Geometry.hpp File Reference

#include <Eigen/Dense>
#include "dart/common/Deprecated.hpp"
#include "dart/math/Constants.hpp"
#include "dart/math/MathTypes.hpp"

Go to the source code of this file.

Classes
class	dart::math::BoundingBox

Namespaces
	dart
	dart::math

Typedefs
typedef std::vector< Eigen::Vector3d >	dart::math::SupportGeometry
typedef common::aligned_vector< Eigen::Vector2d >	dart::math::SupportPolygon

Enumerations
enum	dart::math::AxisType { dart::math::AXIS_X = 0 , dart::math::AXIS_Y = 1 , dart::math::AXIS_Z = 2 }
enum	dart::math::IntersectionResult { dart::math::INTERSECTING = 0 , dart::math::PARALLEL , dart::math::BEYOND_ENDPOINTS }
	Intersection_t is returned by the computeIntersection() function to indicate whether there was a valid intersection between the two line segments. More...

Functions
Eigen::Matrix3d	dart::math::makeSkewSymmetric (const Eigen::Vector3d &_v)
Eigen::Vector3d	dart::math::fromSkewSymmetric (const Eigen::Matrix3d &_m)
Eigen::Quaterniond	dart::math::expToQuat (const Eigen::Vector3d &_v)
Eigen::Vector3d	dart::math::quatToExp (const Eigen::Quaterniond &_q)
Eigen::Vector3d	dart::math::rotatePoint (const Eigen::Quaterniond &_q, const Eigen::Vector3d &_pt)
Eigen::Vector3d	dart::math::rotatePoint (const Eigen::Quaterniond &_q, double _x, double _y, double _z)
Eigen::Matrix3d	dart::math::quatDeriv (const Eigen::Quaterniond &_q, int _el)
Eigen::Matrix3d	dart::math::quatSecondDeriv (const Eigen::Quaterniond &_q, int _el1, int _el2)
Eigen::Matrix3d	dart::math::eulerXYXToMatrix (const Eigen::Vector3d &_angle)
	Given Euler XYX angles, return a 3x3 rotation matrix, which is equivalent to RotX(angle(0)) * RotY(angle(1)) * RotX(angle(2)). More...
Eigen::Matrix3d	dart::math::eulerXYZToMatrix (const Eigen::Vector3d &_angle)
	Given EulerXYZ angles, return a 3x3 rotation matrix, which is equivalent to RotX(angle(0)) * RotY(angle(1)) * RotZ(angle(2)). More...
Eigen::Matrix3d	dart::math::eulerXZXToMatrix (const Eigen::Vector3d &_angle)
	Given EulerXZX angles, return a 3x3 rotation matrix, which is equivalent to RotX(angle(0)) * RotZ(angle(1)) * RotX(angle(2)). More...
Eigen::Matrix3d	dart::math::eulerXZYToMatrix (const Eigen::Vector3d &_angle)
	Given EulerXZY angles, return a 3x3 rotation matrix, which is equivalent to RotX(angle(0)) * RotZ(angle(1)) * RotY(angle(2)). More...
Eigen::Matrix3d	dart::math::eulerYXYToMatrix (const Eigen::Vector3d &_angle)
	Given EulerYXY angles, return a 3x3 rotation matrix, which is equivalent to RotY(angle(0)) * RotX(angle(1)) * RotY(angle(2)). More...
Eigen::Matrix3d	dart::math::eulerYXZToMatrix (const Eigen::Vector3d &_angle)
	Given EulerYXZ angles, return a 3x3 rotation matrix, which is equivalent to RotY(angle(0)) * RotX(angle(1)) * RotZ(angle(2)). More...
Eigen::Matrix3d	dart::math::eulerYZXToMatrix (const Eigen::Vector3d &_angle)
	Given EulerYZX angles, return a 3x3 rotation matrix, which is equivalent to RotY(angle(0)) * RotZ(angle(1)) * RotX(angle(2)). More...
Eigen::Matrix3d	dart::math::eulerYZYToMatrix (const Eigen::Vector3d &_angle)
	Given EulerYZY angles, return a 3x3 rotation matrix, which is equivalent to RotY(angle(0)) * RotZ(angle(1)) * RotY(angle(2)). More...
Eigen::Matrix3d	dart::math::eulerZXYToMatrix (const Eigen::Vector3d &_angle)
