mm::cad_helpers Namespace Reference

Detailed Description

Namespace for helper functions used in CAD.

Functions
template<typename scalar_t , int dim>
Vec< scalar_t, dim >	evaluate_b_spline (scalar_t t, int p, const Range< Vec< scalar_t, dim >> &control_points, const Range< scalar_t > &knots, int k)
	Evaluate B-spline in one point using De Boor's algorithm - \(\mathcal{O}(d p^2)\), where \(d\) is the number of dimensions. More...
template<typename scalar_t , int dim>
Vec< scalar_t, dim >	evaluate_b_spline (scalar_t t, int p, const Range< Vec< scalar_t, dim >> &control_points, const Range< scalar_t > &knots, scalar_t epsilon=1e-10)
	Overload with binary search for position of t in knots. More...
template<typename scalar_t , int dim>
void	generate_b_spline_derivative (int p, const Range< Vec< scalar_t, dim >> &control_points, const Range< scalar_t > &knots, Range< Vec< scalar_t, dim >> &der_control_points, Range< scalar_t > &der_knots)
	Generate control points and knot vector of a B-spline that is the first derivative of the inputed B-spline. More...
template<typename scalar_t , int dim>
void	generate_b_spline_derivative_control_points (int p, const Range< Vec< scalar_t, dim >> &control_points, const Range< scalar_t > &knots, Range< Vec< scalar_t, dim >> &der_control_points)
	Generate control points of a B-spline that is the first derivative of the inputed B-spline. More...
template<typename scalar_t >
void	generate_b_spline_derivative_knots (const Range< scalar_t > &knots, Range< scalar_t > &der_knots)
	Generate knots of a B-spline that is the first derivative of the inputed B-spline. More...

Function Documentation

evaluate_b_spline() [1/2]

template<typename scalar_t , int dim>

Vec< scalar_t, dim > mm::cad_helpers::evaluate_b_spline	(	scalar_t	t,
		int	p,
		const Range< Vec< scalar_t, dim >> &	control_points,
		const Range< scalar_t > &	knots,
		int	k
	)

Evaluate B-spline in one point using De Boor's algorithm - \(\mathcal{O}(d p^2)\), where \(d\) is the number of dimensions.

Adds additional time complexity of \(\mathcal{O}(\log |\mathrm{knots}|)\) if k is not given.

Template Parameters

scalar_t	Numeric scalar type, e.g. double or float.
dim	Space dimension.

Parameters

p	B-spline order (starting from order 0).
t	Point of evaluation.
control_points	Range of control points.
knots	Knot vector.
k	Position of t in the knot vector, such that control_points[k] <= t < control_points[k]

Returns

Vector to the point on the B-spline corresponding to parameter t.

Examples

test/domains/cad_helpers_test.cpp.

Definition at line 18 of file cad_helpers.hpp.

evaluate_b_spline() [2/2]

template<typename scalar_t , int dim>

Vec< scalar_t, dim > mm::cad_helpers::evaluate_b_spline	(	scalar_t	t,
		int	p,
		const Range< Vec< scalar_t, dim >> &	control_points,
		const Range< scalar_t > &	knots,
		scalar_t	epsilon = 1e-10
	)

Overload with binary search for position of t in knots.

If parameter is outside the domain by epsilon, translate it back to the edge of the domain.

Definition at line 44 of file cad_helpers.hpp.

generate_b_spline_derivative()

template<typename scalar_t , int dim>

void mm::cad_helpers::generate_b_spline_derivative	(	int	p,
		const Range< Vec< scalar_t, dim >> &	control_points,
		const Range< scalar_t > &	knots,
		Range< Vec< scalar_t, dim >> &	der_control_points,
		Range< scalar_t > &	der_knots
	)

Generate control points and knot vector of a B-spline that is the first derivative of the inputed B-spline.

Note that its degree is p - 1.

Template Parameters

scalar_t	Numeric scalar type, e.g. double or float.
dim	Space dimension.

Parameters

p	B-spline order (starting from order 0).
control_points	Range of control points.
knots	Knot vector.
der_control_points	Range for derivative control points.
der_knots	Range for derivative knots.

Examples

test/domains/cad_helpers_test.cpp.

Definition at line 61 of file cad_helpers.hpp.

generate_b_spline_derivative_control_points()

template<typename scalar_t , int dim>

void mm::cad_helpers::generate_b_spline_derivative_control_points	(	int	p,
		const Range< Vec< scalar_t, dim >> &	control_points,
		const Range< scalar_t > &	knots,
		Range< Vec< scalar_t, dim >> &	der_control_points
	)

Generate control points of a B-spline that is the first derivative of the inputed B-spline.

Note that its degree is p - 1.

Template Parameters

scalar_t	Numeric scalar type, e.g. double or float.
dim	Space dimension.

Parameters

p	B-spline order (starting from order 0).
control_points	Range of control points.
knots	Knot vector.
der_control_points	Range for derivative control points.

Definition at line 69 of file cad_helpers.hpp.

generate_b_spline_derivative_knots()

template<typename scalar_t >

void mm::cad_helpers::generate_b_spline_derivative_knots	(	const Range< scalar_t > &	knots,
		Range< scalar_t > &	der_knots
	)

Generate knots of a B-spline that is the first derivative of the inputed B-spline.

Note that its degree is p - 1.

Template Parameters

scalar_t

Numeric scalar type, e.g. double or float.

Parameters

knots	Knot vector.
der_knots	Range for derivative knots.

Definition at line 85 of file cad_helpers.hpp.