public void Drag(Vector2d pt)
{
edPt = pt;
edVec = MapToSphere(pt);
double epsilon = 1.0e-5;
Vector3d prep = stVec.Cross(edVec);
if (prep.Length() > epsilon)
quat = new Vector4d(prep, stVec.Dot(edVec));
else
quat = new Vector4d();
}
public Quaternion(Matrix3d m)
{
double T = 1.0 + m.Trace();
double S, W, X, Y, Z;
if (T > eps)
{
S = Math.Sqrt(T) * 2.0;
X = (m[5] - m[7]) / S;
Y = (m[6] - m[2]) / S;
Z = (m[1] - m[3]) / S;
W = 0.25 * S;
}
else if (m[0] > m[4] && m[0] > m[8])
{
S = Math.Sqrt(1.0 + m[0] - m[4] - m[8]) * 2.0;
X = 0.25 * S;
Y = (m[1] + m[3]) / S;
Z = (m[6] + m[2]) / S;
W = (m[5] - m[7]) / S;
}
else if (m[4] > m[8])
{
S = Math.Sqrt(1.0 + m[4] - m[0] - m[8]) * 2;
X = (m[1] + m[3]) / S;
Y = 0.25 * S;
Z = (m[5] + m[7]) / S;
W = (m[6] - m[2]) / S;
}
else
{
S = Math.Sqrt(1.0 + m[8] - m[0] - m[4]) * 2;
X = (m[6] + m[2]) / S;
Y = (m[5] + m[7]) / S;
Z = 0.25 * S;
W = (m[1] - m[3]) / S;
}
this.s = W;
this.v = new Vector3d(X, Y, Z);
}
public double Dot(Vector3d v)
{
return x*v.x + y*v.y + z*v.z;
}
public double AverageFaceArea()
{
double tot = 0;
for (int i = 0, j = 0; i < faceCount; i++, j += 3)
{
Vector3d v1 = new Vector3d(VertexPos, faceIndex[j] * 3);
Vector3d v2 = new Vector3d(VertexPos, faceIndex[j + 1] * 3);
Vector3d v3 = new Vector3d(VertexPos, faceIndex[j + 2] * 3);
tot += ((v2 - v1).Cross(v3 - v1)).Length() / 2.0;
}
return (tot / faceCount);
}
public Vector3d Cross(Vector3d v)
{
return new Vector3d(
y * v.z - v.y * z,
z * v.x - v.z * x,
x * v.y - v.x * y
);
}
private double Face_wij(int i, int j)
{
double[] normal = this.new_normals == null ? mesh.FaceNormal : this.new_normals;
int b = i * 3, c = j * 3;
Vector3d ni = new Vector3d(normal, b);
Vector3d nj = new Vector3d(normal, c);
Vector3d vi = new Vector3d(mesh.DualVertexPos, b);
Vector3d vj = new Vector3d(mesh.DualVertexPos, c);
Vector3d eij = (vj - vi).Normalize();
double d = (nj - ni).Length();
double e = Math.Abs((ni).Dot(eij));
return (1+e)*d;
}
/*s is the \sigma*/
private void FilterFaceNormals(double s, int iterations)
{
// -- precompute normals based on NII, as a smoothing step --
int n = mesh.FaceCount; double denominator = s*s*2;
old_normals = mesh.FaceNormal.Clone() as double[];
new_normals = new double[n*3];
for (int k = 0; k < iterations; ++k)
{
for (int i = 0; i < n; ++i)
{
// -- get two-ring neighbors
Set<int> nbrs = this.neighbors[i]; nbrs.Remove(i);
int count = nbrs.Count, b = i * 3;
Vector3d ni = new Vector3d(mesh.FaceNormal, b);
Vector3d nn = new Vector3d();
foreach (int f in nbrs)
{
Vector3d nj = new Vector3d(mesh.FaceNormal, f * 3);
double d = (ni - nj).Length();
