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-rw-r--r--thirdparty/bullet/BulletInverseDynamics/IDMath.cpp351
1 files changed, 212 insertions, 139 deletions
diff --git a/thirdparty/bullet/BulletInverseDynamics/IDMath.cpp b/thirdparty/bullet/BulletInverseDynamics/IDMath.cpp
index d279d3435c..2f120ed489 100644
--- a/thirdparty/bullet/BulletInverseDynamics/IDMath.cpp
+++ b/thirdparty/bullet/BulletInverseDynamics/IDMath.cpp
@@ -3,25 +3,30 @@
#include <cmath>
#include <limits>
-namespace btInverseDynamics {
+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) {
+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++) {
+void setZero(vecx &v)
+{
+ for (int i = 0; i < v.size(); i++)
+ {
v(i) = 0;
}
}
-void setZero(mat33 &m) {
+void setZero(mat33 &m)
+{
m(0, 0) = 0;
m(0, 1) = 0;
m(0, 2) = 0;
@@ -33,7 +38,8 @@ void setZero(mat33 &m) {
m(2, 2) = 0;
}
-void skew(vec3& v, mat33* result) {
+void skew(vec3 &v, mat33 *result)
+{
(*result)(0, 0) = 0.0;
(*result)(0, 1) = -v(2);
(*result)(0, 2) = v(1);
@@ -45,22 +51,28 @@ void skew(vec3& v, mat33* result) {
(*result)(2, 2) = 0.0;
}
-idScalar maxAbs(const vecx &v) {
+idScalar maxAbs(const vecx &v)
+{
idScalar result = 0.0;
- for (int i = 0; i < v.size(); i++) {
+ for (int i = 0; i < v.size(); i++)
+ {
const idScalar tmp = BT_ID_FABS(v(i));
- if (tmp > result) {
+ if (tmp > result)
+ {
result = tmp;
}
}
return result;
}
-idScalar maxAbs(const vec3 &v) {
+idScalar maxAbs(const vec3 &v)
+{
idScalar result = 0.0;
- for (int i = 0; i < 3; i++) {
+ for (int i = 0; i < 3; i++)
+ {
const idScalar tmp = BT_ID_FABS(v(i));
- if (tmp > result) {
+ if (tmp > result)
+ {
result = tmp;
}
}
@@ -68,60 +80,75 @@ idScalar maxAbs(const vec3 &v) {
}
#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;
+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()) {
- bt_id_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 mul(const mat33 &a, const mat3x &b, mat3x *result)
+{
+ if (b.cols() != result->cols())
+ {
+ bt_id_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()) {
- bt_id_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 add(const mat3x &a, const mat3x &b, mat3x *result)
+{
+ if (a.cols() != b.cols())
+ {
+ bt_id_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()) {
- bt_id_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())
+ {
+ bt_id_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 transformX(const idScalar &alpha)
+{
mat33 T;
const idScalar cos_alpha = BT_ID_COS(alpha);
const idScalar sin_alpha = BT_ID_SIN(alpha);
@@ -143,7 +170,8 @@ mat33 transformX(const idScalar &alpha) {
return T;
}
-mat33 transformY(const idScalar &beta) {
+mat33 transformY(const idScalar &beta)
+{
mat33 T;
const idScalar cos_beta = BT_ID_COS(beta);
const idScalar sin_beta = BT_ID_SIN(beta);
@@ -165,7 +193,8 @@ mat33 transformY(const idScalar &beta) {
return T;
}
-mat33 transformZ(const idScalar &gamma) {
+mat33 transformZ(const idScalar &gamma)
+{
mat33 T;
const idScalar cos_gamma = BT_ID_COS(gamma);
const idScalar sin_gamma = BT_ID_SIN(gamma);
@@ -187,7 +216,8 @@ mat33 transformZ(const idScalar &gamma) {
return T;
}
-mat33 tildeOperator(const vec3 &v) {
+mat33 tildeOperator(const vec3 &v)
+{
mat33 m;
m(0, 0) = 0.0;
m(0, 1) = -v(2);
@@ -201,7 +231,8 @@ mat33 tildeOperator(const vec3 &v) {
return m;
}
-void getVecMatFromDH(idScalar theta, idScalar d, idScalar a, idScalar alpha, vec3 *r, mat33 *T) {
+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);
@@ -224,7 +255,8 @@ void getVecMatFromDH(idScalar theta, idScalar d, idScalar a, idScalar alpha, vec
(*T)(2, 2) = ca;
}
-void bodyTParentFromAxisAngle(const vec3 &axis, const idScalar &angle, mat33 *T) {
+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;
@@ -246,175 +278,214 @@ void bodyTParentFromAxisAngle(const vec3 &axis, const idScalar &angle, mat33 *T)
(*T)(2, 2) = z * z * one_m_c + c;
}
-bool isPositiveDefinite(const mat33 &m) {
+bool isPositiveDefinite(const mat33 &m)
+{
// test if all upper left determinants are positive
- if (m(0, 0) <= 0) { // upper 1x1
+ 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
+ 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) {
