igl::cycodebase Namespace Reference

Functions
template<typename DerivedC, typename DerivedB>
void	box_cubic (const Eigen::MatrixBase< DerivedC > &C, Eigen::PlainObjectBase< DerivedB > &B1, Eigen::PlainObjectBase< DerivedB > &B2)
	Compute the min/max box corners tightly containing a given cubic bezier curve.
template<typename DerivedP, typename DerivedC, typename DerivedB>
void	box_cubic (const Eigen::MatrixBase< DerivedP > &P, const Eigen::MatrixBase< DerivedC > &C, Eigen::PlainObjectBase< DerivedB > &B1, Eigen::PlainObjectBase< DerivedB > &B2)
	overload
template<typename DerivedQ, typename DerivedC, typename DerivedsqrD, typename DerivedS, typename DerivedK>
void	point_cubic_squared_distance (const Eigen::MatrixBase< DerivedQ > &Q, const Eigen::MatrixBase< DerivedC > &C, Eigen::PlainObjectBase< DerivedsqrD > &sqrD, Eigen::PlainObjectBase< DerivedS > &S, Eigen::PlainObjectBase< DerivedK > &K)
	Compute the squared distance from a set of points to a cubic Bezier curve.
template<typename DerivedQ, typename DerivedC, typename DerivedD, typename DerivedB, typename DerivedsqrD, typename DerivedS, typename DerivedK>
void	point_cubic_squared_distance (const Eigen::MatrixBase< DerivedQ > &Q, const Eigen::MatrixBase< DerivedC > &C, const Eigen::MatrixBase< DerivedD > &D, const Eigen::MatrixBase< DerivedB > &B, Eigen::PlainObjectBase< DerivedsqrD > &sqrD, Eigen::PlainObjectBase< DerivedS > &S, Eigen::PlainObjectBase< DerivedK > &K)
	overload
template<typename Derivedq, typename DerivedC, typename DerivedD, typename DerivedB, typename Derivedk>
void	point_cubic_squared_distance (const Eigen::MatrixBase< Derivedq > &q, const Eigen::MatrixBase< DerivedC > &C, const Eigen::MatrixBase< DerivedD > &D, const Eigen::MatrixBase< DerivedB > &B, typename Derivedq::Scalar &sqrD, typename Derivedq::Scalar &s, Eigen::PlainObjectBase< Derivedk > &k)
	single point overload
template<typename Derivedq, typename DerivedC, typename Derivedk>
void	point_cubic_squared_distance (const Eigen::MatrixBase< Derivedq > &q, const Eigen::MatrixBase< DerivedC > &C, typename Derivedq::Scalar &sqrD, typename Derivedq::Scalar &s, Eigen::PlainObjectBase< Derivedk > &k)
	single point overload
template<typename DerivedQ, typename DerivedP, typename DerivedC, typename DerivedsqrD, typename DerivedI, typename DerivedS, typename DerivedK>
void	point_spline_squared_distance (const Eigen::MatrixBase< DerivedQ > &Q, const Eigen::MatrixBase< DerivedP > &P, const Eigen::MatrixBase< DerivedC > &C, Eigen::PlainObjectBase< DerivedsqrD > &sqrD, Eigen::PlainObjectBase< DerivedI > &I, Eigen::PlainObjectBase< DerivedS > &S, Eigen::PlainObjectBase< DerivedK > &K)
	Compute the squared distance from a set of points to a spline defined by cubic Bezier curves.
template<typename DerivedQ, typename DerivedP, typename DerivedC, typename DerivedB, typename Derivedleaf, typename DerivedsqrD, typename DerivedI, typename DerivedS, typename DerivedK>
void	point_spline_squared_distance (const Eigen::MatrixBase< DerivedQ > &Q, const Eigen::MatrixBase< DerivedP > &P, const Eigen::MatrixBase< DerivedC > &C, const Eigen::MatrixBase< DerivedB > &B1, const Eigen::MatrixBase< DerivedB > &B2, const Eigen::MatrixBase< Derivedleaf > &leaf, Eigen::PlainObjectBase< DerivedsqrD > &sqrD, Eigen::PlainObjectBase< DerivedI > &I, Eigen::PlainObjectBase< DerivedS > &S, Eigen::PlainObjectBase< DerivedK > &K)
	overload with AABB acceleration structure
template<typename Derivedcoef, typename DerivedR>
int	roots (const Eigen::MatrixBase< Derivedcoef > &coef, const typename Derivedcoef::Scalar xmin, const typename Derivedcoef::Scalar xmax, Eigen::PlainObjectBase< DerivedR > &R)
	Compute the real roots of a polynomial with given coefficients within a given interval [xmin, xmax].
template<typename DerivedP, typename DerivedC, typename DerivedB, typename Derivedleaf>
void	spline_eytzinger_aabb (const Eigen::MatrixBase< DerivedP > &P, const Eigen::MatrixBase< DerivedC > &C, Eigen::PlainObjectBase< DerivedB > &B1, Eigen::PlainObjectBase< DerivedB > &B2, Eigen::PlainObjectBase< Derivedleaf > &leaf)
	Compute an AABB acceleration structure for a spline of cubic Bezier curves in Eytzinger layout.

