1008 lines
40 KiB
C++
1008 lines
40 KiB
C++
// Copyright (C) 2017, Dominik Wodniok
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// This software may be modified and distributed under the terms
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// of the BSD 3-Clause license.
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// See the LICENSE.txt file for details.
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#ifndef DUALMC_H_INCLUDED
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#define DUALMC_H_INCLUDED
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/// \file dualmc.h
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/// \author Dominik Wodniok
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/// \date 2009
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// c includes
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#include <cstdint>
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// stl includes
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#include <robin_hood.h>
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#include <vector>
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namespace dualmc {
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typedef float VertexComponentsType;
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typedef uint32_t PropertyType;
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typedef uint32_t QuadIndexType;
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typedef uint32_t TriIndexType;
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/// vertex structure for dual points
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struct Vertex {
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/// non-initializing constructor
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Vertex();
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/// initializing constructor
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Vertex(VertexComponentsType x, VertexComponentsType y, VertexComponentsType z, PropertyType w);
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/// initializing constructor
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Vertex(Vertex const & v);
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// components
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VertexComponentsType x;
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VertexComponentsType y;
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VertexComponentsType z;
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// texture
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PropertyType w;
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};
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/// tri indices structure
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struct Tri {
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/// non-initializing constructor
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Tri();
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/// initializing constructor
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Tri(TriIndexType i0, TriIndexType i1, TriIndexType i2);
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// tri indices
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TriIndexType i0;
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TriIndexType i1;
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TriIndexType i2;
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};
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/// \class DualMC
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/// \author Dominik Wodniok
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/// \date 2009
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/// Class which implements the dual marching cubes algorithm from Gregory M. Nielson.
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/// Faces and vertices of the standard marching cubes algorithm correspond to
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/// vertices and faces in the dual algorithm. As a vertex in standard marching cubes
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/// usually is shared by 4 faces, the dual mesh is entirely made from quadrangles.
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/// Unfortunately, under rare circumstances the original algorithm can create
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/// non-manifold meshes. See the remarks of the original paper on this.
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/// The class optionally can guarantee manifold meshes by taking the Manifold
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/// Dual Marching Cubes approach from Rephael Wenger as described in
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/// chapter 3.3.5 of his book "Isosurfaces: Geometry, Topology, and Algorithms".
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template<class T> class DualMC {
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public:
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// typedefs
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typedef T VolumeDataType;
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/// point structure for input points
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struct Point {
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/// non-initializing constructor
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Point();
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/// initializing constructor
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Point(VolumeDataType x, PropertyType w);
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/// initializing constructor
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Point(Point const &v);
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// components
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VolumeDataType x;
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// material
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PropertyType w;
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inline bool operator<(const VolumeDataType& b) const { return x < b; }
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inline bool operator>=(const VolumeDataType& b) const { return x >= b; }
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inline std::pair<PropertyType, VolumeDataType> pair() const { return std::make_pair(w, x); }
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};
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/// Extracts the iso surface for a given volume and iso value.
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/// Output is a list of vertices and a list of indices, which connect
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/// vertices to tris.
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void buildTris(
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Point const *data,
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int32_t const dimX, int32_t const dimY, int32_t const dimZ,
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VolumeDataType const iso,
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size_t const *textures_map,
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float const *roughness,
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bool const generateManifold,
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std::vector<Vertex> &vertices,
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std::vector<Tri> &tris);
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private:
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/// Extract tris mesh with shared vertex indices.
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void buildSharedVerticesTris(
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VolumeDataType const iso,
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std::vector<Vertex> & vertices,
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std::vector<Tri> & tris
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);
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protected:
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/// enum with edge codes for a 12-bit voxel edge mask to indicate
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/// grid edges which intersect the ISO surface of classic marching cubes
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enum DMCEdgeCode {
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EDGE0 = 1,
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EDGE1 = 1 << 1,
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EDGE2 = 1 << 2,
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EDGE3 = 1 << 3,
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EDGE4 = 1 << 4,
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EDGE5 = 1 << 5,
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EDGE6 = 1 << 6,
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EDGE7 = 1 << 7,
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EDGE8 = 1 << 8,
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EDGE9 = 1 << 9,
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EDGE10 = 1 << 10,
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EDGE11 = 1 << 11,
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FORCE_32BIT = 0xffffffff
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};
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/// get the 8-bit in-out mask for the voxel corners of the cell cube at (cx,cy,cz)
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/// and the given iso value
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int getCellCode(int32_t const cx, int32_t const cy, int32_t const cz, VolumeDataType const iso) const;
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/// Get the 12-bit dual point code mask, which encodes the traditional
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/// marching cube vertices of the traditional marching cubes face which
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/// corresponds to the dual point.
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/// This is also where the manifold dual marching cubes algorithm is
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/// implemented.
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int getDualPointCode(int32_t const cx, int32_t const cy, int32_t const cz,
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VolumeDataType const iso, DMCEdgeCode const edge) const;
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/// Given a dual point code and iso value, compute the dual point.
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void calculateDualPoint(int32_t const cx, int32_t const cy, int32_t const cz,
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VolumeDataType const iso, int const pointCode, Vertex &v) const;
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/// Get the shared index of a dual point which is uniquly identified by its
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/// cell cube index and a cube edge. The dual point is computed,
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/// if it has not been computed before.
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QuadIndexType getSharedDualPointIndex(int32_t const cx, int32_t const cy, int32_t const cz,
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VolumeDataType const iso, DMCEdgeCode const edge,
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std::vector<Vertex> & vertices);
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/// Compute a linearized cell cube index.
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int32_t gA(int32_t const x, int32_t const y, int32_t const z) const;
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/// Update texture if max.
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void maxProp(int32_t const x, int32_t const y, int32_t const z, Vertex &vertex, VolumeDataType& max) const;
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protected:
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// static lookup tables needed for (manifold) dual marching cubes
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/// Dual Marching Cubes table
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/// Encodes the edge vertices for the 256 marching cubes cases.
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/// A marching cube case produces up to four faces and ,thus, up to four
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/// dual points.
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static int32_t const dualPointsList[256][4];
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/// Table which encodes the ambiguous face of cube configurations, which
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/// can cause non-manifold meshes.
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/// Needed for manifold dual marching cubes.
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static uint8_t const problematicConfigs[256];
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protected:
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/// convenience volume extent array for x-,y-, and z-dimension
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int32_t dims[3];
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/// convenience volume data point
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Point const *data;
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/// point to vertex property table
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size_t const *textures_map;
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/// property roughness table
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float const *roughness;
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/// store whether the manifold dual marching cubes algorithm should be
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/// applied.