+ 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) {
+bool isPositiveSemiDefinite(const mat33 &m)
+{
// test if all upper left determinants are positive
- if (m(0, 0) < 0) { // upper 1x1
+ 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
+ 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) {
+ 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) {
+bool isPositiveSemiDefiniteFuzzy(const mat33 &m)
+{
// test if all upper left determinants are positive
- if (m(0, 0) < -kIsZero) { // upper 1x1
+ 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
+ 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) {
+ 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) {
+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) {
+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)) {
- bt_id_error_message("invalid inertia matrix for body %d, not positive definite "
- "(fixed joint)\n",
- index);
- bt_id_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));
+ if (!isPositiveSemiDefiniteFuzzy(I))
+ {
+ bt_id_error_message(
+ "invalid inertia matrix for body %d, not positive definite "
+ "(fixed joint)\n",
+ index);
+ bt_id_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)) {
+ if (!has_fixed_joint)
+ {
+ if (I(0, 0) + I(1, 1) < I(2, 2))
+ {
bt_id_error_message("invalid inertia tensor for body %d, I(0,0) + I(1,1) < I(2,2)\n", index);
- bt_id_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));
+ bt_id_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)) {
+ if (I(0, 0) + I(1, 1) < I(2, 2))
+ {
bt_id_error_message("invalid inertia tensor for body %d, I(0,0) + I(1,1) < I(2,2)\n", index);
- bt_id_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));
+ bt_id_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)) {
+ if (I(1, 1) + I(2, 2) < I(0, 0))
+ {
bt_id_error_message("invalid inertia tensor for body %d, I(1,1) + I(2,2) < I(0,0)\n", index);
- bt_id_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));
+ bt_id_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
+ for (int i = 0; i < 3; i++)
+ {
+ if (I(i, i) < 0)
+ { // accept zero
bt_id_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) {
- bt_id_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));
+ if (BT_ID_FABS(I(1, 0) - I(0, 1)) > kIsZero)
+ {
+ bt_id_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) {
- bt_id_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));
+ if (BT_ID_FABS(I(2, 0) - I(0, 2)) > kIsZero)
+ {
+ bt_id_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) {
+ if (BT_ID_FABS(I(1, 2) - I(2, 1)) > kIsZero)
+ {
bt_id_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));
+ I(1, 2) - I(2, 1));
return false;
}
return true;
}
-bool isValidTransformMatrix(const mat33 &m) {
-#define print_mat(x) \
- bt_id_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))
+bool isValidTransformMatrix(const mat33 &m)
+{
+#define print_mat(x) \
+ bt_id_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++) {
+ 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) {
- bt_id_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);
+ if (length_minus_1 > kAxisLengthEpsilon)
+ {
+ bt_id_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) {
+ if (BT_ID_FABS(m(0, 0) * m(0, 1) + m(1, 0) * m(1, 1) + m(2, 0) * m(2, 1)) > kAxisLengthEpsilon)
+ {
bt_id_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) {
+ if (BT_ID_FABS(m(0, 0) * m(0, 2) + m(1, 0) * m(1, 2) + m(2, 0) * m(2, 2)) > kAxisLengthEpsilon)
+ {
bt_id_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) {
+ if (BT_ID_FABS(m(0, 1) * m(0, 2) + m(1, 1) * m(1, 2) + m(2, 1) * m(2, 2)) > kAxisLengthEpsilon)
+ {
bt_id_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) {
+ if (determinant(m) <= 0)
+ {
bt_id_error_message("Not a valid rotation matrix (determinant <=0)\n");
print_mat(m);
return false;
@@ -422,16 +493,18 @@ bool isValidTransformMatrix(const mat33 &m) {
return true;
}
-bool isUnitVector(const vec3 &vector) {
+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 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;
}
-}
+} // namespace btInverseDynamics