Math3D Namespace Reference

Contains all the definitions in the Math3D package. More...

Classes
struct	AABB2D
	A 2D axis-aligned bounding box. More...
struct	AABB3D
	A 3D axis-aligned bounding box. More...
struct	AABBTemplate
class	AngleAxisRotation
	Angle-axis 3D rotation parameterization. More...
struct	Box2D
	A 2D boxThe box is the unit square [0,1]^2 set in the scaled local coordinate system. That is, one corner is at the origin, and it has dimensions [dims.x,dims.y] in the coordinates given by {xbasis,ybasis}. More...
struct	Box3D
	A 3D boxThe box is the unit cube [0,1]^3 set in the scaled local coordinate system. That is, one corner is at the origin, and it has dimensions [dims.x,dims.y,dims.z] in the coordinates given by {xbasis,ybasis,zbasis}. More...
struct	Circle2D
	A 2D circle class. More...
struct	Circle3D
	A 2D circle in 3D space class. More...
struct	ConvexPolygon2D
	A convex connected polygon such that the vertices are in ccw order. More...
struct	ConvexPolyhedron3D
	A convex polyhedron given in a dual representation, planes and vertices of convex hull. More...
struct	Cylinder3D
	A 3D cylinder. More...
struct	Ellipsoid3D
	A 3D ellipsoidThe ellipsoid is the centered unit sphere [-1,1]^3 set in the scaled local coordinate system. That is, the center is at the origin, and its major axes are {xbasis,ybasis,zbasis} with radii {dims.x,dims.y,dims.z}. More...
class	EulerAngleRotation
	Euler angle 3D rotation parameterization. More...
class	GeometricPrimitive2D
class	GeometricPrimitive3D
	A generic geometric primitive class. More...
struct	Line2D
	A 2D line class. More...
struct	Line3D
	A 3D line class. More...
struct	LocalCoordinates2D
struct	LocalCoordinates3D
class	Matrix2
	A 2x2 matrix class. More...
class	Matrix3
	A 3x3 matrix class. More...
class	Matrix4
	A 4x4 matrix class. More...
class	MomentRotation
	"Moment", a.k.a. exponential map, 3D rotation parameterization More...
struct	Plane2D
	A 2D plane classRepresents plane with a normal and offset such that x on the plane satisfy dot(normal,x) = offset. More...
struct	Plane3D
	A 3D plane classRepresents plane with a normal and offset such that x on the plane satisfy dot(normal,x) = offset. More...
struct	Polygon2D
	An arbitrary connected polygon given by a vertex list. More...
struct	Polygon3D
	An arbitrary connected polygon in 3D space given by a vertex list. More...
class	QuaternionRotation
	Quaternion, a.k.a. Euler parameter, 3D rotation parameterization. More...
struct	Ray3D
class	RigidTransform
	A rigid-body transformation. More...
class	RigidTransform2D
	Same as above, but in 2D. More...
struct	ScaledLocalCoordinates2D
struct	ScaledLocalCoordinates3D
struct	Segment2D
	A 2D segment class. More...
struct	Segment3D
struct	Sphere3D
	A 3D sphere class. More...
struct	Triangle2D
	A 2D triangle class. More...
struct	Triangle3D
	A 3D triangle class. More...
class	Vector2
	A 2D vector class. More...
class	Vector3
	A 3D vector class. More...
class	Vector4
	A 4D vector class. More...

Typedefs
typedef Real	vec2_t[2]
typedef Real	vec3_t[3]
typedef Real	vec4_t[4]
typedef Real	matrix3_t[3][4]
typedef Real	matrix4_t[4][4]
typedef Line2D	Ray2D
typedef Vector2	Point2D
typedef Vector3	Point3D
typedef Vector4	Point4D
typedef vec4_t	quat_t

Functions
ostream &	operator<< (ostream &out, const AABB3D &bb)
istream &	operator>> (istream &in, AABB3D &bb)
std::ostream &	operator<< (std::ostream &out, const AABB3D &bb)
std::istream &	operator>> (std::istream &in, AABB3D &bb)
void	GetCanonicalBasis (const Vector2 &x, Vector2 &y)
void	GetCanonicalBasis (const Vector3 &x, Vector3 &y, Vector3 &z)
std::ostream &	operator<< (std::ostream &out, const Box3D &b)
std::istream &	operator>> (std::istream &in, Box3D &b)
bool	ClipLine1D (Real q, Real p, Real &umin, Real &umax)
	Clipping primitive in 1D. More...
