BezierTriangle Class Reference

#include </usr1/tp517/Tumble/trunk/src/tumble/cell.h>

Inheritance diagram for BezierTriangle:

[legend]Collaboration diagram for BezierTriangle:[legend]List of all members.


Public Types
typedef FaceCell	super
Public Member Functions
	BezierTriangle (PersistantStore &, BezierEdge *const es[3], const DataStore &, bool inverse_handed=false)
	Create a BezierTriangle.
void	set_boundary_face (BoundaryFace *f)
virtual	~BezierTriangle ()
	Destructor.
int	get_num_cp () const
const Point2D &	get_cp (int i) const
	Get the geometry of the ith control point.
Point2D &	access_cp (int i)
	Read-write access to the geometry.
void	set_cp (int i, const Point2D &p)
	Write access to the geometry.
ControlPoint	get_control_point (int i) const
int	get_num_dp () const
const LinearData &	get_dp (int i) const
	Get the data at the ith control point.
LinearData &	access_dp (int i)
	Read-write access to the data.
void	set_dp (int i, const LinearData &p)
	Write access to the data.
DataPoint	get_data_point (int i) const
int	get_num_edges () const
BezierEdge *	get_edge (int i)
	Since we always have exactly three, allow index-based retrieval of edges.
const BezierEdge *	get_edge (int i) const
bool	has_bdry_face () const
const BoundaryFace *	get_bdry_face () const
BoundaryFace *	get_bdry_face ()
BoundaryFace *	get_bdry_face_or_null ()
double	get_min_angle () const
int	get_color () const
const BezierEdge *	get_edge (int p0, int p1) const
	Get the BezierEdge that is a sub-cell of this Face, which shares the given control points.
BezierEdge *	get_edge (int p0, int p1)
Point2D	eval (double alpha, double beta) const
	Given parameters u, v, interpolate the geometric coordinates in the Bezier Basis.
LinearData	dataeval (double alpha, double beta) const
	Given parameters u, v, interpolate the functional data in the Bezier Basis.
void	evalIntermediate (double alpha, double beta, Point2D &p, Point2D &pc0, Point2D &pc1, Point2D &pc2) const
	Given a parameters u and v, interpolate the geometric coordinates in the Bezier Basis.
void	dataevalIntermediate (double alpha, double beta, LinearData &d, LinearData &dc0, LinearData &dc1, LinearData &dc2) const
	Given a parameters u and v, interpolate the functional data in the Bezier Basis.
double	jacobian (double alpha, double beta) const
	Gives the Jacobian determinate at the given barycentric coordinates.
void	jacobian_matrix (double alpha, double beta, Point2D &pdu, Point2D &pdv) const
	Gives the full Jacobian at the given barycentric coordinates.
void	bound_jacobian (double &min, double &max, double &area) const
	Approximates the jacobian determinate and the area of the triangle.
bool	newton_find (const Point2D &p, double &u, double &v, int &niter, int &edge_num)
double	area () const
	Gives the area of the BezierTriangle.
bool	small_angle () const
	Determine if angle is small.
bool	is_linear_inverted () const
int	is_inverted () const
bool	is_definitely_inverted () const
bool	is_definitely_not_inverted () const
Point2D	circumcenter () const
	Get the circumcenter of this triangle.
Point2D	offcenter () const
	Get the offcenter of this triangle using the angle bound enforced by the BoundaryFace that contains this triangle. Error if no such face or bound exists.
Point2D	offcenter (double beta) const
	Get the offcenter of this triangle (as defined by Ungor et al.).
void	print () const
	Print info.
void	print_mathematica () const
	Print info in a Mathematica friendly format.
	declare_iterators_canon (edge, edges, BezierEdge)
Private Member Functions
int	get_edge_index_by_cps (int p0, int p1) const
	Given the index of two of the triangle's cps, find the edge that spans them.
void	replace_cp (const ControlPoint &oldp, const ControlPoint &newp)
	BezierTriangle (const BezierTriangle &o)
BezierTriangle &	operator= (const BezierTriangle &o)
Private Attributes
ControlPoint	cp_ [6]
	An array of iterators, pointing to the geometric data (Point2D).
DataPoint	dp_ [6]
	An array of iterators, pointing to the functional data (LinearData).
BoundaryFace *	bdry_face_
	A pointer to the BoundaryFace containing this BezierTriangle.
Friends
class	BezierMesh
std::ostream &	operator<< (std::ostream &stream, const BezierTriangle &t)

Detailed Description

The Face type for BezierMesh.

