public static int PolygonizeTransitionCell(Vector3f offset, Vector3i origin,
Vector3i localX, Vector3i localY, Vector3i localZ,
int x, int y, float cellSize,
byte lodIndex, byte axis, byte directionMask,
IVolumeData samples,
ref IList<Vertex> verts, ref IList<int> indices,
ref TransitionCache cache)
{
int lodStep = 1 << lodIndex;
int sampleStep = 1 << (lodIndex - 1);
int lodScale = 1 << lodIndex;
int last = 16 * lodScale;
byte near = 0;
// Compute which of the six faces of the block that the vertex
// is near. (near is defined as being in boundary cell.)
for (int i = 0; i < 3; i++)
{
// Vertex close to negative face.
if (origin[i] == 0) { near |= (byte)(1 << (i * 2 + 0)); }
// Vertex close to positive face.
if (origin[i] == last) { near |= (byte)(1 << (i * 2 + 1)); }
}
Vector3i[] coords =
{
new Vector3i(0,0,0), new Vector3i(1,0,0), new Vector3i(2,0,0), // High-res lower row
new Vector3i(0,1,0), new Vector3i(1,1,0), new Vector3i(2,1,0), // High-res middle row
new Vector3i(0,2,0), new Vector3i(1,2,0), new Vector3i(2,2,0), // High-res upper row
new Vector3i(0,0,2), new Vector3i(2,0,2), // Low-res lower row
new Vector3i(0,2,2), new Vector3i(2,2,2) // Low-res upper row
};
// TODO: Implement Matrix Math
var mx = localX * sampleStep;
var my = localY * sampleStep;
var mz = localZ * sampleStep;
Matrix3X3 basis = new Matrix3X3((Vector3f)mx, (Vector3f)my, (Vector3f)mz);
Vector3i[] pos = {
origin + basis * coords[0x00], origin + basis * coords[0x01], origin + basis * coords[0x02],
origin + basis * coords[0x03], origin + basis * coords[0x04], origin + basis * coords[0x05],
origin + basis * coords[0x06], origin + basis * coords[0x07], origin + basis * coords[0x08],
origin + basis * coords[0x09], origin + basis * coords[0x0A],
origin + basis * coords[0x0B], origin + basis * coords[0x0C]
};
Vector3f[] normals = new Vector3f[13];
for (int i = 0; i < 9; i++)
{
Vector3i p = pos[i];
float nx = (samples[p + Vector3i.UnitX] - samples[p - Vector3i.UnitX]) * 0.5f;
float ny = (samples[p + Vector3i.UnitY] - samples[p - Vector3i.UnitY]) * 0.5f;
float nz = (samples[p + Vector3i.UnitZ] - samples[p - Vector3i.UnitZ]) * 0.5f;
normals[i] = new Vector3f(nx, ny, nz);
normals[i].Normalize();
}
normals[0x9] = normals[0];
normals[0xA] = normals[2];
normals[0xB] = normals[6];
normals[0xC] = normals[8];
Vector3i[] samplePos = {
pos[0], pos[1], pos[2],
pos[3], pos[4], pos[5],
pos[6], pos[7], pos[8],
pos[0], pos[2],
pos[6], pos[8]
};
uint caseCode = (uint)(Sign(samples[pos[0]]) * 0x001 |
Sign(samples[pos[1]]) * 0x002 |
Sign(samples[pos[2]]) * 0x004 |
Sign(samples[pos[5]]) * 0x008 |
Sign(samples[pos[8]]) * 0x010 |
Sign(samples[pos[7]]) * 0x020 |
Sign(samples[pos[6]]) * 0x040 |
Sign(samples[pos[3]]) * 0x080 |
Sign(samples[pos[4]]) * 0x100);
if (caseCode == 0 || caseCode == 511)
return 0;
cache[x, y].CaseIndex = (byte)caseCode;
byte classIndex = Tables.TransitionCellClass[caseCode]; // Equivalence class index.
