/*=========================================================================

  Program:   Visualization Toolkit
  Module:    vtkPolyDataAlgorithm.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 vtkFiberSurface
 * @brief Given a fiber surface control polygon (FSCP) and an
 * unstructured grid composed of tetrahedral cells with two scalar arrays, this filter
 * computes the corresponding fiber surfaces.
 *
 * @section Introduction
 * Fiber surfaces are constructed from sets of fibers, the multivariate analogues
 * of isolines. The original paper [0] offers a general purpose method that produces
 * separating surfaces representing boundaries in bivariate fields. This filter is based
 * on an improvement over [0] which computes accurate and exact fiber surfaces. It can
 * handle arbitrary input polygons including open polygons or self-intersecting polygons.
 * The current implementation can better captures sharp features induced by polygon
 * bends [1].
 *
 * [0] Hamish Carr, Zhao Geng, Julien Tierny, Amit Chattopadhyay and Aaron Knoll,
 *     Fiber Surfaces: Generalizing Isosurfaces to Bivariate Data,
 *     Computer Graphics Forum, Volume 34, Issue 3, Pages 241-250, (EuroVis 2015)
 *
 * [1] Pavol Klacansky, Julien Tierny, Hamish Carr, Zhao Geng,
 *     Fast and Exact Fiber Surfaces for Tetrahedral Meshes,
 *     Paper in submission, 2015
 *
 * @section Algorithm For Extracting An Exact Fiber Surface
 *  Require: R.1 A 3D domain space represented by an unstructured grid composed of
 *               tetrahedral cells
 *           R.2 Two scalar fields, f1 and f2, that map the domain space to a 2D range
 *               space. These fields are assumed to be known at vertices of the
 *               unstructured grid: i.e they are two fields associated with the
 *               unstructured grid.
 *           R.3 A Fiber Surface Control Polygon (FSCP) defined in the range space as a
 *               list of line segments (l1, l2, ..., ln). The FSCP may be an open polyline
 *               or a self-intersecting polygon.
 *
 *   1. For each line segment l in FSCP, we ignore the endpoints of the line and assume
 *      this line extends to infinity. This line will then separate the range and its
 *      inverse image, i.e fiber surfaces, will also separate the domain. Based on the
 *      signed distance d between the image of a cell vertex v and line l in the range,
 *      v can be classified as white (d < 0), grey (d == 0) or black (d>0). The
 *      interpolation parameter between two vertices v1 and v2 in a cell edge can be
 *      computed as |d1| / (|d2|+|d1|), where d1 and d2 are the signed distances between
 *      images of v1,v2 and line l in the range. Once the classification and interpolation
 *      parameters for all vertices in a cell are known, then we can apply the Marching
 *      Tetrahedra algorithm. For each tetrahedron, this produces a planar cut which we
 *      refer to as a base fiber surface.
 *
 *   2. After generating the base fiber surface in each cell, we need a further clipping
 *      process to obtain the accurate fiber surface. Clipping is based on classifying the
 *      vertices of each triangle as follows:
 *      Given a line segment in the fiber surface control polygon (FSCP) parameterised
 *      from 0 to 1, we know that every triangle vertex in the base fiber surface belongs
 *      to the fiber surface, and that the fiber through each vertex can be parameterised
 *      with respect to the line segment. Therefore, we compute the parameter t for each
 *      vertex and use it to classify the vertex as:
 *           0: t < 0        Vertex is below the clipping range [0,1] and will be removed
 *           1: 0 ≤ t ≤ 1    Vertex is inside the clipping range [0,1] and is retained
 *           2: 1 < t        Vertex is above the clipping  range [0,1] and will be removed
 *      Based on the classification, we can further clip the triangle to obtain the final
 *      surface.
 *
 *   3. Repeating steps 1 and 2 for every line segment in FSCP and iterating through each
 *      cell will generate the final fiber surfaces in the domain.
 *
 * @section VTK Filter Design
 * As stated in part B (R.1), we will compute the fiber surface over an unstructured grid.
 * This grid will have to be an input of the VTK filter. The two scalar fields, however,
 * are assumed to be stored in the VTK unstructured grid, and will be specified using the
 * SetField1() and SetField2() accessors. The FSCP will be passed into the filter as a
 * second input port. The data type of FSCP is required to be a vtkPolyData, with each of
 * its cell defined as a line segment and its point coordinates defined in the range of
 * the bivariate fields of the input grid.
 *
 * @section Case Tables
 * @subsection Marching tetrahedra with grey cases
 * In this filter, we have added one vertex classification in Marching Tetrahedra. The
 * reason is because we need a grey classification to ensure that surfaces coincident with
 * the boundary of the tetrahedra will also be included in the output. Given an iso-value,
 * each vertex on the tetrahedron can be classified into three types, including
 * equal-(G)rey, below-(W)hite or above-(B)lack the isovalue.
 * The notation of the classifications are represented as:
 *     W or 0 --- below an iso-value
 *     G or 1 --- equal an iso-value
 *     B or 2 --- above an iso-value
 * The following illustration summarises all of the surface cases (Asterisk * is used to
 * highlight the outline of the triangle):
 * Case A (no triangles): 0000
 *    No triangle is generated.
 *
 *          W
 *         ...
 *        . . .
 *       .  .  .
 *      .  .W.  .
 *     . .     . .
 *    W...........W
 *
 * Case B (one grey vertex): 0001, 0010, 0100, 1000
 *    Only a vertex is kept, no triangle is generated.
 *          W
 *         ...
 *        . . .
 *       .  .  .
 *      .  .G.  .
 *     . .     . .
 *    W...........W
 *
 * Case C (one grey edge): 0011, 0101, 0110, 1001, 1010, 1100
 *    Only an edge is kept, no triangle is generated.
 *          G
 *         ...
 *        . . .
 *       .  .  .
 *      .  .G.  .
 *     . .     . .
 *    W...........W
 *
 * Case D (standard triangle case): 0002, 0020, 0200, 2000
 *    One triangle is generated
 *          W                           W
 *         ...                         ...
 *        . . .                       . * .
 *       .  .  .                     . *.* .
 *      .  .B.  .        ->         . * B * .
