// Given a grid cell and an isolevel, calculate the triangular facets required to represent the isosurface through the cell.
// Return the number of triangular facets, the array "triangles" will be loaded up with the vertices at most 5 triangular facets.
// 0 will be returned if the grid cell is either totally above of totally below the isolevel.
public static void Polygonise(GridCell grid, double isolevel, ref List <Triangle> theTriangleList)
{
// Determine the index into the edge table which tells us which vertices are inside of the surface
int cubeindex = 0;
if (grid.val[0] < isolevel)
{
cubeindex |= 1;
}
if (grid.val[1] < isolevel)
{
cubeindex |= 2;
}
if (grid.val[2] < isolevel)
{
cubeindex |= 4;
}
if (grid.val[3] < isolevel)
{
cubeindex |= 8;
}
if (grid.val[4] < isolevel)
{
cubeindex |= 16;
}
if (grid.val[5] < isolevel)
{
cubeindex |= 32;
}
if (grid.val[6] < isolevel)
{
cubeindex |= 64;
}
if (grid.val[7] < isolevel)
{
cubeindex |= 128;
}
// Cube is entirely in/out of the surface
if (EdgeTable.LookupTable[cubeindex] == 0)
{
return;
}
Point3D[] vertlist = new Point3D[12];
// Find the vertices where the surface intersects the cube
if ((EdgeTable.LookupTable[cubeindex] & 1) > 0)
{
vertlist[0] = VertexInterp(isolevel, grid.p[0], grid.p[1], grid.val[0], grid.val[1]);
}
if ((EdgeTable.LookupTable[cubeindex] & 2) > 0)
{
vertlist[1] = VertexInterp(isolevel, grid.p[1], grid.p[2], grid.val[1], grid.val[2]);
}
if ((EdgeTable.LookupTable[cubeindex] & 4) > 0)
{
vertlist[2] = VertexInterp(isolevel, grid.p[2], grid.p[3], grid.val[2], grid.val[3]);
}
if ((EdgeTable.LookupTable[cubeindex] & 8) > 0)
{
vertlist[3] = VertexInterp(isolevel, grid.p[3], grid.p[0], grid.val[3], grid.val[0]);
}
if ((EdgeTable.LookupTable[cubeindex] & 16) > 0)
{
vertlist[4] = VertexInterp(isolevel, grid.p[4], grid.p[5], grid.val[4], grid.val[5]);
}
if ((EdgeTable.LookupTable[cubeindex] & 32) > 0)
{
vertlist[5] = VertexInterp(isolevel, grid.p[5], grid.p[6], grid.val[5], grid.val[6]);
}
if ((EdgeTable.LookupTable[cubeindex] & 64) > 0)
{
vertlist[6] = VertexInterp(isolevel, grid.p[6], grid.p[7], grid.val[6], grid.val[7]);
}
if ((EdgeTable.LookupTable[cubeindex] & 128) > 0)
{
vertlist[7] = VertexInterp(isolevel, grid.p[7], grid.p[4], grid.val[7], grid.val[4]);
}
if ((EdgeTable.LookupTable[cubeindex] & 256) > 0)
{
vertlist[8] = VertexInterp(isolevel, grid.p[0], grid.p[4], grid.val[0], grid.val[4]);
}
if ((EdgeTable.LookupTable[cubeindex] & 512) > 0)
{
vertlist[9] = VertexInterp(isolevel, grid.p[1], grid.p[5], grid.val[1], grid.val[5]);
}
if ((EdgeTable.LookupTable[cubeindex] & 1024) > 0)
{
vertlist[10] = VertexInterp(isolevel, grid.p[2], grid.p[6], grid.val[2], grid.val[6]);
}
if ((EdgeTable.LookupTable[cubeindex] & 2048) > 0)
{
vertlist[11] = VertexInterp(isolevel, grid.p[3], grid.p[7], grid.val[3], grid.val[7]);
}
// Create the triangle
for (int i = 0; TriTable.LookupTable[cubeindex, i] != -1; i += 3)
{
Triangle aTriangle = new Triangle();
aTriangle.p[0] = vertlist[TriTable.LookupTable[cubeindex, i]];
aTriangle.p[1] = vertlist[TriTable.LookupTable[cubeindex, i + 1]];
aTriangle.p[2] = vertlist[TriTable.LookupTable[cubeindex, i + 2]];
theTriangleList.Add(aTriangle);
}
}
private static List<Triangle> ComputeTriangles(CTSliceInfo[] slices, int theIsoValue)
{
// 1. Calculate the Center Point
// =============================
// For moving the 3D model with the mouse, the implementation is taken from Code Project 'WPF 3D Primer'.
// See also: 'http://www.codeproject.com/Articles/23332/WPF-3D-Primer#'
// However, this implementation needs the 3D model to be centered in the origin of the coordinate system.
// As a consequence, all CT Slices have to be shifted by the Center Point (method 'AdjustPatientPositionToCenterPoint()')
CTSliceInfo firstCT = slices[0];
CTSliceInfo lastCT = slices[slices.Length - 1];
double Center_X = firstCT.UpperLeft_X + (firstCT.PixelSpacing_X * firstCT.ColumnCount / 2);
double Center_Y = firstCT.UpperLeft_Y + (firstCT.PixelSpacing_Y * firstCT.RowCount / 2);
// CT Slices are already sorted ascending in Z direction
double Center_Z = firstCT.UpperLeft_Z + ((lastCT.UpperLeft_Z - firstCT.UpperLeft_Z) / 2);
// Create the Center Point
Point3D aCenterPoint = new Point3D(Center_X, Center_Y, Center_Z);
// 2. The Marching Cubes algorithm
// ===============================
// For each Voxel of the CT Slice, an own GridCell is created.
