Revision 39b13612ebd645a65eda854771b517371f2f858a authored by ennetws on 13 March 2015, 18:17:18 UTC, committed by ennetws on 13 March 2015, 18:17:18 UTC
1 parent c702819
MarchingCubes.cpp
/*
Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
Redistributions of source code must retain the above copyright notice, this list of
conditions and the following disclaimer. Redistributions in binary form must reproduce
the above copyright notice, this list of conditions and the following disclaimer
in the documentation and/or other materials provided with the distribution.
Neither the name of the Johns Hopkins University nor the names of its contributors
may be used to endorse or promote products derived from this software without specific
prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO THE IMPLIED WARRANTIES
OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
DAMAGE.
*/
#include <math.h>
#include "MarchingCubes.h"
////////////
// Square //
////////////
int Square::AntipodalCornerIndex(int idx){
int x,y;
FactorCornerIndex(idx,x,y);
return CornerIndex( (x+1)%2 , (y+1)%2 );
}
int Square::CornerIndex(int x,int y){return (y<<1)|x;}
void Square::FactorCornerIndex(int idx,int& x,int& y){
x=(idx>>0)%2;
y=(idx>>1)%2;
}
int Square::EdgeIndex(int orientation,int i){
switch(orientation){
case 0: // x
if(!i) {return 0;} // (0,0) -> (1,0)
else {return 2;} // (0,1) -> (1,1)
case 1: // y
if(!i) {return 3;} // (0,0) -> (0,1)
else {return 1;} // (1,0) -> (1,1)
};
return -1;
}
void Square::FactorEdgeIndex(int idx,int& orientation,int& i){
switch(idx){
case 0: case 2:
orientation=0;
i=idx/2;
return;
case 1: case 3:
orientation=1;
i=((idx/2)+1)%2;
return;
};
}
void Square::EdgeCorners(int idx,int& c1,int& c2){
int orientation,i;
FactorEdgeIndex(idx,orientation,i);
switch(orientation){
case 0:
c1=CornerIndex(0,i);
c2=CornerIndex(1,i);
break;
case 1:
c1=CornerIndex(i,0);
c2=CornerIndex(i,1);
break;
};
}
int Square::ReflectEdgeIndex(int idx,int edgeIndex){
int orientation=edgeIndex%2;
int o,i;
FactorEdgeIndex(idx,o,i);
if(o!=orientation){return idx;}
else{return EdgeIndex(o,(i+1)%2);}
}
int Square::ReflectCornerIndex(int idx,int edgeIndex){
int orientation=edgeIndex%2;
int x,y;
FactorCornerIndex(idx,x,y);
switch(orientation){
case 0: return CornerIndex((x+1)%2,y);
case 1: return CornerIndex(x,(y+1)%2);
};
return -1;
}
//////////
// Cube //
//////////
int Cube::CornerIndex(int x,int y,int z){return (z<<2)|(y<<1)|x;}
void Cube::FactorCornerIndex(int idx,int& x,int& y,int& z){
x=(idx>>0)%2;
y=(idx>>1)%2;
z=(idx>>2)%2;
}
int Cube::EdgeIndex(int orientation,int i,int j){return (i | (j<<1))|(orientation<<2);}
void Cube::FactorEdgeIndex( int idx , int& orientation , int& i , int &j )
{
orientation=idx>>2;
i = (idx&1);
j = (idx&2)>>1;
}
int Cube::FaceIndex(int x,int y,int z){
if (x<0) {return 0;}
else if (x>0) {return 1;}
else if (y<0) {return 2;}
else if (y>0) {return 3;}
else if (z<0) {return 4;}
else if (z>0) {return 5;}
else {return -1;}
}
int Cube::FaceIndex(int dir,int offSet){return (dir<<1)|offSet;}
void Cube::FactorFaceIndex(int idx,int& x,int& y,int& z){
x=y=z=0;
switch(idx){
case 0: x=-1; break;
case 1: x= 1; break;
case 2: y=-1; break;
case 3: y= 1; break;
case 4: z=-1; break;
case 5: z= 1; break;
};
}
void Cube::FactorFaceIndex(int idx,int& dir,int& offSet){
dir = idx>>1;
offSet=idx &1;
}
int Cube::FaceAdjacentToEdges(int eIndex1,int eIndex2){
int f1,f2,g1,g2;
FacesAdjacentToEdge(eIndex1,f1,f2);
FacesAdjacentToEdge(eIndex2,g1,g2);
if(f1==g1 || f1==g2){return f1;}
if(f2==g1 || f2==g2){return f2;}
return -1;
}
void Cube::FacesAdjacentToEdge(int eIndex,int& f1Index,int& f2Index){
int orientation,i1,i2;
FactorEdgeIndex(eIndex,orientation,i1,i2);
i1<<=1;
i2<<=1;
i1--;
i2--;
switch(orientation){
case 0:
f1Index=FaceIndex( 0,i1, 0);
f2Index=FaceIndex( 0, 0,i2);
break;
case 1:
f1Index=FaceIndex(i1, 0, 0);
f2Index=FaceIndex( 0, 0,i2);
break;
case 2:
f1Index=FaceIndex(i1, 0, 0);
f2Index=FaceIndex( 0,i2, 0);
break;
};
}
void Cube::EdgeCorners(int idx,int& c1,int& c2){
int orientation,i1,i2;
FactorEdgeIndex(idx,orientation,i1,i2);
switch(orientation){
case 0:
c1=CornerIndex(0,i1,i2);
c2=CornerIndex(1,i1,i2);
break;
case 1:
c1=CornerIndex(i1,0,i2);
c2=CornerIndex(i1,1,i2);
break;
case 2:
c1=CornerIndex(i1,i2,0);
c2=CornerIndex(i1,i2,1);
break;
};
}
void Cube::FaceCorners(int idx,int& c1,int& c2,int& c3,int& c4){
int i=idx%2;
switch(idx/2){
case 0:
c1=CornerIndex(i,0,0);
c2=CornerIndex(i,1,0);
c3=CornerIndex(i,0,1);
c4=CornerIndex(i,1,1);
return;
case 1:
c1=CornerIndex(0,i,0);