bool	ClipLine (const Vector2 &x, const Vector2 &v, const Plane2D &b, Real &u1, Real &u2)
bool	ClipLine (const Vector2 &x, const Vector2 &v, const AABB2D &b, Real &u1, Real &u2)
	Clip the line to the interior of the bbox.
bool	ClipLine (const Vector2 &x, const Vector2 &v, const ConvexPolygon2D &b, Real &u1, Real &u2)
	Clip the line to the interior of the convex polygon.
bool	ClipLine (const Vector3 &x, const Vector3 &v, const Plane3D &b, Real &u1, Real &u2)
bool	ClipLine (const Vector3 &x, const Vector3 &v, const Box3D &b, Real &u1, Real &u2)
bool	ClipLine (const Vector3 &x, const Vector3 &v, const AABB3D &b, Real &u1, Real &u2)
bool	ClipLine (const Vector3 &x, const Vector3 &v, const ConvexPolyhedron3D &p, Real &u1, Real &u2)
bool	ClipLine1D (Real x0, Real a, Real b, Real &umin, Real &umax)
std::ostream &	operator<< (std::ostream &out, const Cylinder3D &b)
std::istream &	operator>> (std::istream &in, Cylinder3D &b)
std::ostream &	operator<< (std::ostream &out, const Ellipsoid3D &b)
std::istream &	operator>> (std::istream &in, Ellipsoid3D &b)
Vector3	Unit (const Vector3 &v)
std::ostream &	operator<< (std::ostream &out, const GeometricPrimitive3D &g)
std::istream &	operator>> (std::istream &in, GeometricPrimitive3D &g)
void	interpolateRotation (const Matrix2 &a, const Matrix2 &b, Real u, Matrix2 &x)
void	interpolateRotation (const Matrix3 &a, const Matrix3 &b, Real u, Matrix3 &x)
void	interpolate (const Vector2 &a, const Vector2 &b, Real u, Vector2 &x)
void	interpolate (const Vector3 &a, const Vector3 &b, Real u, Vector3 &x)
void	interpolate (const Vector4 &a, const Vector4 &b, Real u, Vector4 &x)
void	interpolate (const RigidTransform2D &a, const RigidTransform2D &b, Real u, RigidTransform2D &x)
void	interpolate (const RigidTransform &a, const RigidTransform &b, Real u, RigidTransform &x)
template<class VectorT >
void	interpolateDirection (const VectorT &a, const VectorT &b, Real u, VectorT &out)
Real	SegmentZeroCrossing (Real a, Real b)
	if segment is x = a + u*(b-a), returns the value u s.t. x=0
Real	SegmentCrossing (Real a, Real b, Real x0)
	if segment is x = a + u*(b-a), returns the value u s.t. x=x0
ostream &	operator<< (ostream &out, const Line3D &line)
istream &	operator>> (istream &in, Line3D &line)
std::ostream &	operator<< (std::ostream &out, const Line3D &line)
std::istream &	operator>> (std::istream &in, Line3D &line)
void	Copy (Real v, Vector &mat)
void	Copy (const Vector2 &v, Vector &mat)
void	Copy (const Vector3 &v, Vector &mat)
void	Copy (const Vector4 &v, Vector &mat)
void	Copy (const Vector &vec, Real &v)
void	Copy (const Vector &vec, Vector2 &v)
void	Copy (const Vector &vec, Vector3 &v)
void	Copy (const Vector &vec, Vector4 &v)
void	Copy (Real m, Matrix &mat)
void	Copy (const Matrix2 &m, Matrix &mat)
void	Copy (const Matrix3 &m, Matrix &mat)
void	Copy (const Matrix4 &m, Matrix &mat)
void	Copy (const Matrix &mat, Real &m)
void	Copy (const Matrix &mat, Matrix2 &m)
void	Copy (const Matrix &mat, Matrix3 &m)
void	Copy (const Matrix &mat, Matrix4 &m)
void	Lasv2 (double *smin, double *smax, double *sv, double *cv, double *su, double *cu, double f, double g, double h)
bool	SVD (const Matrix2 &A, Matrix2 &U, Vector2 &W, Matrix2 &V)
bool	SVD (const Matrix3 &A, Matrix3 &U, Vector3 &W, Matrix3 &V)
bool	SVD (const Matrix4 &A, Matrix4 &U, Vector4 &W, Matrix4 &V)
void	Eigenvalues (const Matrix2 &A, Complex &lambda1, Complex &lambda2)
bool	Eigenvalues (const Matrix2 &A, Real &lambda1, Real &lambda2)
bool	Eigendecomposition (const Matrix2 &A, Vector2 &lambda, Matrix2 &Q)