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bool generateManifold;
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/// Dual point key structure for hashing of shared vertices
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struct DualPointKey {
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// a dual point can be uniquely identified by ite linearized volume cell
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// id and point code
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int32_t linearizedCellID;
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int pointCode;
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/// Equal operator for unordered map
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bool operator==(DualPointKey const & other) const;
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};
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/// Functor for dual point key hash generation
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struct DualPointKeyHash {
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size_t operator()(DualPointKey const & k) const {
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return size_t(k.linearizedCellID) | (size_t(k.pointCode) << 32u);
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}
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};
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/// Hash map for shared vertex index computations
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robin_hood::unordered_map<DualPointKey,QuadIndexType,DualPointKeyHash> pointToIndex;
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};
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// inline function definitions
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//------------------------------------------------------------------------------
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inline
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Vertex::Vertex(){}
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//------------------------------------------------------------------------------
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inline
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Vertex::Vertex(
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VertexComponentsType x,
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VertexComponentsType y,
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VertexComponentsType z,
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PropertyType w
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) : x(x), y(y), z(z), w(w) {}
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//------------------------------------------------------------------------------
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inline
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Vertex::Vertex(Vertex const & v) : x(v.x), y(v.y), z(v.z), w(v.w) {}
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//------------------------------------------------------------------------------
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inline
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Tri::Tri() {}
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//------------------------------------------------------------------------------
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inline
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Tri::Tri(
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TriIndexType i0,
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TriIndexType i1,
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TriIndexType i2
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) : i0(i0), i1(i1), i2(i2) {}
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//------------------------------------------------------------------------------
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template<class T> inline
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DualMC<T>::Point::Point() {}
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//------------------------------------------------------------------------------
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template<class T> inline
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DualMC<T>::Point::Point(VolumeDataType x, PropertyType w): x(x), w(w) { }
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//------------------------------------------------------------------------------
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template<class T> inline
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DualMC<T>::Point::Point(Point const &v): x(v.x), w(v.w) {}
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//------------------------------------------------------------------------------
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template<class T> inline
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int32_t DualMC<T>::gA(int32_t const x, int32_t const y, int32_t const z) const {
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return x + dims[0] * (y + dims[1] * z);
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}
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//------------------------------------------------------------------------------
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template<class T> inline
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void DualMC<T>::maxProp(int32_t const x, int32_t const y, int32_t const z, Vertex &vertex, VolumeDataType &max) const {
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if(data[gA(x, y, z)].x > max) {
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max = data[gA(x, y, z)].x;
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vertex.w = textures_map[data[gA(x, y, z)].w];
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}
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}
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//------------------------------------------------------------------------------
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template<class T> inline
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bool DualMC<T>::DualPointKey::operator==(typename DualMC<T>::DualPointKey const & other) const {
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return linearizedCellID == other.linearizedCellID && pointCode == other.pointCode;
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}
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// Copyright (C) 2017, Dominik Wodniok
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// This software may be modified and distributed under the terms
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// of the BSD 3-Clause license. See the LICENSE.txt file for details.
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/// \file dualmc.tpp
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/// \author Dominik Wodniok
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/// \date 2009
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//------------------------------------------------------------------------------
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template<class T> inline
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int DualMC<T>::getCellCode(int32_t const cx, int32_t const cy, int32_t const cz, VolumeDataType const iso) const {
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// determine for each cube corner if it is outside or inside
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int code = 0;
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if (data[gA(cx, cy, cz)] >= iso)
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code |= 1;
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if (data[gA(cx + 1, cy, cz)] >= iso)
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code |= 2;
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if (data[gA(cx, cy + 1, cz)] >= iso)
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code |= 4;
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if (data[gA(cx + 1, cy + 1, cz)] >= iso)
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code |= 8;
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if (data[gA(cx, cy, cz + 1)] >= iso)
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code |= 16;
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if (data[gA(cx + 1, cy, cz + 1)] >= iso)
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code |= 32;
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if (data[gA(cx, cy + 1, cz + 1)] >= iso)
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code |= 64;
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if (data[gA(cx + 1, cy + 1, cz + 1)] >= iso)
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code |= 128;
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return code;
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}
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//------------------------------------------------------------------------------
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template<class T> inline
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int DualMC<T>::getDualPointCode(int32_t const cx, int32_t const cy, int32_t const cz, VolumeDataType const iso, DMCEdgeCode const edge) const {
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int cubeCode = getCellCode(cx, cy, cz, iso);
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// is manifold dual marching cubes desired?
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if (generateManifold) {
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// The Manifold Dual Marching Cubes approach from Rephael Wenger as described in
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// chapter 3.3.5 of his book "Isosurfaces: Geometry, Topology, and Algorithms"
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// is implemente here.
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// If a problematic C16 or C19 configuration shares the ambiguous face
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// with another C16 or C19 configuration we simply invert the cube code
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// before looking up dual points. Doing this for these pairs ensures
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// manifold meshes.
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// But this removes the dualism to marching cubes.
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// check if we have a potentially problematic configuration
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uint8_t const direction = problematicConfigs[uint8_t(cubeCode)];
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// If the direction code is in {0,...,5} we have a C16 or C19 configuration.
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if (direction != 255) {
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// We have to check the neighboring cube, which shares the ambiguous
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// face. For this we decode the direction. This could also be done
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// with another lookup table.
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// copy current cube coordinates into an array.
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int32_t neighborCoords[] = { cx,cy,cz };
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// get the dimension of the non-zero coordinate axis
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unsigned int const component = direction >> 1;
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// get the sign of the direction
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int32_t delta = (direction & 1) == 1 ? 1 : -1;
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// modify the correspong cube coordinate
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neighborCoords[component] += delta;
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// have we left the volume in this direction?
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if (neighborCoords[component] >= 0 && neighborCoords[component] < (dims[component] - 1)) {
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// get the cube configuration of the relevant neighbor
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int neighborCubeCode = getCellCode(neighborCoords[0], neighborCoords[1], neighborCoords[2], iso);
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// Look up the neighbor configuration ambiguous face direction.
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// If the direction is valid we have a C16 or C19 neighbor.
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// As C16 and C19 have exactly one ambiguous face this face is
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// guaranteed to be shared for the pair.
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if (problematicConfigs[uint8_t(neighborCubeCode)] != 255) {
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// replace the cube configuration with its inverse.
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cubeCode ^= 0xff;
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}
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}
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}
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}
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for (int i = 0; i < 4; ++i)
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if (dualPointsList[cubeCode][i] & edge) {