c2=CornerIndex(1,i,0);
c3=CornerIndex(0,i,1);
c4=CornerIndex(1,i,1);
return;
case 2:
c1=CornerIndex(0,0,i);
c2=CornerIndex(1,0,i);
c3=CornerIndex(0,1,i);
c4=CornerIndex(1,1,i);
return;
}
}
int Cube::AntipodalCornerIndex(int idx){
int x,y,z;
FactorCornerIndex(idx,x,y,z);
return CornerIndex((x+1)%2,(y+1)%2,(z+1)%2);
}
int Cube::FaceReflectFaceIndex(int idx,int faceIndex){
if(idx/2!=faceIndex/2){return idx;}
else{
if(idx%2) {return idx-1;}
else {return idx+1;}
}
}
int Cube::FaceReflectEdgeIndex(int idx,int faceIndex){
int orientation=faceIndex/2;
int o,i,j;
FactorEdgeIndex(idx,o,i,j);
if(o==orientation){return idx;}
switch(orientation){
case 0: return EdgeIndex(o,(i+1)%2,j);
case 1:
switch(o){
case 0: return EdgeIndex(o,(i+1)%2,j);
case 2: return EdgeIndex(o,i,(j+1)%2);
};
case 2: return EdgeIndex(o,i,(j+1)%2);
};
return -1;
}
int Cube::FaceReflectCornerIndex(int idx,int faceIndex){
int orientation=faceIndex/2;
int x,y,z;
FactorCornerIndex(idx,x,y,z);
switch(orientation){
case 0: return CornerIndex((x+1)%2,y,z);
case 1: return CornerIndex(x,(y+1)%2,z);
case 2: return CornerIndex(x,y,(z+1)%2);
};
return -1;
}
int Cube::EdgeReflectCornerIndex(int idx,int edgeIndex){
int orientation,x,y,z;
FactorEdgeIndex(edgeIndex,orientation,x,y);
FactorCornerIndex(idx,x,y,z);
switch(orientation){
case 0: return CornerIndex( x ,(y+1)%2,(z+1)%2);
case 1: return CornerIndex((x+1)%2, y ,(z+1)%2);
case 2: return CornerIndex((x+1)%2,(y+1)%2, z );
};
return -1;
}
int Cube::EdgeReflectEdgeIndex(int edgeIndex){
int o,i1,i2;
FactorEdgeIndex(edgeIndex,o,i1,i2);
return Cube::EdgeIndex(o,(i1+1)%2,(i2+1)%2);
}
/////////////////////
// MarchingSquares //
/////////////////////
/*
0} // (0,0) -> (1,0)
1} // (1,0) -> (1,1)
2} // (0,1) -> (1,1)
3} // (0,0) -> (0,1)
*/
const int MarchingSquares::edgeMask[1<<Square::CORNERS]={
0, // 0 -> -> ->
9, // 1 -> 0 -> (0,0) -> 0,3 -> 9
3, // 2 -> 1 -> (1,0) -> 0,1 -> 3
10, // 3 -> 0,1 -> (0,0) (1,0) -> 1,3 -> 10
12, // 4 -> 2 -> (0,1) -> 2,3 -> 12
5, // 5 -> 0,2 -> (0,0) (0,1) -> 0,2 -> 5
15, // 6 -> 1,2 -> (1,0) (0,1) -> 0,1,2,3 -> 15
6, // 7 -> 0,1,2 -> (0,0) (1,0) (0,1) -> 1,2 -> 6
6, // 8 -> 3 -> (1,1) -> 1,2 -> 6
15, // 9 -> 0,3 -> (0,0) (1,1) -> 0,1,2,3 -> 15
5, // 10 -> 1,3 -> (1,0) (1,1) -> 0,2 -> 5
12, // 11 -> 0,1,3 -> (0,0) (1,0) (1,1) -> 2,3 -> 12
10, // 12 -> 2,3 -> (0,1) (1,1) -> 1,3 -> 10
3, // 13 -> 0,2,3 -> (0,0) (0,1) (1,1) -> 0,1 -> 3
9, // 14 -> 1,2,3 -> (1,0) (0,1) (1,1) -> 0,3 -> 9
0, // 15 -> 0,1,2,3 -> (0,0) (1,0) (0,1) (1,1) ->
};
const int MarchingSquares::edges[1<<Square::CORNERS][MAX_EDGES*2+1] = {
{ -1, -1, -1, -1, -1}, //
{ 3, 0, -1, -1, -1}, // (0,0)
{ 0, 1, -1, -1, -1}, // (1,0)
{ 3, 1, -1, -1, -1}, // (0,0) (1,0)
{ 2, 3, -1, -1, -1}, // (0,1)
{ 2, 0, -1, -1, -1}, // (0,0) (0,1)
{ 0, 1, 2, 3, -1}, // (1,0) (0,1)
{ 1, 2, -1, -1, -1}, // (0,0) (1,0) (0,1)
{ 2, 1, -1, -1, -1}, // (1,1)
{ 3, 0, 1, 2, -1}, // (0,0) (1,1)
{ 0, 2, -1, -1, -1}, // (1,0) (1,1)
{ 3, 2, -1, -1, -1}, // (0,0) (1,0) (1,1)
{ 1, 3, -1, -1, -1}, // (0,1) (1,1)
{ 1, 0, -1, -1, -1}, // (0,0) (0,1) (1,1)
{ 0, 3, -1, -1, -1}, // (1,0) (0,1) (1,1)
{ -1, -1, -1, -1, -1}, // (0,0) (1,0) (0,1) (1,1)
};
double MarchingSquares::vertexList[Square::EDGES][2];
int MarchingSquares::GetIndex(const double v[Square::CORNERS],double iso){
int idx=0;
for(int i=0;i<Square::CORNERS;i++){if(v[i]<iso){idx|=(1<<i);}}
return idx;
}
int MarchingSquares::IsAmbiguous(const double v[Square::CORNERS],double isoValue){
int idx=GetIndex(v,isoValue);
return (idx==5) || (idx==10);
}
int MarchingSquares::AddEdges(const double v[Square::CORNERS],double iso,Edge* isoEdges){
int idx,nEdges=0;
Edge e;
idx=GetIndex(v,iso);
/* Cube is entirely in/out of the surface */
if (!edgeMask[idx]) return 0;
/* Find the vertices where the surface intersects the cube */
int i,j,ii=1;
for(i=0;i<12;i++){
if(edgeMask[idx] & ii){SetVertex(i,v,iso);}
ii<<=1;
}
/* Create the triangle */
for (i=0;edges[idx][i]!=-1;i+=2) {
for(j=0;j<2;j++){
e.p[0][j]=vertexList[edges[idx][i+0]][j];
e.p[1][j]=vertexList[edges[idx][i+1]][j];
}
isoEdges[nEdges++]=e;
}
return nEdges;
}
int MarchingSquares::AddEdgeIndices(const double v[Square::CORNERS],double iso,int* isoIndices){
int idx,nEdges=0;
idx=GetIndex(v,iso);
/* Cube is entirely in/out of the surface */
if (!edgeMask[idx]) return 0;
/* Create the triangle */
for(int i=0;edges[idx][i]!=-1;i+=2){
for(int j=0;j<2;j++){isoIndices[i+j]=edges[idx][i+j];}
nEdges++;
}
return nEdges;
}
void MarchingSquares::SetVertex(int e,const double values[Square::CORNERS],double iso){
