Bembel::Patch Class Reference

handles a single patch More...

#include <Patch.hpp>

Detailed Description

handles a single patch

Definition at line 20 of file Patch.hpp.

Public Member Functions
	Patch ()
	constructors More...
	Patch (const std::vector< Eigen::Matrix< double, -1, -1 >> &control_points, const std::vector< double > &knots_x, const std::vector< double > &knots_y)
	Constructor of a Patch. More...
void	init_Patch (const std::vector< Eigen::Matrix< double, -1, -1 >> &xyzw, const std::vector< double > &x_knots, const std::vector< double > &y_knots)
	init More...
Eigen::Vector3d	eval (const Eigen::Vector2d &reference_point) const
	Evaluate patch at given point. More...
Eigen::Matrix< double, 3, 2 >	evalJacobian (const Eigen::Vector2d &reference_point) const
	Evaluate Jacobian of the parametrization at given point. More...
Eigen::Matrix< double, 3, 1 >	evalNormal (const Eigen::Vector2d &reference_point) const
	Evaluate normal vector at given point. More...
Eigen::Vector3d	eval (double x, double y) const
	Evaluate patch at given point. More...
Eigen::Matrix< double, 3, 2 >	evalJacobian (double x, double y) const
	Evaluate Jacobian of the parametrization at given point. More...
Eigen::Matrix< double, 3, 1 >	evalNormal (double x, double y) const
	Evaluate normal vector at given point. More...
void	updateSurfacePoint (SurfacePoint *srf_pt, const Eigen::Vector2d &ref_pt, double w, const Eigen::Vector2d &xi) const
	Updates the surface point and returns the physical point and the derivatives there. More...

Public Attributes
std::vector< double >	data_
	getter
int	polynomial_degree_x_
int	polynomial_degree_y_
std::vector< double >	unique_knots_x_
std::vector< double >	unique_knots_y_

Constructor & Destructor Documentation

Patch() [1/2]

Bembel::Patch::Patch ( )

inline

constructors

Default constructor.

Definition at line 28 of file Patch.hpp.

Patch() [2/2]

Bembel::Patch::Patch ( const std::vector< Eigen::Matrix< double, -1, -1 >> &  control_points, const std::vector< double > &  knots_x, const std::vector< double > &  knots_y  )

inline

Constructor of a Patch.

A patch is defined by a set of control points and knot vectors in the x and y directions. It is used to create complex surfaces in computer graphics and CAD applications.

Parameters

control_points	std::vector<Eigen::MatrixXd> {x, y, z, w} where the rows are the control points in x direction.
knots_x	The knot vector in the x direction.
knots_y	The knot vector in the y direction.

Definition at line 42 of file Patch.hpp.

Member Function Documentation

eval() [1/2]

Eigen::Vector3d Bembel::Patch::eval ( const Eigen::Vector2d &  reference_point ) const

inline

Evaluate patch at given point.

I look up the position in the knot vector, scale the input arguments, evaluate the 1D basis functions and sum over them with the control points from data.

Parameters

reference_point

Point in reference domain.

Returns

Point in physical domain.

Definition at line 115 of file Patch.hpp.

eval() [2/2]

Eigen::Vector3d Bembel::Patch::eval ( double  x, double  y  ) const

inline

Evaluate patch at given point.

I look up the position in the knot vector, scale the input arguments, evaluate the 1D basis functions and sum over them with the control points from data.

Parameters

x	Coordinate in reference domain.
y	Coordinate in reference domain.

Returns

Point in physical domain.

Definition at line 257 of file Patch.hpp.

evalJacobian() [1/2]

Eigen::Matrix<double, 3, 2> Bembel::Patch::evalJacobian ( const Eigen::Vector2d &  reference_point ) const

inline

Evaluate Jacobian of the parametrization at given point.

Parameters

reference_point

Point in reference domain.

Returns

3x2 Matrix with the Jacobian.

Definition at line 163 of file Patch.hpp.

evalJacobian() [2/2]

Eigen::Matrix<double, 3, 2> Bembel::Patch::evalJacobian ( double  x, double  y  ) const

inline

Evaluate Jacobian of the parametrization at given point.

Parameters

x	Coordinate in reference domain.
y	Coordinate in reference domain.

Returns

3x2 Matrix with the Jacobian.

Definition at line 267 of file Patch.hpp.

evalNormal() [1/2]

Eigen::Matrix<double, 3, 1> Bembel::Patch::evalNormal ( const Eigen::Vector2d &  reference_point ) const

inline

Evaluate normal vector at given point.

Parameters

reference_point

Point in reference domain.

Returns

3x1 normal vector.

Definition at line 240 of file Patch.hpp.

evalNormal() [2/2]

Eigen::Matrix<double, 3, 1> Bembel::Patch::evalNormal ( double  x, double  y  ) const

inline

Evaluate normal vector at given point.

Parameters

x	Coordinate in reference domain.
y	Coordinate in reference domain.

Returns

3x1 normal vector.

Definition at line 277 of file Patch.hpp.

init_Patch()

void Bembel::Patch::init_Patch ( const std::vector< Eigen::Matrix< double, -1, -1 >> &  xyzw, const std::vector< double > &  x_knots, const std::vector< double > &  y_knots  )

inline

init

Initializes a Patch.

A patch is defined by a set of control points and knot vectors in the x and y directions. It is used to create complex surfaces in computer graphics and CAD applications.

Parameters

xyzw	std::vector<Eigen::MatrixXd> {x, y, z, w} where the rows are the control points in x direction.
x_knots	The knot vector in the x direction.
y_knots	The knot vector in the y direction.

Definition at line 63 of file Patch.hpp.

updateSurfacePoint()

void Bembel::Patch::updateSurfacePoint ( SurfacePoint *  srf_pt, const Eigen::Vector2d &  ref_pt, double  w, const Eigen::Vector2d &  xi  ) const

inline

Updates the surface point and returns the physical point and the derivatives there.

This is a combination of eval und evalJacobian, to avoid duplication of work.

Parameters

srf_pt	Pointer to the SurfacePoint which gets updated.
ref_pt	Point in reference domain with respect to the patch.
w	quadrature weight.
xi	Point in reference domain with respect to the element.

Definition at line 294 of file Patch.hpp.

---

The documentation for this class was generated from the following file:

• Bembel/src/Geometry/Patch.hpp