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BezierEdge Class Reference

The Edge type for BezierMesh. More...

#include </afs/cs.cmu.edu/user/tp517/rio/tumble/trunk/src/tumble/inc/cell.h>

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List of all members.

Public Types

typedef EdgeCell super

Public Member Functions

 BezierEdge (BezierVertex *v1, BezierVertex *v2, const ControlPoint &, const DataStore &)
 Create an empty BezierEdge.
 ~BezierEdge ()
void set_bdry (BoundaryEdge *be, double u0, double u1)
 Destructor.
void set_cp (const Point2D &p, int i)
 Set the value of ControlPoint with given index.
void set_dp (const LinearData &d, int i)
 Set the value of DataPoint with given index.
void set_data (int i, int pos, double data)
 Set the value of DataPoint with given index, at the given position.
int get_num_cp () const
const Point2D & get_cp (int i) const
 Get the value of ControlPoint with given index.
Point2D & access_cp (int i)
 Get read-write access to the point at position i.
ControlPoint get_control_point (int i) const
 Direct access to the ControlPoint pointer.
const LinearData & get_dp (int i) const
 Get the value of DataPoint with given index.
LinearData & access_dp (int i)
 Get the value of DataPoint with given index.
DataPoint get_data_point (int i) const
 Direct access to the DataPoint pointer.
const BezierVertex * get_vertex (int i) const
 Get the BezierVertex that is a sub-cell of this edge, with given index.
BezierVertex * get_vertex (int i)
bool is_boundary () const
 True if this is a boundary edge.
const BoundaryEdge * get_bdry_edge () const
BoundaryEdge * get_bdry_edge ()
double get_u (int i) const
Point2D eval (double u) const
 Given a parameter in [0,1], interpolate the geometric coordinates in the Bezier Basis.
LinearData dataeval (double u) const
 Given a parameter in [0,1], interpolate the functional value in the Bezier Basis.
void evalIntermediate (double u, Point2D &p, Point2D &pc0, Point2D &pc1) const
 Given a parameter in [0,1], interpolate the geometric coordinates in the Bezier Basis.
void dataevalIntermediate (double u, LinearData &d, LinearData &dc0, LinearData &dc1) const
 Given a parameter in [0,1], interpolate the functional data in the Bezier Basis.
bool is_encroached (const Point2D &) const
 Determines id the given point encroaches this edge.
int left_of_curve (Point2D &, int, double &) const
 Determines if the point is left of the curve.
double curvature_angle () const
 Returns the total turning (theta) of this edge For a quadratic bezier edge, this is the absolute value of the angle between control arms.
void print () const
 Print info.
 declare_iterators (vertex, vertices, BezierVertex)
 declare_iterators (face, faces, BezierTriangle)

Static Public Member Functions

template<typename iterator>
static bool encroaches (Point2D p, const iterator &bounding_start, const iterator &bounding_end)
 Test whether the point encroaches on the curve bounded by the bounding polygon defined by points in the range [start, end].

Private Member Functions

void replace_cp (const ControlPoint &oldp, const ControlPoint &newp)
 Replace a control point. Used in bootstrapping. We assert the old point is actually part of the edge. Note: this function does *not* fix up the corresponding triangle or vertex.
 BezierEdge (const BezierEdge &o)
BezierEdge & operator= (const BezierEdge &o)

Private Attributes

ControlPoint cp_ [3]
 An array of iterators, pointing to the geometric data (Point2D).
DataPoint dp_ [3]
 An array of iterators, pointing to the functional data (LinearData).
BoundaryEdge * bdry_edge_
 The BoundaryEdge this edge is part of (NULL if no such BoundaryEdge).
double u_ [2]
 If on a boundary, then this is the u-value of the first and last vertex along the boundary.

Friends

class BezierMesh
std::ostream & operator<< (std::ostream &stream, const BezierEdge &e)

Detailed Description

The Edge type for BezierMesh.

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

$ \forall \alpha \in [0,1], B(\alpha) = (cp[0])\cdot \alpha^2 + (cp[1])\cdot 2\alpha (1 - \alpha) + (cp[2])\cdot (1-\alpha)^2 $

bedge.png

BezierEdge

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 the iterator functions (begin_vertices, begin_faces, etc) to access the sub-cells and super-cells of this edge.

Also contains information about the boundary. If this edge is part of a BoundaryEdge, then bdry points to that BoundaryEdge and u0 and u1 are the u-values of the vertex with index 0 and the vertex with index 1 respectivly. Thus, we should have that:

 edge->get_vertex(0)->get_u(edge->bdry, edge) == edge->u0

 edge->get_vertex(1)->get_u(edge->bdry, edge) == edge->u1

Note:
In the above code, we could not use simply, edge->get_vertex(0)->u , because that vertex might have been on a D0 vertex, and thus not have a unique u-value.
The u0 and u1 values for this edge will tell us how the mapping domains line-up between this edge and the BoundaryEdge. The following assertion will hold for i in 0...1: 
 edge->evaluate(i) == edge->bdry->evaluate(edge->u0 + i * (edge->u1 - edge->u0))

Definition at line 575 of file cell.h.