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return dualPointsList[cubeCode][i];
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}
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return 0;
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}
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//------------------------------------------------------------------------------
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template<class T> inline
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void DualMC<T>::calculateDualPoint(int32_t const cx, int32_t const cy, int32_t const cz, VolumeDataType const iso, int const pointCode, Vertex & v) const {
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// initialize the point with lower voxel coordinates
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v.x = static_cast<VertexComponentsType>(cx);
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v.y = static_cast<VertexComponentsType>(cy);
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v.z = static_cast<VertexComponentsType>(cz);
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// compute the dual point as the mean of the face vertices belonging to the
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// original marching cubes face
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Vertex p(0, 0, 0, 0);
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int points = 0;
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T max = 0;
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// sum edge intersection vertices using the point code
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if (pointCode & EDGE0) {
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p.x += ((float)iso - data[gA(cx, cy, cz)].x) / (data[gA(cx + 1, cy, cz)].x - data[gA(cx, cy, cz)].x);
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points++;
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maxProp(cx, cy, cz, v, max);
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maxProp(cx + 1, cy, cz, v, max);
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}
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if (pointCode & EDGE1) {
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p.x += 1.0f;
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p.z += ((float)iso - data[gA(cx + 1, cy, cz)].x) / (data[gA(cx + 1, cy, cz + 1)].x - data[gA(cx + 1, cy, cz)].x);
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points++;
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maxProp(cx + 1, cy, cz, v, max);
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maxProp(cx + 1, cy, cz + 1, v, max);
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}
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if (pointCode & EDGE2) {
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p.x += ((float)iso - data[gA(cx, cy, cz + 1)].x) / (data[gA(cx + 1, cy, cz + 1)].x - data[gA(cx, cy, cz + 1)].x);
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p.z += 1.0f;
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points++;
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maxProp(cx, cy, cz + 1, v, max);
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maxProp(cx + 1, cy, cz + 1, v, max);
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}
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if (pointCode & EDGE3) {
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p.z += ((float)iso - data[gA(cx, cy, cz)].x) / (data[gA(cx, cy, cz + 1)].x - data[gA(cx, cy, cz)].x);
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points++;
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maxProp(cx, cy, cz, v, max);
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maxProp(cx, cy, cz + 1, v, max);
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}
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if (pointCode & EDGE4) {
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p.x += ((float)iso - data[gA(cx, cy + 1, cz)].x) / (data[gA(cx + 1, cy + 1, cz)].x - data[gA(cx, cy + 1, cz)].x);
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p.y += 1.0f;
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points++;
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maxProp(cx, cy+1, cz, v, max);
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maxProp(cx + 1, cy+1, cz, v, max);
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}
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if (pointCode & EDGE5) {
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p.x += 1.0f;
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p.z += ((float)iso - data[gA(cx + 1, cy + 1, cz)].x) / (data[gA(cx + 1, cy + 1, cz + 1)].x - data[gA(cx + 1, cy + 1, cz)].x);
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p.y += 1.0f;
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points++;
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maxProp(cx+1, cy+1, cz, v, max);
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maxProp(cx + 1, cy+1, cz+1, v, max);
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}
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if (pointCode & EDGE6) {
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p.x += ((float)iso - data[gA(cx, cy + 1, cz + 1)].x) / (data[gA(cx + 1, cy + 1, cz + 1)].x - data[gA(cx, cy + 1, cz + 1)].x);
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p.z += 1.0f;
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p.y += 1.0f;
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points++;
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maxProp(cx, cy+1, cz+1, v, max);
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maxProp(cx + 1, cy+1, cz+1, v, max);
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}
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if (pointCode & EDGE7) {
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p.z += ((float)iso - data[gA(cx, cy + 1, cz)].x) / (data[gA(cx, cy + 1, cz + 1)].x - data[gA(cx, cy + 1, cz)].x);
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p.y += 1.0f;
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points++;
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maxProp(cx, cy+1, cz, v, max);
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maxProp(cx, cy+1, cz+1, v, max);
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}
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if (pointCode & EDGE8) {
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p.y += ((float)iso - data[gA(cx, cy, cz)].x) / (data[gA(cx, cy + 1, cz)].x - data[gA(cx, cy, cz)].x);
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points++;
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maxProp(cx, cy, cz, v, max);
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maxProp(cx, cy+1, cz, v, max);
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}
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if (pointCode & EDGE9) {
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p.x += 1.0f;
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p.y += ((float)iso - data[gA(cx + 1, cy, cz)].x) / (data[gA(cx + 1, cy + 1, cz)].x - data[gA(cx + 1, cy, cz)].x);
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points++;
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maxProp(cx+1, cy, cz, v, max);
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maxProp(cx + 1, cy+1, cz, v, max);
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}
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if (pointCode & EDGE10) {
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p.x += 1.0f;
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p.y += ((float)iso - data[gA(cx + 1, cy, cz + 1)].x) / (data[gA(cx + 1, cy + 1, cz + 1)].x - data[gA(cx + 1, cy, cz + 1)].x);
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p.z += 1.0f;
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points++;
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maxProp(cx+1, cy, cz+1, v, max);
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maxProp(cx + 1, cy+1, cz+1, v, max);
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}
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|
if (pointCode & EDGE11) {
|
|
p.z += 1.0f;
|
|
p.y += ((float)iso - data[gA(cx, cy, cz + 1)].x) / (data[gA(cx, cy + 1, cz + 1)].x - data[gA(cx, cy, cz + 1)].x);
|
|
points++;
|
|
maxProp(cx, cy, cz+1, v, max);
|
|
maxProp(cx, cy+1, cz+1, v, max);
|
|
}
|
|
|
|
// divide by number of accumulated points
|
|
float invPoints = (1.f - roughness[v.w]) / (float)points;
|
|
p.x *= invPoints;
|
|
p.y *= invPoints;
|
|
p.z *= invPoints;
|
|
|
|
// offset point by voxel coordinates
|
|
v.x += p.x;
|
|
v.y += p.y;
|
|
v.z += p.z;
|
|
}
|
|
|
|
//------------------------------------------------------------------------------
|
|
|
|
template<class T> inline
|
|
QuadIndexType DualMC<T>::getSharedDualPointIndex(
|
|
int32_t const cx, int32_t const cy, int32_t const cz,
|
|
VolumeDataType const iso, DMCEdgeCode const edge,
|
|
std::vector<Vertex> & vertices
|
|
) {
|
|
// create a key for the dual point from its linearized cell ID and point code
|
|
DualPointKey key;
|
|
key.linearizedCellID = gA(cx, cy, cz);
|
|
key.pointCode = getDualPointCode(cx, cy, cz, iso, edge);
|
|
|
|
// have we already computed the dual point?
|
|
auto iterator = pointToIndex.find(key);
|
|
if (iterator != pointToIndex.end()) {
|
|
// just return the dual point index
|
|
return iterator->second;
|
|
}
|
|
else {
|
|
// create new vertex and vertex id
|
|
QuadIndexType newVertexId = static_cast<QuadIndexType>(vertices.size());
|
|
vertices.emplace_back();
|
|
calculateDualPoint(cx, cy, cz, iso, key.pointCode, vertices.back());
|
|
// insert vertex ID into map and also return it
|
|
pointToIndex[key] = newVertexId;
|
|
return newVertexId;
|
|
}
|
|
}
|
|
|
|
//------------------------------------------------------------------------------
|
|
|
|
template<class T> inline
|
|
void DualMC<T>::buildTris(
|
|
Point const * data,
|
|
int32_t const dimX, int32_t const dimY, int32_t const dimZ,
|
|
VolumeDataType const iso,
|
|
size_t const * textures_map,
|
|
float const * roughness,
|
|
bool const generateManifold,
|
|
std::vector<Vertex> & vertices,
|
|
std::vector<Tri> & tris
|
|
) {
|
|
|
|
// set members
|
|
this->dims[0] = dimX;
|
|
this->dims[1] = dimY;
|
|
this->dims[2] = dimZ;
|
|
this->data = data;
|
|
this->textures_map = textures_map;
|
|
this->roughness = roughness;
|
|
this->generateManifold = generateManifold;
|
|
|
|
// clear vertices and quad indices
|
|
vertices.clear();
|
|
tris.clear();
|
|
|
|
buildSharedVerticesTris(iso, vertices, tris);
|
|
}
|
|
|
|
template<class T> inline
|
|
void DualMC<T>::buildSharedVerticesTris(
|
|
VolumeDataType const iso,
|
|
std::vector<Vertex> & vertices,
|
|
std::vector<Tri> & tris
|
|
) {
|
|
int32_t const reducedX = dims[0] - 2;
|
|
int32_t const reducedY = dims[1] - 2;
|
|
int32_t const reducedZ = dims[2] - 2;
|
|
|
|
TriIndexType i0, i1, i2, i3;
|
|
|
|
pointToIndex.clear();
|
|
|
|
// iterate voxels
|
|
for (int32_t z = 0; z < reducedZ; ++z)
|
|
for (int32_t y = 0; y < reducedY; ++y)
|
|
for (int32_t x = 0; x < reducedX; ++x) {
|
|
// construct quads for x edge
|
|
if (z > 0 && y > 0) {
|
|
bool const entering = data[gA(x, y, z)] < iso && data[gA(x + 1, y, z)] >= iso;
|
|
bool const exiting = data[gA(x, y, z)] >= iso && data[gA(x + 1, y, z)] < iso;
|
|
if (entering || exiting) {
|
|
// get quad
|
|
i0 = getSharedDualPointIndex(x, y, z, iso, EDGE0, vertices);
|
|
i1 = getSharedDualPointIndex(x, y, z - 1, iso, EDGE2, vertices);
|
|
i2 = getSharedDualPointIndex(x, y - 1, z - 1, iso, EDGE6, vertices);
|
|
i3 = getSharedDualPointIndex(x, y - 1, z, iso, EDGE4, vertices);
|
|
|
|
if (entering) {
|
|
tris.emplace_back(i0, i1, i2);
|
|
tris.emplace_back(i2, i3, i0);
|
|
}
|
|
else {
|
|
tris.emplace_back(i2, i1, i0);
|
|
tris.emplace_back(i0, i3, i2);
|
|
}
|
|
}
|
|
}
|
|
|
|
// construct quads for y edge
|
|
if (z > 0 && x > 0) {
|
|
bool const entering = data[gA(x, y, z)] < iso && data[gA(x, y + 1, z)] >= iso;
|
|
bool const exiting = data[gA(x, y, z)] >= iso && data[gA(x, y + 1, z)] < iso;
|
|
if (entering || exiting) {
|
|
// generate quad
|
|
i0 = getSharedDualPointIndex(x, y, z, iso, EDGE8, vertices);
|
|
i1 = getSharedDualPointIndex(x, y, z - 1, iso, EDGE11, vertices);
|
|
i2 = getSharedDualPointIndex(x - 1, y, z - 1, iso, EDGE10, vertices);
|
|
i3 = getSharedDualPointIndex(x - 1, y, z, iso, EDGE9, vertices);
|
|
|
|
if (exiting) {
|
|
tris.emplace_back(i0, i1, i2);
|
|
tris.emplace_back(i2, i3, i0);
|
|
}
|
|
else {
|
|
tris.emplace_back(i2, i1, i0);
|
|
tris.emplace_back(i0, i3, i2);
|
|
}
|
|
}
|
|
}
|
|
|
|
// construct quads for z edge
|
|
if (x > 0 && y > 0) {
|
|
bool const entering = data[gA(x, y, z)] < iso && data[gA(x, y, z + 1)] >= iso;
|
|
bool const exiting = data[gA(x, y, z)] >= iso && data[gA(x, y, z + 1)] < iso;
|
|
if (entering || exiting) {
|
|
// generate quad
|
|
i0 = getSharedDualPointIndex(x, y, z, iso, EDGE3, vertices);
|
|
i1 = getSharedDualPointIndex(x - 1, y, z, iso, EDGE1, vertices);
|
|
i2 = getSharedDualPointIndex(x - 1, y - 1, z, iso, EDGE5, vertices);
|
|
i3 = getSharedDualPointIndex(x, y - 1, z, iso, EDGE7, vertices);
|
|
|
|
if (exiting) {
|
|
tris.emplace_back(i0, i1, i2);
|
|
tris.emplace_back(i2, i3, i0);
|
|
}
|
|
else {
|
|
tris.emplace_back(i2, i1, i0);
|
|
tris.emplace_back(i0, i3, i2);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Copyright (C) 2018, Dominik Wodniok
|
|
// This software may be modified and distributed under the terms
|
|
// of the BSD 3-Clause license.
