text: /*=========================================================================
  
    Program:   Visualization Toolkit
    Module:    vtkLine.h
  
    Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
    All rights reserved.
    See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
  
       This software is distributed WITHOUT ANY WARRANTY; without even
       the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
       PURPOSE.  See the above copyright notice for more information.
  
  =========================================================================*/
  /**
   * @class   vtkLine
   * @brief   cell represents a 1D line
   *
   * vtkLine is a concrete implementation of vtkCell to represent a 1D line.
  */
  
  #ifndef vtkLine_h
  #define vtkLine_h
  
  #include "vtkCommonDataModelModule.h" // For export macro
  #include "vtkCell.h"
  class vtkIncrementalPointLocator;
  
  class VTKCOMMONDATAMODEL_EXPORT vtkLine : public vtkCell
  {
  public:
    static vtkLine *New();
    vtkTypeMacro(vtkLine,vtkCell);
    void PrintSelf(ostream& os, vtkIndent indent) override;
  
    //@{
    /**
     * See the vtkCell API for descriptions of these methods.
     */
    int GetCellType() override {return VTK_LINE;};
    int GetCellDimension() override {return 1;};
    int GetNumberOfEdges() override {return 0;};
    int GetNumberOfFaces() override {return 0;};
    vtkCell *GetEdge(int) override  {return nullptr;};
    vtkCell *GetFace(int) override  {return nullptr;};
    int CellBoundary(int subId, double pcoords[3], vtkIdList *pts) override;
    void Contour(double value, vtkDataArray *cellScalars,
                 vtkIncrementalPointLocator *locator, vtkCellArray *verts,
                 vtkCellArray *lines, vtkCellArray *polys,
                 vtkPointData *inPd, vtkPointData *outPd,
                 vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd) override;
    int EvaluatePosition(double x[3], double* closestPoint,
                         int& subId, double pcoords[3],
                         double& dist2, double *weights) override;
    void EvaluateLocation(int& subId, double pcoords[3], double x[3],
                          double *weights) override;
    int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts) override;
    void Derivatives(int subId, double pcoords[3], double *values,
                     int dim, double *derivs) override;
    double *GetParametricCoords() override;
    //@}
  
    /**
     * Clip this line using scalar value provided. Like contouring, except
     * that it cuts the line to produce other lines.
     */
    void Clip(double value, vtkDataArray *cellScalars,
              vtkIncrementalPointLocator *locator, vtkCellArray *lines,
              vtkPointData *inPd, vtkPointData *outPd,
              vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd,
              int insideOut) override;
  
    /**
     * Return the center of the triangle in parametric coordinates.
     */
    int GetParametricCenter(double pcoords[3]) override;
  
    /**
     * Line-line intersection. Intersection has to occur within [0,1] parametric
     * coordinates and with specified tolerance.
     */
    int IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
                          double x[3], double pcoords[3], int& subId) override;
  
  
    /**
     * Performs intersection of the projection of two finite 3D lines onto a 2D
     * plane. An intersection is found if the projection of the two lines onto
     * the plane perpendicular to the cross product of the two lines intersect.
     * The parameters (u,v) are the parametric coordinates of the lines at the
     * position of closest approach.
     */
    static int Intersection(const double p1[3], const double p2[3],
                            const double x1[3], const double x2[3],
                            double& u, double& v);
  
  
    /**
     * Performs intersection of two finite 3D lines. An intersection is found if
     * the projection of the two lines onto the plane perpendicular to the cross
     * product of the two lines intersect, and if the distance between the
     * closest points of approach are within a relative tolerance. The parameters
     * (u,v) are the parametric coordinates of the lines at the position of
     * closest approach.
  
     * NOTE: "Unlike Intersection(), which determines whether the projections of
     * two lines onto a plane intersect, Intersection3D() determines whether the
     * lines themselves in 3D space intersect, within a tolerance.
     */
    static int Intersection3D(double p1[3], double p2[3],
                              double x1[3], double x2[3],
                              double& u, double& v);
  
  
    /**
     * Compute the distance of a point x to a finite line (p1,p2). The method
     * computes the parametric coordinate t and the point location on the
     * line. Note that t is unconstrained (i.e., it may lie outside the range
     * [0,1]) but the closest point will lie within the finite line [p1,p2], if
     * it is defined. Also, the method returns the distance squared between x and
     * the line (p1,p2).
     */
    static double DistanceToLine(const double x[3], const double p1[3], const double p2[3],
                                double &t, double* closestPoint=nullptr);
  
  
    /**
     * Determine the distance of the current vertex to the edge defined by
     * the vertices provided.  Returns distance squared. Note: line is assumed
     * infinite in extent.
     */
    static double DistanceToLine(const double x[3], const double p1[3], const double p2[3]);
  
    /**
     * Computes the shortest distance squared between two infinite lines, each
     * defined by a pair of points (l0,l1) and (m0,m1).
     * Upon return, the closest points on the two line segments will be stored
     * in closestPt1 and closestPt2. Their parametric coords
     * (-inf <= t0, t1 <= inf) will be stored in t0 and t1. The return value is
     * the shortest distance squared between the two line-segments.
     */
    static double DistanceBetweenLines(
                  double l0[3], double l1[3],
                  double m0[3], double m1[3],
                  double closestPt1[3], double closestPt2[3],
                  double &t1, double &t2 );
  
    /**
     * Computes the shortest distance squared between two finite line segments
     * defined by their end points (l0,l1) and (m0,m1).
     * Upon return, the closest points on the two line segments will be stored
     * in closestPt1 and closestPt2. Their parametric coords (0 <= t0, t1 <= 1)
     * will be stored in t0 and t1. The return value is the shortest distance
     * squared between the two line-segments.
     */
    static double DistanceBetweenLineSegments(
                  double l0[3], double l1[3],
                  double m0[3], double m1[3],
                  double closestPt1[3], double closestPt2[3],
                  double &t1, double &t2 );
  
    /**
     * @deprecated Replaced by vtkLine::InterpolateFunctions as of VTK 5.2
     */
    static void InterpolationFunctions(double pcoords[3], double weights[2]);
    /**
     * @deprecated Replaced by vtkLine::InterpolateDerivs as of VTK 5.2
     */
    static void InterpolationDerivs(double pcoords[3], double derivs[2]);
    //@{
    /**
     * Compute the interpolation functions/derivatives
     * (aka shape functions/derivatives)
     */
    void InterpolateFunctions(double pcoords[3], double weights[2]) override
    {
      vtkLine::InterpolationFunctions(pcoords,weights);
    }
    void InterpolateDerivs(double pcoords[3], double derivs[2]) override
    {
      vtkLine::InterpolationDerivs(pcoords,derivs);
    }
    //@}
  
  protected:
    vtkLine();
    ~vtkLine() override {}
  
  private:
    vtkLine(const vtkLine&) = delete;
    void operator=(const vtkLine&) = delete;
  };
  
  //----------------------------------------------------------------------------
  inline int vtkLine::GetParametricCenter(double pcoords[3])
  {
    pcoords[0] = 0.5;
    pcoords[1] = pcoords[2] = 0.0;
    return 0;
  }
  
  #endif
  