c - z * s;
+ (*T)(0, 2) = x * z * one_m_c + y * s;
+
+ (*T)(1, 0) = x * y * one_m_c + z * s;
+ (*T)(1, 1) = y * y * one_m_c + c;
+ (*T)(1, 2) = y * z * one_m_c - x * s;
+
+ (*T)(2, 0) = x * z * one_m_c - y * s;
+ (*T)(2, 1) = y * z * one_m_c + x * s;
+ (*T)(2, 2) = z * z * one_m_c + c;
+}
+
+bool isPositiveDefinite(const mat33 &m) {
+ // test if all upper left determinants are positive
+ if (m(0, 0) <= 0) { // upper 1x1
+ return false;
+ }
+ if (m(0, 0) * m(1, 1) - m(0, 1) * m(1, 0) <= 0) { // upper 2x2
+ return false;
+ }
+ if ((m(0, 0) * (m(1, 1) * m(2, 2) - m(1, 2) * m(2, 1)) -
+ m(0, 1) * (m(1, 0) * m(2, 2) - m(1, 2) * m(2, 0)) +
+ m(0, 2) * (m(1, 0) * m(2, 1) - m(1, 1) * m(2, 0))) < 0) {
+ return false;
+ }
+ return true;
+}
+
+bool isPositiveSemiDefinite(const mat33 &m) {
+ // test if all upper left determinants are positive
+ if (m(0, 0) < 0) { // upper 1x1
+ return false;
+ }
+ if (m(0, 0) * m(1, 1) - m(0, 1) * m(1, 0) < 0) { // upper 2x2
+ return false;
+ }
+ if ((m(0, 0) * (m(1, 1) * m(2, 2) - m(1, 2) * m(2, 1)) -
+ m(0, 1) * (m(1, 0) * m(2, 2) - m(1, 2) * m(2, 0)) +
+ m(0, 2) * (m(1, 0) * m(2, 1) - m(1, 1) * m(2, 0))) < 0) {
+ return false;
+ }
+ return true;
+}
+
+bool isPositiveSemiDefiniteFuzzy(const mat33 &m) {
+ // test if all upper left determinants are positive
+ if (m(0, 0) < -kIsZero) { // upper 1x1
+ return false;
+ }
+ if (m(0, 0) * m(1, 1) - m(0, 1) * m(1, 0) < -kIsZero) { // upper 2x2
+ return false;
+ }
+ if ((m(0, 0) * (m(1, 1) * m(2, 2) - m(1, 2) * m(2, 1)) -
+ m(0, 1) * (m(1, 0) * m(2, 2) - m(1, 2) * m(2, 0)) +
+ m(0, 2) * (m(1, 0) * m(2, 1) - m(1, 1) * m(2, 0))) < -kIsZero) {
+ return false;
+ }
+ return true;
+}
+
+idScalar determinant(const mat33 &m) {
+ return m(0, 0) * m(1, 1) * m(2, 2) + m(0, 1) * m(1, 2) * m(2, 0) + m(0, 2) * m(1, 0) * m(2, 1) -
+ m(0, 2) * m(1, 1) * m(2, 0) - m(0, 0) * m(1, 2) * m(2, 1) - m(0, 1) * m(1, 0) * m(2, 2);
+}
+
+bool isValidInertiaMatrix(const mat33 &I, const int index, bool has_fixed_joint) {
+ // TODO(Thomas) do we really want this?
+ // in cases where the inertia tensor about the center of mass is zero,
+ // the determinant of the inertia tensor about the joint axis is almost
+ // zero and can have a very small negative value.
+ if (!isPositiveSemiDefiniteFuzzy(I)) {
+ error_message("invalid inertia matrix for body %d, not positive definite "
+ "(fixed joint)\n",
+ index);
+ error_message("matrix is:\n"
+ "[%.20e %.20e %.20e;\n"
+ "%.20e %.20e %.20e;\n"
+ "%.20e %.20e %.20e]\n",
+ I(0, 0), I(0, 1), I(0, 2), I(1, 0), I(1, 1), I(1, 2), I(2, 0), I(2, 1),
+ I(2, 2));
+
+ return false;
+ }
+
+ // check triangle inequality, must have I(i,i)+I(j,j)>=I(k,k)
+ if (!has_fixed_joint) {
+ if (I(0, 0) + I(1, 1) < I(2, 2)) {
+ error_message("invalid inertia tensor for body %d, I(0,0) + I(1,1) < I(2,2)\n", index);
+ error_message("matrix is:\n"
+ "[%.20e %.20e %.20e;\n"
+ "%.20e %.20e %.20e;\n"
+ "%.20e %.20e %.20e]\n",
+ I(0, 0), I(0, 1), I(0, 2), I(1, 0), I(1, 1), I(1, 2), I(2, 0), I(2, 1),
+ I(2, 2));
+ return false;
+ }
+ if (I(0, 0) + I(1, 1) < I(2, 2)) {
+ error_message("invalid inertia tensor for body %d, I(0,0) + I(1,1) < I(2,2)\n", index);
+ error_message("matrix is:\n"
+ "[%.20e %.20e %.20e;\n"
+ "%.20e %.20e %.20e;\n"
+ "%.20e %.20e %.20e]\n",