	Given EulerZXY angles, return a 3x3 rotation matrix, which is equivalent to RotZ(angle(0)) * RotX(angle(1)) * RotY(angle(2)). More...
Eigen::Matrix3d	dart::math::eulerZYXToMatrix (const Eigen::Vector3d &_angle)
	Given EulerZYX angles, return a 3x3 rotation matrix, which is equivalent to RotZ(angle(0)) * RotY(angle(1)) * RotX(angle(2)). More...
Eigen::Matrix3d	dart::math::eulerZXZToMatrix (const Eigen::Vector3d &_angle)
	Given EulerZXZ angles, return a 3x3 rotation matrix, which is equivalent to RotZ(angle(0)) * RotX(angle(1)) * RotZ(angle(2)). More...
Eigen::Matrix3d	dart::math::eulerZYZToMatrix (const Eigen::Vector3d &_angle)
	Given EulerZYZ angles, return a 3x3 rotation matrix, which is equivalent to RotZ(angle(0)) * RotY(angle(1)) * RotZ(angle(2)). More...
Eigen::Vector3d	dart::math::matrixToEulerXYX (const Eigen::Matrix3d &_R)
	get the Euler XYX angle from R More...
Eigen::Vector3d	dart::math::matrixToEulerXYZ (const Eigen::Matrix3d &_R)
	get the Euler XYZ angle from R More...
Eigen::Vector3d	dart::math::matrixToEulerXZY (const Eigen::Matrix3d &_R)
	get the Euler XZY angle from R More...
Eigen::Vector3d	dart::math::matrixToEulerYXZ (const Eigen::Matrix3d &_R)
	get the Euler YXZ angle from R More...
Eigen::Vector3d	dart::math::matrixToEulerYZX (const Eigen::Matrix3d &_R)
	get the Euler YZX angle from R More...
Eigen::Vector3d	dart::math::matrixToEulerZXY (const Eigen::Matrix3d &_R)
	get the Euler ZXY angle from R More...
Eigen::Vector3d	dart::math::matrixToEulerZYX (const Eigen::Matrix3d &_R)
	get the Euler ZYX angle from R More...
Eigen::Isometry3d	dart::math::expMap (const Eigen::Vector6d &_S)
	Exponential mapping. More...
Eigen::Isometry3d	dart::math::expAngular (const Eigen::Vector3d &_s)
	fast version of Exp(se3(s, 0)) More...
Eigen::Matrix3d	dart::math::expMapRot (const Eigen::Vector3d &_expmap)
	Computes the Rotation matrix from a given expmap vector. More...
Eigen::Matrix3d	dart::math::expMapJac (const Eigen::Vector3d &_expmap)
	Computes the Jacobian of the expmap. More...
Eigen::Matrix3d	dart::math::expMapJacDot (const Eigen::Vector3d &_expmap, const Eigen::Vector3d &_qdot)
	Computes the time derivative of the expmap Jacobian. More...
Eigen::Matrix3d	dart::math::expMapJacDeriv (const Eigen::Vector3d &_expmap, int _qi)
	computes the derivative of the Jacobian of the expmap wrt to _qi indexed dof; _qi \in {0,1,2} More...
Eigen::Vector3d	dart::math::logMap (const Eigen::Matrix3d &_R)
	Log mapping. More...
Eigen::Vector6d	dart::math::logMap (const Eigen::Isometry3d &_T)
	Log mapping. More...
Eigen::Vector6d	dart::math::AdT (const Eigen::Isometry3d &_T, const Eigen::Vector6d &_V)
	Rectify the rotation part so as that it satifies the orthogonality condition. More...
Eigen::Matrix6d	dart::math::getAdTMatrix (const Eigen::Isometry3d &T)
	Get linear transformation matrix of Adjoint mapping. More...
template<typename Derived >
Derived::PlainObject	dart::math::AdTJac (const Eigen::Isometry3d &_T, const Eigen::MatrixBase< Derived > &_J)
	Adjoint mapping for dynamic size Jacobian. More...
template<typename Derived >
Derived::PlainObject	dart::math::AdTJacFixed (const Eigen::Isometry3d &_T, const Eigen::MatrixBase< Derived > &_J)
	Adjoint mapping for fixed size Jacobian. More...
Eigen::Vector6d	dart::math::AdR (const Eigen::Isometry3d &_T, const Eigen::Vector6d &_V)