|
|
// See the LICENSE.txt file for details.
|
|
|
|
/// \file dualmc_table.tpp
|
|
/// \author Dominik Wodniok
|
|
/// \date 2009
|
|
|
|
// TODO: invert y and z
|
|
// Coordinate system
|
|
//
|
|
// y
|
|
// |
|
|
// |
|
|
// |
|
|
// 0-----x
|
|
// /
|
|
// /
|
|
// z
|
|
//
|
|
|
|
// Cell Corners
|
|
// (Corners are voxels. Number correspond to Morton codes of corner coordinates)
|
|
//
|
|
// 2-------------------3
|
|
// /| /|
|
|
// / | / |
|
|
// / | / |
|
|
// 6-------------------7 |
|
|
// | | | |
|
|
// | | | |
|
|
// | | | |
|
|
// | | | |
|
|
// | 0---------------|---1
|
|
// | / | /
|
|
// | / | /
|
|
// |/ |/
|
|
// 4-------------------5
|
|
//
|
|
|
|
|
|
// Cell Edges
|
|
//
|
|
// o--------4----------o
|
|
// /| /|
|
|
// 7 | 5 |
|
|
// / | / |
|
|
// o--------6----------o |
|
|
// | 8 | 9
|
|
// | | | |
|
|
// | | | |
|
|
// 11 | 10 |
|
|
// | o--------0------|---o
|
|
// | / | /
|
|
// | 3 | 1
|
|
// |/ |/
|
|
// o--------2----------o
|
|
//
|
|
|
|
// Encodes the edge vertices for the 256 marching cubes cases.
|
|
// A marching cube case produces up to four faces and ,thus, up to four
|
|
// dual points.
|
|
template<class T>
|
|
int32_t const DualMC<T>::dualPointsList[256][4] = {
|
|
{0, 0, 0, 0}, // 0
|
|
{EDGE0 | EDGE3 | EDGE8, 0, 0, 0}, // 1
|
|
{EDGE0 | EDGE1 | EDGE9, 0, 0, 0}, // 2
|
|
{EDGE1 | EDGE3 | EDGE8 | EDGE9, 0, 0, 0}, // 3
|
|
{EDGE4 | EDGE7 | EDGE8, 0, 0, 0}, // 4
|
|
{EDGE0 | EDGE3 | EDGE4 | EDGE7, 0, 0, 0}, // 5
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE4 | EDGE7 | EDGE8, 0, 0}, // 6
|
|
{EDGE1 | EDGE3 | EDGE4 | EDGE7 | EDGE9, 0, 0, 0}, // 7
|
|
{EDGE4 | EDGE5 | EDGE9, 0, 0, 0}, // 8
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE4 | EDGE5 | EDGE9, 0, 0}, // 9
|
|
{EDGE0 | EDGE1 | EDGE4 | EDGE5, 0, 0, 0}, // 10
|
|
{EDGE1 | EDGE3 | EDGE4 | EDGE5 | EDGE8, 0, 0, 0}, // 11
|
|
{EDGE5 | EDGE7 | EDGE8 | EDGE9, 0, 0, 0}, // 12
|
|
{EDGE0 | EDGE3 | EDGE5 | EDGE7 | EDGE9, 0, 0, 0}, // 13
|
|
{EDGE0 | EDGE1 | EDGE5 | EDGE7 | EDGE8, 0, 0, 0}, // 14
|
|
{EDGE1 | EDGE3 | EDGE5 | EDGE7, 0, 0, 0}, // 15
|
|
{EDGE2 | EDGE3 | EDGE11, 0, 0, 0}, // 16
|
|
{EDGE0 | EDGE2 | EDGE8 | EDGE11, 0, 0, 0}, // 17
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE2 | EDGE3 | EDGE11, 0, 0}, // 18
|
|
{EDGE1 | EDGE2 | EDGE8 | EDGE9 | EDGE11, 0, 0, 0}, // 19
|
|
{EDGE4 | EDGE7 | EDGE8, EDGE2 | EDGE3 | EDGE11, 0, 0}, // 20
|
|
{EDGE0 | EDGE2 | EDGE4 | EDGE7 | EDGE11, 0, 0, 0}, // 21
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE4 | EDGE7 | EDGE8, EDGE2 | EDGE3 | EDGE11, 0}, // 22
|
|
{EDGE1 | EDGE2 | EDGE4 | EDGE7 | EDGE9 | EDGE11, 0, 0, 0}, // 23
|
|
{EDGE4 | EDGE5 | EDGE9, EDGE2 | EDGE3 | EDGE11, 0, 0}, // 24
|
|
{EDGE0 | EDGE2 | EDGE8 | EDGE11, EDGE4 | EDGE5 | EDGE9, 0, 0}, // 25
|
|
{EDGE0 | EDGE1 | EDGE4 | EDGE5, EDGE2 | EDGE3 | EDGE11, 0, 0}, // 26
|
|
{EDGE1 | EDGE2 | EDGE4 | EDGE5 | EDGE8 | EDGE11, 0, 0, 0}, // 27
|
|
{EDGE5 | EDGE7 | EDGE8 | EDGE9, EDGE2 | EDGE3 | EDGE11, 0, 0}, // 28
|
|
{EDGE0 | EDGE2 | EDGE5 | EDGE7 | EDGE9 | EDGE11, 0, 0, 0}, // 29
|
|
{EDGE0 | EDGE1 | EDGE5 | EDGE7 | EDGE8, EDGE2 | EDGE3 | EDGE11, 0, 0}, // 30
|
|
{EDGE1 | EDGE2 | EDGE5 | EDGE7 | EDGE11, 0, 0, 0}, // 31
|
|
{EDGE1 | EDGE2 | EDGE10, 0, 0, 0}, // 32
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE1 | EDGE2 | EDGE10, 0, 0}, // 33
|
|
{EDGE0 | EDGE2 | EDGE9 | EDGE10, 0, 0, 0}, // 34
|
|
{EDGE2 | EDGE3 | EDGE8 | EDGE9 | EDGE10, 0, 0, 0}, // 35
|
|
{EDGE4 | EDGE7 | EDGE8, EDGE1 | EDGE2 | EDGE10, 0, 0}, // 36
|
|
{EDGE0 | EDGE3 | EDGE4 | EDGE7, EDGE1 | EDGE2 | EDGE10, 0, 0}, // 37
|
|
{EDGE0 | EDGE2 | EDGE9 | EDGE10, EDGE4 | EDGE7 | EDGE8, 0, 0}, // 38
|
|
{EDGE2 | EDGE3 | EDGE4 | EDGE7 | EDGE9 | EDGE10, 0, 0, 0}, // 39
|
|
{EDGE4 | EDGE5 | EDGE9, EDGE1 | EDGE2 | EDGE10, 0, 0}, // 40
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE4 | EDGE5 | EDGE9, EDGE1 | EDGE2 | EDGE10, 0}, // 41
|
|
{EDGE0 | EDGE2 | EDGE4 | EDGE5 | EDGE10, 0, 0, 0}, // 42
|
|
{EDGE2 | EDGE3 | EDGE4 | EDGE5 | EDGE8 | EDGE10, 0, 0, 0}, // 43
|
|
{EDGE5 | EDGE7 | EDGE8 | EDGE9, EDGE1 | EDGE2 | EDGE10, 0, 0}, // 44
|
|
{EDGE0 | EDGE3 | EDGE5 | EDGE7 | EDGE9, EDGE1 | EDGE2 | EDGE10, 0, 0}, // 45