bool	Eigendecomposition (const Matrix3 &A, Vector3 &lambda, Matrix3 &Q)
bool	Eigendecomposition (const Matrix4 &A, Vector4 &lambda, Matrix4 &Q)
void	Eigenvalues (const Matrix3 &A, Complex &lambda1, Complex &lambda2, Complex &lambda3)
bool	Eigenvalues (const Matrix3 &A, Real &lambda1, Real &lambda2, Real &lambda3)
template<class VT , int n>
bool	LinearlyDependent_Robust_Template (const VT &a, const VT &b, Real &c, bool &cb, Real eps)
bool	LinearlyDependent_Robust (const Vector2 &a, const Vector2 &b, Real &c, bool &cb, Real eps)
bool	LinearlyDependent_Robust (const Vector3 &a, const Vector3 &b, Real &c, bool &cb, Real eps)
bool	LinearlyDependent_Robust (const Vector4 &a, const Vector4 &b, Real &c, bool &cb, Real eps)
void	matrix4_zero (matrix4_t x)
void	matrix4_identity (matrix4_t x)
void	matrix4_from_basis (matrix4_t x, const vec4_t xbasis, const vec4_t ybasis, const vec4_t zbasis, const vec4_t trans)
void	matrix4_to_basis (const matrix4_t x, vec4_t xbasis, vec4_t ybasis, vec4_t zbasis, vec4_t trans)
void	matrix4_equal (matrix4_t x, const matrix4_t a)
void	matrix4_add (matrix4_t x, const matrix4_t a, const matrix4_t b)
void	matrix4_sub (matrix4_t x, const matrix4_t a, const matrix4_t b)
void	matrix4_multiply (matrix4_t x, const matrix4_t a, const matrix4_t b)
void	matrix4_transpose (matrix4_t x, const matrix4_t a)
void	matrix4_vec3_multiply (vec3_t x, const matrix4_t a, const vec3_t v)
void	matrix4_normal_multiply (vec3_t x, const matrix4_t a, const vec3_t v)
void	matrix4_vec3_multiply_transpose (vec3_t x, const matrix4_t a, const vec3_t v)
void	matrix4_vec4_multiply (vec4_t x, const matrix4_t a, const vec4_t v)
void	matrix4_scale3 (matrix4_t x, Real scale)
void	matrix4_scale3 (matrix4_t x, const vec3_t v_scale)
Real	matrix3_determinant (const matrix4_t a)
void	matrix4_cross_product (matrix4_t x, const vec3_t v)
void	matrix4_uncross (vec3_t x, const matrix4_t a)
void	matrix4_invert (matrix4_t x, const matrix4_t a)
void	matrix4_rotation (matrix4_t x, const vec3_t r)
void	matrix4_rotation_axis (vec3_t r, const matrix4_t R)
void	matrix4_rotate_x (matrix4_t x, Real fRads)
void	matrix4_rotate_y (matrix4_t x, Real fRads)
void	matrix4_rotate_z (matrix4_t x, Real fRads)
void	matrix4_projection (matrix4_t x, const vec3_t v)
void	matrix4_plane_projection (matrix4_t x, const vec4_t p, vec3_t v)
void	matrix4_rigid_body_inverse (matrix4_t x, const matrix4_t a)
bool	IsFinite (const Vector2 &x)
bool	IsFinite (const Vector3 &x)
bool	IsFinite (const Vector4 &x)
bool	IsFinite (const Matrix2 &R)
bool	IsFinite (const Matrix3 &R)
bool	IsFinite (const Matrix4 &R)
bool	IsInf (const Vector2 &x)
bool	IsInf (const Vector3 &x)
bool	IsInf (const Vector4 &x)
bool	IsInf (const Matrix2 &R)
bool	IsInf (const Matrix3 &R)
bool	IsInf (const Matrix4 &R)
bool	FuzzyZero (const Vector2 &x, Real tol=Epsilon)
bool	FuzzyZero (const Vector3 &x, Real tol=Epsilon)
bool	FuzzyZero (const Vector4 &x, Real tol=Epsilon)
template<class V >
bool	NormLess (const V &x, Real d)
template<class V >
bool	NormLEQ (const V &x, Real d)
template<class V >
bool	NormGreater (const V &x, Real d)
template<class V >
bool	NormGEQ (const V &x, Real d)
template<class V >
bool	DistanceLess (const V &x, const V &y, Real d)
template<class V >
bool	DistanceLEQ (const V &x, const V &y, Real d)
template<class V >
bool	DistanceGreater (const V &x, const V &y, Real d)
template<class V >
bool	DistanceGEQ (const V &x, const V &y, Real d)
Real	Orient2D (const Vector2 &p0, const Vector2 &p1, const Vector2 &p2)
	Orientation test for 2d points. More...