Function Documentation

box_cubic() [1/2]

template<typename DerivedC, typename DerivedB>

void igl::cycodebase::box_cubic	(	const Eigen::MatrixBase< DerivedC > &	C,
		Eigen::PlainObjectBase< DerivedB > &	B1,
		Eigen::PlainObjectBase< DerivedB > &	B2 )

Compute the min/max box corners tightly containing a given cubic bezier curve.

Parameters

[in]	C	4 by dim matrix of control points defining the cubic bezier curve
[out]	B1	1 by dim min corner of the bounding box
[out]	B2	1 by dim max corner of the bounding box

See also

igl::box_simplices

box_cubic() [2/2]

template<typename DerivedP, typename DerivedC, typename DerivedB>

void igl::cycodebase::box_cubic	(	const Eigen::MatrixBase< DerivedP > &	P,
		const Eigen::MatrixBase< DerivedC > &	C,
		Eigen::PlainObjectBase< DerivedB > &	B1,
		Eigen::PlainObjectBase< DerivedB > &	B2 )

overload

Parameters

[in]	P	#P by dim matrix of control point locations
[in]	C	#C by 4 matrix of indices into P defining the cubics
[out]	B1	#C by dim matrix of min corners of the bounding boxes
[out]	B2	#C by dim matrix of max corners of the bounding boxes

point_cubic_squared_distance() [1/4]

template<typename DerivedQ, typename DerivedC, typename DerivedsqrD, typename DerivedS, typename DerivedK>

void igl::cycodebase::point_cubic_squared_distance	(	const Eigen::MatrixBase< DerivedQ > &	Q,
		const Eigen::MatrixBase< DerivedC > &	C,
		Eigen::PlainObjectBase< DerivedsqrD > &	sqrD,
		Eigen::PlainObjectBase< DerivedS > &	S,
		Eigen::PlainObjectBase< DerivedK > &	K )

Compute the squared distance from a set of points to a cubic Bezier curve.

Parameters

[in]	Q	#Q by dim matrix of query points
[in]	C	4 by dim matrix of control points defining the cubic bezier curve
[out]	sqrD	#Q vector of squared distances from each query point to the cubic bezier curve
[out]	S	#Q vector of parametric locations on the cubic bezier curve of the closest point to each query point
[out]	K	#Q by dim matrix of closest point locations

See also

igl::cubic_monomial_bases, igl::cycodebase::point_spline_squared_distance

point_cubic_squared_distance() [2/4]

template<typename DerivedQ, typename DerivedC, typename DerivedD, typename DerivedB, typename DerivedsqrD, typename DerivedS, typename DerivedK>

void igl::cycodebase::point_cubic_squared_distance	(	const Eigen::MatrixBase< DerivedQ > &	Q,
		const Eigen::MatrixBase< DerivedC > &	C,
		const Eigen::MatrixBase< DerivedD > &	D,
		const Eigen::MatrixBase< DerivedB > &	B,
		Eigen::PlainObjectBase< DerivedsqrD > &	sqrD,
		Eigen::PlainObjectBase< DerivedS > &	S,
		Eigen::PlainObjectBase< DerivedK > &	K )

overload

Parameters

[in]	D	3 by dim matrix of monomial coefficients for dC/dt
[in]	B	6-vector of inner products of monomial coefficients of C and dCdt

point_cubic_squared_distance() [3/4]

template<typename Derivedq, typename DerivedC, typename DerivedD, typename DerivedB, typename Derivedk>

void igl::cycodebase::point_cubic_squared_distance	(	const Eigen::MatrixBase< Derivedq > &	q,
		const Eigen::MatrixBase< DerivedC > &	C,
		const Eigen::MatrixBase< DerivedD > &	D,
		const Eigen::MatrixBase< DerivedB > &	B,
		typename Derivedq::Scalar &	sqrD,
		typename Derivedq::Scalar &	s,
		Eigen::PlainObjectBase< Derivedk > &	k )

single point overload

Parameters

[in]

q

dim vector of a query point

point_cubic_squared_distance() [4/4]

template<typename Derivedq, typename DerivedC, typename Derivedk>

void igl::cycodebase::point_cubic_squared_distance	(	const Eigen::MatrixBase< Derivedq > &	q,
		const Eigen::MatrixBase< DerivedC > &	C,
		typename Derivedq::Scalar &	sqrD,
		typename Derivedq::Scalar &	s,
		Eigen::PlainObjectBase< Derivedk > &	k )

