add real-time safe Inverse Dynamics library+test+utils

an example for the example browser will follow.
thanks to Thomas Buschmann

src/BulletInverseDynamics/IDMath.hpp

@@ -0,0 +1,88 @@
+/// @file Math utility functions used in inverse dynamics library.
+///       Defined here as they may not be provided by the math library.
+
+#ifndef IDMATH_HPP_
+#define IDMATH_HPP_
+#include "IDConfig.hpp"
+
+namespace btInverseDynamics {
+/// set all elements to zero
+void setZero(vec3& v);
+/// set all elements to zero
+void setZero(vecx& v);
+/// set all elements to zero
+void setZero(mat33& m);
+
+/// return maximum absolute value
+idScalar maxAbs(const vecx& v);
+#ifndef ID_LINEAR_MATH_USE_EIGEN
+/// return maximum absolute value
+idScalar maxAbs(const vec3& v);
+#endif  //ID_LINEAR_MATH_USE_EIGEN
+/// get offset vector & transform matrix from DH parameters
+/// TODO: add documentation
+void getVecMatFromDH(idScalar theta, idScalar d, idScalar a, idScalar alpha, vec3* r, mat33* T);
+
+/// Check if a 3x3 matrix is positive definite
+/// @param m a 3x3 matrix
+/// @return true if m>0, false otherwise
+bool isPositiveDefinite(const mat33& m);
+
+/// Check if a 3x3 matrix is positive semi definite
+/// @param m a 3x3 matrix
+/// @return true if m>=0, false otherwise
+bool isPositiveSemiDefinite(const mat33& m);
+/// Check if a 3x3 matrix is positive semi definite within numeric limits
+/// @param m a 3x3 matrix
+/// @return true if m>=-eps, false otherwise
+bool isPositiveSemiDefiniteFuzzy(const mat33& m);
+
+/// Determinant of 3x3 matrix
+/// NOTE: implemented here for portability, as determinant operation
+///       will be implemented differently for various matrix/vector libraries
+/// @param m a 3x3 matrix
+/// @return det(m)
+idScalar determinant(const mat33& m);
+
+/// Test if a 3x3 matrix satisfies some properties of inertia matrices
+/// @param I a 3x3 matrix
+/// @param index body index (for error messages)
+/// @param has_fixed_joint: if true, positive semi-definite matrices are accepted
+/// @return true if I satisfies inertia matrix properties, false otherwise.
+bool isValidInertiaMatrix(const mat33& I, int index, bool has_fixed_joint);
+
+/// Check if a 3x3 matrix is a valid transform (rotation) matrix
+/// @param m a 3x3 matrix
+/// @return true if m is a rotation matrix, false otherwise
+bool isValidTransformMatrix(const mat33& m);
+/// Transform matrix from parent to child frame,
+/// when the child frame is rotated about @param axis by @angle
+/// (mathematically positive)
+/// @param axis the axis of rotation
+/// @param angle rotation angle
+/// @param T pointer to transform matrix
+void bodyTParentFromAxisAngle(const vec3& axis, const idScalar& angle, mat33* T);
+
+/// Check if this is a unit vector
+/// @param vector
+/// @return true if |vector|=1 within numeric limits
+bool isUnitVector(const vec3& vector);
+
+/// @input a vector in R^3
+/// @returns corresponding spin tensor
+mat33 tildeOperator(const vec3& v);
+/// @param alpha angle in radians
+/// @returns transform matrix for ratation with @param alpha about x-axis
+mat33 transformX(const idScalar& alpha);
+/// @param beta angle in radians
+/// @returns transform matrix for ratation with @param beta about y-axis
+mat33 transformY(const idScalar& beta);
+/// @param gamma angle in radians
+/// @returns transform matrix for ratation with @param gamma about z-axis
+mat33 transformZ(const idScalar& gamma);
+///calculate rpy angles (x-y-z Euler angles) from a given rotation matrix
+/// @param rot rotation matrix
+/// @returns x-y-z Euler angles
+vec3 rpyFromMatrix(const mat33&rot);
+}
+#endif  // IDMATH_HPP_