Real	DistanceSquared2D (Real x1, Real y1, Real x2, Real y2)
Real	Distance2D (Real x1, Real y1, Real x2, Real y2)
bool	IsSymmetric (const Matrix2 &R, Real tol=Epsilon)
bool	IsSymmetric (const Matrix3 &R, Real tol=Epsilon)
bool	IsSymmetric (const Matrix4 &R, Real tol=Epsilon)
bool	IsUpperTriangular (const Matrix2 &R, Real tol=Epsilon)
bool	IsUpperTriangular (const Matrix3 &R, Real tol=Epsilon)
bool	IsUpperTriangular (const Matrix4 &R, Real tol=Epsilon)
ostream &	operator<< (ostream &out, const Plane3D &p)
istream &	operator>> (istream &in, Plane3D &p)
std::ostream &	operator<< (std::ostream &out, const Plane3D &p)
std::istream &	operator>> (std::istream &out, Plane3D &p)
void	PolarToRectangular (const Vector2 &polar, Vector2 &rect)
void	RectangularToPolar (const Vector2 &rect, Vector2 &polar)
void	CylindricalToRectangular (const Vector3 &cyl, Vector3 &rect)
void	RectangularToCylindrical (const Vector3 &rect, Vector3 &cyl)
void	SphericalToRectangular (const Vector3 &sphere, Vector3 &rect)
void	RectangularToSpherical (const Vector3 &rect, Vector3 &sphere)
void	PolarDR (const Vector2 &polar, Vector2 &drect)
void	PolarDTheta (const Vector2 &polar, Vector2 &drect)
void	CylindricalDR (const Vector3 &cyl, Vector3 &drect)
void	CylindricalDTheta (const Vector3 &cyl, Vector3 &drect)
void	CylindricalDZ (const Vector3 &cyl, Vector3 &drect)
void	SphericalDR (const Vector3 &sphere, Vector3 &drect)
void	SphericalDTheta (const Vector3 &sphere, Vector3 &drect)
void	SphericalDPhi (const Vector3 &sphere, Vector3 &drect)
std::ostream &	operator<< (std::ostream &out, const Polygon3D &b)
std::istream &	operator>> (std::istream &in, Polygon3D &b)
std::ostream &	operator<< (std::ostream &out, const Vector2 &v)
std::istream &	operator>> (std::istream &in, Vector2 &v)
std::ostream &	operator<< (std::ostream &out, const Vector3 &v)
std::istream &	operator>> (std::istream &in, Vector3 &v)
std::ostream &	operator<< (std::ostream &out, const Vector4 &v)
std::istream &	operator>> (std::istream &in, Vector4 &v)
std::ostream &	operator<< (std::ostream &out, const Matrix2 &m)
std::istream &	operator>> (std::istream &in, Matrix2 &m)
std::ostream &	operator<< (std::ostream &out, const Matrix3 &m)
std::istream &	operator>> (std::istream &in, Matrix3 &m)
std::ostream &	operator<< (std::ostream &out, const Matrix4 &m)
std::istream &	operator>> (std::istream &in, Matrix4 &m)
std::ostream &	operator<< (std::ostream &out, const RigidTransform &x)
std::istream &	operator>> (std::istream &in, RigidTransform &x)
std::ostream &	operator<< (std::ostream &out, const RigidTransform2D &x)