|
|
{EDGE0 | EDGE2 | EDGE5 | EDGE7 | EDGE8 | EDGE10, 0, 0, 0}, // 46
|
|
{EDGE2 | EDGE3 | EDGE5 | EDGE7 | EDGE10, 0, 0, 0}, // 47
|
|
{EDGE1 | EDGE3 | EDGE10 | EDGE11, 0, 0, 0}, // 48
|
|
{EDGE0 | EDGE1 | EDGE8 | EDGE10 | EDGE11, 0, 0, 0}, // 49
|
|
{EDGE0 | EDGE3 | EDGE9 | EDGE10 | EDGE11, 0, 0, 0}, // 50
|
|
{EDGE8 | EDGE9 | EDGE10 | EDGE11, 0, 0, 0}, // 51
|
|
{EDGE4 | EDGE7 | EDGE8, EDGE1 | EDGE3 | EDGE10 | EDGE11, 0, 0}, // 52
|
|
{EDGE0 | EDGE1 | EDGE4 | EDGE7 | EDGE10 | EDGE11, 0, 0, 0}, // 53
|
|
{EDGE0 | EDGE3 | EDGE9 | EDGE10 | EDGE11, EDGE4 | EDGE7 | EDGE8, 0, 0}, // 54
|
|
{EDGE4 | EDGE7 | EDGE9 | EDGE10 | EDGE11, 0, 0, 0}, // 55
|
|
{EDGE4 | EDGE5 | EDGE9, EDGE1 | EDGE3 | EDGE10 | EDGE11, 0, 0}, // 56
|
|
{EDGE0 | EDGE1 | EDGE8 | EDGE10 | EDGE11, EDGE4 | EDGE5 | EDGE9, 0, 0}, // 57
|
|
{EDGE0 | EDGE3 | EDGE4 | EDGE5 | EDGE10 | EDGE11, 0, 0, 0}, // 58
|
|
{EDGE4 | EDGE5 | EDGE8 | EDGE10 | EDGE11, 0, 0, 0}, // 59
|
|
{EDGE5 | EDGE7 | EDGE8 | EDGE9, EDGE1 | EDGE3 | EDGE10 | EDGE11, 0, 0}, // 60
|
|
{EDGE0 | EDGE1 | EDGE5 | EDGE7 | EDGE9 | EDGE10 | EDGE11, 0, 0, 0}, // 61
|
|
{EDGE0 | EDGE3 | EDGE5 | EDGE7 | EDGE8 | EDGE10 | EDGE11, 0, 0, 0}, // 62
|
|
{EDGE5 | EDGE7 | EDGE10 | EDGE11, 0, 0, 0}, // 63
|
|
{EDGE6 | EDGE7 | EDGE11, 0, 0, 0}, // 64
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE6 | EDGE7 | EDGE11, 0, 0}, // 65
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE6 | EDGE7 | EDGE11, 0, 0}, // 66
|
|
{EDGE1 | EDGE3 | EDGE8 | EDGE9, EDGE6 | EDGE7 | EDGE11, 0, 0}, // 67
|
|
{EDGE4 | EDGE6 | EDGE8 | EDGE11, 0, 0, 0}, // 68
|
|
{EDGE0 | EDGE3 | EDGE4 | EDGE6 | EDGE11, 0, 0, 0}, // 69
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE4 | EDGE6 | EDGE8 | EDGE11, 0, 0}, // 70
|
|
{EDGE1 | EDGE3 | EDGE4 | EDGE6 | EDGE9 | EDGE11, 0, 0, 0}, // 71
|
|
{EDGE4 | EDGE5 | EDGE9, EDGE6 | EDGE7 | EDGE11, 0, 0}, // 72
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE4 | EDGE5 | EDGE9, EDGE6 | EDGE7 | EDGE11, 0}, // 73
|
|
{EDGE0 | EDGE1 | EDGE4 | EDGE5, EDGE6 | EDGE7 | EDGE11, 0, 0}, // 74
|
|
{EDGE1 | EDGE3 | EDGE4 | EDGE5 | EDGE8, EDGE6 | EDGE7 | EDGE11, 0, 0}, // 75
|
|
{EDGE5 | EDGE6 | EDGE8 | EDGE9 | EDGE11, 0, 0, 0}, // 76
|
|
{EDGE0 | EDGE3 | EDGE5 | EDGE6 | EDGE9 | EDGE11, 0, 0, 0}, // 77
|
|
{EDGE0 | EDGE1 | EDGE5 | EDGE6 | EDGE8 | EDGE11, 0, 0, 0}, // 78
|
|
{EDGE1 | EDGE3 | EDGE5 | EDGE6 | EDGE11, 0, 0, 0}, // 79
|
|
{EDGE2 | EDGE3 | EDGE6 | EDGE7, 0, 0, 0}, // 80
|
|
{EDGE0 | EDGE2 | EDGE6 | EDGE7 | EDGE8, 0, 0, 0}, // 81
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE2 | EDGE3 | EDGE6 | EDGE7, 0, 0}, // 82
|
|
{EDGE1 | EDGE2 | EDGE6 | EDGE7 | EDGE8 | EDGE9, 0, 0, 0}, // 83
|
|
{EDGE2 | EDGE3 | EDGE4 | EDGE6 | EDGE8, 0, 0, 0}, // 84
|
|
{EDGE0 | EDGE2 | EDGE4 | EDGE6, 0, 0, 0}, // 85
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE2 | EDGE3 | EDGE4 | EDGE6 | EDGE8, 0, 0}, // 86
|
|
{EDGE1 | EDGE2 | EDGE4 | EDGE6 | EDGE9, 0, 0, 0}, // 87
|
|
{EDGE4 | EDGE5 | EDGE9, EDGE2 | EDGE3 | EDGE6 | EDGE7, 0, 0}, // 88
|
|
{EDGE0 | EDGE2 | EDGE6 | EDGE7 | EDGE8, EDGE4 | EDGE5 | EDGE9, 0, 0}, // 89
|
|
{EDGE0 | EDGE1 | EDGE4 | EDGE5, EDGE2 | EDGE3 | EDGE6 | EDGE7, 0, 0}, // 90
|
|
{EDGE1 | EDGE2 | EDGE4 | EDGE5 | EDGE6 | EDGE7 | EDGE8, 0, 0, 0}, // 91
|
|
{EDGE2 | EDGE3 | EDGE5 | EDGE6 | EDGE8 | EDGE9, 0, 0, 0}, // 92
|
|
{EDGE0 | EDGE2 | EDGE5 | EDGE6 | EDGE9, 0, 0, 0}, // 93
|
|
{EDGE0 | EDGE1 | EDGE2 | EDGE3 | EDGE5 | EDGE6 | EDGE8, 0, 0, 0}, // 94
|
|
{EDGE1 | EDGE2 | EDGE5 | EDGE6, 0, 0, 0}, // 95
|
|
{EDGE1 | EDGE2 | EDGE10, EDGE6 | EDGE7 | EDGE11, 0, 0}, // 96
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE1 | EDGE2 | EDGE10, EDGE6 | EDGE7 | EDGE11, 0}, // 97
|
|
{EDGE0 | EDGE2 | EDGE9 | EDGE10, EDGE6 | EDGE7 | EDGE11, 0, 0}, // 98
|
|
{EDGE2 | EDGE3 | EDGE8 | EDGE9 | EDGE10, EDGE6 | EDGE7 | EDGE11, 0, 0}, // 99
|
|
{EDGE4 | EDGE6 | EDGE8 | EDGE11, EDGE1 | EDGE2 | EDGE10, 0, 0}, // 100
|
|
{EDGE0 | EDGE3 | EDGE4 | EDGE6 | EDGE11, EDGE1 | EDGE2 | EDGE10, 0, 0}, // 101
|
|
{EDGE0 | EDGE2 | EDGE9 | EDGE10, EDGE4 | EDGE6 | EDGE8 | EDGE11, 0, 0}, // 102
|
|
{EDGE2 | EDGE3 | EDGE4 | EDGE6 | EDGE9 | EDGE10 | EDGE11, 0, 0, 0}, // 103