 *     . .     . .                 . ** * ** .
 *    W...........W               W...........W
 *
 * Case E (one grey face): 0111, 1011, 1101, 1110
 *    The triangle on one face of the tetra is generated.
 *          G                          G
 *         ...                        .**
 *        . . .                      . * *
 *       .  .  .         ->         .  *  *
 *      .  .G.  .                  .  .G*  *
 *     . .     . .                . .     * *
 *    W...........G              W...........G
 *
 * Case F (triangle through vertex):  0012 0021 0102 0120 0201 0210
 *                                    1002 1020 1200 2001 2010 2100
 *    A triangle connecting one of the tetra vertex is generated.
 *          G                          G
 *         ...                        .*.
 *        . . .                      .*.*.
 *       .  .  .         ->         . *.* .
 *      .  .B.  .                  . *.B.* .
 *     . .     . .                . * * * * .
 *    W...........W              W...........W
 *
 * Case G (grey tet - treat as empty): 1111
 *    No triangle is generated.
 *          G
 *         ...
 *        . . .
 *       .  .  .
 *      .  .G.  .
 *     . .     . .
 *    G...........G
 *
 * Case H (triangle through edge): 0112 0121 0211 1012 1021 1102
 *                                 1120 1201 1210 2011 2101 2110
 *    A triangle containing an edge of the tetra is generated.
 *
 *          G                                      G
 *         ...                                    ..*
 *        . . .                                  . . *
 *       .  .  .                                . *.  *
 *      .   .   .                              .   .   *
 *     .    .    .           ->               . *  .    *
 *    .   . W .   .                          .   . W .   *
 *   .  .      .   .                        .  *      .   *
 *  . .          .  .                      . .      *   .  *
 *  B.............. G                      B...............G
 *
 * Case I (standard quad case): 0022 0202 0220 2002 2020 2200
 *   A quand is generated, which can be split to two triangles.
 *
 *          W                                      W
 *         ...                                    ...
 *        . . .                                  . . .
 *       .  .  .                                .  .  .
 *      .   .   .                              *  *. * *
 *     .    .    .           ->               .*   .   *.
 *    .   . W .   .                          . * . W . * .
 *   .  .      .   .                        .  * *  *  *   .
 *  . .          .  .                      . .            . .
 *  B.............. B                     B..................B
 *
 * Case J (complement of Case E): 1112 1121 1211 2111
 * Case K (complement of Case F): 0122 0212 0221 1022 1202
 *                                1220 2012 2021 2102 2120 2201 2210
 * Case L (complement of Case C): 1122 1212 1221 2112 2121 2211
 * Case M (complement of Case D): 0222 2022 2202 2220
 * Case N (complement of Case B): 1222 2122 2212 2221
 * Case O (complement of Case A): 2222
 *
 * @subsection Clipping cases of the base fiber surface
 * After generating the base fiber surface in each cell, we need a further clipping
 * process to obtain the accurate fiber surface. Clipping is based on classifying the
 * vertices of each triangle to several cases, which will be described in this section.
 * In order to keep things consistent, we assume that the vertices are ordered CCW, and
 * that edges are numbered according to the opposing vertex:
 *
 *      v0
 *     /  \
 *   e2    e1
 *   /      \
 * v1---e0---v2
 *
 * =======================================================================
 * There are six cases for clipping the base fiber surface (subject to the usual
 * symmetries & complementarity)
 *------------------------------------------------------------------------
 * Case A (No triangles): Cases 000 & 222
 * Here, the entire triangle is discarded
 *
 * 000(A):  0
 *         . .
 *        .   .
 *       .     .
 *      .       .
 *     .         .
 *    0...........0
 *
 *------------------------------------------------------------------------
 * Case B (Point-triangle): Cases 001, 010, 100, 122, 212, 221
 * One vertex is kept, and a single triangle is extracted
 *
 * 001(B):  1
 *         / \
 *        /   \
 *       E-----E
 *      .       .
 *     .         .
 *    0...........0
 *
 *------------------------------------------------------------------------
 * Case C (Edge Quad): Cases 011, 101, 110, 112, 121, 211
 * Two vertices are kept, and a quad is extracted based on the edge
 *
 * 011(C):  1
 *         /|\
 *        / | \
 *       /  |  E
 *      /   | / .
 *     /    |/   .
 *    1-----E.....0
 *
 *------------------------------------------------------------------------
 * Case D (Stripe): Cases 002, 020, 022, 200, 202, 220
 * No vertices are kept, but a stripe across the middle is generated
 *
 * 022(D):  2
 *         . .
 *        .   E
 *       .   /|\
 *      .   / | E
 *     .   /  |/ .
 *    2...E---E...0
 *
 *------------------------------------------------------------------------
 * Case E (Point-Stripe): Cases 012, 021, 102, 120, 201, 210
 * One vertex is kept, with a stripe through the triangle
 *
 * 021(E):  1
 *         / \
 *        E---E
 *       .|\  |.
 *      . | \ | .
 *     .  |  \|  .
 *    2...E---E...0
 *
 *------------------------------------------------------------------------
 * Case F (Entire): Case 111
 * All three vertices are kept, along with the triangle
 *
 * 111(F):  1
 *         / \
 *        /   \
 *       /     \
 *      /       \
 *     /         \
 *    1-----------1
 *
 *
 * @section How to use this filter
 * Suppose we have a tetrahedral mesh stored in a vtkUnstructuredGrid, we call this
 * data set "inputData". This data set has two scalar arrays whose names are "f1"
 * and "f2" respectively. Assume the "inputPoly" is a valid input polygon. Given
 * these input above, this filter can be used as follows in c++ sample code:
 *
 *     vtkSmartPointer<vtkFiberSurface> fiberSurface =
 *                            vtkSmartPointer<vtkFiberSurface>::New();
 *     fiberSurface->SetInputData(0,inputData);
 *     fiberSurface->SetInputData(1,inputPoly);
 *     fiberSurface->SetField1("f1");
 *     fiberSurface->SetField2("f2");
 *     fiberSurface->Update();
 *
 * The filter output which can be called by "fiberSurface->GetOutput()", will be a
 * vtkPolyData containing the output fiber surfaces.
 */