std::istream &	operator>> (std::istream &in, RigidTransform2D &x)
Real	dot (const Vector2 &a, const Vector2 &b)
Real	cross (const Vector2 &a, const Vector2 &b)
void	normalize (Vector2 &a)
Vector2	project (const Vector2 &a, const Vector2 &b)
Vector2	operator- (const Vector2 &a)
Vector2	operator+ (const Vector2 &a, const Vector2 &b)
Vector2	operator- (const Vector2 &a, const Vector2 &b)
Vector2	operator* (const Vector2 &a, Real b)
Vector2	operator* (Real a, const Vector2 &b)
Vector2	operator/ (const Vector2 &a, Real b)
Real	dot (const Vector3 &a, const Vector3 &b)
Vector3	cross (const Vector3 &a, const Vector3 &b)
void	normalize (Vector3 &a)
Vector3	project (const Vector3 &a, const Vector3 &b)
Vector3	operator- (const Vector3 &a)
Vector3	operator+ (const Vector3 &a, const Vector3 &b)
Vector3	operator- (const Vector3 &a, const Vector3 &b)
Vector3	operator* (const Vector3 &a, Real b)
Vector3	operator* (Real a, const Vector3 &b)
Vector3	operator/ (const Vector3 &a, Real b)
Real	dot (const Vector4 &a, const Vector4 &b)
Real	dot3 (const Vector4 &a, const Vector4 &b)
Real	dot3 (const Vector4 &a, const Vector3 &b)
Real	dot3 (const Vector3 &a, const Vector4 &b)
void	normalize (Vector4 &a)
Vector4	project (const Vector4 &a, const Vector4 &b)
Vector4	operator- (const Vector4 &a)
Vector4	operator+ (const Vector4 &a, const Vector4 &b)
Vector4	operator- (const Vector4 &a, const Vector4 &b)
Vector4	operator* (const Vector4 &a, Real b)
Vector4	operator* (Real a, const Vector4 &b)
Vector4	operator/ (const Vector4 &a, Real b)
Real	determinant (const Matrix2 &)
Real	trace (const Matrix2 &)
Matrix2	operator+ (const Matrix2 &a, const Matrix2 &b)
Matrix2	operator- (const Matrix2 &a, const Matrix2 &b)
Matrix2	operator* (const Matrix2 &a, const Matrix2 &b)
Vector2	operator* (const Matrix2 &a, const Vector2 &b)
Vector2	operator* (const Vector2 &a, const Matrix2 &b)
Real	determinant (const Matrix3 &)
Real	trace (const Matrix3 &)
Matrix3	operator+ (const Matrix3 &a, const Matrix3 &b)
Matrix3	operator- (const Matrix3 &a, const Matrix3 &b)
Matrix3	operator* (const Matrix3 &a, const Matrix3 &b)
Vector3	operator* (const Matrix3 &a, const Vector3 &b)
Vector3	operator* (const Vector3 &a, const Matrix3 &b)
Real	determinant (const Matrix4 &)
Real	trace (const Matrix4 &)
Matrix4	operator+ (const Matrix4 &a, const Matrix4 &b)
Matrix4	operator- (const Matrix4 &a, const Matrix4 &b)
Matrix4	operator* (const Matrix4 &a, const Matrix4 &b)
Vector4	operator* (const Matrix4 &a, const Vector4 &b)
Vector4	operator* (const Vector4 &a, const Matrix4 &b)
Vector3	operator* (const Matrix4 &a, const Vector3 &b)
	WARNING: vector multiply.
