322 lines
13 KiB
C
322 lines
13 KiB
C
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/*=========================================================================
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Program: Visualization Toolkit
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Module: vtkPolygon.h
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Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
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All rights reserved.
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See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
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This software is distributed WITHOUT ANY WARRANTY; without even
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the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
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PURPOSE. See the above copyright notice for more information.
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=========================================================================*/
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/**
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* @class vtkPolygon
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* @brief a cell that represents an n-sided polygon
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*
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* vtkPolygon is a concrete implementation of vtkCell to represent a 2D
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* n-sided polygon. The polygons cannot have any internal holes, and cannot
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* self-intersect. Define the polygon with n-points ordered in the counter-
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* clockwise direction; do not repeat the last point.
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*/
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#ifndef vtkPolygon_h
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#define vtkPolygon_h
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#include "vtkCell.h"
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#include "vtkCommonDataModelModule.h" // For export macro
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class vtkDoubleArray;
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class vtkIdTypeArray;
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class vtkLine;
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class vtkPoints;
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class vtkQuad;
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class vtkTriangle;
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class vtkIncrementalPointLocator;
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class VTKCOMMONDATAMODEL_EXPORT vtkPolygon : public vtkCell
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{
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public:
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static vtkPolygon* New();
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vtkTypeMacro(vtkPolygon, vtkCell);
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void PrintSelf(ostream& os, vtkIndent indent) override;
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///@{
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/**
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* See the vtkCell API for descriptions of these methods.
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*/
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int GetCellType() override { return VTK_POLYGON; }
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int GetCellDimension() override { return 2; }
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int GetNumberOfEdges() override { return this->GetNumberOfPoints(); }
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int GetNumberOfFaces() override { return 0; }
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vtkCell* GetEdge(int edgeId) override;
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vtkCell* GetFace(int) override { return nullptr; }
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int CellBoundary(int subId, const double pcoords[3], vtkIdList* pts) override;
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void Contour(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
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vtkCellArray* verts, vtkCellArray* lines, vtkCellArray* polys, vtkPointData* inPd,
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vtkPointData* outPd, vtkCellData* inCd, vtkIdType cellId, vtkCellData* outCd) override;
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void Clip(double value, vtkDataArray* cellScalars, vtkIncrementalPointLocator* locator,
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vtkCellArray* tris, vtkPointData* inPd, vtkPointData* outPd, vtkCellData* inCd,
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vtkIdType cellId, vtkCellData* outCd, int insideOut) override;
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int EvaluatePosition(const double x[3], double closestPoint[3], int& subId, double pcoords[3],
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double& dist2, double weights[]) override;
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void EvaluateLocation(int& subId, const double pcoords[3], double x[3], double* weights) override;
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int IntersectWithLine(const double p1[3], const double p2[3], double tol, double& t, double x[3],
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double pcoords[3], int& subId) override;
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int Triangulate(int index, vtkIdList* ptIds, vtkPoints* pts) override;
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void Derivatives(
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int subId, const double pcoords[3], const double* values, int dim, double* derivs) override;
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int IsPrimaryCell() override { return 0; }
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///@}
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/**
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* Compute the area of a polygon. This is a convenience function
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* which simply calls static double ComputeArea(vtkPoints *p,
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* vtkIdType numPts, vtkIdType *pts, double normal[3]);
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* with the appropriate parameters from the instantiated vtkPolygon.
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*/
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double ComputeArea();
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/**
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* Compute the interpolation functions/derivatives.
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* (aka shape functions/derivatives)
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* Two interpolation algorithms are available: 1/r^2 and Mean Value
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* Coordinate. The former is used by default. To use the second algorithm,
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* set UseMVCInterpolation to be true.
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* The function assumes the input point lies on the polygon plane without
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* checking that.
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*/
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void InterpolateFunctions(const double x[3], double* sf) override;
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///@{
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/**
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* Computes the unit normal to the polygon. If pts=nullptr, point indexing is
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* assumed to be {0, 1, ..., numPts-1}.
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*/
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static void ComputeNormal(vtkPoints* p, int numPts, const vtkIdType* pts, double n[3]);
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static void ComputeNormal(vtkPoints* p, double n[3]);
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static void ComputeNormal(vtkIdTypeArray* ids, vtkPoints* pts, double n[3]);
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///@}
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/**
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* Compute the polygon normal from an array of points. This version assumes
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* that the polygon is convex, and looks for the first valid normal.