|
|
{EDGE4 | EDGE5 | EDGE9, EDGE1 | EDGE2 | EDGE10, EDGE6 | EDGE7 | EDGE11, 0}, // 104
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE4 | EDGE5 | EDGE9, EDGE1 | EDGE2 | EDGE10, EDGE6 | EDGE7 | EDGE11}, // 105
|
|
{EDGE0 | EDGE2 | EDGE4 | EDGE5 | EDGE10, EDGE6 | EDGE7 | EDGE11, 0, 0}, // 106
|
|
{EDGE2 | EDGE3 | EDGE4 | EDGE5 | EDGE8 | EDGE10, EDGE6 | EDGE7 | EDGE11, 0, 0}, // 107
|
|
{EDGE5 | EDGE6 | EDGE8 | EDGE9 | EDGE11, EDGE1 | EDGE2 | EDGE10, 0, 0}, // 108
|
|
{EDGE0 | EDGE3 | EDGE5 | EDGE6 | EDGE9 | EDGE11, EDGE1 | EDGE2 | EDGE10, 0, 0}, // 109
|
|
{EDGE0 | EDGE2 | EDGE5 | EDGE6 | EDGE8 | EDGE10 | EDGE11, 0, 0, 0}, // 110
|
|
{EDGE2 | EDGE3 | EDGE5 | EDGE6 | EDGE10 | EDGE11, 0, 0, 0}, // 111
|
|
{EDGE1 | EDGE3 | EDGE6 | EDGE7 | EDGE10, 0, 0, 0}, // 112
|
|
{EDGE0 | EDGE1 | EDGE6 | EDGE7 | EDGE8 | EDGE10, 0, 0, 0}, // 113
|
|
{EDGE0 | EDGE3 | EDGE6 | EDGE7 | EDGE9 | EDGE10, 0, 0, 0}, // 114
|
|
{EDGE6 | EDGE7 | EDGE8 | EDGE9 | EDGE10, 0, 0, 0}, // 115
|
|
{EDGE1 | EDGE3 | EDGE4 | EDGE6 | EDGE8 | EDGE10, 0, 0, 0}, // 116
|
|
{EDGE0 | EDGE1 | EDGE4 | EDGE6 | EDGE10, 0, 0, 0}, // 117
|
|
{EDGE0 | EDGE3 | EDGE4 | EDGE6 | EDGE8 | EDGE9 | EDGE10, 0, 0, 0}, // 118
|
|
{EDGE4 | EDGE6 | EDGE9 | EDGE10, 0, 0, 0}, // 119
|
|
{EDGE4 | EDGE5 | EDGE9, EDGE1 | EDGE3 | EDGE6 | EDGE7 | EDGE10, 0, 0}, // 120
|
|
{EDGE0 | EDGE1 | EDGE6 | EDGE7 | EDGE8 | EDGE10, EDGE4 | EDGE5 | EDGE9, 0, 0}, // 121
|
|
{EDGE0 | EDGE3 | EDGE4 | EDGE5 | EDGE6 | EDGE7 | EDGE10, 0, 0, 0}, // 122
|
|
{EDGE4 | EDGE5 | EDGE6 | EDGE7 | EDGE8 | EDGE10, 0, 0, 0}, // 123
|
|
{EDGE1 | EDGE3 | EDGE5 | EDGE6 | EDGE8 | EDGE9 | EDGE10, 0, 0, 0}, // 124
|
|
{EDGE0 | EDGE1 | EDGE5 | EDGE6 | EDGE9 | EDGE10, 0, 0, 0}, // 125
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE5 | EDGE6 | EDGE10, 0, 0}, // 126
|
|
{EDGE5 | EDGE6 | EDGE10, 0, 0, 0}, // 127
|
|
{EDGE5 | EDGE6 | EDGE10, 0, 0, 0}, // 128
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE5 | EDGE6 | EDGE10, 0, 0}, // 129
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE5 | EDGE6 | EDGE10, 0, 0}, // 130
|
|
{EDGE1 | EDGE3 | EDGE8 | EDGE9, EDGE5 | EDGE6 | EDGE10, 0, 0}, // 131
|
|
{EDGE4 | EDGE7 | EDGE8, EDGE5 | EDGE6 | EDGE10, 0, 0}, // 132
|
|
{EDGE0 | EDGE3 | EDGE4 | EDGE7, EDGE5 | EDGE6 | EDGE10, 0, 0}, // 133
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE4 | EDGE7 | EDGE8, EDGE5 | EDGE6 | EDGE10, 0}, // 134
|
|
{EDGE1 | EDGE3 | EDGE4 | EDGE7 | EDGE9, EDGE5 | EDGE6 | EDGE10, 0, 0}, // 135
|
|
{EDGE4 | EDGE6 | EDGE9 | EDGE10, 0, 0, 0}, // 136
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE4 | EDGE6 | EDGE9 | EDGE10, 0, 0}, // 137
|
|
{EDGE0 | EDGE1 | EDGE4 | EDGE6 | EDGE10, 0, 0, 0}, // 138
|
|
{EDGE1 | EDGE3 | EDGE4 | EDGE6 | EDGE8 | EDGE10, 0, 0, 0}, // 139
|
|
{EDGE6 | EDGE7 | EDGE8 | EDGE9 | EDGE10, 0, 0, 0}, // 140
|
|
{EDGE0 | EDGE3 | EDGE6 | EDGE7 | EDGE9 | EDGE10, 0, 0, 0}, // 141
|
|
{EDGE0 | EDGE1 | EDGE6 | EDGE7 | EDGE8 | EDGE10, 0, 0, 0}, // 142
|
|
{EDGE1 | EDGE3 | EDGE6 | EDGE7 | EDGE10, 0, 0, 0}, // 143
|
|
{EDGE2 | EDGE3 | EDGE11, EDGE5 | EDGE6 | EDGE10, 0, 0}, // 144
|
|
{EDGE0 | EDGE2 | EDGE8 | EDGE11, EDGE5 | EDGE6 | EDGE10, 0, 0}, // 145
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE2 | EDGE3 | EDGE11, EDGE5 | EDGE6 | EDGE10, 0}, // 146
|
|
{EDGE1 | EDGE2 | EDGE8 | EDGE9 | EDGE11, EDGE5 | EDGE6 | EDGE10, 0, 0}, // 147
|
|
{EDGE4 | EDGE7 | EDGE8, EDGE2 | EDGE3 | EDGE11, EDGE5 | EDGE6 | EDGE10, 0}, // 148
|
|
{EDGE0 | EDGE2 | EDGE4 | EDGE7 | EDGE11, EDGE5 | EDGE6 | EDGE10, 0, 0}, // 149
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE4 | EDGE7 | EDGE8, EDGE2 | EDGE3 | EDGE11, EDGE5 | EDGE6 | EDGE10}, // 150
|
|
{EDGE1 | EDGE2 | EDGE4 | EDGE7 | EDGE9 | EDGE11, EDGE5 | EDGE6 | EDGE10, 0, 0}, // 151
|
|
{EDGE4 | EDGE6 | EDGE9 | EDGE10, EDGE2 | EDGE3 | EDGE11, 0, 0}, // 152
|
|
{EDGE0 | EDGE2 | EDGE8 | EDGE11, EDGE4 | EDGE6 | EDGE9 | EDGE10, 0, 0}, // 153
|
|
{EDGE0 | EDGE1 | EDGE4 | EDGE6 | EDGE10, EDGE2 | EDGE3 | EDGE11, 0, 0}, // 154
|
|
{EDGE1 | EDGE2 | EDGE4 | EDGE6 | EDGE8 | EDGE10 | EDGE11, 0, 0, 0}, // 155
|
|
{EDGE6 | EDGE7 | EDGE8 | EDGE9 | EDGE10, EDGE2 | EDGE3 | EDGE11, 0, 0}, // 156