Vector3	operator* (const Vector3 &a, const Matrix4 &b)
	WARNING: vector multiply (transpose)
RigidTransform	operator* (const RigidTransform &, const RigidTransform &)
RigidTransform	operator* (const RigidTransform &, const Matrix3 &)
RigidTransform	operator* (const Matrix3 &a, const RigidTransform &b)
Vector3	operator* (const RigidTransform &, const Vector3 &)
RigidTransform	operator+ (const RigidTransform &, const Vector3 &)
RigidTransform	operator- (const RigidTransform &, const Vector3 &)
RigidTransform2D	operator* (const RigidTransform2D &, const RigidTransform2D &)
Vector2	operator* (const RigidTransform2D &, const Vector2 &)
Matrix2	transpose (const Matrix2 &m)
Matrix2	inverse (const Matrix2 &m)
Matrix2	outerProduct (const Vector2 &a, const Vector2 &b)
Matrix2	operator* (const Matrix2 &a, Real b)
Matrix2	operator/ (const Matrix2 &a, Real b)
Matrix3	transpose (const Matrix3 &m)
Matrix3	inverse (const Matrix3 &m)
Matrix3	outerProduct (const Vector3 &a, const Vector3 &b)
Matrix3	operator* (const Matrix3 &a, Real b)
Matrix3	operator/ (const Matrix3 &a, Real b)
Matrix4	transpose (const Matrix4 &m)
Matrix4	inverse (const Matrix4 &m)
Matrix4	outerProduct (const Vector4 &a, const Vector4 &b)
Matrix4	operator* (const Matrix4 &a, Real b)
Matrix4	operator/ (const Matrix4 &a, Real b)
void	quat_slerp (quat_t out, const quat_t a, const quat_t b, Real t)
void	RandRotation (Quaternion &q)
void	SampleCircle (Real r, Vector2 &v)
void	SampleDisk (Real r, Vector2 &v)
void	SampleSphere (Real r, Vector3 &v)
void	SampleBall (Real r, Vector3 &v)
void	SampleSquare (Real d, Vector2 &v)
void	SampleCube (Real d, Vector3 &v)
void	SampleHyperCube (Real d, Vector4 &v)
void	SampleAABB (const Vector2 &bmin, const Vector2 &bmax, Vector2 &v)
void	SampleAABB (const Vector3 &bmin, const Vector3 &bmax, Vector3 &v)
void	SampleAABB (const Vector4 &bmin, const Vector4 &bmax, Vector4 &v)
Vector2	SampleCircle (Real r)
Vector2	SampleDisk (Real r)
Vector3	SampleSphere (Real r)
Vector3	SampleBall (Real r)
Vector2	SampleSquare (Real d)
Vector3	SampleCube (Real d)
Vector4	SampleHyperCube (Real d)
Vector2	SampleAABB (const Vector2 &bmin, const Vector2 &bmax)
Vector3	SampleAABB (const Vector3 &bmin, const Vector3 &bmax)
Vector4	SampleAABB (const Vector4 &bmin, const Vector4 &bmax)
Quaternion	RandRotation ()
void	SLerp (const Quaternion &q0, const Quaternion &q1, Quaternion &out, Real t)
	Linear quaternion rotation interpolation.
void	SCerp (const Quaternion &q_1, const Quaternion &q0, const Quaternion &q1, const Quaternion &q2, Quaternion &out, Real t)
	Cubic quaternion rotation interpolation.
void	SBezier (const Quaternion &q0, const Quaternion &c0, const Quaternion &c1, const Quaternion &q1, Quaternion &out, Real t)
	Bezier-style quaternion rotation interpolation. More...
void	SetMatrixRotationZYX (Matrix3 &m, const Vector3 &v)
void	SetMatrixRotationZYX (Matrix4 &m, const Vector3 &v)
void	SetMatrixRotationVector (Matrix3 &m, const Vector3 &v)
void	SetMatrixRotationVector (Matrix4 &m, const Vector3 &v)
void	SetMatrixRotationVector (Matrix3 &m, const Vector3 &v, Real angle)
void	SetMatrixRotationVector (Matrix4 &m, const Vector3 &v, Real angle)
void	SetMatrixRotationQuaternion (Matrix3 &m, const Quaternion &q)
void	SetMatrixRotationQuaternion (Matrix4 &m, const Quaternion &q)
Real	RotationFit (const vector< Vector3 > &a, const vector< Vector3 > &b, Matrix3 &R)
	Calculates the least squares rotation fit min_R sum||R*a[i]-b[i]||^2. Returns the sum-of-squared errors.
void	AxisRotationFit (const std::vector< Vector3 > &a, const std::vector< Vector3 > &b, const Vector3 &z, Real &theta)
	Calculates the least squares rotation angle min_theta sum||R(theta,z)*a[i]-b[i]||^2.
Real	TransformFit (vector< Vector3 > &a, vector< Vector3 > &b, Matrix3 &R, Vector3 &t)
	Calculate the least squares rotation fit min_R,t sum||R*a[i]+t-b[i]||^2. Returns the sum-of-squared errors. More...
Real	WeightedTransformFit (const vector< Point3D > &a, const vector< Point3D > &b, const vector< Real > &w, const vector< Vector3 > &c, const vector< Vector3 > &d, const vector< Real > &v, Matrix3 &R, Vector3 &t)
	Solve the mixed point/vector fitting problem min sum_j wj||R*aj+t-bj||^2 + sum_k vk||Rc-d||^2. More...