#ifndef vtkFiberSurface_h
#define vtkFiberSurface_h

#include "vtkFiltersTopologyModule.h" // For export macro
#include "vtkPolyDataAlgorithm.h"

class VTKFILTERSTOPOLOGY_EXPORT vtkFiberSurface : public vtkPolyDataAlgorithm
{
public:
  static vtkFiberSurface* New();
  vtkTypeMacro(vtkFiberSurface, vtkPolyDataAlgorithm);
  void PrintSelf(ostream& os, vtkIndent indent) override;

  /**
   * Specify the first field name to be used in this filter.
   */
  void SetField1(const char* fieldName);

  /**
   * Specify the second field name to be used in the filter.
   */
  void SetField2(const char* fieldName);

  /**
   * This structure lists the vertices to use for the marching tetrahedra,
   * Some of these vertices need to be interpolated, but others are the vertices of
   * the tetrahedron already, and for this we need to store the type of vertex.
   * bv_not_used: Symbol for an unused entry
   * bv_vertex_*: Vertices on a tetrahedron
   * bv_edge_*: Vertices on the edges of a tetrahedron
   */
  enum BaseVertexType
  {
    bv_not_used,
    bv_vertex_0,
    bv_vertex_1,
    bv_vertex_2,
    bv_vertex_3,
    bv_edge_01,
    bv_edge_02,
    bv_edge_03,
    bv_edge_12,
    bv_edge_13,
    bv_edge_23
  };

  /**
   * After generating the base fiber surface in each cell, we need a further clipping
   * process to obtain the accurate fiber surface. Clipping is based on classifying the
   * vertices of each triangle, this structure lists the type of vertices to be used for
   * the clipping triangles.
   * Some of these vertices need to be interpolated, but others are the vertices of
   * the triangle already, and for this we need to store the type of vertex.
   * Moreover, vertices along the edges of the triangle may be interpolated either at
   * parameter value 0 or at parameter value 1. In other words, there are three classes
   * of vertex with three choices of each, with a total of nine vertices. We therefore
   * store an ID code for each possibility as follows:
   */
  enum ClipVertexType
  {
    not_used,
    vertex_0,
    vertex_1,
    vertex_2,
    edge_0_parm_0,
    edge_1_parm_0,
    edge_2_parm_0,
    edge_0_parm_1,
    edge_1_parm_1,
    edge_2_parm_1,
  };

protected:
  vtkFiberSurface();
  int FillInputPortInformation(int port, vtkInformation* info) override;
  int RequestData(vtkInformation*, vtkInformationVector**, vtkInformationVector*) override;

  // name of the input array names.
  const char* Fields[2];

private:
  vtkFiberSurface(const vtkFiberSurface&) = delete;
  void operator=(const vtkFiberSurface&) = delete;
};
#endif