int o,i,c1,c2;
Square::FactorEdgeIndex(e,o,i);
Square::EdgeCorners(e,c1,c2);
switch(o){
case 0:
vertexList[e][0]=Interpolate(values[c1]-iso,values[c2]-iso);
vertexList[e][1]=i;
break;
case 1:
vertexList[e][1]=Interpolate(values[c1]-iso,values[c2]-iso);
vertexList[e][0]=i;
break;
}
}
double MarchingSquares::Interpolate(double v1,double v2){return v1/(v1-v2);}
///////////////////
// MarchingCubes //
///////////////////
const int MarchingCubes::edgeMask[1<<Cube::CORNERS]={
0, 273, 545, 816, 2082, 2355, 2563, 2834,
1042, 1283, 1587, 1826, 3120, 3361, 3601, 3840,
324, 85, 869, 628, 2406, 2167, 2887, 2646,
1366, 1095, 1911, 1638, 3444, 3173, 3925, 3652,
644, 917, 165, 436, 2726, 2999, 2183, 2454,
1686, 1927, 1207, 1446, 3764, 4005, 3221, 3460,
960, 721, 481, 240, 3042, 2803, 2499, 2258,
2002, 1731, 1523, 1250, 4080, 3809, 3537, 3264,
2184, 2457, 2729, 3000, 170, 443, 651, 922,
3226, 3467, 3771, 4010, 1208, 1449, 1689, 1928,
2508, 2269, 3053, 2812, 494, 255, 975, 734,
3550, 3279, 4095, 3822, 1532, 1261, 2013, 1740,
2572, 2845, 2093, 2364, 558, 831, 15, 286,
3614, 3855, 3135, 3374, 1596, 1837, 1053, 1292,
2888, 2649, 2409, 2168, 874, 635, 331, 90,
3930, 3659, 3451, 3178, 1912, 1641, 1369, 1096,
1096, 1369, 1641, 1912, 3178, 3451, 3659, 3930,
90, 331, 635, 874, 2168, 2409, 2649, 2888,
1292, 1053, 1837, 1596, 3374, 3135, 3855, 3614,
286, 15, 831, 558, 2364, 2093, 2845, 2572,
1740, 2013, 1261, 1532, 3822, 4095, 3279, 3550,
734, 975, 255, 494, 2812, 3053, 2269, 2508,
1928, 1689, 1449, 1208, 4010, 3771, 3467, 3226,
922, 651, 443, 170, 3000, 2729, 2457, 2184,
3264, 3537, 3809, 4080, 1250, 1523, 1731, 2002,
2258, 2499, 2803, 3042, 240, 481, 721, 960,
3460, 3221, 4005, 3764, 1446, 1207, 1927, 1686,
2454, 2183, 2999, 2726, 436, 165, 917, 644,
3652, 3925, 3173, 3444, 1638, 1911, 1095, 1366,
2646, 2887, 2167, 2406, 628, 869, 85, 324,
3840, 3601, 3361, 3120, 1826, 1587, 1283, 1042,
2834, 2563, 2355, 2082, 816, 545, 273, 0
};
const int MarchingCubes::triangles[1<<Cube::CORNERS][MAX_TRIANGLES*3+1] = {
{ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 0, 4, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 5, 0, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 8, 9, 5, 8, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 1, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 0, 4, 8, 1, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 9, 11, 1, 9, 1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 8, 9, 11, 8, 11, 1, 8, 1, 4, -1, -1, -1, -1, -1, -1, -1},
{ 4, 1, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 10, 8, 0, 10, 0, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 5, 0, 9, 4, 1, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 10, 8, 9, 10, 9, 5, 10, 5, 1, -1, -1, -1, -1, -1, -1, -1},
{ 11, 10, 4, 11, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 11, 10, 8, 11, 8, 0, 11, 0, 5, -1, -1, -1, -1, -1, -1, -1},
{ 9, 11, 10, 9, 10, 4, 9, 4, 0, -1, -1, -1, -1, -1, -1, -1},
{ 8, 9, 11, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 8, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 6, 2, 0, 4, 6, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 6, 2, 8, 5, 0, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 5, 4, 6, 9, 5, 6, 2, 9, 6, -1, -1, -1, -1, -1, -1, -1},
{ 1, 5, 11, 8, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 1, 5, 11, 6, 2, 0, 4, 6, 0, -1, -1, -1, -1, -1, -1, -1},
{ 6, 2, 8, 9, 11, 1, 9, 1, 0, -1, -1, -1, -1, -1, -1, -1},
{ 9, 11, 2, 2, 11, 1, 2, 1, 6, 6, 1, 4, -1, -1, -1, -1},
{ 1, 10, 4, 2, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 2, 0, 1, 6, 2, 1, 10, 6, 1, -1, -1, -1, -1, -1, -1, -1},
{ 5, 0, 9, 4, 1, 10, 8, 6, 2, -1, -1, -1, -1, -1, -1, -1},
{ 5, 2, 9, 5, 6, 2, 5, 1, 6, 1, 10, 6, -1, -1, -1, -1},
{ 2, 8, 6, 4, 5, 11, 4, 11, 10, -1, -1, -1, -1, -1, -1, -1},
{ 5, 2, 0, 6, 2, 5, 11, 6, 5, 10, 6, 11, -1, -1, -1, -1},
{ 9, 11, 10, 9, 10, 4, 9, 4, 0, 8, 6, 2, -1, -1, -1, -1},
{ 9, 11, 2, 2, 11, 6, 10, 6, 11, -1, -1, -1, -1, -1, -1, -1},
{ 9, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 7, 9, 2, 4, 8, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 0, 2, 7, 0, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 7, 5, 4, 2, 7, 4, 8, 2, 4, -1, -1, -1, -1, -1, -1, -1},
{ 7, 9, 2, 5, 11, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 1, 5, 11, 0, 4, 8, 9, 2, 7, -1, -1, -1, -1, -1, -1, -1},
{ 1, 0, 2, 1, 2, 7, 1, 7, 11, -1, -1, -1, -1, -1, -1, -1},
{ 1, 7, 11, 1, 2, 7, 1, 4, 2, 4, 8, 2, -1, -1, -1, -1},
{ 4, 1, 10, 9, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 7, 9, 2, 0, 1, 10, 0, 10, 8, -1, -1, -1, -1, -1, -1, -1},