Real	FitFrames (const std::vector< Vector3 > &a, const std::vector< Vector3 > &b, RigidTransform &Ta, RigidTransform &Tb, Vector3 &cov)
	Calculate the translations and rotations that match a,b in an axis-aligned frame. The cov vector stores the covariance in each axis.
Real	RotationFit (const std::vector< Vector3 > &a, const std::vector< Vector3 > &b, Matrix3 &R)
	Calculates the least squares rotation fit min_R sum||R*a[i]-b[i]||^2. Returns the sum-of-squared errors.
Real	TransformFit (std::vector< Vector3 > &a, std::vector< Vector3 > &b, Matrix3 &R, Vector3 &t)
	Calculate the least squares rotation fit min_R,t sum||R*a[i]+t-b[i]||^2. Returns the sum-of-squared errors. More...
Real	WeightedTransformFit (const std::vector< Point3D > &a, const std::vector< Point3D > &b, const std::vector< Real > &w, const std::vector< Vector3 > &c, const std::vector< Vector3 > &d, const std::vector< Real > &v, Matrix3 &R, Vector3 &t)
	Solve the mixed point/vector fitting problem min sum_j wj||R*aj+t-bj||^2 + sum_k vk||Rc-d||^2. More...
ostream &	operator<< (ostream &out, const Segment3D &s)
istream &	operator>> (istream &in, Segment3D &s)
std::ostream &	operator<< (std::ostream &out, const Segment3D &s)
std::istream &	operator>> (std::istream &in, Segment3D &s)
ostream &	operator<< (ostream &out, const Triangle3D &tri)
istream &	operator>> (istream &in, Triangle3D &tri)
std::ostream &	operator<< (std::ostream &out, const Triangle3D &tri)
std::istream &	operator>> (std::istream &in, Triangle3D &tri)
void	vec2_zero (vec2_t x)
void	vec2_make (vec2_t x, Real a, Real b)
void	vec2_equal (vec2_t x, const vec2_t a)
void	vec2_add (vec2_t x, const vec2_t a, const vec2_t b)
void	vec2_sub (vec2_t x, const vec2_t a, const vec2_t b)
void	vec2_multiply (vec2_t x, const vec2_t a, Real c)
void	vec2_madd (vec2_t x, const vec2_t a, Real c)
void	vec2_negate (vec2_t x, const vec2_t a)
Real	vec2_dot (const vec2_t a, const vec2_t b)
float	vec2_cross (const vec2_t a, const vec2_t b)
Real	vec2_length (const vec2_t x)
void	vec2_normalize (vec2_t x)
void	vec2_project (vec2_t x, const vec2_t a, const vec2_t b)
void	vec3_zero (vec3_t x)
void	vec3_make (vec3_t x, Real a, Real b, Real c)
void	vec3_equal (vec3_t x, const vec3_t a)
void	vec3_add (vec3_t x, const vec3_t a, const vec3_t b)
void	vec3_sub (vec3_t x, const vec3_t a, const vec3_t b)
void	vec3_multiply (vec3_t x, const vec3_t a, Real c)
void	vec3_madd (vec3_t x, const vec3_t a, Real c)
void	vec3_negate (vec3_t x, const vec3_t a)
Real	vec3_dot (const vec3_t a, const vec3_t b)
void	vec3_cross (vec3_t x, const vec3_t a, const vec3_t b)
Real	vec3_length (const vec3_t x)
void	vec3_normalize (vec3_t x)
void	vec3_project (vec3_t x, const vec3_t a, const vec3_t b)
void	vec4_zero (vec4_t x)
void	vec4_make (vec4_t x, Real a, Real b, Real c, Real d)
void	vec4_equal (vec4_t x, const vec4_t a)
void	vec4_add (vec4_t x, const vec4_t a, const vec4_t b)
void	vec4_sub (vec4_t x, const vec4_t a, const vec4_t b)
void	vec4_multiply (vec4_t x, const vec4_t a, Real c)
void	vec4_madd (vec4_t x, const vec4_t a, Real c)
void	vec4_negate (vec4_t x, const vec4_t a)
Real	vec4_dot (const vec4_t a, const vec4_t b)
void	vec4_normalize (vec4_t x)
void	vec4_plane_project (vec4_t x, const vec4_t a, const vec4_t b)

Detailed Description

Contains all the definitions in the Math3D package.