|
|
{EDGE0 | EDGE2 | EDGE6 | EDGE7 | EDGE9 | EDGE10 | EDGE11, 0, 0, 0}, // 157
|
|
{EDGE0 | EDGE1 | EDGE6 | EDGE7 | EDGE8 | EDGE10, EDGE2 | EDGE3 | EDGE11, 0, 0}, // 158
|
|
{EDGE1 | EDGE2 | EDGE6 | EDGE7 | EDGE10 | EDGE11, 0, 0, 0}, // 159
|
|
{EDGE1 | EDGE2 | EDGE5 | EDGE6, 0, 0, 0}, // 160
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE1 | EDGE2 | EDGE5 | EDGE6, 0, 0}, // 161
|
|
{EDGE0 | EDGE2 | EDGE5 | EDGE6 | EDGE9, 0, 0, 0}, // 162
|
|
{EDGE2 | EDGE3 | EDGE5 | EDGE6 | EDGE8 | EDGE9, 0, 0, 0}, // 163
|
|
{EDGE4 | EDGE7 | EDGE8, EDGE1 | EDGE2 | EDGE5 | EDGE6, 0, 0}, // 164
|
|
{EDGE0 | EDGE3 | EDGE4 | EDGE7, EDGE1 | EDGE2 | EDGE5 | EDGE6, 0, 0}, // 165
|
|
{EDGE0 | EDGE2 | EDGE5 | EDGE6 | EDGE9, EDGE4 | EDGE7 | EDGE8, 0, 0}, // 166
|
|
{EDGE2 | EDGE3 | EDGE4 | EDGE5 | EDGE6 | EDGE7 | EDGE9, 0, 0, 0}, // 167
|
|
{EDGE1 | EDGE2 | EDGE4 | EDGE6 | EDGE9, 0, 0, 0}, // 168
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE1 | EDGE2 | EDGE4 | EDGE6 | EDGE9, 0, 0}, // 169
|
|
{EDGE0 | EDGE2 | EDGE4 | EDGE6, 0, 0, 0}, // 170
|
|
{EDGE2 | EDGE3 | EDGE4 | EDGE6 | EDGE8, 0, 0, 0}, // 171
|
|
{EDGE1 | EDGE2 | EDGE6 | EDGE7 | EDGE8 | EDGE9, 0, 0, 0}, // 172
|
|
{EDGE0 | EDGE1 | EDGE2 | EDGE3 | EDGE6 | EDGE7 | EDGE9, 0, 0, 0}, // 173
|
|
{EDGE0 | EDGE2 | EDGE6 | EDGE7 | EDGE8, 0, 0, 0}, // 174
|
|
{EDGE2 | EDGE3 | EDGE6 | EDGE7, 0, 0, 0}, // 175
|
|
{EDGE1 | EDGE3 | EDGE5 | EDGE6 | EDGE11, 0, 0, 0}, // 176
|
|
{EDGE0 | EDGE1 | EDGE5 | EDGE6 | EDGE8 | EDGE11, 0, 0, 0}, // 177
|
|
{EDGE0 | EDGE3 | EDGE5 | EDGE6 | EDGE9 | EDGE11, 0, 0, 0}, // 178
|
|
{EDGE5 | EDGE6 | EDGE8 | EDGE9 | EDGE11, 0, 0, 0}, // 179
|
|
{EDGE4 | EDGE7 | EDGE8, EDGE1 | EDGE3 | EDGE5 | EDGE6 | EDGE11, 0, 0}, // 180
|
|
{EDGE0 | EDGE1 | EDGE4 | EDGE5 | EDGE6 | EDGE7 | EDGE11, 0, 0, 0}, // 181
|
|
{EDGE0 | EDGE3 | EDGE5 | EDGE6 | EDGE9 | EDGE11, EDGE4 | EDGE7 | EDGE8, 0, 0}, // 182
|
|
{EDGE4 | EDGE5 | EDGE6 | EDGE7 | EDGE9 | EDGE11, 0, 0, 0}, // 183
|
|
{EDGE1 | EDGE3 | EDGE4 | EDGE6 | EDGE9 | EDGE11, 0, 0, 0}, // 184
|
|
{EDGE0 | EDGE1 | EDGE4 | EDGE6 | EDGE8 | EDGE9 | EDGE11, 0, 0, 0}, // 185
|
|
{EDGE0 | EDGE3 | EDGE4 | EDGE6 | EDGE11, 0, 0, 0}, // 186
|
|
{EDGE4 | EDGE6 | EDGE8 | EDGE11, 0, 0, 0}, // 187
|
|
{EDGE1 | EDGE3 | EDGE6 | EDGE7 | EDGE8 | EDGE9 | EDGE11, 0, 0, 0}, // 188
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE6 | EDGE7 | EDGE11, 0, 0}, // 189
|
|
{EDGE0 | EDGE3 | EDGE6 | EDGE7 | EDGE8 | EDGE11, 0, 0, 0}, // 190
|
|
{EDGE6 | EDGE7 | EDGE11, 0, 0, 0}, // 191
|
|
{EDGE5 | EDGE7 | EDGE10 | EDGE11, 0, 0, 0}, // 192
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE5 | EDGE7 | EDGE10 | EDGE11, 0, 0}, // 193
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE5 | EDGE7 | EDGE10 | EDGE11, 0, 0}, // 194
|
|
{EDGE1 | EDGE3 | EDGE8 | EDGE9, EDGE5 | EDGE7 | EDGE10 | EDGE11, 0, 0}, // 195
|
|
{EDGE4 | EDGE5 | EDGE8 | EDGE10 | EDGE11, 0, 0, 0}, // 196
|
|
{EDGE0 | EDGE3 | EDGE4 | EDGE5 | EDGE10 | EDGE11, 0, 0, 0}, // 197
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE4 | EDGE5 | EDGE8 | EDGE10 | EDGE11, 0, 0}, // 198
|
|
{EDGE1 | EDGE3 | EDGE4 | EDGE5 | EDGE9 | EDGE10 | EDGE11, 0, 0, 0}, // 199
|
|
{EDGE4 | EDGE7 | EDGE9 | EDGE10 | EDGE11, 0, 0, 0}, // 200
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE4 | EDGE7 | EDGE9 | EDGE10 | EDGE11, 0, 0}, // 201
|
|
{EDGE0 | EDGE1 | EDGE4 | EDGE7 | EDGE10 | EDGE11, 0, 0, 0}, // 202
|
|
{EDGE1 | EDGE3 | EDGE4 | EDGE7 | EDGE8 | EDGE10 | EDGE11, 0, 0, 0}, // 203
|
|
{EDGE8 | EDGE9 | EDGE10 | EDGE11, 0, 0, 0}, // 204
|
|
{EDGE0 | EDGE3 | EDGE9 | EDGE10 | EDGE11, 0, 0, 0}, // 205
|
|
{EDGE0 | EDGE1 | EDGE8 | EDGE10 | EDGE11, 0, 0, 0}, // 206
|
|
{EDGE1 | EDGE3 | EDGE10 | EDGE11, 0, 0, 0}, // 207
|
|
{EDGE2 | EDGE3 | EDGE5 | EDGE7 | EDGE10, 0, 0, 0}, // 208
|
|
{EDGE0 | EDGE2 | EDGE5 | EDGE7 | EDGE8 | EDGE10, 0, 0, 0}, // 209
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE2 | EDGE3 | EDGE5 | EDGE7 | EDGE10, 0, 0}, // 210
|
|
{EDGE1 | EDGE2 | EDGE5 | EDGE7 | EDGE8 | EDGE9 | EDGE10, 0, 0, 0}, // 211
|
|
{EDGE2 | EDGE3 | EDGE4 | EDGE5 | EDGE8 | EDGE10, 0, 0, 0}, // 212
|
|
{EDGE0 | EDGE2 | EDGE4 | EDGE5 | EDGE10, 0, 0, 0}, // 213