{ 4, 1, 10, 2, 7, 5, 0, 2, 5, -1, -1, -1, -1, -1, -1, -1},
{ 2, 10, 8, 1, 10, 2, 7, 1, 2, 5, 1, 7, -1, -1, -1, -1},
{ 7, 9, 2, 10, 4, 5, 11, 10, 5, -1, -1, -1, -1, -1, -1, -1},
{ 11, 10, 8, 11, 8, 0, 11, 0, 5, 9, 2, 7, -1, -1, -1, -1},
{ 11, 10, 7, 7, 10, 4, 7, 4, 2, 2, 4, 0, -1, -1, -1, -1},
{ 11, 10, 7, 7, 10, 2, 8, 2, 10, -1, -1, -1, -1, -1, -1, -1},
{ 7, 9, 8, 6, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 4, 6, 7, 0, 4, 7, 9, 0, 7, -1, -1, -1, -1, -1, -1, -1},
{ 6, 7, 5, 8, 6, 5, 0, 8, 5, -1, -1, -1, -1, -1, -1, -1},
{ 4, 6, 7, 5, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 5, 11, 1, 8, 6, 7, 9, 8, 7, -1, -1, -1, -1, -1, -1, -1},
{ 4, 6, 7, 0, 4, 7, 9, 0, 7, 11, 1, 5, -1, -1, -1, -1},
{ 8, 1, 0, 11, 1, 8, 6, 11, 8, 7, 11, 6, -1, -1, -1, -1},
{ 11, 6, 7, 1, 6, 11, 6, 1, 4, -1, -1, -1, -1, -1, -1, -1},
{ 1, 10, 4, 6, 7, 9, 6, 9, 8, -1, -1, -1, -1, -1, -1, -1},
{ 0, 1, 9, 9, 1, 10, 9, 10, 7, 7, 10, 6, -1, -1, -1, -1},
{ 6, 7, 5, 8, 6, 5, 0, 8, 5, 1, 10, 4, -1, -1, -1, -1},
{ 1, 7, 5, 10, 7, 1, 7, 10, 6, -1, -1, -1, -1, -1, -1, -1},
{ 11, 10, 4, 11, 4, 5, 7, 9, 8, 6, 7, 8, -1, -1, -1, -1},
{ 0, 6, 9, 9, 6, 7, 6, 0, 5, 5, 11, 10, 5, 10, 6, -1},
{ 8, 7, 0, 6, 7, 8, 4, 0, 7, 11, 10, 4, 7, 11, 4, -1},
{ 11, 10, 6, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 11, 7, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 0, 4, 8, 11, 7, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 9, 5, 0, 11, 7, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 11, 7, 3, 4, 8, 9, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1},
{ 3, 1, 5, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 0, 4, 8, 7, 3, 1, 5, 7, 1, -1, -1, -1, -1, -1, -1, -1},
{ 3, 1, 0, 3, 0, 9, 3, 9, 7, -1, -1, -1, -1, -1, -1, -1},
{ 7, 8, 9, 4, 8, 7, 3, 4, 7, 1, 4, 3, -1, -1, -1, -1},
{ 1, 10, 4, 3, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 3, 11, 7, 8, 0, 1, 10, 8, 1, -1, -1, -1, -1, -1, -1, -1},
{ 4, 1, 10, 5, 0, 9, 11, 7, 3, -1, -1, -1, -1, -1, -1, -1},
{ 10, 8, 9, 10, 9, 5, 10, 5, 1, 11, 7, 3, -1, -1, -1, -1},
{ 4, 5, 7, 4, 7, 3, 4, 3, 10, -1, -1, -1, -1, -1, -1, -1},
{ 10, 8, 3, 3, 8, 0, 3, 0, 7, 7, 0, 5, -1, -1, -1, -1},
{ 4, 3, 10, 4, 7, 3, 4, 0, 7, 0, 9, 7, -1, -1, -1, -1},
{ 10, 8, 3, 3, 8, 7, 9, 7, 8, -1, -1, -1, -1, -1, -1, -1},
{ 11, 7, 3, 8, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 11, 7, 3, 2, 0, 4, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1},
{ 11, 7, 3, 8, 6, 2, 5, 0, 9, -1, -1, -1, -1, -1, -1, -1},
{ 5, 4, 6, 9, 5, 6, 2, 9, 6, 3, 11, 7, -1, -1, -1, -1},
{ 8, 6, 2, 3, 1, 5, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1},
{ 3, 1, 5, 3, 5, 7, 6, 2, 0, 4, 6, 0, -1, -1, -1, -1},
{ 3, 1, 0, 3, 0, 9, 3, 9, 7, 2, 8, 6, -1, -1, -1, -1},
{ 9, 4, 2, 2, 4, 6, 4, 9, 7, 7, 3, 1, 7, 1, 4, -1},
{ 8, 6, 2, 11, 7, 3, 4, 1, 10, -1, -1, -1, -1, -1, -1, -1},
{ 2, 0, 1, 6, 2, 1, 10, 6, 1, 11, 7, 3, -1, -1, -1, -1},
{ 5, 0, 9, 4, 1, 10, 8, 6, 2, 11, 7, 3, -1, -1, -1, -1},
{ 11, 7, 3, 5, 2, 9, 5, 6, 2, 5, 1, 6, 1, 10, 6, -1},
{ 4, 5, 7, 4, 7, 3, 4, 3, 10, 6, 2, 8, -1, -1, -1, -1},
{ 10, 5, 3, 3, 5, 7, 5, 10, 6, 6, 2, 0, 6, 0, 5, -1},
{ 8, 6, 2, 4, 3, 10, 4, 7, 3, 4, 0, 7, 0, 9, 7, -1},
{ 9, 7, 10, 10, 7, 3, 10, 6, 9, 6, 2, 9, -1, -1, -1, -1},
{ 3, 11, 9, 2, 3, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 4, 8, 0, 2, 3, 11, 2, 11, 9, -1, -1, -1, -1, -1, -1, -1},
{ 0, 2, 3, 0, 3, 11, 0, 11, 5, -1, -1, -1, -1, -1, -1, -1},
{ 2, 3, 8, 8, 3, 11, 8, 11, 4, 4, 11, 5, -1, -1, -1, -1},
{ 2, 3, 1, 2, 1, 5, 2, 5, 9, -1, -1, -1, -1, -1, -1, -1},
{ 2, 3, 1, 2, 1, 5, 2, 5, 9, 0, 4, 8, -1, -1, -1, -1},
{ 0, 2, 3, 0, 3, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 2, 3, 8, 8, 3, 4, 1, 4, 3, -1, -1, -1, -1, -1, -1, -1},
{ 1, 10, 4, 9, 2, 3, 11, 9, 3, -1, -1, -1, -1, -1, -1, -1},
{ 10, 8, 0, 10, 0, 1, 3, 11, 9, 2, 3, 9, -1, -1, -1, -1},
{ 0, 2, 3, 0, 3, 11, 0, 11, 5, 1, 10, 4, -1, -1, -1, -1},
{ 5, 2, 11, 11, 2, 3, 2, 5, 1, 1, 10, 8, 1, 8, 2, -1},
{ 10, 2, 3, 9, 2, 10, 4, 9, 10, 5, 9, 4, -1, -1, -1, -1},
{ 5, 10, 0, 0, 10, 8, 10, 5, 9, 9, 2, 3, 9, 3, 10, -1},
{ 0, 2, 4, 4, 2, 10, 3, 10, 2, -1, -1, -1, -1, -1, -1, -1},
{ 10, 8, 2, 10, 2, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 11, 9, 8, 3, 11, 8, 6, 3, 8, -1, -1, -1, -1, -1, -1, -1},
{ 0, 11, 9, 3, 11, 0, 4, 3, 0, 6, 3, 4, -1, -1, -1, -1},
{ 11, 5, 3, 5, 0, 3, 0, 6, 3, 0, 8, 6, -1, -1, -1, -1},
{ 3, 4, 6, 11, 4, 3, 4, 11, 5, -1, -1, -1, -1, -1, -1, -1},
{ 3, 1, 6, 6, 1, 5, 6, 5, 8, 8, 5, 9, -1, -1, -1, -1},