double w = Math.Exp(-d * d / denominator);
nn = nn + w * nj;
}
nn = nn.Normalize();
new_normals[b] = nn.x;
new_normals[b + 1] = nn.y;
new_normals[b + 2] = nn.z;
}
//mesh.FaceNormal = new_normals.Clone() as double[];
}
}
public void ComputeFaceNormal()
{
for (int i=0,j=0; i<faceCount; i++,j+=3)
{
int c1 = faceIndex[j] * 3;
int c2 = faceIndex[j+1] * 3;
int c3 = faceIndex[j+2] * 3;
Vector3d v1 = new Vector3d(vertexPos, c1);
Vector3d v2 = new Vector3d(vertexPos, c2);
Vector3d v3 = new Vector3d(vertexPos, c3);
Vector3d normal = (v2-v1).Cross(v3-v1).Normalize();
faceNormal[j] = normal.x;
faceNormal[j+1] = normal.y;
faceNormal[j+2] = normal.z;
}
}
private void ApplyHarmonicSolver_Cholmod()
{
// --- build up lefthand side matrix A
int vn = mesh.VertexCount;
int fn = mesh.FaceCount;
int bn = this.sourceVertices.Count + this.sinkVertices.Count;
int m = vn+bn;
if (this.sparseSolver != null) this.sparseSolver.Release();
this.sparseSolver = new CholmodSolver();
this.sparseSolver.InitializeMatrixA(m, vn);
for (int i = 0, j = 0; i < fn; i++, j += 3)
{
int c1 = mesh.FaceIndex[j];
int c2 = mesh.FaceIndex[j + 1];
int c3 = mesh.FaceIndex[j + 2];
Vector3d v1 = new Vector3d(mesh.VertexPos, c1 * 3);
Vector3d v2 = new Vector3d(mesh.VertexPos, c2 * 3);
Vector3d v3 = new Vector3d(mesh.VertexPos, c3 * 3);
double cot1 = (v2 - v1).Dot(v3 - v1) / (v2 - v1).Cross(v3 - v1).Length();
double cot2 = (v3 - v2).Dot(v1 - v2) / (v3 - v2).Cross(v1 - v2).Length();
double cot3 = (v1 - v3).Dot(v2 - v3) / (v1 - v3).Cross(v2 - v3).Length();
sparseSolver.Add_Coef(c2, c2, -cot1); sparseSolver.Add_Coef(c2, c3, cot1);
sparseSolver.Add_Coef(c3, c3, -cot1); sparseSolver.Add_Coef(c3, c2, cot1);
sparseSolver.Add_Coef(c3, c3, -cot2); sparseSolver.Add_Coef(c3, c1, cot2);
sparseSolver.Add_Coef(c1, c1, -cot2); sparseSolver.Add_Coef(c1, c3, cot2);
sparseSolver.Add_Coef(c1, c1, -cot3); sparseSolver.Add_Coef(c1, c2, cot3);
sparseSolver.Add_Coef(c2, c2, -cot3); sparseSolver.Add_Coef(c2, c1, cot3);
}
// add positional weights
int index = 0;
foreach (int v in sourceVertices)
{
sparseSolver.Add_Coef(vn + index, v, 1.0 * ConstantWeight);
++index;
}
foreach (int v in sinkVertices)
{
sparseSolver.Add_Coef(vn + index, v, 1.0 * ConstantWeight);
++index;
}
if (!opt.UseAtb) m = vn;
double[] b = new double[m];
double[] x = new double[vn];
// -- assign values to the right hand side b,-- Ax=b
if (opt.UseAtb)
{
for (int j = 0; j < b.Length; j++) b[j] = 0;
int count = 0;
for (int j = 0; j < sourceVertices.Count; ++j, ++count)
b[vn + j] = 1.0 * ConstantWeight;
for (int j = 0; j < sinkVertices.Count; ++j)
b[vn + count + j] = 0.0;
}
else // set by user..