single point overload

point_spline_squared_distance() [1/2]

template<typename DerivedQ, typename DerivedP, typename DerivedC, typename DerivedsqrD, typename DerivedI, typename DerivedS, typename DerivedK>

void igl::cycodebase::point_spline_squared_distance	(	const Eigen::MatrixBase< DerivedQ > &	Q,
		const Eigen::MatrixBase< DerivedP > &	P,
		const Eigen::MatrixBase< DerivedC > &	C,
		Eigen::PlainObjectBase< DerivedsqrD > &	sqrD,
		Eigen::PlainObjectBase< DerivedI > &	I,
		Eigen::PlainObjectBase< DerivedS > &	S,
		Eigen::PlainObjectBase< DerivedK > &	K )

Compute the squared distance from a set of points to a spline defined by cubic Bezier curves.

Parameters

[in]	Q	#Q by dim matrix of query points
[in]	P	#P by dim matrix of spline control points
[in]	C	#C by 4 matrix of indices into P defining the cubic bezier curves making up the spline
[out]	sqrD	#Q vector of squared distances from each query point to the spline
[out]	I	#Q vector of indices of the closest cubic bezier curve in the spline to each query point
[out]	S	#Q vector of parametric locations on the closest cubic bezier curve of the closest point to each query point
[out]	K	#Q by dim matrix of closest point locations

See also

igl::cycodebase::point_cubic_squared_distance, igl::cycodebase::spline_eytzinger_aabb

point_spline_squared_distance() [2/2]

template<typename DerivedQ, typename DerivedP, typename DerivedC, typename DerivedB, typename Derivedleaf, typename DerivedsqrD, typename DerivedI, typename DerivedS, typename DerivedK>

void igl::cycodebase::point_spline_squared_distance	(	const Eigen::MatrixBase< DerivedQ > &	Q,
		const Eigen::MatrixBase< DerivedP > &	P,
		const Eigen::MatrixBase< DerivedC > &	C,
		const Eigen::MatrixBase< DerivedB > &	B1,
		const Eigen::MatrixBase< DerivedB > &	B2,
		const Eigen::MatrixBase< Derivedleaf > &	leaf,
		Eigen::PlainObjectBase< DerivedsqrD > &	sqrD,
		Eigen::PlainObjectBase< DerivedI > &	I,
		Eigen::PlainObjectBase< DerivedS > &	S,
		Eigen::PlainObjectBase< DerivedK > &	K )

overload with AABB acceleration structure

Parameters

[in]	B1	#B by dim matrix of AABB min box corners
[in]	B2	#B by dim matrix of AABB max box corners
[in]	leaf	#B by 1 matrix of AABB leaf node indices/flags

See also

igl::eytzinger_aabb

roots()

template<typename Derivedcoef, typename DerivedR>

int igl::cycodebase::roots	(	const Eigen::MatrixBase< Derivedcoef > &	coef,
		const typename Derivedcoef::Scalar	xmin,
		const typename Derivedcoef::Scalar	xmax,
		Eigen::PlainObjectBase< DerivedR > &	R )

Compute the real roots of a polynomial with given coefficients within a given interval [xmin, xmax].

Parameters

[in]	coef	Vector of polynomial coefficients in increasing order of degree (i.e., coef[0] + coef[1]*x + coef[2]*x^2 + ... )
[in]	xmin	Minimum x value of the interval
[in]	xmax	Maximum x value of the interval
[out]	R	Vector of real roots within [xmin, xmax]

Returns

Number of real roots found within [xmin, xmax]

spline_eytzinger_aabb()

template<typename DerivedP, typename DerivedC, typename DerivedB, typename Derivedleaf>

void igl::cycodebase::spline_eytzinger_aabb	(	const Eigen::MatrixBase< DerivedP > &	P,
		const Eigen::MatrixBase< DerivedC > &	C,
		Eigen::PlainObjectBase< DerivedB > &	B1,
		Eigen::PlainObjectBase< DerivedB > &	B2,
		Eigen::PlainObjectBase< Derivedleaf > &	leaf )

Compute an AABB acceleration structure for a spline of cubic Bezier curves in Eytzinger layout.

Parameters

[in]	P	#P by dim matrix of spline control points
[in]	C	#C by 4 matrix of indices into P defining the cubic Bézier curves making up the spline
[out]	B1	#B by dim matrix of AABB min box corners
[out]	B2	#B by dim matrix of AABB max box corners
[out]	leaf	#B by 1 matrix of AABB leaf node indices/flags

See also

igl::cycodebase::box_cubic, igl::eytzinger_aabb