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

  Program:   Visualization Toolkit
  Module:    TestPolyhedronConvexity.cxx

  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.

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

#include <vector>

#include "vtkCellArray.h"
#include "vtkCellData.h"
#include "vtkDataArray.h"
#include "vtkDoubleArray.h"
#include "vtkExtractEdges.h"
#include "vtkMath.h"
#include "vtkPointData.h"
#include "vtkPoints.h"
#include "vtkPolyhedron.h"
#include "vtkProperty.h"
#include "vtkSmartPointer.h"
#include "vtkTestUtilities.h"
#include "vtkUnstructuredGrid.h"

enum Shape
{
  dodecahedron,
  u_shape,
  cube,
  colinear_cube,
  degenerate_cube,
  convex_pyramid,
  nonconvex_pyramid
};

bool IsConvex(Shape shape)
{
  vtkSmartPointer<vtkPoints> polyhedronPoints = vtkSmartPointer<vtkPoints>::New();

  vtkSmartPointer<vtkCellArray> polyhedronFaces = vtkSmartPointer<vtkCellArray>::New();

  std::vector<vtkIdType> polyhedronPointsIds;

  if (shape == dodecahedron)
  {
    // create a dodecahedron
    const int nPoints = 20;
    const int nFaces = 12;

    double dodechedronPoint[nPoints][3] = {
      { 1.21412, 0, 1.58931 },
      { 0.375185, 1.1547, 1.58931 },
      { -0.982247, 0.713644, 1.58931 },
      { -0.982247, -0.713644, 1.58931 },
      { 0.375185, -1.1547, 1.58931 },
      { 1.96449, 0, 0.375185 },
      { 0.607062, 1.86835, 0.375185 },
      { -1.58931, 1.1547, 0.375185 },
      { -1.58931, -1.1547, 0.375185 },
      { 0.607062, -1.86835, 0.375185 },
      { 1.58931, 1.1547, -0.375185 },
      { -0.607062, 1.86835, -0.375185 },
      { -1.96449, 0, -0.375185 },
      { -0.607062, -1.86835, -0.375185 },
      { 1.58931, -1.1547, -0.375185 },
      { 0.982247, 0.713644, -1.58931 },
      { -0.375185, 1.1547, -1.58931 },
      { -1.21412, 0, -1.58931 },
      { -0.375185, -1.1547, -1.58931 },
      { 0.982247, -0.713644, -1.58931 },
    };
    polyhedronPoints->SetNumberOfPoints(nPoints);
    for (int i = 0; i < nPoints; i++)
    {
      polyhedronPoints->SetPoint(i, dodechedronPoint[i]);
      polyhedronPointsIds.push_back(i);
    }

    vtkIdType dodechedronFace[nFaces][5] = {
      { 0, 1, 2, 3, 4 },
      { 0, 5, 10, 6, 1 },
      { 1, 6, 11, 7, 2 },
      { 2, 7, 12, 8, 3 },
      { 3, 8, 13, 9, 4 },
      { 4, 9, 14, 5, 0 },
      { 15, 10, 5, 14, 19 },
      { 16, 11, 6, 10, 15 },
      { 17, 12, 7, 11, 16 },
      { 18, 13, 8, 12, 17 },
      { 19, 14, 9, 13, 18 },
      { 19, 18, 17, 16, 15 },
    };

    for (int i = 0; i < nFaces; i++)
    {
      polyhedronFaces->InsertNextCell(5, dodechedronFace[i]);
    }
  }
  else if (shape == u_shape)
  {
    // create a concave shape
    const int nPoints = 16;
    const int nFaces = 10;

    double concaveShapePoint[nPoints][3] = {
      { .5, -.5, .25 },
      { .5, .5, .25 },
      { .25, .5, .25 },
      { .25, -.25, .25 },
      { -.25, -.25, .25 },
      { -.25, .5, .25 },
      { -.5, .5, .25 },
      { -.5, -.5, .25 },
      { .5, -.5, -.25 },
      { .5, .5, -.25 },
      { .25, .5, -.25 },
      { .25, -.25, -.25 },
      { -.25, -.25, -.25 },
      { -.25, .5, -.25 },
      { -.5, .5, -.25 },
      { -.5, -.5, -.25 },
    };

    polyhedronPoints->SetNumberOfPoints(nPoints);
    for (int i = 0; i < nPoints; i++)
    {
      polyhedronPoints->SetPoint(i, concaveShapePoint[i]);
      polyhedronPointsIds.push_back(i);
    }

    vtkIdType f1[8] = { 0, 1, 2, 3, 4, 5, 6, 7 };
    vtkIdType f2[8] = { 15, 14, 13, 12, 11, 10, 9, 8 };
    vtkIdType f3[4] = { 0, 7, 15, 8 };
    vtkIdType f4[4] = { 1, 0, 8, 9 };
    vtkIdType f5[4] = { 2, 1, 9, 10 };
    vtkIdType f6[4] = { 3, 2, 10, 11 };
    vtkIdType f7[4] = { 4, 3, 11, 12 };
    vtkIdType f8[4] = { 5, 4, 12, 13 };
    vtkIdType f9[4] = { 6, 5, 13, 14 };
    vtkIdType f10[4] = { 7, 6, 14, 15 };

