MarchingSquaresTable.h

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/*************************************************************************
> File Name: MarchingSquaresTable.h
> Project Name: CubbyFlow
> Author: Chan-Ho Chris Ohk
> Purpose: A simple, portable and complete implementation of the Marching Cubes
>          and Marching Tetrahedrons algorithms.
> Created Time: 2017/07/09
> Copyright (c) 2018, Chan-Ho Chris Ohk
*************************************************************************/
#ifndef CUBBYFLOW_MARCHING_SQUARES_TABLE_H
#define CUBBYFLOW_MARCHING_SQUARES_TABLE_H

namespace CubbyFlow
{
    // VertexOffset lists the positions, relative to vertex0, of each of the 4
    // vertices of a Rect
    static const float vertexOffset2D[4][2] =
    {
        { 0.0f, 0.0f }, { 1.0f, 0.0f }, { 1.0f, 1.0f }, { 0.0f, 1.0f }
    };

    // EdgeConnection lists the index of the endpoint vertices for each of the 4
    // edges of the Rect
    static const int edgeConnection2D[4][2] =
    {
        { 0, 1 }, { 1, 2 }, { 2, 3 }, { 3, 0 }
    };

    // EdgeDirection lists the direction unit vector for each edge in the Rect
    static const float edgeDirection2D[4][2] =
    {
        { 1.0f, 0.0f }, { 0.0f, 1.0f }, { -1.0f, 0.0f }, { 0.0f, -1.0f }
    };

    // For any edge, if one vertex is inside of the surface and the other is outside
    // of the surface then the edge intersects the surface
    // For each of the 4 vertices of the Rect can be two possible states : either
    // inside or outside of the surface
    // For any cube there are 2^4=16 possible sets of vertex states
    // This table lists the edges intersected by the surface for all 16 possible
    // vertex states
    // There are 4 edges. For each entry in the table, if edge #n is intersected,
    // then bit #n is set to 1
    static const int squareEdgeFlags[16] =
    {
        0x000, 0x009, 0x003, 0x00a, 0x006, 0x00f, 0x005, 0x00c,
        0x00c, 0x005, 0x00f, 0x006, 0x00a, 0x003, 0x009, 0x000
    };

    // For each of the possible vertex states listed in RectEdgeFlags there is a
    // specific triangulation of the edge intersection points.
    // TriangleConnectionTable lists all of them in the form of 0-4 edge triples
    // with the list terminated by the invalid value -1.
    // For example: TriangleConnectionTable[3] list the 2 triangles formed when
    // corner[0] and corner[1] are inside of the surface, but the rest of the cube
    // is not.
    // The notation of vertex is as follow.
    //       6
    // 3-----------2
    // |           |
    // |           |
    // |7          |5
    // |           |
    // |           |
    // 0-----------1
    //       4
    // vertices at 0~1 nodes : 0~1
    // vertices on 0~1 edges : 4~7
    // Three vertices compose a triangle.

    static const int triangleConnectionTable2D[16][13] =
    {
        {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
        { 0,  4,  7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
        { 4,  1,  5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
        { 0,  1,  7,  1,  5,  7, -1, -1, -1, -1, -1, -1, -1 },
        { 5,  2,  6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
        { 0,  4,  7,  2,  6,  5, -1, -1, -1, -1, -1, -1, -1 },
        { 4,  1,  6,  1,  2,  6, -1, -1, -1, -1, -1, -1, -1 },
        { 0,  1,  7,  7,  1,  6,  1,  2,  6, -1, -1, -1, -1 },
        { 7,  6,  3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1 },
        { 0,  4,  6,  0,  6,  3, -1, -1, -1, -1, -1, -1, -1 },
        { 3,  7,  6,  6,  7,  4,  6,  4,  5,  1,  5,  4, -1 },
        { 0,  6,  3,  0,  5,  6,  0,  1,  5, -1, -1, -1, -1 },
        { 7,  5,  3,  5,  2,  3, -1, -1, -1, -1, -1, -1, -1 },
        { 3,  0,  4,  3,  4,  5,  3,  5,  2, -1, -1, -1, -1 },
        { 2,  3,  7,  2,  7,  4,  2,  4,  1, -1, -1, -1, -1 },
        { 0,  1,  3,  1,  2,  3, -1, -1, -1, -1, -1, -1, -1 },
    };
}

#endif