{ 0, 6, 9, 4, 6, 0, 5, 9, 6, 3, 1, 5, 6, 3, 5, -1},
{ 3, 1, 6, 6, 1, 8, 0, 8, 1, -1, -1, -1, -1, -1, -1, -1},
{ 3, 1, 4, 3, 4, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 11, 9, 8, 3, 11, 8, 6, 3, 8, 4, 1, 10, -1, -1, -1, -1},
{ 3, 9, 6, 11, 9, 3, 10, 6, 9, 0, 1, 10, 9, 0, 10, -1},
{ 4, 1, 10, 11, 5, 3, 5, 0, 3, 0, 6, 3, 0, 8, 6, -1},
{ 5, 10, 6, 1, 10, 5, 6, 11, 5, 6, 3, 11, -1, -1, -1, -1},
{ 10, 5, 3, 4, 5, 10, 6, 3, 5, 9, 8, 6, 5, 9, 6, -1},
{ 6, 3, 10, 9, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 3, 10, 0, 0, 10, 4, 0, 8, 3, 8, 6, 3, -1, -1, -1, -1},
{ 6, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 10, 3, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 3, 6, 10, 0, 4, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 5, 0, 9, 10, 3, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 3, 6, 10, 8, 9, 5, 8, 5, 4, -1, -1, -1, -1, -1, -1, -1},
{ 11, 1, 5, 10, 3, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 0, 4, 8, 1, 5, 11, 10, 3, 6, -1, -1, -1, -1, -1, -1, -1},
{ 10, 3, 6, 0, 9, 11, 1, 0, 11, -1, -1, -1, -1, -1, -1, -1},
{ 8, 9, 11, 8, 11, 1, 8, 1, 4, 10, 3, 6, -1, -1, -1, -1},
{ 4, 1, 3, 6, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 0, 1, 3, 8, 0, 3, 6, 8, 3, -1, -1, -1, -1, -1, -1, -1},
{ 5, 0, 9, 3, 6, 4, 1, 3, 4, -1, -1, -1, -1, -1, -1, -1},
{ 8, 9, 6, 6, 9, 5, 6, 5, 3, 3, 5, 1, -1, -1, -1, -1},
{ 6, 4, 5, 6, 5, 11, 6, 11, 3, -1, -1, -1, -1, -1, -1, -1},
{ 0, 6, 8, 0, 3, 6, 0, 5, 3, 5, 11, 3, -1, -1, -1, -1},
{ 3, 9, 11, 0, 9, 3, 6, 0, 3, 4, 0, 6, -1, -1, -1, -1},
{ 8, 9, 6, 6, 9, 3, 11, 3, 9, -1, -1, -1, -1, -1, -1, -1},
{ 2, 8, 10, 3, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 3, 2, 0, 10, 3, 0, 4, 10, 0, -1, -1, -1, -1, -1, -1, -1},
{ 5, 0, 9, 8, 10, 3, 8, 3, 2, -1, -1, -1, -1, -1, -1, -1},
{ 9, 3, 2, 10, 3, 9, 5, 10, 9, 4, 10, 5, -1, -1, -1, -1},
{ 11, 1, 5, 2, 8, 10, 3, 2, 10, -1, -1, -1, -1, -1, -1, -1},
{ 3, 2, 0, 10, 3, 0, 4, 10, 0, 5, 11, 1, -1, -1, -1, -1},
{ 9, 11, 1, 9, 1, 0, 2, 8, 10, 3, 2, 10, -1, -1, -1, -1},
{ 10, 2, 4, 3, 2, 10, 1, 4, 2, 9, 11, 1, 2, 9, 1, -1},
{ 1, 3, 2, 4, 1, 2, 8, 4, 2, -1, -1, -1, -1, -1, -1, -1},
{ 0, 1, 3, 2, 0, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 1, 3, 2, 4, 1, 2, 8, 4, 2, 9, 5, 0, -1, -1, -1, -1},
{ 9, 3, 2, 5, 3, 9, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1},
{ 3, 2, 11, 11, 2, 8, 11, 8, 5, 5, 8, 4, -1, -1, -1, -1},
{ 5, 2, 0, 11, 2, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1},
{ 4, 3, 8, 8, 3, 2, 3, 4, 0, 0, 9, 11, 0, 11, 3, -1},
{ 9, 11, 3, 9, 3, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 10, 3, 6, 9, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 9, 2, 7, 10, 3, 6, 0, 4, 8, -1, -1, -1, -1, -1, -1, -1},
{ 10, 3, 6, 7, 5, 0, 7, 0, 2, -1, -1, -1, -1, -1, -1, -1},
{ 7, 5, 4, 2, 7, 4, 8, 2, 4, 10, 3, 6, -1, -1, -1, -1},
{ 10, 3, 6, 9, 2, 7, 1, 5, 11, -1, -1, -1, -1, -1, -1, -1},
{ 10, 3, 6, 9, 2, 7, 1, 5, 11, 0, 4, 8, -1, -1, -1, -1},
{ 1, 0, 2, 1, 2, 7, 1, 7, 11, 3, 6, 10, -1, -1, -1, -1},
{ 10, 3, 6, 1, 7, 11, 1, 2, 7, 1, 4, 2, 4, 8, 2, -1},
{ 9, 2, 7, 6, 4, 1, 6, 1, 3, -1, -1, -1, -1, -1, -1, -1},
{ 0, 1, 3, 8, 0, 3, 6, 8, 3, 7, 9, 2, -1, -1, -1, -1},
{ 0, 2, 7, 0, 7, 5, 4, 1, 3, 6, 4, 3, -1, -1, -1, -1},
{ 2, 5, 8, 7, 5, 2, 6, 8, 5, 1, 3, 6, 5, 1, 6, -1},
{ 6, 4, 5, 6, 5, 11, 6, 11, 3, 7, 9, 2, -1, -1, -1, -1},
{ 9, 2, 7, 0, 6, 8, 0, 3, 6, 0, 5, 3, 5, 11, 3, -1},
{ 3, 4, 11, 6, 4, 3, 7, 11, 4, 0, 2, 7, 4, 0, 7, -1},
{ 11, 3, 8, 8, 3, 6, 8, 2, 11, 2, 7, 11, -1, -1, -1, -1},
{ 9, 8, 10, 7, 9, 10, 3, 7, 10, -1, -1, -1, -1, -1, -1, -1},
{ 9, 0, 7, 0, 4, 7, 4, 3, 7, 4, 10, 3, -1, -1, -1, -1},
{ 8, 10, 0, 0, 10, 3, 0, 3, 5, 5, 3, 7, -1, -1, -1, -1},
{ 10, 5, 4, 3, 5, 10, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1},
{ 9, 8, 10, 7, 9, 10, 3, 7, 10, 1, 5, 11, -1, -1, -1, -1},
{ 1, 5, 11, 9, 0, 7, 0, 4, 7, 4, 3, 7, 4, 10, 3, -1},
{ 11, 0, 7, 1, 0, 11, 3, 7, 0, 8, 10, 3, 0, 8, 3, -1},
{ 7, 1, 4, 11, 1, 7, 4, 3, 7, 4, 10, 3, -1, -1, -1, -1},
{ 4, 9, 8, 7, 9, 4, 1, 7, 4, 3, 7, 1, -1, -1, -1, -1},
{ 7, 1, 3, 9, 1, 7, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1},
{ 8, 7, 0, 0, 7, 5, 7, 8, 4, 4, 1, 3, 4, 3, 7, -1},
{ 5, 1, 3, 7, 5, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 3, 4, 11, 11, 4, 5, 4, 3, 7, 7, 9, 8, 7, 8, 4, -1},
{ 3, 9, 0, 7, 9, 3, 0, 11, 3, 0, 5, 11, -1, -1, -1, -1},
{ 3, 7, 11, 8, 4, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 3, 7, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 6, 10, 11, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 0, 4, 8, 10, 11, 7, 10, 7, 6, -1, -1, -1, -1, -1, -1, -1},