{
foreach (int v in this.sourceVertices)
b[v] = 1.0 * ConstantWeight * ConstantWeight;
}
fixed (double* _b = b)
{
sparseSolver.InitializeMatrixB(_b, m, 1);
}
sparseSolver.InitializeSolver();
sparseSolver.SetFinalPack(0);
sparseSolver.Factorize();
fixed (double* _x = x)
{
sparseSolver.Linear_Solve(_x, !opt.UseAtb);
}
this.harmonicField = x;
}
public void Click(Vector2d pt, MotionType type)
{
this.stPt = pt;
this.stVec = MapToSphere(pt);
this.type = type;
}
public Vector4d(Vector3d v)
{
this.x = v.x;
this.y = v.y;
this.z = v.z;
this.w = 0;
}
public Vector3d MinCoord()
{
Vector3d minCoord = new Vector3d(double.MaxValue, double.MaxValue, double.MaxValue);
for (int i=0,j=0; i<vertexCount; i++,j+=3)
{
Vector3d v = new Vector3d(vertexPos, j);
minCoord = Vector3d.Min(minCoord, v);
}
return minCoord;
}
public double Volume()
{
double totVolume = 0;
for (int i = 0, j = 0; i < faceCount; i++, j += 3)
{
int c1 = faceIndex[j] * 3;
int c2 = faceIndex[j + 1] * 3;
int c3 = faceIndex[j + 2] * 3;
Vector3d a = new Vector3d(vertexPos, c1);
Vector3d b = new Vector3d(vertexPos, c2);
Vector3d c = new Vector3d(vertexPos, c3);
totVolume +=
a.x * b.y * c.z -
a.x * b.z * c.y -
a.y * b.x * c.z +
a.y * b.z * c.x +
a.z * b.x * c.y -
a.z * b.y * c.x;
}
return totVolume;
}
public void ComputeVertexNormal()
{
Array.Clear(vertexNormal, 0, vertexNormal.Length);
for (int i=0,j=0; i<faceCount; i++,j+=3)
{
int c1 = faceIndex[j] * 3;
int c2 = faceIndex[j+1] * 3;
int c3 = faceIndex[j+2] * 3;
vertexNormal[c1] += faceNormal[j];
vertexNormal[c2] += faceNormal[j];
vertexNormal[c3] += faceNormal[j];
vertexNormal[c1+1] += faceNormal[j+1];
vertexNormal[c2+1] += faceNormal[j+1];
vertexNormal[c3+1] += faceNormal[j+1];
vertexNormal[c1+2] += faceNormal[j+2];
vertexNormal[c2+2] += faceNormal[j+2];
vertexNormal[c3+2] += faceNormal[j+2];
}
for (int i=0,j=0; i<vertexCount; i++,j+=3)
{
Vector3d n = new Vector3d(vertexNormal, j);
n = n.Normalize();
vertexNormal[j] = n.x;
vertexNormal[j+1] = n.y;
vertexNormal[j+2] = n.z;
}
}
public void ComputeNormals2Ring()
{
int nf = faceCount;
Vector3d[] vnormals = new Vector3d[VertexCount];
for (int i = 0, j = 0; i < nf; i++, j += 3)
{
int v0 = faceIndex[j];
int v1 = faceIndex[j + 1];
int v2 = faceIndex[j + 2];
Vector3d p0 = new Vector3d(vertexPos, v0 * 3);
Vector3d p1 = new Vector3d(vertexPos, v1 * 3);
Vector3d p2 = new Vector3d(vertexPos, v2 * 3);
Vector3d a = p0 - p1, b = p1 - p2, c = p2 - p0;
double l2a = a.Dot(a), l2b = b.Dot(b), l2c = c.Dot(c);
Vector3d facenormal = a.Cross(b);
// assign face normals
facenormal = facenormal.Normalize();
faceNormal[j] = facenormal.x;
faceNormal[j + 1] = facenormal.y;
faceNormal[j + 2] = facenormal.z;
}
for (int i = 0, j = 0; i < vertexCount; ++i, j += 3)
{
Set<int> fset = new Set<int>();
foreach (int adj in adjVV[i])
{
foreach (int f in adjVF[adj])
{
fset.Add(f);
}
}
vnormals[i] = new Vector3d();
foreach (int f in fset)
{
Vector3d fnormal = new Vector3d(faceNormal, f * 3);
double s = ComputeFaceArea(f);
vnormals[i] = vnormals[i] + s*fnormal;
}
vnormals[i] = vnormals[i].Normalize();
vertexNormal[j] = vnormals[i].x;
vertexNormal[j + 1] = vnormals[i].y;
vertexNormal[j + 2] = vnormals[i].z;
}
}
// compute both face normals and vertex normals, from trimesh2.