As we are using a second order BezierBasis for our geometric and functional basis, each BezierTriangle will have six ControlPoints and six DataPoints. Interpolation is done with the basis functions as:

$\forall u,v \in [0,1]$ such that $ u+v <= 1 $

$B(u, v) = (cp0)\cdot (1-u-v)^2 + (cp1)\cdot 2 v (1-u-v) + (cp2)\cdot v^2 + (cp3)\cdot 2 u (1-u-v) +(cp4)\cdot 2 u v + (cp5)\cdot u^2$

BezierTriangle

A BezierTriangle contains ControlPoints which point to the geometric Point2D information, and a DataPoints which point to the functional (LinearData) information. To get direct access to the information use the get_cp(int) and get_dp(int) methods.

Use get_edge(int) to get the edges of this face.

Also contains a pointer to the BoundaryFace containing this BezierTriangle.

Definition at line 719 of file cell.h.

Member Typedef Documentation

typedef FaceCell BezierTriangle::super

Definition at line 722 of file cell.h.

Constructor & Destructor Documentation

BezierTriangle::BezierTriangle	(	PersistantStore &	,
		BezierEdge *const	es[3],
		const DataStore &	,
		bool	inverse_handed = `false`
	)

Create a BezierTriangle.

Definition at line 1472 of file cell.C.

References cp_, dp_, BezierEdge::get_control_point(), get_control_point(), BezierEdge::get_vertex(), and map_idx().

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virtual BezierTriangle::~BezierTriangle ( ) [inline, virtual]

Destructor.

Definition at line 731 of file cell.h.

BezierTriangle::BezierTriangle ( const BezierTriangle & o ) [private]

Member Function Documentation

void BezierTriangle::set_boundary_face ( BoundaryFace * f )

Definition at line 1558 of file cell.C.

References bdry_face_.

Referenced by BezierMesh::add_bezier_triangle().

int BezierTriangle::get_num_cp ( ) const [inline]

Definition at line 734 of file cell.h.

Referenced by access_cp(), access_dp(), get_control_point(), get_cp(), get_num_dp(), and replace_cp().

const Point2D & BezierTriangle::get_cp ( int i ) const

Get the geometry of the ith control point.

Definition at line 1566 of file cell.C.

References cp_, and get_num_cp().

Referenced by bound_jacobian(), circumcenter(), Visualization::draw_control_net(), BezierMesh::draw_insert_error(), eval(), evalIntermediate(), BezierMesh::find_start_triangle(), GhostTriangle::GhostTriangle(), is_definitely_not_inverted(), is_linear_inverted(), Visualization::is_visible(), jacobian_matrix(), offcenter(), operator<<(), and print_mathematica().

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Point2D & BezierTriangle::access_cp ( int i )

Read-write access to the geometry.

Definition at line 1573 of file cell.C.

References PersistantList< Value >::iterator::access(), cp_, and get_num_cp().

Referenced by set_cp().

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void BezierTriangle::set_cp	(	int	i,
		const Point2D &	p
	)

Write access to the geometry.

Definition at line 1580 of file cell.C.

References access_cp().

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ControlPoint BezierTriangle::get_control_point ( int i ) const

Definition at line 1585 of file cell.C.

References cp_, and get_num_cp().

Referenced by BezierTriangle(), BezierMesh::consistency_check_helper(), get_edge_index_by_cps(), BezierMesh::locate_point_in_quadratic_triangle(), BezierMesh::orient_edge_triangle(), replace_cp(), and BezierMesh::tri_cps_off_edge().

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int BezierTriangle::get_num_dp ( ) const [inline]

Definition at line 741 of file cell.h.

References get_num_cp().

Referenced by get_data_point(), and get_dp().

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const LinearData & BezierTriangle::get_dp ( int i ) const

Get the data at the ith control point.

Definition at line 1592 of file cell.C.

References dp_, and get_num_dp().

Referenced by dataeval(), dataevalIntermediate(), GhostTriangle::GhostTriangle(), and operator<<().

