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Program: Visualization Toolkit
Module: vtkPolygon.h
Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
All rights reserved.
See Copyright.txt or for details.
This software is distributed WITHOUT ANY WARRANTY; without even
PURPOSE. See the above copyright notice for more information.
// .NAME vtkPolygon - a cell that represents an n-sided polygon
// .SECTION Description
// vtkPolygon is a concrete implementation of vtkCell to represent a 2D
// n-sided polygon. The polygons cannot have any internal holes, and cannot
// self-intersect. Define the polygon with n-points ordered in the counter-
// clockwise direction; do not repeat the last point.
#ifndef __vtkPolygon_h
#define __vtkPolygon_h
#include "vtkCell.h"
class vtkDoubleArray;
class vtkIdTypeArray;
class vtkLine;
class vtkPoints;
class vtkQuad;
class vtkTriangle;
class vtkIncrementalPointLocator;
class VTK_FILTERING_EXPORT vtkPolygon : public vtkCell
static vtkPolygon *New();
void PrintSelf(ostream& os, vtkIndent indent);
// Description:
// See the vtkCell API for descriptions of these methods.
int GetCellType() {return VTK_POLYGON;};
int GetCellDimension() {return 2;};
int GetNumberOfEdges() {return this->GetNumberOfPoints();};
int GetNumberOfFaces() {return 0;};
vtkCell *GetEdge(int edgeId);
vtkCell *GetFace(int) {return 0;};
int CellBoundary(int subId, double pcoords[3], vtkIdList *pts);
void Contour(double value, vtkDataArray *cellScalars,
vtkIncrementalPointLocator *locator,vtkCellArray *verts,
vtkCellArray *lines, vtkCellArray *polys,
vtkPointData *inPd, vtkPointData *outPd,
vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd);
void Clip(double value, vtkDataArray *cellScalars,
vtkIncrementalPointLocator *locator, vtkCellArray *tris,
vtkPointData *inPd, vtkPointData *outPd,
vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd,
int insideOut);
int EvaluatePosition(double x[3], double* closestPoint,
int& subId, double pcoords[3],
double& dist2, double *weights);
void EvaluateLocation(int& subId, double pcoords[3], double x[3],
double *weights);
int IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
double x[3], double pcoords[3], int& subId);
int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts);
void Derivatives(int subId, double pcoords[3], double *values,
int dim, double *derivs);
int IsPrimaryCell() {return 0;}
// Description:
// Compute the area of a polygon. This is a convenience function
// which simply calls static double ComputeArea(vtkPoints *p,
// vtkIdType numPts, vtkIdType *pts, double normal[3]);
// with the appropriate parameters from the instantiated vtkPolygon.
double ComputeArea();
// Description:
// Compute the interpolation functions/derivatives.
// (aka shape functions/derivatives)
// Two interpolation algorithms are available: 1/r^2 and Mean Value
// Coordinate. The former is used by default. To use the second algorithm,
// set UseMVCInterpolation to be true.
// The function assumes the input point lies on the polygon plane without
// checking that.
virtual void InterpolateFunctions(double x[3], double *sf);
virtual void InterpolateDerivs(double x[3], double *derivs);
// Description:
// Polygon specific methods.
static void ComputeNormal(vtkPoints *p, int numPts, vtkIdType *pts,
double n[3]);
static void ComputeNormal(vtkPoints *p, double n[3]);
static void ComputeNormal(vtkIdTypeArray *ids, vtkPoints *pts, double n[3]);
// Description:
// Compute the polygon normal from an array of points. This version assumes
// that the polygon is convex, and looks for the first valid normal.
static void ComputeNormal(int numPts, double *pts, double n[3]);
// Description:
// Compute the centroid of a set of points.
static void ComputeCentroid(vtkIdTypeArray *ids, vtkPoints *pts,
double centroid[3]);
// Description:
// Compute interpolation weights using 1/r**2 normalized sum.
// @deprecated Replaced by vtkPolygon::InterpolateFunctions as of VTK 5.2
VTK_LEGACY(void ComputeWeights(double x[3], double *weights));
// Description:
// Compute the area of a polygon in 3D. The area is returned, as well as
// the normal (a side effect of using this method). If you desire to
// compute the area of a triangle, use vtkTriangleArea which is faster.