Member Typedef Documentation

typedef EdgeCell BezierEdge::super
 

Definition at line 577 of file cell.h.

Constructor & Destructor Documentation

BezierEdge::BezierEdge (  BezierVertex *  v1,
BezierVertex *  v2,
const ControlPoint &  ,
const DataStore & 
) 
 

Create an empty BezierEdge.

Definition at line 1047 of file cell.C.

References cp_, dp_, get_control_point(), BezierVertex::get_control_point(), get_num_cp(), and u_.

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BezierEdge::~BezierEdge (   )  [inline]
 

Definition at line 585 of file cell.h.

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

Member Function Documentation

Point2D & BezierEdge::access_cp (  int  i  ) 
 

Get read-write access to the point at position i.

Definition at line 1305 of file cell.C.

References cp_, and get_num_cp().

Referenced by Simulation::move(), and set_cp().

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LinearData & BezierEdge::access_dp (  int  i  ) 
 

Get the value of DataPoint with given index.

Parameters:
i The index of the DataPoint [0<= i <=2]
Returns:
The value of the DataPoint

Definition at line 1332 of file cell.C.

References dp_, and get_num_cp().

Referenced by BezierMesh::reinterpolate(), set_data(), and set_dp().

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double BezierEdge::curvature_angle (   )  const
 

Returns the total turning (theta) of this edge For a quadratic bezier edge, this is the absolute value of the angle between control arms.

Returns:
the curvature angle in degrees

Definition at line 1202 of file cell.C.

References Point2D::dot(), get_cp(), and Point2D::mag().

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LinearData BezierEdge::dataeval (  double  u  )  const
 

Given a parameter in [0,1], interpolate the functional value in the Bezier Basis.

returns: $ B(\alpha) = (dp2) \cdot u^2 + (dp1)\cdot 2u (1 - u) + (dp0)\cdot (1-u)^2 $

Parameters:
u The parameter (u in [0, 1])
Returns:
The interpolated functional values

Definition at line 1120 of file cell.C.

References get_dp().

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void BezierEdge::dataevalIntermediate (  double  u,
LinearData &  d,
LinearData &  dc0,
LinearData &  dc1
)  const
 

Given a parameter in [0,1], 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 parameter (u in [0, 1])
[out] d The interpolated data point
[out] dc0 The first intermediate
[out] dc1 The second intermediate

Definition at line 1162 of file cell.C.

References get_dp().

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BezierEdge::declare_iterators (  face  ,
faces  ,
BezierTriangle 
) 
 

BezierEdge::declare_iterators (  vertex  ,
vertices  ,
BezierVertex 
) 
 

template<typename iterator>
bool BezierEdge::encroaches (  Point2D  p,
const iterator &  bounding_start,
const iterator &  bounding_end
)  [inline, static]
 

Test whether the point encroaches on the curve bounded by the bounding polygon defined by points in the range [start, end].

Encroachment on curve is defined by encroachment on the dimetral circle of any pair of points on the curve. To compute this, we compute whether there is encroachment on the bounding polygon (is the point in the circumcircle of any pair of points on the polygon -- in particular, its vertices).

iterator::operator*() must return something on which operator-(Point2D) is defined and returns something on which a dot product is defined. For example: Point2D* has its * operator return a Point2D, on which operator-(Point2D) returns a Point2D, on which the dot product is defined.

Definition at line 862 of file cell.h.

Referenced by is_encroached().

Point2D BezierEdge::eval (  double  u  )  const
 

Given a parameter in [0,1], interpolate the geometric coordinates in the Bezier Basis.

returns: $ B(\alpha) = (cp2) \cdot u^2 + (cp1)\cdot 2u (1 - u) + (cp0)\cdot (1-u)^2 $

Parameters:
u The parameter (u in [0, 1])
Returns:
The interpolated coordinates

Definition at line 1103 of file cell.C.

References get_cp().

Referenced by BezierMesh::clean_insert_edge_midpoint(), Visualization::draw_bezier_edge(), Visualization::draw_point(), and BezierMesh::insert_edge_midpoint().

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void BezierEdge::evalIntermediate (  double  u,
Point2D &  p,
Point2D &  pc0,
Point2D &  pc1
)  const
 

Given a parameter in [0,1], 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 parameter (u in [0, 1])
[out] p The interpolated geometric point
[out] pc0 The first intermediate
[out] pc1 The second intermediate

Definition at line 1139 of file cell.C.