{ 9, 5, 0, 6, 10, 11, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1},
{ 8, 9, 5, 8, 5, 4, 6, 10, 11, 7, 6, 11, -1, -1, -1, -1},
{ 5, 7, 6, 5, 6, 10, 5, 10, 1, -1, -1, -1, -1, -1, -1, -1},
{ 5, 7, 6, 5, 6, 10, 5, 10, 1, 4, 8, 0, -1, -1, -1, -1},
{ 1, 0, 10, 10, 0, 9, 10, 9, 6, 6, 9, 7, -1, -1, -1, -1},
{ 1, 7, 10, 10, 7, 6, 7, 1, 4, 4, 8, 9, 4, 9, 7, -1},
{ 7, 6, 4, 7, 4, 1, 7, 1, 11, -1, -1, -1, -1, -1, -1, -1},
{ 11, 0, 1, 8, 0, 11, 7, 8, 11, 6, 8, 7, -1, -1, -1, -1},
{ 7, 6, 4, 7, 4, 1, 7, 1, 11, 5, 0, 9, -1, -1, -1, -1},
{ 11, 6, 1, 7, 6, 11, 5, 1, 6, 8, 9, 5, 6, 8, 5, -1},
{ 4, 5, 7, 4, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 5, 7, 0, 0, 7, 8, 6, 8, 7, -1, -1, -1, -1, -1, -1, -1},
{ 7, 6, 9, 9, 6, 0, 4, 0, 6, -1, -1, -1, -1, -1, -1, -1},
{ 8, 9, 7, 8, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 8, 10, 11, 2, 8, 11, 7, 2, 11, -1, -1, -1, -1, -1, -1, -1},
{ 10, 11, 4, 4, 11, 7, 4, 7, 0, 0, 7, 2, -1, -1, -1, -1},
{ 8, 10, 11, 2, 8, 11, 7, 2, 11, 5, 0, 9, -1, -1, -1, -1},
{ 9, 4, 2, 5, 4, 9, 7, 2, 4, 10, 11, 7, 4, 10, 7, -1},
{ 1, 8, 10, 2, 8, 1, 5, 2, 1, 7, 2, 5, -1, -1, -1, -1},
{ 1, 7, 10, 5, 7, 1, 4, 10, 7, 2, 0, 4, 7, 2, 4, -1},
{ 7, 1, 9, 9, 1, 0, 1, 7, 2, 2, 8, 10, 2, 10, 1, -1},
{ 7, 2, 9, 10, 1, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 8, 4, 2, 4, 1, 2, 1, 7, 2, 1, 11, 7, -1, -1, -1, -1},
{ 11, 0, 1, 7, 0, 11, 0, 7, 2, -1, -1, -1, -1, -1, -1, -1},
{ 5, 0, 9, 8, 4, 2, 4, 1, 2, 1, 7, 2, 1, 11, 7, -1},
{ 2, 5, 1, 9, 5, 2, 1, 7, 2, 1, 11, 7, -1, -1, -1, -1},
{ 4, 5, 8, 8, 5, 2, 7, 2, 5, -1, -1, -1, -1, -1, -1, -1},
{ 7, 2, 0, 5, 7, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 7, 2, 4, 4, 2, 8, 4, 0, 7, 0, 9, 7, -1, -1, -1, -1},
{ 7, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 10, 11, 9, 6, 10, 9, 2, 6, 9, -1, -1, -1, -1, -1, -1, -1},
{ 10, 11, 9, 6, 10, 9, 2, 6, 9, 0, 4, 8, -1, -1, -1, -1},
{ 5, 10, 11, 6, 10, 5, 0, 6, 5, 2, 6, 0, -1, -1, -1, -1},
{ 2, 5, 8, 8, 5, 4, 5, 2, 6, 6, 10, 11, 6, 11, 5, -1},
{ 10, 1, 6, 1, 5, 6, 5, 2, 6, 5, 9, 2, -1, -1, -1, -1},
{ 0, 4, 8, 10, 1, 6, 1, 5, 6, 5, 2, 6, 5, 9, 2, -1},
{ 1, 0, 10, 10, 0, 6, 2, 6, 0, -1, -1, -1, -1, -1, -1, -1},
{ 2, 6, 1, 1, 6, 10, 1, 4, 2, 4, 8, 2, -1, -1, -1, -1},
{ 11, 9, 1, 1, 9, 2, 1, 2, 4, 4, 2, 6, -1, -1, -1, -1},
{ 8, 1, 6, 0, 1, 8, 2, 6, 1, 11, 9, 2, 1, 11, 2, -1},
{ 11, 6, 1, 1, 6, 4, 6, 11, 5, 5, 0, 2, 5, 2, 6, -1},
{ 2, 6, 8, 11, 5, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 6, 4, 2, 2, 4, 9, 5, 9, 4, -1, -1, -1, -1, -1, -1, -1},
{ 5, 9, 6, 6, 9, 2, 6, 8, 5, 8, 0, 5, -1, -1, -1, -1},
{ 0, 2, 6, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 2, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 8, 10, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 0, 11, 9, 4, 11, 0, 11, 4, 10, -1, -1, -1, -1, -1, -1, -1},
{ 5, 10, 11, 0, 10, 5, 10, 0, 8, -1, -1, -1, -1, -1, -1, -1},
{ 4, 10, 11, 5, 4, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 1, 8, 10, 5, 8, 1, 8, 5, 9, -1, -1, -1, -1, -1, -1, -1},
{ 9, 4, 10, 0, 4, 9, 10, 5, 9, 10, 1, 5, -1, -1, -1, -1},
{ 0, 8, 10, 1, 0, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 10, 1, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 4, 9, 8, 1, 9, 4, 9, 1, 11, -1, -1, -1, -1, -1, -1, -1},
{ 1, 11, 9, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 11, 0, 8, 5, 0, 11, 8, 1, 11, 8, 4, 1, -1, -1, -1, -1},
{ 11, 5, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 5, 9, 8, 4, 5, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 9, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ 8, 4, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
{ -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}
};
const int MarchingCubes::cornerMap[Cube::CORNERS]={0,1,3,2,4,5,7,6};
double MarchingCubes::vertexList[Cube::EDGES][3];
int MarchingCubes::GetIndex(const double v[Cube::CORNERS],double iso){
int idx=0;
if (v[Cube::CornerIndex(0,0,0)] < iso) idx |= 1;
if (v[Cube::CornerIndex(1,0,0)] < iso) idx |= 2;
if (v[Cube::CornerIndex(1,1,0)] < iso) idx |= 4;
if (v[Cube::CornerIndex(0,1,0)] < iso) idx |= 8;
if (v[Cube::CornerIndex(0,0,1)] < iso) idx |= 16;
if (v[Cube::CornerIndex(1,0,1)] < iso) idx |= 32;
if (v[Cube::CornerIndex(1,1,1)] < iso) idx |= 64;
if (v[Cube::CornerIndex(0,1,1)] < iso) idx |= 128;
return idx;
}
int MarchingCubes::GetFaceIndex(const double values[Cube::CORNERS],double iso,int faceIndex){
int i,j,x,y,z,idx=0;
double v[2][2];
Cube::FactorFaceIndex(faceIndex,x,y,z);