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LinearData & BezierTriangle::access_dp ( int i )

Read-write access to the data.

Definition at line 1599 of file cell.C.

References PersistantList< Value >::iterator::access(), dp_, and get_num_cp().

Referenced by set_dp().

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void BezierTriangle::set_dp	(	int	i,
		const LinearData &	p
	)

Write access to the data.

Definition at line 1606 of file cell.C.

References access_dp().

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DataPoint BezierTriangle::get_data_point ( int i ) const

Definition at line 1611 of file cell.C.

References dp_, and get_num_dp().

Referenced by BezierMesh::consistency_check_helper().

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int BezierTriangle::get_num_edges ( ) const [inline]

Definition at line 749 of file cell.h.

Referenced by get_edge(), and get_edge_index_by_cps().

BezierEdge * BezierTriangle::get_edge ( int i )

Since we always have exactly three, allow index-based retrieval of edges.

Definition at line 1619 of file cell.C.

References FaceCell::begin_edges(), and get_num_edges().

Referenced by BezierMesh::check_consistency(), MeshOutput::ele_to_file(), get_edge(), get_edge_index_by_cps(), BezierMesh::locate_point_in_quadratic_triangle(), small_angle(), and BezierMesh::smooth_mesh().

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const BezierEdge * BezierTriangle::get_edge ( int i ) const

Definition at line 1623 of file cell.C.

References FaceCell::begin_edges(), and get_num_edges().

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bool BezierTriangle::has_bdry_face ( ) const

Definition at line 1628 of file cell.C.

References bdry_face_.

Referenced by get_bdry_face(), and operator<<().

const BoundaryFace * BezierTriangle::get_bdry_face ( ) const

Definition at line 1631 of file cell.C.

References bdry_face_, and has_bdry_face().

Referenced by get_color(), get_min_angle(), and operator<<().

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BoundaryFace * BezierTriangle::get_bdry_face ( )

Definition at line 1635 of file cell.C.

References bdry_face_, and has_bdry_face().

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BoundaryFace * BezierTriangle::get_bdry_face_or_null ( )

Definition at line 1639 of file cell.C.

References bdry_face_.

Referenced by MeshOutput::ele_to_file(), BezierMesh::flip(), BezierMesh::insert_edge_midpoint(), and BezierMesh::insert_point().

double BezierTriangle::get_min_angle ( ) const

Definition at line 1643 of file cell.C.

References get_bdry_face(), and BoundaryFace::get_min_angle().

Referenced by offcenter(), and small_angle().

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int BezierTriangle::get_color ( ) const

Definition at line 1646 of file cell.C.

References get_bdry_face(), and BoundaryFace::get_color().

Referenced by Visualization::draw_bezier_triangle(), and EPSWrite::shade_triangle().

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const BezierEdge * BezierTriangle::get_edge	(	int	p0,
		int	p1
	)			const

Get the BezierEdge that is a sub-cell of this Face, which shares the given control points.

Parameters:

	p0	The index in cps of the edge's first control point
	p1	The index in cps of the edge's second control point

Returns:: The edge with the given control points

Definition at line 1655 of file cell.C.

References get_edge(), and get_edge_index_by_cps().

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BezierEdge * BezierTriangle::get_edge	(	int	p0,
		int	p1
	)

Definition at line 1659 of file cell.C.

References get_edge(), and get_edge_index_by_cps().

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Point2D BezierTriangle::eval	(	double	u,
		double	v
	)			const `[virtual]`

Given parameters u, v, interpolate the geometric coordinates in the Bezier Basis.

Assumes that $u,v,u+v \in [0,1]$ .

returns: $B(u, v) = (cp0)\cdot (1-u-v)^2 + (cp1)\cdot 2 v (1-u-v) + (cp2)\cdot v^2 + (cp3)\cdot 2 u (1-u-v) +(cp4)\cdot 2 u v + (cp5)\cdot u^2$

Parameters:

	u	The first parameter (u in [0,1] )
	v	The second parameter (v in [0,1] )

Returns:: The interpolated coordinates

Implements CurvedTriangle.

Definition at line 1675 of file cell.C.

References get_cp().