References get_cp().

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BoundaryEdge * BezierEdge::get_bdry_edge (   ) 
 

Definition at line 1380 of file cell.C.

References bdry_edge_, and is_boundary().

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const BoundaryEdge * BezierEdge::get_bdry_edge (   )  const
 

Definition at line 1375 of file cell.C.

References bdry_edge_, and is_boundary().

Referenced by BezierVertex::get_u(), BezierMesh::insert_edge_midpoint(), operator<<(), BezierTriangle::small_angle(), and MeshBinaryOutput::write().

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ControlPoint BezierEdge::get_control_point (  int  i  )  const
 

Direct access to the ControlPoint pointer.

Definition at line 1312 of file cell.C.

References cp_, and get_num_cp().

Referenced by BezierEdge(), BezierTriangle::BezierTriangle(), BezierMesh::consistency_check_helper(), BezierMesh::delete_edge(), BezierMesh::orient_edge_triangle(), BezierMesh::replace_control_point(), MeshBinaryOutput::write(), and MeshOutput::write().

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

Get the value of ControlPoint with given index.

Parameters:
i The index of the ControlPoint [0<= i <=2]
Returns:
The value of the ControlPoint

Definition at line 1299 of file cell.C.

References cp_, and get_num_cp().

Referenced by BezierMesh::can_flip(), BezierMesh::can_smooth(), curvature_angle(), BezierMesh::debug_flip(), BezierMesh::debug_smooth(), EPSWrite::draw_edge(), eval(), evalIntermediate(), BezierMesh::flip(), BezierMesh::function_angle(), BezierMesh::get_flip_polygon(), BezierMesh::get_smooth_polygon(), Visualization::is_visible(), left_of_curve(), operator<<(), EPSWrite::shade_triangle(), BezierMesh::should_refine_func_angle(), BezierMesh::smooth_edge(), and MeshBinaryOutput::write().

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DataPoint BezierEdge::get_data_point (  int  i  )  const
 

Direct access to the DataPoint pointer.

Definition at line 1339 of file cell.C.

References dp_, and get_num_cp().

Referenced by BezierMesh::consistency_check_helper(), BezierMesh::delete_edge(), and MeshOutput::write().

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

Get the value of DataPoint with given index.

Parameters:
i The index of the DataPoint [0<= i <=2]
Returns:
The value of the DataPoint

Definition at line 1322 of file cell.C.

References dp_, and get_num_cp().

Referenced by dataeval(), dataevalIntermediate(), BezierMesh::flip(), BezierMesh::function_angle(), Simulation::move(), operator<<(), BezierMesh::remove_vertex(), and MeshBinaryOutput::write().

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int BezierEdge::get_num_cp (   )  const [inline]
 

Definition at line 594 of file cell.h.

Referenced by access_cp(), access_dp(), BezierEdge(), get_control_point(), get_cp(), get_data_point(), get_dp(), is_encroached(), and replace_cp().

double BezierEdge::get_u (  int  i  )  const
 

Definition at line 1090 of file cell.C.

References u_.

Referenced by operator<<().

BezierVertex * BezierEdge::get_vertex (  int  i  ) 
 

Reimplemented from EdgeCell.

Definition at line 1364 of file cell.C.

References EdgeCell::get_vertex().

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const BezierVertex * BezierEdge::get_vertex (  int  i  )  const
 

Get the BezierVertex that is a sub-cell of this edge, with given index.

Parameters:
i The index into the edge's set of vertexs [0<= i <=1]
Returns:
The BezierVertex that is a vertex of this edge, with given index

Reimplemented from EdgeCell.

Definition at line 1360 of file cell.C.

References EdgeCell::get_vertex().

Referenced by BezierTriangle::BezierTriangle(), BezierMesh::coarsen_calculate_edge_lengths(), BezierMesh::coarsen_keep_large_function_angles(), BezierMesh::consistency_check_helper(), BezierTriangle::get_edge_index_by_cps(), BezierVertex::get_u(), BezierTriangle::small_angle(), and MeshBinaryOutput::write().

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bool BezierEdge::is_boundary (   )  const
 

True if this is a boundary edge.

Definition at line 1370 of file cell.C.

References bdry_edge_.