+ I(0, 0), I(0, 1), I(0, 2), I(1, 0), I(1, 1), I(1, 2), I(2, 0), I(2, 1),
+ I(2, 2));
+ return false;
+ }
+ if (I(1, 1) + I(2, 2) < I(0, 0)) {
+ error_message("invalid inertia tensor for body %d, I(1,1) + I(2,2) < I(0,0)\n", index);
+ error_message("matrix is:\n"
+ "[%.20e %.20e %.20e;\n"
+ "%.20e %.20e %.20e;\n"
+ "%.20e %.20e %.20e]\n",
+ I(0, 0), I(0, 1), I(0, 2), I(1, 0), I(1, 1), I(1, 2), I(2, 0), I(2, 1),
+ I(2, 2));
+ return false;
+ }
+ }
+ // check positive/zero diagonal elements
+ for (int i = 0; i < 3; i++) {
+ if (I(i, i) < 0) { // accept zero
+ error_message("invalid inertia tensor, I(%d,%d)= %e <0\n", i, i, I(i, i));
+ return false;
+ }
+ }
+ // check symmetry
+ if (BT_ID_FABS(I(1, 0) - I(0, 1)) > kIsZero) {
+ error_message("invalid inertia tensor for body %d I(1,0)!=I(0,1). I(1,0)-I(0,1)= "
+ "%e\n",
+ index, I(1, 0) - I(0, 1));
+ return false;
+ }
+ if (BT_ID_FABS(I(2, 0) - I(0, 2)) > kIsZero) {
+ error_message("invalid inertia tensor for body %d I(2,0)!=I(0,2). I(2,0)-I(0,2)= "
+ "%e\n",
+ index, I(2, 0) - I(0, 2));
+ return false;
+ }
+ if (BT_ID_FABS(I(1, 2) - I(2, 1)) > kIsZero) {
+ error_message("invalid inertia tensor body %d I(1,2)!=I(2,1). I(1,2)-I(2,1)= %e\n", index,
+ I(1, 2) - I(2, 1));
+ return false;
+ }
+ return true;
+}
+
+bool isValidTransformMatrix(const mat33 &m) {
+#define print_mat(x) \
+ error_message("matrix is [%e, %e, %e; %e, %e, %e; %e, %e, %e]\n", x(0, 0), x(0, 1), x(0, 2), \
+ x(1, 0), x(1, 1), x(1, 2), x(2, 0), x(2, 1), x(2, 2))
+
+ // check for unit length column vectors
+ for (int i = 0; i < 3; i++) {
+ const idScalar length_minus_1 =
+ BT_ID_FABS(m(0, i) * m(0, i) + m(1, i) * m(1, i) + m(2, i) * m(2, i) - 1.0);
+ if (length_minus_1 > kAxisLengthEpsilon) {
+ error_message("Not a valid rotation matrix (column %d not unit length)\n"
+ "column = [%.18e %.18e %.18e]\n"
+ "length-1.0= %.18e\n",
+ i, m(0, i), m(1, i), m(2, i), length_minus_1);
+ print_mat(m);
+ return false;
+ }
+ }
+ // check for orthogonal column vectors
+ if (BT_ID_FABS(m(0, 0) * m(0, 1) + m(1, 0) * m(1, 1) + m(2, 0) * m(2, 1)) > kAxisLengthEpsilon) {
+ error_message("Not a valid rotation matrix (columns 0 and 1 not orthogonal)\n");
+ print_mat(m);
+ return false;
+ }
+ if (BT_ID_FABS(m(0, 0) * m(0, 2) + m(1, 0) * m(1, 2) + m(2, 0) * m(2, 2)) > kAxisLengthEpsilon) {
+ error_message("Not a valid rotation matrix (columns 0 and 2 not orthogonal)\n");
+ print_mat(m);
+ return false;
+ }
+ if (BT_ID_FABS(m(0, 1) * m(0, 2) + m(1, 1) * m(1, 2) + m(2, 1) * m(2, 2)) > kAxisLengthEpsilon) {
+ error_message("Not a valid rotation matrix (columns 0 and 2 not orthogonal)\n");
+ print_mat(m);
+ return false;
+ }
+ // check determinant (rotation not reflection)
+ if (determinant(m) <= 0) {
+ error_message("Not a valid rotation matrix (determinant <=0)\n");
+ print_mat(m);
+ return false;
+ }
+ return true;
+}
+
+bool isUnitVector(const vec3 &vector) {
+ return BT_ID_FABS(vector(0) * vector(0) + vector(1) * vector(1) + vector(2) * vector(2) - 1.0) <
+ kIsZero;
+}
+
+vec3 rpyFromMatrix(const mat33 &rot) {
+ vec3 rpy;
+ rpy(2) = BT_ID_ATAN2(-rot(1, 0), rot(0, 0));
+ rpy(1) = BT_ID_ATAN2(rot(2, 0), BT_ID_COS(rpy(2)) * rot(0, 0) - BT_ID_SIN(rpy(0)) * rot(1, 0));
+ rpy(0) = BT_ID_ATAN2(-rot(2, 0), rot(2, 2));
+ return rpy;
+}
+}
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