	Fast version of Ad([R 0; 0 1], V) More...
Eigen::Vector6d	dart::math::AdTAngular (const Eigen::Isometry3d &_T, const Eigen::Vector3d &_w)
	fast version of Ad(T, se3(w, 0)) More...
Eigen::Vector6d	dart::math::AdTLinear (const Eigen::Isometry3d &_T, const Eigen::Vector3d &_v)
	fast version of Ad(T, se3(0, v)) More...
template<typename Derived >
Derived::PlainObject	dart::math::AdRJac (const Eigen::Isometry3d &_T, const Eigen::MatrixBase< Derived > &_J)
	Change coordinate Frame of a Jacobian. More...
template<typename Derived >
Derived::PlainObject	dart::math::AdRInvJac (const Eigen::Isometry3d &_T, const Eigen::MatrixBase< Derived > &_J)
template<typename Derived >
Derived::PlainObject	dart::math::adJac (const Eigen::Vector6d &_V, const Eigen::MatrixBase< Derived > &_J)
Eigen::Vector6d	dart::math::AdInvT (const Eigen::Isometry3d &_T, const Eigen::Vector6d &_V)
	fast version of Ad(Inv(T), V) More...
template<typename Derived >
Derived::PlainObject	dart::math::AdInvTJac (const Eigen::Isometry3d &_T, const Eigen::MatrixBase< Derived > &_J)
	Adjoint mapping for dynamic size Jacobian. More...
template<typename Derived >
Derived::PlainObject	dart::math::AdInvTJacFixed (const Eigen::Isometry3d &_T, const Eigen::MatrixBase< Derived > &_J)
	Adjoint mapping for fixed size Jacobian. More...
Eigen::Vector6d	dart::math::AdInvRLinear (const Eigen::Isometry3d &_T, const Eigen::Vector3d &_v)
	Fast version of Ad(Inv([R 0; 0 1]), se3(0, v)) More...
Eigen::Vector6d	dart::math::dAdT (const Eigen::Isometry3d &_T, const Eigen::Vector6d &_F)
	dual adjoint mapping More...
Eigen::Vector6d	dart::math::dAdInvT (const Eigen::Isometry3d &_T, const Eigen::Vector6d &_F)
	fast version of dAd(Inv(T), F) More...
Eigen::Vector6d	dart::math::dAdInvR (const Eigen::Isometry3d &_T, const Eigen::Vector6d &_F)
	fast version of dAd(Inv([R 0; 0 1]), F) More...
Eigen::Vector6d	dart::math::ad (const Eigen::Vector6d &_X, const Eigen::Vector6d &_Y)
	adjoint mapping More...
Eigen::Vector6d	dart::math::dad (const Eigen::Vector6d &_s, const Eigen::Vector6d &_t)
	fast version of ad(se3(Eigen_Vec3(0), v), S) More...
Inertia	dart::math::transformInertia (const Eigen::Isometry3d &_T, const Inertia &_AI)
Eigen::Matrix3d	dart::math::parallelAxisTheorem (const Eigen::Matrix3d &_original, const Eigen::Vector3d &_comShift, double _mass)
	Use the Parallel Axis Theorem to compute the moment of inertia of a body whose center of mass has been shifted from the origin. More...
Eigen::Matrix3d	dart::math::computeRotation (const Eigen::Vector3d &axis, AxisType axisType=AxisType::AXIS_X)
	Compute a rotation matrix from a vector. More...
Eigen::Isometry3d	dart::math::computeTransform (const Eigen::Vector3d &axis, const Eigen::Vector3d &translation, AxisType axisType=AxisType::AXIS_X)
	Compute a transform from a vector and a position. More...
Eigen::Isometry3d	dart::math::getFrameOriginAxisZ (const Eigen::Vector3d &_origin, const Eigen::Vector3d &_axisZ)
	Generate frame given origin and z-axis. More...
bool	dart::math::verifyRotation (const Eigen::Matrix3d &_R)
	Check if determinant of _R is equat to 1 and all the elements are not NaN values. More...
bool	dart::math::verifyTransform (const Eigen::Isometry3d &_T)