var data = Tables.TransitionRegularCellData[classIndex & 0x7F];
bool inverse = (classIndex & 128) != 0;
int[] localVertexMapping = new int[12];
int nv = (int)data.GetVertexCount();
int nt = (int)data.GetTriangleCount();
Debug.Assert(nv <= 12);
var vert = new Vertex();
for (int i = 0; i < nv; i++)
{
ushort edgeCode = Tables.TransitionVertexData[caseCode][i];
byte v0 = HiNibble((byte)edgeCode);
byte v1 = LoNibble((byte)edgeCode);
bool lowside = (v0 > 8) && (v1 > 8);
int d0 = samples[samplePos[v0]];
int d1 = samples[samplePos[v1]];
int t = (d1 << 8) / (d1 - d0);
int u = 0x0100 - t;
float t0 = t * S;
float t1 = u * S;
Vector3f n0 = normals[v0];
Vector3f n1 = normals[v1];
vert.Near = near;
vert.Normal = n0 * t0 + n1 * t1;
if ((t & 0x00ff) != 0)
{
// Use the reuse information in transitionVertexData
byte dir = HiNibble((byte)(edgeCode >> 8));
byte idx = LoNibble((byte)(edgeCode >> 8));
bool present = (dir & directionMask) == dir;
if (present)
{
// The previous cell is available. Retrieve the cached cell
// from which to retrieve the reused vertex index from.
var prev = cache[x - (dir & 1), y - ((dir >> 1) & 1)];
if (prev.CaseIndex == 0 || prev.CaseIndex == 511)
{
// Previous cell does not contain any geometry.
localVertexMapping[i] = -1;
}
else
{
// Reuse the vertex index from the previous cell.
localVertexMapping[i] = prev.Verts[idx];
}
}
if (!present || localVertexMapping[i] < 0)
{
Vector3f p0 = (Vector3f)pos[v0];
Vector3f p1 = (Vector3f)pos[v1];
Vector3f pi = Interp(p0, p1, samplePos[v0], samplePos[v1], samples, lowside ? (byte)lodIndex : (byte)(lodIndex - 1));
if (lowside)
{
switch (axis)
{
case 0:
pi.X = (float)origin.X;
break;
case 1:
pi.Y = (float)origin.Y;
break;
case 2:
pi.Z = (float)origin.Z;
break;
}
Vector3f delta = ComputeDelta(pi, lodIndex, 16);
Vector3f proj = ProjectNormal(vert.Normal, delta);
vert.Primary = Unused;
vert.Secondary = offset + pi + proj;
}
else
{
vert.Near = 0;
vert.Primary = offset + pi;
vert.Secondary = Unused;
}
localVertexMapping[i] = verts.Count;
verts.Add(vert);
if ((dir & 8) != 0)
{
// The vertex can be reused.
cache[x, y].Verts[idx] = localVertexMapping[i];
}
}
}
else
{
// Try to reuse corner vertex from a preceding cell.
// Use the reuse information in transitionCornerData.
byte v = t == 0 ? v1 : v0;
byte cornerData = Tables.TransitionCornerData[v];
byte dir = HiNibble(cornerData); // High nibble contains direction code.
byte idx = LoNibble((cornerData)); // Low nibble contains storage slot for vertex.
bool present = (dir & directionMask) == dir;
if (present)
{
// The previous cell is available. Retrieve the cached cell
// from which to retrieve the reused vertex index from.
var prev = cache[x - (dir & 1), y - ((dir >> 1) & 1)];
if (prev.CaseIndex == 0 || prev.CaseIndex == 511)
{
// Previous cell does not contain any geometry.
localVertexMapping[i] = -1;
}
else
{
// Reuse the vertex index from the previous cell.
localVertexMapping[i] = prev.Verts[idx];
}
}
if (!present || localVertexMapping[i] < 0)
{
// A vertex has to be created.
Vector3f pi = (Vector3f)pos[v];
if (v > 8)
{
// On low-resolution side.
// Necessary to translate the intersection point to the
// high-res side so that it is transformed the same way
// as the vertices in the regular cell.
switch (axis)
{
case 0:
pi.X = (float)origin.X;
break;
case 1:
pi.Y = (float)origin.Y;
break;
case 2:
pi.Z = (float)origin.Z;
break;
}
Vector3f delta = ComputeDelta(pi, lodIndex, 16);
Vector3f proj = ProjectNormal(vert.Normal, delta);
vert.Primary = Unused;
vert.Secondary = offset + pi + proj;
}
else
{
// On high-resolution side.
vert.Near = 0; // Vertices on high-res side are never moved.