Referenced by BezierMesh::clean_insert_edge_midpoint(), BezierMesh::clean_insert_point(), BezierMesh::delete_edge(), Visualization::draw_flippable_edges(), Visualization::draw_smoothable_edges(), MeshOutput::edge_to_file(), BezierMesh::flip(), get_bdry_edge(), BezierMesh::get_edge_neighbor_cells(), BezierMesh::insert_edge_midpoint(), BezierMesh::locate_point_in_linear_mesh(), Simulation::move(), operator<<(), BezierMesh::protect_boundarys(), BezierMesh::should_flip(), BezierMesh::should_refine_func_angle(), BezierTriangle::small_angle(), BezierMesh::smooth_edge(), BezierMesh::smooth_mesh(), and MeshBinaryOutput::write().

bool BezierEdge::is_encroached (  const Point2D &  p  )  const
 

Determines id the given point encroaches this edge.

In the classic Delaunay refinement algorithms, one of the key procedures is checking an edge for encroachment. This occurs when a point enters the circumcircle of an edge.

For curved segments, we define encroachment using a convex bounding polygon for the curve. A point encroaches if it lies inside the diametral circle of any pair of point of the bounding polygon.

For Bezier segments, the control points define the bounding polygon.

Parameters:
p The point to test for encroachment
Returns:
true if this edge is encroached by given point

Definition at line 1191 of file cell.C.

References cp_, encroaches(), and get_num_cp().

Referenced by BezierMesh::clean_insert_edge_midpoint(), BezierMesh::clean_insert_point(), and BezierMesh::protect_boundarys().

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int BezierEdge::left_of_curve (  Point2D &  p,
int  stop,
double &  approx
)  const
 

Determines if the point is left of the curve.

Ask Todd about this one.

Definition at line 1224 of file cell.C.

References get_cp(), Point2D::is_left_of(), p1, and p2.

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BezierEdge& BezierEdge::operator= (  const BezierEdge &  o  )  [private]
 

void BezierEdge::print (   )  const
 

Print info.

Definition at line 1386 of file cell.C.

void BezierEdge::replace_cp (  const ControlPoint &  oldp,
const ControlPoint &  newp
)  [private]
 

Replace a control point. Used in bootstrapping. We assert the old point is actually part of the edge. Note: this function does *not* fix up the corresponding triangle or vertex.

Definition at line 1079 of file cell.C.

References cp_, and get_num_cp().

Referenced by BezierMesh::replace_control_point().

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void BezierEdge::set_bdry (  BoundaryEdge *  b,
double  u0,
double  u1
) 
 

Destructor.

Parameters:
b The BoundaryEdge this edge is part of
_u0 The u-value along b of vertexs[0]
_u1 The v-value along b of vertexs[1]

Definition at line 1067 of file cell.C.

References bdry_edge_, and u_.

Referenced by BezierMesh::insert_edge_midpoint(), MeshBinaryInput::read(), MeshInput::read(), BezierMesh::remove_vertex(), and ConformalMesher::reticulate_splines().

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

Set the value of ControlPoint with given index.

Parameters:
p The new value at the ControlPoint
i The index of the control point [0<= i <=2]

Definition at line 1279 of file cell.C.

References access_cp().

Referenced by BezierMesh::smooth_edge().

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void BezierEdge::set_data (  int  i,
int  pos,
double  data
) 
 

Set the value of DataPoint with given index, at the given position.

Parameters:
i The index of the DataPoint [0<= i <=2]
pos The position within the LinearData to set
data The value to set at the given position

Definition at line 1350 of file cell.C.

References access_dp(), and LinearData::set().

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void BezierEdge::set_dp (  const LinearData &  d,
int  i
) 
 

Set the value of DataPoint with given index.

Parameters:
d The new value at the DataPoint
i The index of the DataPoint [0<= i <=2]

Definition at line 1289 of file cell.C.

References access_dp().

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Friends And Related Function Documentation

friend class BezierMesh [friend]
 

Definition at line 578 of file cell.h.

std::ostream& operator<< (  std::ostream &  stream,
const BezierEdge &  e
)  [friend]
 

Member Data Documentation

BoundaryEdge* BezierEdge::bdry_edge_ [private]
 

The BoundaryEdge this edge is part of (NULL if no such BoundaryEdge).

Definition at line 638 of file cell.h.

Referenced by get_bdry_edge(), is_boundary(), and set_bdry().

ControlPoint BezierEdge::cp_[3] [private]
 

An array of iterators, pointing to the geometric data (Point2D).

Definition at line 636 of file cell.h.

Referenced by access_cp(), BezierEdge(), get_control_point(), get_cp(), is_encroached(), and replace_cp().

DataPoint BezierEdge::dp_[3] [private]
 

An array of iterators, pointing to the functional data (LinearData).

Definition at line 637 of file cell.h.

Referenced by access_dp(), BezierEdge(), get_data_point(), and get_dp().

double BezierEdge::u_[2] [private]
 

If on a boundary, then this is the u-value of the first and last vertex along the boundary.

Definition at line 639 of file cell.h.

Referenced by BezierEdge(), get_u(), and set_bdry().

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