// The IsoValue and the x/y/z information for each corner of the GridCell is taken from the direct neighbor voxels (of the same or adjacant CT Slice).
// Looping has to be done over all CT Slices.
List<Triangle> triangles = new List<Triangle>();
CTSliceInfo slice1 = null;
CTSliceInfo slice2 = slices[0];
slice2.AdjustPatientPositionToCenterPoint(aCenterPoint);
for (int sliceIdx = 1; sliceIdx != slices.Length; ++sliceIdx)
{
slice1 = slice2;
slice2 = slices[sliceIdx];
slice2.AdjustPatientPositionToCenterPoint(aCenterPoint);
for (int r = 0; r != slice1.RowCount - 1; ++r)
{
for (int c = 0; c != slice1.ColumnCount - 1; ++c)
{
GridCell aGridCell = new GridCell(sliceIdx, r, c, slice1, slice2);
MarchingCubes.Polygonise(aGridCell, theIsoValue, ref triangles);
}
}
}
return triangles;
}
// Given a grid cell and an isolevel, calculate the triangular facets required to represent the isosurface through the cell.
// Return the number of triangular facets, the array "triangles" will be loaded up with the vertices at most 5 triangular facets.
// 0 will be returned if the grid cell is either totally above of totally below the isolevel.
public static void Polygonise(GridCell grid, double isolevel, ref List<Triangle> theTriangleList)
{
// Determine the index into the edge table which tells us which vertices are inside of the surface
int cubeindex = 0;
if (grid.val[0] < isolevel) cubeindex |= 1;
if (grid.val[1] < isolevel) cubeindex |= 2;
if (grid.val[2] < isolevel) cubeindex |= 4;
if (grid.val[3] < isolevel) cubeindex |= 8;
if (grid.val[4] < isolevel) cubeindex |= 16;
if (grid.val[5] < isolevel) cubeindex |= 32;
if (grid.val[6] < isolevel) cubeindex |= 64;
if (grid.val[7] < isolevel) cubeindex |= 128;
// Cube is entirely in/out of the surface
if (EdgeTable.LookupTable[cubeindex] == 0)
return;
Point3D[] vertlist = new Point3D[12];
// Find the vertices where the surface intersects the cube
if ((EdgeTable.LookupTable[cubeindex] & 1) > 0)
vertlist[0] = VertexInterp(isolevel, grid.p[0], grid.p[1], grid.val[0], grid.val[1]);
if ((EdgeTable.LookupTable[cubeindex] & 2) > 0)
vertlist[1] = VertexInterp(isolevel, grid.p[1], grid.p[2], grid.val[1], grid.val[2]);
if ((EdgeTable.LookupTable[cubeindex] & 4) > 0)
vertlist[2] = VertexInterp(isolevel, grid.p[2], grid.p[3], grid.val[2], grid.val[3]);
if ((EdgeTable.LookupTable[cubeindex] & 8) > 0)
vertlist[3] = VertexInterp(isolevel, grid.p[3], grid.p[0], grid.val[3], grid.val[0]);
if ((EdgeTable.LookupTable[cubeindex] & 16) > 0)
vertlist[4] = VertexInterp(isolevel, grid.p[4], grid.p[5], grid.val[4], grid.val[5]);
if ((EdgeTable.LookupTable[cubeindex] & 32) > 0)
vertlist[5] = VertexInterp(isolevel, grid.p[5], grid.p[6], grid.val[5], grid.val[6]);
if ((EdgeTable.LookupTable[cubeindex] & 64) > 0)
vertlist[6] = VertexInterp(isolevel, grid.p[6], grid.p[7], grid.val[6], grid.val[7]);
if ((EdgeTable.LookupTable[cubeindex] & 128) > 0)
vertlist[7] = VertexInterp(isolevel, grid.p[7], grid.p[4], grid.val[7], grid.val[4]);
if ((EdgeTable.LookupTable[cubeindex] & 256) > 0)
vertlist[8] = VertexInterp(isolevel, grid.p[0], grid.p[4], grid.val[0], grid.val[4]);
if ((EdgeTable.LookupTable[cubeindex] & 512) > 0)
vertlist[9] = VertexInterp(isolevel, grid.p[1], grid.p[5], grid.val[1], grid.val[5]);
if ((EdgeTable.LookupTable[cubeindex] & 1024) > 0)
vertlist[10] = VertexInterp(isolevel, grid.p[2], grid.p[6], grid.val[2], grid.val[6]);
if ((EdgeTable.LookupTable[cubeindex] & 2048) > 0)
vertlist[11] = VertexInterp(isolevel, grid.p[3], grid.p[7], grid.val[3], grid.val[7]);
// Create the triangle
for (int i = 0; TriTable.LookupTable[cubeindex, i] != -1; i += 3)
{
Triangle aTriangle = new Triangle();
aTriangle.p[0] = vertlist[TriTable.LookupTable[cubeindex, i]];
aTriangle.p[1] = vertlist[TriTable.LookupTable[cubeindex, i + 1]];
aTriangle.p[2] = vertlist[TriTable.LookupTable[cubeindex, i + 2]];
theTriangleList.Add(aTriangle);
}
}