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*/
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static void ComputeNormal(int numPts, double* pts, double n[3]);
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/**
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* Determine whether or not a polygon is convex. This is a convenience
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* function that simply calls static bool IsConvex(int numPts,
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* vtkIdType *pts, vtkPoints *p) with the appropriate parameters from the
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* instantiated vtkPolygon.
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*/
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bool IsConvex();
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///@{
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/**
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* Determine whether or not a polygon is convex. If pts=nullptr, point indexing
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* is assumed to be {0, 1, ..., numPts-1}.
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*/
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static bool IsConvex(vtkPoints* p, int numPts, const vtkIdType* pts);
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static bool IsConvex(vtkIdTypeArray* ids, vtkPoints* p);
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static bool IsConvex(vtkPoints* p);
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///@}
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///@{
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/**
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* Compute the centroid of a set of points. Returns false if the computation
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* is invalid (this occurs when numPts=0 or when ids is empty).
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*/
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static bool ComputeCentroid(vtkPoints* p, int numPts, const vtkIdType* pts, double centroid[3]);
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static bool ComputeCentroid(vtkIdTypeArray* ids, vtkPoints* pts, double centroid[3]);
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///@}
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/**
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* Compute the area of a polygon in 3D. The area is returned, as well as
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* the normal (a side effect of using this method). If you desire to
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* compute the area of a triangle, use vtkTriangleArea which is faster.
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* If pts==nullptr, point indexing is supposed to be {0, 1, ..., numPts-1}.
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* If you already have a vtkPolygon instantiated, a convenience function,
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* ComputeArea() is provided.
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*/
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static double ComputeArea(vtkPoints* p, vtkIdType numPts, const vtkIdType* pts, double normal[3]);
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/**
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* Create a local s-t coordinate system for a polygon. The point p0 is
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* the origin of the local system, p10 is s-axis vector, and p20 is the
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* t-axis vector. (These are expressed in the modeling coordinate system and
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* are vectors of dimension [3].) The values l20 and l20 are the lengths of
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* the vectors p10 and p20, and n is the polygon normal.
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*/
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int ParameterizePolygon(
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double p0[3], double p10[3], double& l10, double p20[3], double& l20, double n[3]);
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/**
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* Determine whether a point is inside the specified polygon. The function
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* computes the winding number to assess inclusion. It works for arbitrary
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* polygon shapes (e.g., non-convex) oriented arbitrarily in 3D
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* space. Returns 0 if the point is not in the polygon; 1 if it is. Can
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* also return -1 to indicate a degenerate polygon. Parameters passed into
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* the method include the point in question x[3]; the polygon defined by
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* (npts,pts); the bounds of the polygon bounds[6]; and the normal n[3] to
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* the polygon. (The implementation was inspired by Dan Sunday's book
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* Practical Geometry Algorithms.) This method is thread safe.
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*/
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static int PointInPolygon(double x[3], int numPts, double* pts, double bounds[6], double n[3]);
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/**
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* Triangulate this polygon. The user must provide the vtkIdList outTris.
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* On output, the outTris list contains the ids of the points defining the
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* triangulation (i.e., not the associated polygon->PointIds, rather the
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* index into the polygon->Points array). The ids are ordered into groups
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* of three: each three-group defines one triangle. The method returns
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* non-zero if the triangulation is successful.
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*/
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int Triangulate(vtkIdList* outTris);
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/**
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* Same as Triangulate(vtkIdList *outTris)
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* but with a first pass to split the polygon into non-degenerate polygons.
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*/
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int NonDegenerateTriangulate(vtkIdList* outTris);
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/**
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* Triangulate polygon and enforce that the ratio of the smallest triangle
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* area to the polygon area is greater than a user-defined tolerance. The user
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* must provide the vtkIdList outTris. On output, the outTris list contains
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* the ids of the points defining the triangulation. The ids are ordered into
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* groups of three: each three-group defines one triangle.
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*/
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int BoundedTriangulate(vtkIdList* outTris, double tol);
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/**
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* Compute the distance of a point to a polygon. The closest point on
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* the polygon is also returned. The bounds should be provided to
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* accelerate the computation.
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*/
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static double DistanceToPolygon(
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double x[3], int numPts, double* pts, double bounds[6], double closest[3]);
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/**
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* Method intersects two polygons. You must supply the number of points and
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* point coordinates (npts, *pts) and the bounding box (bounds) of the two
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* polygons. Also supply a tolerance squared for controlling
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* error. The method returns 1 if there is an intersection, and 0 if
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* not. A single point of intersection x[3] is also returned if there
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* is an intersection.