if (x<0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=values[Cube::CornerIndex(0,i,j)];}}}
else if (x>0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=values[Cube::CornerIndex(1,i,j)];}}}
else if (y<0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=values[Cube::CornerIndex(i,0,j)];}}}
else if (y>0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=values[Cube::CornerIndex(i,1,j)];}}}
else if (z<0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=values[Cube::CornerIndex(i,j,0)];}}}
else if (z>0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=values[Cube::CornerIndex(i,j,1)];}}}
if (v[0][0] < iso) idx |= 1;
if (v[1][0] < iso) idx |= 2;
if (v[1][1] < iso) idx |= 4;
if (v[0][1] < iso) idx |= 8;
return idx;
}
int MarchingCubes::IsAmbiguous(const double v[Cube::CORNERS],double isoValue,int faceIndex){
int idx=GetFaceIndex(v,isoValue,faceIndex);
return (idx==5) || (idx==10);
}
int MarchingCubes::HasRoots(const double v[Cube::CORNERS],double isoValue,int faceIndex){
int idx=GetFaceIndex(v,isoValue,faceIndex);
return (idx!=0) && (idx !=15);
}
int MarchingCubes::HasRoots(const double v[Cube::CORNERS],double isoValue){
int idx=GetIndex(v,isoValue);
if(idx==0 || idx==255){return 0;}
else{return 1;}
}
int MarchingCubes::HasRoots(int mcIndex){
if(mcIndex==0 || mcIndex==255){return 0;}
else{return 1;}
}
int MarchingCubes::AddTriangles( const double v[Cube::CORNERS] , double iso , Triangle* isoTriangles )
{
int idx,ntriang=0;
Triangle tri;
idx=GetIndex(v,iso);
/* Cube is entirely in/out of the surface */
if (!edgeMask[idx]) return 0;
/* Find the vertices where the surface intersects the cube */
int i,j,ii=1;
for(i=0;i<12;i++){
if(edgeMask[idx] & ii){SetVertex(i,v,iso);}
ii<<=1;
}
/* Create the triangle */
for( i=0 ; triangles[idx][i]!=-1 ; i+=3 )
{
for(j=0;j<3;j++){
tri.p[0][j]=vertexList[triangles[idx][i+0]][j];
tri.p[1][j]=vertexList[triangles[idx][i+1]][j];
tri.p[2][j]=vertexList[triangles[idx][i+2]][j];
}
isoTriangles[ntriang++]=tri;
}
return ntriang;
}
int MarchingCubes::AddTriangleIndices(const double v[Cube::CORNERS],double iso,int* isoIndices){
int idx,ntriang=0;
idx=GetIndex(v,iso);
/* Cube is entirely in/out of the surface */
if (!edgeMask[idx]) return 0;
/* Create the triangle */
for(int i=0;triangles[idx][i]!=-1;i+=3){
for(int j=0;j<3;j++){isoIndices[i+j]=triangles[idx][i+j];}
ntriang++;
}
return ntriang;
}
void MarchingCubes::SetVertex( int e , const double values[Cube::CORNERS] , double iso )
{
double t;
int o , i1 , i2;
Cube::FactorEdgeIndex( e , o , i1 , i2 );
switch( o )
{
case 0:
t = Interpolate( values[ Cube::CornerIndex( 0 , i1 , i2 ) ] - iso , values[ Cube::CornerIndex( 1 , i1 , i2 ) ] - iso );
vertexList[e][0] = t , vertexList[e][1] = i1 , vertexList[e][2] = i2;
break;
case 1:
t = Interpolate( values[ Cube::CornerIndex( i1 , 0 , i2 ) ] - iso , values[ Cube::CornerIndex( i1 , 1 , i2 ) ] - iso );
vertexList[e][0] = i1 , vertexList[e][1] = t , vertexList[e][2] = i2;
break;
case 2:
t = Interpolate( values[ Cube::CornerIndex( i1 , i2 , 0 ) ] - iso , values[ Cube::CornerIndex( i1 , i2 , 1 ) ] - iso );
vertexList[e][0] = i1 , vertexList[e][1] = i2 , vertexList[e][2] = t;
break;
}
}
double MarchingCubes::Interpolate( double v1 , double v2 ) { return v1/(v1-v2); }
///////////////////////////////////
int MarchingCubes::GetIndex(const float v[Cube::CORNERS],float iso){
int idx=0;
if (v[Cube::CornerIndex(0,0,0)] < iso) idx |= 1;
if (v[Cube::CornerIndex(1,0,0)] < iso) idx |= 2;
if (v[Cube::CornerIndex(1,1,0)] < iso) idx |= 4;
if (v[Cube::CornerIndex(0,1,0)] < iso) idx |= 8;
if (v[Cube::CornerIndex(0,0,1)] < iso) idx |= 16;
if (v[Cube::CornerIndex(1,0,1)] < iso) idx |= 32;
if (v[Cube::CornerIndex(1,1,1)] < iso) idx |= 64;
if (v[Cube::CornerIndex(0,1,1)] < iso) idx |= 128;
return idx;
}
int MarchingCubes::GetFaceIndex(const float values[Cube::CORNERS],float iso,int faceIndex){
int i,j,x,y,z,idx=0;
double v[2][2];
Cube::FactorFaceIndex(faceIndex,x,y,z);
if (x<0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=values[Cube::CornerIndex(0,i,j)];}}}
else if (x>0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=values[Cube::CornerIndex(1,i,j)];}}}
else if (y<0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=values[Cube::CornerIndex(i,0,j)];}}}
else if (y>0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=values[Cube::CornerIndex(i,1,j)];}}}
else if (z<0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=values[Cube::CornerIndex(i,j,0)];}}}
else if (z>0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=values[Cube::CornerIndex(i,j,1)];}}}