Referenced by BezierMesh::clean_insert_point(), Visualization::draw_bezier_triangle(), Visualization::draw_point(), and BezierMesh::interpolant_error().

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LinearData BezierTriangle::dataeval	(	double	u,
		double	v
	)			const

Given parameters u, v, interpolate the functional data in the Bezier Basis.

Assumes that $u,v,u+v \in [0,1]$ .

returns: $B(u, v) = (dp0)\cdot (1-u-v)^2 + (dp1)\cdot 2 v (1-u-v) + (dp2)\cdot v^2 + (dp3)\cdot 2 u (1-u-v) +(dp4)\cdot 2 u v + (dp5)\cdot u^2$

Parameters:

	u	The first parameter (u in [0,1] )
	v	The second parameter (v in [0,1] )

Returns:: The interpolated functional value

Definition at line 1699 of file cell.C.

References get_dp().

Referenced by Visualization::draw_bezier_triangle(), and BezierMesh::interpolant_error().

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void BezierTriangle::evalIntermediate	(	double	u,
		double	v,
		Point2D &	p,
		Point2D &	pc0,
		Point2D &	pc1,
		Point2D &	pc2
	)			const

Given a parameters u and v, interpolate the geometric coordinates in the Bezier Basis.

Runs the de Casteljau algorithm, and returns intermediates as well as the final interpolated value.

Parameters:

	u	The first parameter (u in [0, 1])
	v	The second parameter (v in [0, 1])
`[out]`	p	The interpolated geometric point
`[out]`	pc0	The first intermediate
`[out]`	pc1	The second intermediate
`[out]`	pc2	The third intermediate

Definition at line 1723 of file cell.C.

References get_cp().

Referenced by BezierMesh::insert_edge_midpoint(), and BezierMesh::insert_point().

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void BezierTriangle::dataevalIntermediate	(	double	u,
		double	v,
		LinearData &	d,
		LinearData &	dc0,
		LinearData &	dc1,
		LinearData &	dc2
	)			const

Given a parameters u and v, interpolate the functional data in the Bezier Basis.

Runs the de Casteljau algorithm, and returns intermediates as well as the final interpolated value.

Parameters:

	u	The first parameter (u in [0, 1])
	v	The second parameter (v in [0, 1])
`[out]`	d	The interpolated functional data
`[out]`	dc0	The first intermediate
`[out]`	dc1	The second intermediate
`[out]`	dc2	The third intermediate

Definition at line 1755 of file cell.C.

References get_dp().

Referenced by BezierMesh::insert_edge_midpoint(), and BezierMesh::insert_point().

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double BezierTriangle::jacobian	(	double	u,
		double	v
	)			const

Gives the Jacobian determinate at the given barycentric coordinates.

Parameters:

	u	The first parameter
	v	The second parameter

Returns:: The Jacobian determinate

Definition at line 1781 of file cell.C.

References Point2D::cross(), and jacobian_matrix().

Referenced by is_definitely_inverted(), and BezierMesh::reinterpolate().

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void BezierTriangle::jacobian_matrix	(	double	u,
		double	v,
		Point2D &	pdu,
		Point2D &	pdv
	)			const `[virtual]`

Gives the full Jacobian at the given barycentric coordinates.

This returns the matrix as a pair of column vectors, where each column vector represents the partial with repsect to one of the two parameters.

Parameters:

	u	The first parameter
	v	The second parameter
`[out]`	pdu	A vector with coordinates representing the partial derivative with respect to u
`[out]`	pdv	A vector with coordinates representing the partial derivative with respect to v

Implements CurvedTriangle.

Definition at line 1798 of file cell.C.

References get_cp().

Referenced by jacobian().

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void BezierTriangle::bound_jacobian	(	double &	min,
		double &	max,
		double &	area
	)			const

Approximates the jacobian determinate and the area of the triangle.

Returns a range [min, max ] for the Jacobian Determinate over the whole triangle. Thus, at no pair (u , v ) will the Jacobian determinate be less than min or more than max.

Also calculates the exact area as a side effect.

Parameters:

	min	The lower bound for the Jacobian determinate
	max	The upper bound for the Jacobian determinate
	area	The area of the BezierTriangle

Definition at line 1825 of file cell.C.

References get_cp().

Referenced by area(), and BezierMesh::smooth_mesh().