    vtkIdType* concaveShapeFace[nFaces] = { f1, f2, f3, f4, f5, f6, f7, f8, f9, f10 };

    for (int i = 0; i < nFaces; i++)
    {
      polyhedronFaces->InsertNextCell((i >= 2 ? 4 : 8), concaveShapeFace[i]);
    }
  }
  else if (shape == cube)
  {
    // create a cube
    const int nPoints = 8;
    const int nFaces = 6;

    double cubeShapePoint[nPoints][3] = {
      { .5, .5, .5 },
      { -.5, .5, .5 },
      { -.5, -.5, .5 },
      { .5, -.5, .5 },
      { .5, .5, -.5 },
      { -.5, .5, -.5 },
      { -.5, -.5, -.5 },
      { .5, -.5, -.5 },
    };

    polyhedronPoints->SetNumberOfPoints(nPoints);
    for (int i = 0; i < nPoints; i++)
    {
      polyhedronPoints->SetPoint(i, cubeShapePoint[i]);
      polyhedronPointsIds.push_back(i);
    }

    vtkIdType f1[4] = { 0, 1, 2, 3 };
    vtkIdType f2[4] = { 7, 6, 5, 4 };
    vtkIdType f3[4] = { 0, 3, 7, 4 };
    vtkIdType f4[4] = { 5, 1, 0, 4 };
    vtkIdType f5[4] = { 6, 2, 1, 5 };
    vtkIdType f6[4] = { 7, 3, 2, 6 };

    vtkIdType* cubeShapeFace[nFaces] = { f1, f2, f3, f4, f5, f6 };

    for (int i = 0; i < nFaces; i++)
    {
      polyhedronFaces->InsertNextCell(4, cubeShapeFace[i]);
    }
  }
  else if (shape == colinear_cube)
  {
    // create a cube with two rectangles comprising one of the faces.
    const int nPoints = 10;
    const int nFaces = 7;

    double cubeShapePoint[nPoints][3] = {
      { .5, .5, .5 },
      { 0., .5, .5 },
      { -.5, .5, .5 },
      { -.5, -.5, .5 },
      { .5, -.5, .5 },
      { .5, .5, -.5 },
      { 0., .5, -.5 },
      { -.5, .5, -.5 },
      { -.5, -.5, -.5 },
      { .5, -.5, -.5 },
    };

    polyhedronPoints->SetNumberOfPoints(nPoints);
    for (int i = 0; i < nPoints; i++)
    {
      polyhedronPoints->SetPoint(i, cubeShapePoint[i]);
      polyhedronPointsIds.push_back(i);
    }

    vtkIdType f1[5] = { 0, 1, 2, 3, 4 };
    vtkIdType f2[5] = { 9, 8, 7, 6, 5 };
    vtkIdType f3[4] = { 0, 4, 9, 5 };
    vtkIdType f4[4] = { 7, 2, 1, 6 };
    vtkIdType f5[4] = { 5, 6, 1, 0 };
    vtkIdType f6[4] = { 8, 3, 2, 7 };
    vtkIdType f7[4] = { 9, 4, 3, 8 };

    vtkIdType* cubeShapeFace[nFaces] = { f1, f2, f3, f4, f5, f6, f7 };

    for (int i = 0; i < nFaces; i++)
    {
      if (i < 2)
      {
        polyhedronFaces->InsertNextCell(5, cubeShapeFace[i]);
      }
      else
      {
        polyhedronFaces->InsertNextCell(4, cubeShapeFace[i]);
      }
    }
  }
  else if (shape == degenerate_cube)
  {
    // create a cube with two degenerate points.
    const int nPoints = 10;
    const int nFaces = 7;

    double cubeShapePoint[nPoints][3] = {
      { .5, .5, .5 },
      { .5, .5, .5 },
      { -.5, .5, .5 },
      { -.5, -.5, .5 },
      { .5, -.5, .5 },
      { .5, .5, -.5 },
      { .5, .5, -.5 },
      { -.5, .5, -.5 },
      { -.5, -.5, -.5 },
      { .5, -.5, -.5 },
    };

    polyhedronPoints->SetNumberOfPoints(nPoints);
    for (int i = 0; i < nPoints; i++)
    {
      polyhedronPoints->SetPoint(i, cubeShapePoint[i]);
      polyhedronPointsIds.push_back(i);
    }

    vtkIdType f1[5] = { 0, 1, 2, 3, 4 };
    vtkIdType f2[5] = { 9, 8, 7, 6, 5 };
    vtkIdType f3[4] = { 0, 4, 9, 5 };
    vtkIdType f4[4] = { 7, 2, 1, 6 };
    vtkIdType f5[4] = { 5, 6, 1, 0 };
    vtkIdType f6[4] = { 8, 3, 2, 7 };
    vtkIdType f7[4] = { 9, 4, 3, 8 };