public void ComputeNormals()
{
int nf = faceCount;
Vector3d[] vnormals = new Vector3d[VertexCount];
for (int i = 0, j = 0; i < nf; i++, j+=3) {
int v0 = faceIndex[j];
int v1 = faceIndex[j+1];
int v2 = faceIndex[j+2];
Vector3d p0 = new Vector3d(vertexPos, v0*3);
Vector3d p1 = new Vector3d(vertexPos, v1*3);
Vector3d p2 = new Vector3d(vertexPos, v2*3);
Vector3d a = p0-p1, b = p1-p2, c = p2-p0;
double l2a = a.Dot(a), l2b = b.Dot(b), l2c = c.Dot(c);
Vector3d facenormal = a.Cross(b);
// assign vertex normals
vnormals[v0] = vnormals[v0] + facenormal * (1.0 / (l2a * l2c));
vnormals[v1] = vnormals[v1] + facenormal * (1.0 / (l2b * l2a));
vnormals[v2] = vnormals[v2] + facenormal * (1.0 / (l2c * l2b));
// assign face normals
facenormal = facenormal.Normalize();
faceNormal[j] = facenormal.x;
faceNormal[j+1] = facenormal.y;
faceNormal[j+2] = facenormal.z;
}
for (int i = 0, j = 0; i < vertexCount; ++i, j += 3) {
vnormals[i] = vnormals[i].Normalize();
vertexNormal[j] = vnormals[i].x;
vertexNormal[j+1] = vnormals[i].y;
vertexNormal[j+2] = vnormals[i].z;
}
}
public Matrix3d OuterCross(Vector3d v)
{
Matrix3d m = new Matrix3d();
m[0, 0] = x * v.x;
m[0, 1] = x * v.y;
m[0, 2] = x * v.z;
m[1, 0] = y * v.x;
m[1, 1] = y * v.y;
m[1, 2] = y * v.z;
m[2, 0] = z * v.x;
m[2, 1] = z * v.y;
m[2, 2] = z * v.z;
return m;
}
private void LocateFacesIsoPosition(double[] f, double[] isovals)
{
if (f == null) throw new ArgumentException();
// initialize isofaces
this.isofaces = new IsoFaceRec[mesh.FaceCount];
for (int i = 0; i < mesh.FaceCount; ++i)
this.isofaces[i] = new IsoFaceRec();
for (int i = 0; i < isovalues.Length; ++i)
{
double v = isovals[i];
for (int k = 0, m = 0; k < this.mesh.FaceCount; ++k, m += 3)
{
int c1 = this.mesh.FaceIndex[m];
int c2 = this.mesh.FaceIndex[m + 1];
int c3 = this.mesh.FaceIndex[m + 2];
PQPairs r = null;
if ((f[c1] <= v && f[c2] >= v) || (f[c2] <= v && f[c1] >= v))
{
if (r == null) { r = new PQPairs(); r.findex = k; }
if (r.e1 == -1)
{
r.e1 = 0; r.ratio1 = (v - f[c1]) / (f[c2] - f[c1]);
}
else
{
r.e2 = 0; r.ratio2 = (v - f[c1]) / (f[c2] - f[c1]);
}
}
if ((f[c2] <= v && f[c3] >= v) || (f[c3] <= v && f[c2] >= v))
{
if (r == null) { r = new PQPairs(); r.findex = k; }
if (r.e1 == -1)
{
r.e1 = 1; r.ratio1 = (v - f[c2]) / (f[c3] - f[c2]);
}
else
{
r.e2 = 1; r.ratio2 = (v - f[c2]) / (f[c3] - f[c2]);
}
}
if ((f[c3] <= v && f[c1] >= v) || (f[c1] <= v && f[c3] >= v))
{
if (r == null) { r = new PQPairs(); r.findex = k; }
if (r.e1 == -1)
{
r.e1 = 2; r.ratio1 = (v - f[c3]) / (f[c1] - f[c3]);
}
else
{
r.e2 = 2; r.ratio2 = (v - f[c3]) / (f[c1] - f[c3]);
}
}
if (r == null) continue;
if (r.e1 == -1 || r.e2 == -1) continue;
r.isovalue = v;
r.lindex = i;
Vector3d v1 = new Vector3d(mesh.VertexPos, c1 * 3);
Vector3d v2 = new Vector3d(mesh.VertexPos, c2 * 3);
Vector3d v3 = new Vector3d(mesh.VertexPos, c3 * 3);