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bool BezierTriangle::newton_find	(	const Point2D &	p,
		double &	u,
		double &	v,
		int &	niter,
		int &	edge_num
	)

Definition at line 1855 of file cell.C.

References get_edge_index_by_cps(), and CurvedTriangle::newton_find().

Referenced by BezierMesh::locate_point_in_quadratic_triangle().

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double BezierTriangle::area ( ) const

Gives the area of the BezierTriangle.

Definition at line 1873 of file cell.C.

References bound_jacobian().

Referenced by BezierMesh::remove_large_triangles().

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bool BezierTriangle::small_angle ( ) const

Determine if angle is small.

This function looks up the angle bound from the Triangle's face. It then examines each of the three angles in the triangle, treating the edges as linear. If two edges are both on a boundary, then we ignore that angle, so as not to recurse on small angles.

Returns:: true if the angle is small

Definition at line 1888 of file cell.C.

References Point2D::angle(), BezierEdge::get_bdry_edge(), BezierVertex::get_cp(), get_edge(), get_min_angle(), BezierEdge::get_vertex(), BezierEdge::is_boundary(), and PI.

Referenced by BezierMesh::remove_small_angles().

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bool BezierTriangle::is_linear_inverted ( ) const

Definition at line 1940 of file cell.C.

References get_cp(), and Point2D::is_left_of().

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int BezierTriangle::is_inverted ( ) const

Definition at line 1949 of file cell.C.

References is_definitely_inverted(), and is_definitely_not_inverted().

Referenced by MeshOutput::ele_to_file(), BezierMesh::insert_point(), and BezierMesh::print_check_inverted().

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bool BezierTriangle::is_definitely_inverted ( ) const

Definition at line 1971 of file cell.C.

References ALPHA, BETA, and jacobian().

Referenced by is_inverted().

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bool BezierTriangle::is_definitely_not_inverted ( ) const

Definition at line 1984 of file cell.C.

References get_cp().

Referenced by is_inverted().

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Point2D BezierTriangle::circumcenter ( ) const

Get the circumcenter of this triangle.

Returns:: The circumcenter of the BezierTriangle

Definition at line 2019 of file cell.C.

References get_cp().

Referenced by BezierMesh::clean_insert_circumcenter(), and offcenter().

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Point2D BezierTriangle::offcenter ( ) const

Get the offcenter of this triangle using the angle bound enforced by the BoundaryFace that contains this triangle. Error if no such face or bound exists.

Returns:: the offcenter of the BezierTriangle

Definition at line 2039 of file cell.C.

References get_min_angle(), and PI.

Referenced by offcenter().

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Point2D BezierTriangle::offcenter ( double beta ) const

Get the offcenter of this triangle (as defined by Ungor et al.).

Parameters:

beta

: The radius-edge ratio for the offcenter

Returns:: the offcenter of the BezierTriangle

Definition at line 2052 of file cell.C.

References circumcenter(), get_cp(), Point2D::mag(), and offcenter().

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void BezierTriangle::print ( ) const

Print info.

Definition at line 2093 of file cell.C.

void BezierTriangle::print_mathematica ( ) const

Print info in a Mathematica friendly format.

Definition at line 2099 of file cell.C.

References get_cp(), Point2D::x(), and Point2D::y().

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BezierTriangle::declare_iterators_canon	(	edge	,
		edges	,
		BezierEdge
	)

int BezierTriangle::get_edge_index_by_cps	(	int	p0,
		int	p1
	)			const `[private]`

Given the index of two of the triangle's cps, find the edge that spans them.

p0 and p1 must correspond to the vertices of a single edge.

As the numbering of control points has been done in a counter-clockwise manner, this may not coorsepond to the ordering of edges. This is the case if the triangle is in the inverted set of the BezierMesh.

In all triangles, get_edge(0) spans control points 0-2; get_edge(1) however may span either 2-5 or 5-0 (get_edge(2) spans the other).

TODO: this should be abolished and the edge numbers made to agree with the control point numbers.

Definition at line 2165 of file cell.C.

References BezierVertex::get_control_point(), get_control_point(), get_edge(), get_num_edges(), and BezierEdge::get_vertex().

Referenced by get_edge(), and newton_find().

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