	Check if determinant of the rotational part of _T is equat to 1 and all the elements are not NaN values. More...
double	dart::math::wrapToPi (double angle)
	Compute the angle (in the range of -pi to +pi) which ignores any full rotations. More...
template<typename MatrixType , typename ReturnType >
void	dart::math::extractNullSpace (const Eigen::JacobiSVD< MatrixType > &_SVD, ReturnType &_NS)
template<typename MatrixType , typename ReturnType >
void	dart::math::computeNullSpace (const MatrixType &_M, ReturnType &_NS)
SupportPolygon	dart::math::computeSupportPolgyon (const SupportGeometry &_geometry, const Eigen::Vector3d &_axis1=Eigen::Vector3d::UnitX(), const Eigen::Vector3d &_axis2=Eigen::Vector3d::UnitY())
	Project the support geometry points onto a plane with the given axes and then compute their convex hull, which will take the form of a polgyon. More...
SupportPolygon	dart::math::computeSupportPolgyon (std::vector< std::size_t > &_originalIndices, const SupportGeometry &_geometry, const Eigen::Vector3d &_axis1=Eigen::Vector3d::UnitX(), const Eigen::Vector3d &_axis2=Eigen::Vector3d::UnitY())
	Same as computeSupportPolgyon, except you can pass in a std::vector<std::size_t> which will have the same size as the returned SupportPolygon, and each entry will contain the original index of each point in the SupportPolygon. More...
SupportPolygon	dart::math::computeConvexHull (const SupportPolygon &_points)
	Computes the convex hull of a set of 2D points. More...
SupportPolygon	dart::math::computeConvexHull (std::vector< std::size_t > &_originalIndices, const SupportPolygon &_points)
	Computes the convex hull of a set of 2D points and fills in _originalIndices with the original index of each entry in the returned SupportPolygon. More...
Eigen::Vector2d	dart::math::computeCentroidOfHull (const SupportPolygon &_convexHull)
	Compute the centroid of a polygon, assuming the polygon is a convex hull. More...
IntersectionResult	dart::math::computeIntersection (Eigen::Vector2d &_intersectionPoint, const Eigen::Vector2d &a1, const Eigen::Vector2d &a2, const Eigen::Vector2d &b1, const Eigen::Vector2d &b2)
	Compute the intersection between a line segment that goes from a1 -> a2 and a line segment that goes from b1 -> b2. More...
double	dart::math::cross (const Eigen::Vector2d &_v1, const Eigen::Vector2d &_v2)
	Compute a 2D cross product. More...
bool	dart::math::isInsideSupportPolygon (const Eigen::Vector2d &_p, const SupportPolygon &_support, bool _includeEdge=true)
	Returns true if the point _p is inside the support polygon. More...
Eigen::Vector2d	dart::math::computeClosestPointOnLineSegment (const Eigen::Vector2d &_p, const Eigen::Vector2d &_s1, const Eigen::Vector2d &_s2)
	Returns the point which is closest to _p that also lays on the line segment that goes from _s1 -> _s2. More...
Eigen::Vector2d	dart::math::computeClosestPointOnSupportPolygon (const Eigen::Vector2d &_p, const SupportPolygon &_support)
	Returns the point which is closest to _p that also lays on the edge of the support polygon. More...
Eigen::Vector2d	dart::math::computeClosestPointOnSupportPolygon (std::size_t &_index1, std::size_t &_index2, const Eigen::Vector2d &_p, const SupportPolygon &_support)
	Same as closestPointOnSupportPolygon, but also fills in _index1 and _index2 with the indices of the line segment. More...