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*/
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static int IntersectPolygonWithPolygon(int npts, double* pts, double bounds[6], int npts2,
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double* pts2, double bounds2[3], double tol, double x[3]);
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/**
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* Intersect two convex 2D polygons to produce a line segment as output.
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* The return status of the methods indicated no intersection (returns 0);
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* a single point of intersection (returns 1); or a line segment (i.e., two
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* points of intersection, returns 2). The points of intersection are
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* returned in the arrays p0 and p1. If less than two points of
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* intersection are generated then p1 and/or p0 may be
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* indeterminiate. Finally, if the two convex polygons are parallel, then
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* "0" is returned (i.e., no intersection) even if the triangles lie on one
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* another.
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*/
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static int IntersectConvex2DCells(
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vtkCell* cell1, vtkCell* cell2, double tol, double p0[3], double p1[3]);
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///@{
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/**
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* Set/Get the flag indicating whether to use Mean Value Coordinate for the
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* interpolation. If true, InterpolateFunctions() uses the Mean Value
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* Coordinate to compute weights. Otherwise, the conventional 1/r^2 method
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* is used. The UseMVCInterpolation parameter is set to false by default.
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*/
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vtkGetMacro(UseMVCInterpolation, bool);
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vtkSetMacro(UseMVCInterpolation, bool);
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///@}
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//@{
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/**
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* Specify an internal tolerance for operations requiring polygon
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* triangulation. (For example, clipping and contouring operations proceed
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* by first triangulating the polygon, and then clipping/contouring the
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* resulting triangles.) This is a normalized tolerance value multiplied
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* by the diagonal length of the polygon bounding box. Is it used to
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* determine whether potential triangulation edges intersect one another.
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*/
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vtkSetClampMacro(Tolerance, double, 0.0, 1.0);
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vtkGetMacro(Tolerance, double);
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//@}
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protected:
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vtkPolygon();
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~vtkPolygon() override;
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// Compute the interpolation functions using Mean Value Coordinate.
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void InterpolateFunctionsUsingMVC(const double x[3], double* weights);
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// variables used by instances of this class
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double Tolerance; // Intersection tolerance set by public API
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double Tol; // Internal tolerance set by ComputeBounds()
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void ComputeTolerance(); // Compute the internal tolerance Tol
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int SuccessfulTriangulation; // Stops recursive triangulation if necessary
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vtkIdList* Tris; // Output triangulation placed here
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// These are used for internal computation.
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vtkTriangle* Triangle;
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vtkQuad* Quad;
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vtkDoubleArray* TriScalars;
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vtkLine* Line;
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// Parameter indicating whether to use Mean Value Coordinate algorithm
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// for interpolation. The parameter is false by default.
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bool UseMVCInterpolation;
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// Helper methods for triangulation------------------------------
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// Made public for external access
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public:
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// Ear cut triangulation options. The order in which vertices are
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// removed are controlled by different measures. Changing this can
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// make subtle differences in some cases. Historically the
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// PERIMETER2_TO_AREA_RATIO has been used.
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enum EarCutMeasureTypes
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{
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PERIMETER2_TO_AREA_RATIO = 0,
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DOT_PRODUCT = 1,
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BEST_QUALITY = 2
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};
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///@{
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/**
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* A fast triangulation method. Uses recursive divide and
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* conquer based on plane splitting to reduce loop into triangles.
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* The cell (e.g., triangle) is presumed properly initialized (i.e.,
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* Points and PointIds). Ears can be removed using different measures
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* (the measures indicate convexity plus characterize the local
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* geometry around each vertex).
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*/
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int EarCutTriangulation(int measure = PERIMETER2_TO_AREA_RATIO);
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int EarCutTriangulation(vtkIdList* outTris, int measure = PERIMETER2_TO_AREA_RATIO);
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///@}
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///@{
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/**
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* A fast triangulation method. Uses recursive divide and
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* conquer based on plane splitting to reduce loop into triangles.
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* The cell (e.g., triangle) is presumed properly initialized (i.e.,
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* Points and PointIds). Unlike EarCutTriangulation(), vertices are visited
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* sequentially without preference to angle.
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*/
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int UnbiasedEarCutTriangulation(int seed, int measure = PERIMETER2_TO_AREA_RATIO);
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int UnbiasedEarCutTriangulation(
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int seed, vtkIdList* outTris, int measure = PERIMETER2_TO_AREA_RATIO);
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///@}
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private:
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vtkPolygon(const vtkPolygon&) = delete;
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void operator=(const vtkPolygon&) = delete;
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};
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#endif
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