if (v[0][0] < iso) idx |= 1;
if (v[1][0] < iso) idx |= 2;
if (v[1][1] < iso) idx |= 4;
if (v[0][1] < iso) idx |= 8;
return idx;
}
int MarchingCubes::GetFaceIndex(int mcIndex,int faceIndex){
int i,j,x,y,z,idx=0;
int v[2][2];
Cube::FactorFaceIndex(faceIndex,x,y,z);
if (x<0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=mcIndex&(1<<MarchingCubes::cornerMap[Cube::CornerIndex(0,i,j)]);}}}
else if (x>0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=mcIndex&(1<<MarchingCubes::cornerMap[Cube::CornerIndex(1,i,j)]);}}}
else if (y<0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=mcIndex&(1<<MarchingCubes::cornerMap[Cube::CornerIndex(i,0,j)]);}}}
else if (y>0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=mcIndex&(1<<MarchingCubes::cornerMap[Cube::CornerIndex(i,1,j)]);}}}
else if (z<0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=mcIndex&(1<<MarchingCubes::cornerMap[Cube::CornerIndex(i,j,1)]);}}}
else if (z>0){for(i=0;i<2;i++){for(j=0;j<2;j++){v[i][j]=mcIndex&(1<<MarchingCubes::cornerMap[Cube::CornerIndex(i,j,1)]);}}}
if (v[0][0]) idx |= 1;
if (v[1][0]) idx |= 2;
if (v[1][1]) idx |= 4;
if (v[0][1]) idx |= 8;
return idx;
}
int MarchingCubes::IsAmbiguous(const float v[Cube::CORNERS],float isoValue,int faceIndex){
int idx=GetFaceIndex(v,isoValue,faceIndex);
return (idx==5) || (idx==10);
}
int MarchingCubes::IsAmbiguous(int mcIndex,int faceIndex){
int idx=GetFaceIndex(mcIndex,faceIndex);
return (idx==5) || (idx==10);
}
int MarchingCubes::HasRoots(const float v[Cube::CORNERS],float isoValue){
int idx=GetIndex(v,isoValue);
if(idx==0 || idx==255){return 0;}
else{return 1;}
}
int MarchingCubes::HasRoots(const float v[Cube::CORNERS],float isoValue,int faceIndex){
int idx=GetFaceIndex(v,isoValue,faceIndex);
return (idx!=0) && (idx!=15);
}
int MarchingCubes::HasFaceRoots(int mcIndex,int faceIndex){
int idx=GetFaceIndex(mcIndex,faceIndex);
return (idx!=0) && (idx!=15);
}
int MarchingCubes::HasEdgeRoots(int mcIndex,int edgeIndex){
int c1,c2;
Cube::EdgeCorners(edgeIndex,c1,c2);
if( ( (mcIndex&(1<<MarchingCubes::cornerMap[c1])) && (mcIndex&(1<<MarchingCubes::cornerMap[c2]))) ||
(!(mcIndex&(1<<MarchingCubes::cornerMap[c1])) && !(mcIndex&(1<<MarchingCubes::cornerMap[c2])))){return 0;}
else{return 1;}
}
int MarchingCubes::AddTriangles(const float v[Cube::CORNERS],float iso,Triangle* isoTriangles){
int idx,ntriang=0;
Triangle tri;
idx=GetIndex(v,iso);
/* Cube is entirely in/out of the surface */
if (!edgeMask[idx]) return 0;
/* Find the vertices where the surface intersects the cube */
int i,j,ii=1;
for( i=0 ; i<12 ; i++ )
{
if(edgeMask[idx] & ii) SetVertex( i , v , iso );
ii<<=1;
}
/* Create the triangle */
for (i=0;triangles[idx][i]!=-1;i+=3) {
for(j=0;j<3;j++){
tri.p[0][j]=vertexList[triangles[idx][i+0]][j];
tri.p[1][j]=vertexList[triangles[idx][i+1]][j];
tri.p[2][j]=vertexList[triangles[idx][i+2]][j];
}
isoTriangles[ntriang++]=tri;
}
return ntriang;
}
int MarchingCubes::AddTriangleIndices( const float v[Cube::CORNERS] , float iso , int* isoIndices )
{
int idx,ntriang=0;
idx=GetIndex(v,iso);
/* Cube is entirely in/out of the surface */
if (!edgeMask[idx]) return 0;
/* Create the triangle */
for(int i=0;triangles[idx][i]!=-1;i+=3){
for(int j=0;j<3;j++){isoIndices[i+j]=triangles[idx][i+j];}
ntriang++;
}
return ntriang;
}
int MarchingCubes::AddTriangleIndices( int idx , int* isoIndices )
{
int ntriang=0;
/* Cube is entirely in/out of the surface */
if (!edgeMask[idx]) return 0;
/* Create the triangle */
for(int i=0;triangles[idx][i]!=-1;i+=3){
for(int j=0;j<3;j++){isoIndices[i+j]=triangles[idx][i+j];}
ntriang++;
}
return ntriang;
}
void MarchingCubes::SetVertex( int e , const float values[Cube::CORNERS] , float iso )
{
double t;
int o , i1 , i2;
Cube::FactorEdgeIndex( e , o , i1 , i2 );
switch( o )
{
case 0:
t = Interpolate( values[ Cube::CornerIndex( 0 , i1 , i2 ) ] - iso , values[ Cube::CornerIndex( 1 , i1 , i2 ) ] - iso );
vertexList[e][0] = t , vertexList[e][1] = i1 , vertexList[e][2] = i2;
break;
case 1:
t = Interpolate( values[ Cube::CornerIndex( i1 , 0 , i2 ) ] - iso , values[ Cube::CornerIndex( i1 , 1 , i2 ) ] - iso );
vertexList[e][0] = i1 , vertexList[e][1] = t , vertexList[e][2] = i2;
break;
case 2:
t = Interpolate( values[ Cube::CornerIndex( i1 , i2 , 0 ) ] - iso , values[ Cube::CornerIndex( i1 , i2 , 1 ) ] - iso );
vertexList[e][0] = i1 , vertexList[e][1] = i2 , vertexList[e][2] = t;
break;
}
}
float MarchingCubes::Interpolate( float v1 , float v2 ){ return v1/(v1-v2); }
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