vert.Primary = offset + pi;
vert.Secondary = Unused;
}
localVertexMapping[i] = verts.Count;
cache[x, y].Verts[idx] = localVertexMapping[i];
verts.Add(vert);
}
}
}
for (long t = 0; t < nt; ++t)
{
if (inverse)
{
indices.Add(localVertexMapping[data.Indizes()[t * 3 + 2]]);
indices.Add(localVertexMapping[data.Indizes()[t * 3 + 1]]);
indices.Add(localVertexMapping[data.Indizes()[t * 3 + 0]]);
//indices.push_back(localVertexMapping[ptr[2]]);
//indices.push_back(localVertexMapping[ptr[1]]);
//indices.push_back(localVertexMapping[ptr[0]]);
}
else
{
indices.Add(localVertexMapping[data.Indizes()[t * 3 + 0]]);
indices.Add(localVertexMapping[data.Indizes()[t * 3 + 1]]);
indices.Add(localVertexMapping[data.Indizes()[t * 3 + 2]]);
// indices.push_back(localVertexMapping[ptr[0]]);
// indices.push_back(localVertexMapping[ptr[1]]);
// indices.push_back(localVertexMapping[ptr[2]]);
}
}
return nt;
}
public static int PolygonizeRegularCell(Vector3i min, Vector3f offset, Vector3i xyz,
IVolumeData samples, byte lodIndex, float cellSize,
ref IList<Vertex> verts, ref IList<int> indices, ref RegularCache cache)
{
int lodScale = 1 << lodIndex;
int last = 15 * lodScale;
byte directionMask = (byte)((xyz.X > 0 ? 1 : 0) | ((xyz.Y > 0 ? 1 : 0) << 1) | ((xyz.Z > 0 ? 1 : 0) << 2));
byte near = 0;
// Compute which of the six faces of the block that the vertex
// is near. (near is defined as being in boundary cell.)
for (int i = 0; i < 3; i++)
{
//Vertex close to negative face.
if (min[i] == 0) { near |= (byte)(1 << (i * 2 + 0)); }
//Vertex close to positive face.
if (min[i] == last) { near |= (byte)(1 << (i * 2 + 1)); }
}
Vector3i[] cornerPositions = Tables.CornerIndex;
for (int i = 0; i < cornerPositions.Length; i++)
{
cornerPositions[i] = min + cornerPositions[i] * lodScale;
}
// new Vector3i[]
// {
// min + new Vector3i(0, 0, 0)*lodScale,
// min + new Vector3i(1, 0, 0)*lodScale,
// min + new Vector3i(0, 1, 0)*lodScale,
// min + new Vector3i(1, 1, 0)*lodScale,
//
// min + new Vector3i(0, 0, 1)*lodScale,
// min + new Vector3i(1, 0, 1)*lodScale,
// min + new Vector3i(0, 1, 1)*lodScale,
// min + new Vector3i(1, 1, 1)*lodScale
// };
Vector3i dif = cornerPositions[7] - cornerPositions[1];
// Retrieve sample values for all the corners.
sbyte[] cornerSamples =
new sbyte[]
{
samples[cornerPositions[0]],
samples[cornerPositions[1]],
samples[cornerPositions[2]],
samples[cornerPositions[3]],
samples[cornerPositions[4]],
samples[cornerPositions[5]],
samples[cornerPositions[6]],
samples[cornerPositions[7]],
};
Vector3f[] cornerNormals = new Vector3f[8];
// Determine the index into the edge table which
// tells us which vertices are inside of the surface
uint caseCode = (uint)(((cornerSamples[0] >> 7) & 0x01)
| ((cornerSamples[1] >> 6) & 0x02)
| ((cornerSamples[2] >> 5) & 0x04)
| ((cornerSamples[3] >> 4) & 0x08)
| ((cornerSamples[4] >> 3) & 0x10)
| ((cornerSamples[5] >> 2) & 0x20)
| ((cornerSamples[6] >> 1) & 0x40)
| (cornerSamples[7] & 0x80));
cache[xyz].CaseIndex = (byte)caseCode;
if ((caseCode ^ ((cornerSamples[7] >> 7) & 0xff)) == 0)
return 0;
// Compute the normals at the cell corners using central difference.
for (int i = 0; i < 8; ++i)
{
var p = cornerPositions[i];
float nx = (samples[p + Vector3i.UnitX] - samples[p - Vector3i.UnitX]) * 0.5f;
float ny = (samples[p + Vector3i.UnitY] - samples[p - Vector3i.UnitY]) * 0.5f;
float nz = (samples[p + Vector3i.UnitZ] - samples[p - Vector3i.UnitZ]) * 0.5f;
cornerNormals[i] = new Vector3f(nx, ny, nz);
cornerNormals[i].Normalize();
}
var c = Tables.RegularCellClass[caseCode];
var data = Tables.RegularCellData[c];
byte nt = (byte)data.GetTriangleCount();
byte nv = (byte)data.GetVertexCount();
int[] localVertexMapping = new int[12];
var vert = new Vertex();
vert.Near = near;
// Generate all the vertex positions by interpolating along
// each of the edges that intersect the isosurface.