Vector3d n1 = new Vector3d(mesh.FaceNormal, k * 3);
Vector3d p = new Vector3d(), q = new Vector3d();
switch (r.e1)
{
case 0: p = v2 * r.ratio1 + v1 * (1.0 - r.ratio1); break;
case 1: p = v3 * r.ratio1 + v2 * (1.0 - r.ratio1); break;
case 2: p = v1 * r.ratio1 + v3 * (1.0 - r.ratio1); break;
}
switch (r.e2)
{
case 0: q = v2 * r.ratio2 + v1 * (1.0 - r.ratio2); break;
case 1: q = v3 * r.ratio2 + v2 * (1.0 - r.ratio2); break;
case 2: q = v1 * r.ratio2 + v3 * (1.0 - r.ratio2); break;
}
r.n = n1; r.p = p; r.q = q;
isofaces[k].pqPairs.Add(r);
isofaces[k].index = k;
isofaces[k].valid = true;
}
}
}
public Vector3d Rotate(Vector3d axis, double cos, double sin)
{
return this * cos + (axis.Cross(this)) * sin +
axis * ((1.0 - cos) * (axis.Dot(this)));
}
public double ComputeFaceArea(int fIndex)
{
int b = fIndex * 3;
Vector3d v1 = new Vector3d(VertexPos, faceIndex[b] * 3);
Vector3d v2 = new Vector3d(VertexPos, faceIndex[b+1] * 3);
Vector3d v3 = new Vector3d(VertexPos, faceIndex[b+2] * 3);
return ((v2-v1).Cross(v3-v1)).Length() / 2.0;
}
public Vector4d(Vector3d v, double w)
{
this.x = v.x;
this.y = v.y;
this.z = v.z;
this.w = w;
}
public static void Print3DText(Vector3d pos, string s)
{
FormMain f = FormMain.ActiveForm as FormMain;
if (f != null)
f.Print3DText(pos, s);
}
private double Vrt_wij(int i, int j)
{
int b = i * 3, c = j * 3;
Vector3d s = new Vector3d(mesh.VertexPos, b);
Vector3d t = new Vector3d(mesh.VertexPos, c);
Vector3d e = t-s;
Vector3d ns = new Vector3d(mesh.VertexNormal, b);
Vector3d nt = new Vector3d(mesh.VertexNormal, c);
double w = (1 + ns.Dot(e) / e.Length()) * (1 + ns.Cross(nt).Length());
return w;
}
public Quaternion(double s, Vector3d v)
{
this.s = s;
this.v = v;
}
private double Face_dij(int i, int j)
{
Vector3d ci = new Vector3d(mesh.DualVertexPos, i * 3);
Vector3d cj = new Vector3d(mesh.DualVertexPos, j * 3);
double d = (cj - ci).Length();
return d;
}
public static Vector3d Max(Vector3d v1, Vector3d v2)
{
return new Vector3d( (v1.x > v2.x) ? v1.x : v2.x,
(v1.y > v2.y) ? v1.y : v2.y,
(v1.z > v2.z) ? v1.z : v2.z );
}
private double Face_wij1(int i, int j)
{
Vector3d ns = new Vector3d(mesh.FaceNormal, i * 3);
Vector3d nt = new Vector3d(mesh.FaceNormal, j * 3);
return -ns.Dot(nt);
}
public static Vector3d Min(Vector3d v1, Vector3d v2)
{
return new Vector3d( (v1.x < v2.x) ? v1.x : v2.x,
(v1.y < v2.y) ? v1.y : v2.y,
(v1.z < v2.z) ? v1.z : v2.z );
}
private bool IsTheSamePosition(Vector3d s, Vector3d t)
{
if ((s - t).Length() < 1e-08)
return true;
return false;
}
public void Print3DText(Vector3d pos, string s)
{
GL.glRasterPos3d(pos.x, pos.y, pos.z);
GL.glPushAttrib(GL.GL_LIST_BIT); // Pushes The Display List Bits
GL.glListBase(this.meshView1.fontBase); // Sets The Base Character to 32
GL.glCallLists(s.Length, GL.GL_UNSIGNED_SHORT, s); // Draws The Display List Text
GL.glPopAttrib(); // Pops The Display List Bits
}