// If you already have a vtkPolygon instantiated, a convenience function,
// ComputeArea() is provided.
static double ComputeArea(vtkPoints *p, vtkIdType numPts, vtkIdType *pts,
double normal[3]);
// Description:
// Create a local s-t coordinate system for a polygon. The point p0 is
// the origin of the local system, p10 is s-axis vector, and p20 is the
// t-axis vector. (These are expressed in the modeling coordinate system and
// are vectors of dimension [3].) The values l20 and l20 are the lengths of
// the vectors p10 and p20, and n is the polygon normal.
int ParameterizePolygon(double p0[3], double p10[3], double &l10,
double p20[3], double &l20, double n[3]);
// Description:
// Determine whether point is inside polygon. Function uses ray-casting
// to determine if point is inside polygon. Works for arbitrary polygon shape
// (e.g., non-convex). Returns 0 if point is not in polygon; 1 if it is.
// Can also return -1 to indicate degenerate polygon.
static int PointInPolygon(double x[3], int numPts, double *pts,
double bounds[6], double n[3]);
// Description:
// Triangulate this polygon. The user must provide the vtkIdList outTris.
// On output, the outTris list contains the ids of the points defining
// the triangulation. The ids are ordered into groups of three: each
// three-group defines one triangle.
int Triangulate(vtkIdList *outTris);
// Description:
// Same as Triangulate(vtkIdList *outTris)
// but with a first pass to split the polygon into non-degenerate polygons.
int NonDegenerateTriangulate(vtkIdList *outTris);
// Description:
// Compute the distance of a point to a polygon. The closest point on
// the polygon is also returned. The bounds should be provided to
// accelerate the computation.
static double DistanceToPolygon(double x[3], int numPts, double *pts,
double bounds[6], double closest[3]);
// Description:
// Method intersects two polygons. You must supply the number of points and
// point coordinates (npts, *pts) and the bounding box (bounds) of the two
// polygons. Also supply a tolerance squared for controlling
// error. The method returns 1 if there is an intersection, and 0 if
// not. A single point of intersection x[3] is also returned if there
// is an intersection.
static int IntersectPolygonWithPolygon(int npts, double *pts, double bounds[6],
int npts2, double *pts2,
double bounds2[3], double tol,
double x[3]);
// Description:
// Intersect two convex 2D polygons to produce a line segment as output.
// The return status of the methods indicated no intersection (returns 0);
// a single point of intersection (returns 1); or a line segment (i.e., two
// points of intersection, returns 2). The points of intersection are
// returned in the arrays p0 and p1. If less than two points of
// intersection are generated then p1 and/or p0 may be
// indeterminiate. Finally, if the two convex polygons are parallel, then
// "0" is returned (i.e., no intersection) even if the triangles lie on one
// another.
static int IntersectConvex2DCells(vtkCell *cell1, vtkCell *cell2,
double tol, double p0[3], double p1[3]);
// Description:
// Set/Get the flag indicating whether to use Mean Value Coordinate for the
// interpolation. If true, InterpolateFunctions() uses the Mean Value
// Coordinate to compute weights. Otherwise, the conventional 1/r^2 method
// is used. The UseMVCInterpolation parameter is set to false by default.
vtkGetMacro(UseMVCInterpolation, bool);
vtkSetMacro(UseMVCInterpolation, bool);
// Compute the interpolation functions using Mean Value Coordinate.
void InterpolateFunctionsUsingMVC(double x[3], double *weights);
// variables used by instances of this class
double Tolerance; // Intersection tolerance
int SuccessfulTriangulation; // Stops recursive tri. if necessary
double Normal[3]; //polygon normal
vtkIdList *Tris;
vtkTriangle *Triangle;
vtkQuad *Quad;
vtkDoubleArray *TriScalars;
vtkLine *Line;
// Parameter indicating whether to use Mean Value Coordinate algorithm
// for interpolation. The parameter is false by default.
bool UseMVCInterpolation;
// Helper methods for triangulation------------------------------
// Description:
// A fast triangulation method. Uses recursive divide and
// conquer based on plane splitting to reduce loop into triangles.
// The cell (e.g., triangle) is presumed properly initialized (i.e.,
// Points and PointIds).
int EarCutTriangulation();
vtkPolygon(const vtkPolygon&); // Not implemented.
void operator=(const vtkPolygon&); // Not implemented.