    vtkIdType* cubeShapeFace[nFaces] = { f1, f2, f3, f4, f5, f6, f7 };

    for (int i = 0; i < nFaces; i++)
    {
      if (i < 2)
      {
        polyhedronFaces->InsertNextCell(5, cubeShapeFace[i]);
      }
      else
      {
        polyhedronFaces->InsertNextCell(4, cubeShapeFace[i]);
      }
    }
  }
  else if (shape == convex_pyramid)
  {
    // create a simple convex pyramid
    const int nPoints = 5;
    const int nFaces = 5;

    double pyramidShapePoint[nPoints][3] = {
      { 0., 0., -.5 },
      { 0., 1., -.5 },
      { 1., 1., -.5 },
      { 1., 0., -.5 },
      { .5, .5, .5 },
    };

    polyhedronPoints->SetNumberOfPoints(nPoints);
    for (int i = 0; i < nPoints; i++)
    {
      polyhedronPoints->SetPoint(i, pyramidShapePoint[i]);
      polyhedronPointsIds.push_back(i);
    }

    vtkIdType f1[4] = { 0, 1, 2, 3 };
    vtkIdType f2[3] = { 0, 4, 1 };
    vtkIdType f3[3] = { 1, 4, 2 };
    vtkIdType f4[3] = { 2, 4, 3 };
    vtkIdType f5[3] = { 3, 4, 0 };

    vtkIdType* pyramidShapeFace[nFaces] = { f1, f2, f3, f4, f5 };

    for (int i = 0; i < nFaces; i++)
    {
      polyhedronFaces->InsertNextCell((i == 0 ? 4 : 3), pyramidShapeFace[i]);
    }
  }
  else if (shape == nonconvex_pyramid)
  {
    // create a simple non-convex pyramid
    const int nPoints = 5;
    const int nFaces = 5;

    double pyramidShapePoint[nPoints][3] = {
      { 0., 0., -.5 },
      { 0., 1., -.5 },
      { .25, .25, -.5 },
      { 1., 0., -.5 },
      { 0., 0., .5 },
    };

    polyhedronPoints->SetNumberOfPoints(nPoints);
    for (int i = 0; i < nPoints; i++)
    {
      polyhedronPoints->SetPoint(i, pyramidShapePoint[i]);
      polyhedronPointsIds.push_back(i);
    }

    vtkIdType f1[4] = { 0, 1, 2, 3 };
    vtkIdType f2[3] = { 0, 4, 1 };
    vtkIdType f3[3] = { 1, 4, 2 };
    vtkIdType f4[3] = { 2, 4, 3 };
    vtkIdType f5[3] = { 3, 4, 0 };

    vtkIdType* pyramidShapeFace[nFaces] = { f1, f2, f3, f4, f5 };

    for (int i = 0; i < nFaces; i++)
    {
      polyhedronFaces->InsertNextCell((i == 0 ? 4 : 3), pyramidShapeFace[i]);
    }
  }

  vtkNew<vtkIdTypeArray> legacyFaces;
  polyhedronFaces->ExportLegacyFormat(legacyFaces);

  vtkSmartPointer<vtkUnstructuredGrid> ugrid = vtkSmartPointer<vtkUnstructuredGrid>::New();
  ugrid->SetPoints(polyhedronPoints);
  ugrid->InsertNextCell(VTK_POLYHEDRON, polyhedronPoints->GetNumberOfPoints(),
    polyhedronPointsIds.data(), polyhedronFaces->GetNumberOfCells(), legacyFaces->GetPointer(0));

  vtkPolyhedron* polyhedron = static_cast<vtkPolyhedron*>(ugrid->GetCell(0));

  return polyhedron->IsConvex();
}

int TestPolyhedronConvexity(int argc, char* argv[])
{
  (void)argc;
  (void)argv;

  if (!IsConvex(dodecahedron))
  {
    cerr << "convex dodehecahedron incorrectly classified as non-convex" << std::endl;
    return EXIT_FAILURE;
  }

  if (IsConvex(u_shape))
  {
    cerr << "non-convex u-shape incorrectly classified as convex" << std::endl;
    return EXIT_FAILURE;
  }

  if (!IsConvex(cube))
  {
    cerr << "convex cube incorrectly classified as non-convex" << std::endl;
    return EXIT_FAILURE;
  }

  if (!IsConvex(colinear_cube))
  {
    cerr << "convex colinear cube incorrectly classified as non-convex" << std::endl;
    return EXIT_FAILURE;
  }

  if (!IsConvex(degenerate_cube))
  {
    cerr << "convex degenerate cube incorrectly classified as non-convex" << std::endl;
    return EXIT_FAILURE;
  }

  if (!IsConvex(convex_pyramid))
  {
    cerr << "convex pyramid incorrectly classified as non-convex" << std::endl;
    return EXIT_FAILURE;
  }

  if (IsConvex(nonconvex_pyramid))
  {
    cerr << "non-convex pyramid incorrectly classified as convex" << std::endl;
    return EXIT_FAILURE;
  }

  return EXIT_SUCCESS;
}