for (int i = 0; i < nv; i++)
{
ushort edgeCode = Tables.RegularVertexData[caseCode][i];
byte v0 = HiNibble((byte)(edgeCode & 0xFF));
byte v1 = LoNibble((byte)(edgeCode & 0xFF));
Vector3i p0 = cornerPositions[v0];
Vector3i p1 = cornerPositions[v1];
Vector3f n0 = cornerNormals[v0];
Vector3f n1 = cornerNormals[v1];
int d0 = samples[p0];
int d1 = samples[p1];
Debug.Assert(v0 < v1);
int t = (d1 << 8) / (d1 - d0);
int u = 0x0100 - t;
float t0 = t * S;
float t1 = u * S;
if ((t & 0x00ff) != 0)
{
// Vertex lies in the interior of the edge.
byte dir = HiNibble((byte)(edgeCode >> 8));
byte idx = LoNibble((byte)(edgeCode >> 8));
bool present = (dir & directionMask) == dir;
if (present)
{
var prev = cache[xyz + PrevOffset(dir)];
// I don't think this can happen for non-corner vertices.
if (prev.CaseIndex == 0 || prev.CaseIndex == 255)
{
localVertexMapping[i] = -1;
}
else
{
localVertexMapping[i] = prev.Verts[idx];
}
}
if (!present || localVertexMapping[i] < 0)
{
localVertexMapping[i] = verts.Count;
Vector3f pi = Interp(p0, p1, p0, p1, samples, lodIndex);
vert.Primary = offset + pi;
vert.Normal = n0 * t0 + n1 * t1;
if (near > 0)
{
Vector3f delta = ComputeDelta(pi, lodIndex, 16);
vert.Secondary = vert.Primary + ProjectNormal(vert.Normal, delta);
}
else
{
// The vertex is not in a boundary cell, so the
// secondary position will never be used.
vert.Secondary = Unused; //vert.Primary;
}
verts.Add(vert);
if ((dir & 8) != 0)
{
// Store the generated vertex so that other cells can reuse it.
cache[xyz].Verts[idx] = localVertexMapping[i];
}
}
}
else if (t == 0 && v1 == 7)
{
// This cell owns the vertex, so it should be created.
localVertexMapping[i] = verts.Count;
Vector3f pi = (Vector3f)p1 * t0 + (Vector3f)p1 * t1;
vert.Primary = offset + pi;
vert.Normal = n0 * t0 + n1 * t1;
if (near > 0)
{
Vector3f delta = ComputeDelta(pi, lodIndex, 16);
vert.Secondary = vert.Primary + ProjectNormal(vert.Normal, delta);
}
else
{
// The vertex is not in a boundary cell, so the secondary
// position will never be used.
vert.Secondary = Unused;
}
verts.Add(vert);
cache[xyz].Verts[0] = localVertexMapping[i];
}
else
{
// A 3-bit direction code leading to the proper cell can easily be obtained by
// inverting the 3-bit corner index (bitwise, by exclusive ORing with the number 7).
// The corner index depends on the value of t, t = 0 means that we're at the higher
// numbered endpoint.
byte dir = t == 0 ? (byte)(v1 ^ 7) : (byte)(v0 ^ 7);
bool present = (dir & directionMask) == dir;
if (present)
{
var prev = cache[xyz + PrevOffset(dir)];
// The previous cell might not have any geometry, and we
// might therefore have to create a new vertex anyway.
if (prev.CaseIndex == 0 || prev.CaseIndex == 255)
{
localVertexMapping[i] = -1;
}
else
{
localVertexMapping[i] = prev.Verts[0];
}
}
if (!present || (localVertexMapping[i] < 0))
{
localVertexMapping[i] = verts.Count;
Vector3f pi = (Vector3f)p0 * t0 + (Vector3f)p1 * t1;
vert.Primary = offset + pi;
vert.Normal = n0 * t0 + n1 * t1;
if (near > 0)
{
Vector3f delta = ComputeDelta(pi, lodIndex, 16);
vert.Secondary = vert.Primary + ProjectNormal(vert.Normal, delta);
}
else
{
vert.Secondary = Unused;
}
verts.Add(vert);
}
}
}
for (int t = 0; t < nt; t++)
{
for (int i = 0; i < 3; i++)
{
indices.Add(localVertexMapping[data.Indizes()[t * 3 + i]]);
}
}
return nt;
}