|
|
{EDGE0 | EDGE1 | EDGE9, EDGE2 | EDGE3 | EDGE4 | EDGE5 | EDGE8 | EDGE10, 0, 0}, // 214
|
|
{EDGE1 | EDGE2 | EDGE4 | EDGE5 | EDGE9 | EDGE10, 0, 0, 0}, // 215
|
|
{EDGE2 | EDGE3 | EDGE4 | EDGE7 | EDGE9 | EDGE10, 0, 0, 0}, // 216
|
|
{EDGE0 | EDGE2 | EDGE4 | EDGE7 | EDGE8 | EDGE9 | EDGE10, 0, 0, 0}, // 217
|
|
{EDGE0 | EDGE1 | EDGE2 | EDGE3 | EDGE4 | EDGE7 | EDGE10, 0, 0, 0}, // 218
|
|
{EDGE4 | EDGE7 | EDGE8, EDGE1 | EDGE2 | EDGE10, 0, 0}, // 219
|
|
{EDGE2 | EDGE3 | EDGE8 | EDGE9 | EDGE10, 0, 0, 0}, // 220
|
|
{EDGE0 | EDGE2 | EDGE9 | EDGE10, 0, 0, 0}, // 221
|
|
{EDGE0 | EDGE1 | EDGE2 | EDGE3 | EDGE8 | EDGE10, 0, 0, 0}, // 222
|
|
{EDGE1 | EDGE2 | EDGE10, 0, 0, 0}, // 223
|
|
{EDGE1 | EDGE2 | EDGE5 | EDGE7 | EDGE11, 0, 0, 0}, // 224
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE1 | EDGE2 | EDGE5 | EDGE7 | EDGE11, 0, 0}, // 225
|
|
{EDGE0 | EDGE2 | EDGE5 | EDGE7 | EDGE9 | EDGE11, 0, 0, 0}, // 226
|
|
{EDGE2 | EDGE3 | EDGE5 | EDGE7 | EDGE8 | EDGE9 | EDGE11, 0, 0, 0}, // 227
|
|
{EDGE1 | EDGE2 | EDGE4 | EDGE5 | EDGE8 | EDGE11, 0, 0, 0}, // 228
|
|
{EDGE0 | EDGE1 | EDGE2 | EDGE3 | EDGE4 | EDGE5 | EDGE11, 0, 0, 0}, // 229
|
|
{EDGE0 | EDGE2 | EDGE4 | EDGE5 | EDGE8 | EDGE9 | EDGE11, 0, 0, 0}, // 230
|
|
{EDGE4 | EDGE5 | EDGE9, EDGE2 | EDGE3 | EDGE11, 0, 0}, // 231
|
|
{EDGE1 | EDGE2 | EDGE4 | EDGE7 | EDGE9 | EDGE11, 0, 0, 0}, // 232
|
|
{EDGE0 | EDGE3 | EDGE8, EDGE1 | EDGE2 | EDGE4 | EDGE7 | EDGE9 | EDGE11, 0, 0}, // 233
|
|
{EDGE0 | EDGE2 | EDGE4 | EDGE7 | EDGE11, 0, 0, 0}, // 234
|
|
{EDGE2 | EDGE3 | EDGE4 | EDGE7 | EDGE8 | EDGE11, 0, 0, 0}, // 235
|
|
{EDGE1 | EDGE2 | EDGE8 | EDGE9 | EDGE11, 0, 0, 0}, // 236
|
|
{EDGE0 | EDGE1 | EDGE2 | EDGE3 | EDGE9 | EDGE11, 0, 0, 0}, // 237
|
|
{EDGE0 | EDGE2 | EDGE8 | EDGE11, 0, 0, 0}, // 238
|
|
{EDGE2 | EDGE3 | EDGE11, 0, 0, 0}, // 239
|
|
{EDGE1 | EDGE3 | EDGE5 | EDGE7, 0, 0, 0}, // 240
|
|
{EDGE0 | EDGE1 | EDGE5 | EDGE7 | EDGE8, 0, 0, 0}, // 241
|
|
{EDGE0 | EDGE3 | EDGE5 | EDGE7 | EDGE9, 0, 0, 0}, // 242
|
|
{EDGE5 | EDGE7 | EDGE8 | EDGE9, 0, 0, 0}, // 243
|
|
{EDGE1 | EDGE3 | EDGE4 | EDGE5 | EDGE8, 0, 0, 0}, // 244
|
|
{EDGE0 | EDGE1 | EDGE4 | EDGE5, 0, 0, 0}, // 245
|
|
{EDGE0 | EDGE3 | EDGE4 | EDGE5 | EDGE8 | EDGE9, 0, 0, 0}, // 246
|
|
{EDGE4 | EDGE5 | EDGE9, 0, 0, 0}, // 247
|
|
{EDGE1 | EDGE3 | EDGE4 | EDGE7 | EDGE9, 0, 0, 0}, // 248
|
|
{EDGE0 | EDGE1 | EDGE4 | EDGE7 | EDGE8 | EDGE9, 0, 0, 0}, // 249
|
|
{EDGE0 | EDGE3 | EDGE4 | EDGE7, 0, 0, 0}, // 250
|
|
{EDGE4 | EDGE7 | EDGE8, 0, 0, 0}, // 251
|
|
{EDGE1 | EDGE3 | EDGE8 | EDGE9, 0, 0, 0}, // 252
|
|
{EDGE0 | EDGE1 | EDGE9, 0, 0, 0}, // 253
|
|
{EDGE0 | EDGE3 | EDGE8, 0, 0, 0}, // 254
|
|
{0, 0, 0, 0} // 255
|
|
};
|
|
|
|
/// Encodes the ambiguous face of cube configurations, which
|
|
/// can cause non-manifold meshes.
|
|
/// Non-problematic configurations have a value of 255.
|
|
/// The first bit of each value actually encodes a positive or negative
|
|
/// direction while the second and third bit enumerate the axis.
|
|
template<class T>
|
|
uint8_t const DualMC<T>::problematicConfigs[256] = {
|
|
255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
|
|
255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
|
|
255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
|
|
255,255,255,255,255,255,255,255,255,255,255,255,255,1,0,255,
|
|
255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
|
|
255,255,255,255,255,255,255,255,255,255,255,3,255,255,2,255,
|
|
255,255,255,255,255,255,255,5,255,255,255,255,255,255,5,5,
|
|
255,255,255,255,255,255,4,255,255,255,3,3,1,1,255,255,
|
|
255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,255,
|
|
255,255,255,255,255,255,255,255,255,255,255,5,255,5,255,5,
|
|
255,255,255,255,255,255,255,3,255,255,255,255,255,2,255,255,
|
|
255,255,255,255,255,3,255,3,255,4,255,255,0,255,0,255,
|
|
255,255,255,255,255,255,255,1,255,255,255,0,255,255,255,255,
|
|
255,255,255,1,255,255,255,1,255,4,2,255,255,255,2,255,
|
|
255,255,255,0,255,2,4,255,255,255,255,0,255,2,255,255,
|
|
255,255,255,255,255,255,4,255,255,4,255,255,255,255,255,255
|
|
};
|
|
|
|
|
|
} // END: namespace dualmc
|
|
#endif // DUALMC_H_INCLUDED
|