510 lines
12 KiB
C++
510 lines
12 KiB
C++
#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())
|
|
{
|
|
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 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 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))
|
|
{
|
|
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))
|
|
{
|
|
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));
|
|
return false;
|
|
}
|
|
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));
|
|
return false;
|
|
}
|
|
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));
|
|
return false;
|
|
}
|
|
}
|
|
// check positive/zero diagonal elements
|
|
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));
|
|
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));
|
|
return false;
|
|
}
|
|
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));
|
|
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))
|
|
|
|
// 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)
|
|
{
|
|
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)
|
|
{
|
|
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)
|
|
{
|
|
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)
|
|
{
|
|
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)
|
|
{
|
|
bt_id_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(0) = BT_ID_ATAN2(-rot(2, 0), rot(2, 2));
|
|
rpy(1) = BT_ID_ATAN2(rot(2, 0), BT_ID_COS(rpy(2)) * rot(0, 0) - BT_ID_SIN(rpy(0)) * rot(1, 0));
|
|
return rpy;
|
|
}
|
|
} // namespace btInverseDynamics
|