internal bool Optimize(MxVector3 vec1, MxVector3 vec2, ref MxVector3 opt)
{
var diff = vec1 - vec2;
var tens = Tensor;
var tV2 = tens * vec2;
var tDiff = tens * diff;
var denom = 2.0 * diff * tDiff;
if (denom.IsSqCloseEnoughTo(0.0))
{
return(false);
}
var a = (-2.0 * (Vector * diff) - (diff * tV2) - (vec2 * tDiff)) / (2.0 * (diff * tDiff));
if (a < 0.0)
{
a = 0.0;
}
else if (a > 1.0)
{
a = 1.0;
}
opt = a * diff + vec2;
return(true);
}
internal double CheckLocalCompactness(int vertId, double[] vNew)
{
var n1 = model.Neighbors(vertId);
var cMin = 1.0;
foreach (var faceId in n1)
{
if (!model.FaceIsValid(faceId))
{
continue;
}
var face = model.Face(faceId);
MxVector3[] fAfter = new MxVector3[3];
for (var i = 0; i < 3; i++)
{
fAfter[i] = (face[i] == vertId)
? new MxVector3(vNew)
: new MxVector3(model.Vertex(face[i]));
}
var c = MxGeom3d.TriangleCompactness(fAfter[0], fAfter[1], fAfter[2]);
if (c < cMin)
{
cMin = c;
}
}
return(cMin);
}
internal static MxVector3 TriangleNormal(MxVector3 v1, MxVector3 v2, MxVector3 v3)
{
var n = TriangleRawNormal(v1, v2, v3);
MxVector3.Unitize(ref n);
return(n);
}
internal static double TriangleCompactness(MxVector3 v1, MxVector3 v2, MxVector3 v3)
{
var area = TriangleArea(v1, v2, v3);
var denom = MxVector3.NormSquared(v2 - v1) + MxVector3.NormSquared(v3 - v2) + MxVector3.NormSquared(v1 - v3);
return (FourRootThree*area/denom);
}
internal static MxMatrix4 TranslationMatrix(MxVector3 delta)
{
return(new MxMatrix4(new MxVector4(1.0, 0.0, 0.0, delta[0]),
new MxVector4(0.0, 1.0, 0.0, delta[1]),
new MxVector4(0.0, 0.0, 1.0, delta[2]),
new MxVector4(0.0, 0.0, 0.0, 1.0)));
}
protected void DiscontinuityConstraint(int vertI, int vertJ, List <int> faceList)
{
foreach (var faceId in faceList)
{
var orig = new MxVector3(model.Vertex(vertI));
var dest = new MxVector3(model.Vertex(vertJ));
var edge = dest - orig;
var nml = new[] { 0.0, 0.0, 0.0 };
model.ComputeFaceNormal(faceId, ref nml);
var n = new MxVector3(nml);
var n2 = edge ^ n;
MxVector3.Unitize(ref n2);
var quad = new MxQuadric3(n2, -(n2 * orig));
quad *= BoundaryWeight;
if (WeightingPolicy == MxWeighting.Area || WeightingPolicy == MxWeighting.AreaAverage)
{
quad.Area = MxVector3.Norm(edge);
quad *= quad.Area;
}
quadrics[vertI] += quad;
quadrics[vertJ] += quad;
}
}
internal static double TriangleCompactness(MxVector3 v1, MxVector3 v2, MxVector3 v3)
{
var area = TriangleArea(v1, v2, v3);
var denom = MxVector3.NormSquared(v2 - v1) + MxVector3.NormSquared(v3 - v2) + MxVector3.NormSquared(v1 - v3);
return(FourRootThree * area / denom);
}
internal double CheckLocalInversion(int vertId, double[] vNew)
{
var nMin = 1.0;
var n1 = model.Neighbors(vertId);
foreach (var faceId in n1)
{
if (!model.FaceIsValid(faceId))
{
continue;
}
var face = model.Face(faceId);
var nml = new double[3];
model.ComputeFaceNormal(faceId, ref nml);
var nBefore = new MxVector3(nml);
var fAfter = new MxVector3[3];
for (var i = 0; i < 3; i++)
{
fAfter[i] = (face[i] == vertId)
? new MxVector3(vNew)
: new MxVector3(model.Vertex(face[i]));
}
var newNml = MxGeom3d.TriangleNormal(fAfter[0], fAfter[1], fAfter[2]);
var delta = nBefore * newNml;
if (delta < nMin)
{
nMin = delta;
}
}
return(nMin);
}
internal static MxMatrix4 ScalingMatrix(MxVector3 scale)
{
return(new MxMatrix4(new MxVector4(scale[0], 0.0, 0.0, 0.0),
new MxVector4(0.0, scale[1], 0.0, 0.0),
new MxVector4(0.0, 0.0, scale[2], 0.0),
new MxVector4(0.0, 0.0, 0.0, 1.0)));
}
public static MxVector3 operator *(MxVector3 vec, double scalar)
{
var newVec = new MxVector3(0.0, 0.0, 0.0);
newVec[0] = vec[0]*scalar;
newVec[1] = vec[1]*scalar;
newVec[2] = vec[2]*scalar;
return newVec;
}
public static MxVector3 operator +(MxVector3 vec1, MxVector3 vec2)
{
var newVec = new MxVector3(0.0, 0.0, 0.0);
newVec[0] = vec1[0] + vec2[0];
newVec[1] = vec1[1] + vec2[1];
newVec[2] = vec1[2] + vec2[2];
return newVec;
}
protected void CollectQuadrics()
{
foreach (var quad in quadrics)
{
quad.Clear();
}
for (var i = 0; i < model.FaceCount; i++)
{
var face = model.Face(i);
var vert0 = new MxVector3(model.Vertex(face[0]));
var vert1 = new MxVector3(model.Vertex(face[1]));
var vert2 = new MxVector3(model.Vertex(face[2]));
var plane = (WeightingPolicy == MxWeighting.RawNormals)
? MxGeom3d.TriangleRawPlane(vert0, vert1, vert2)
: MxGeom3d.TrianglePlane(vert0, vert1, vert2);
var quad = new MxQuadric3(plane[0], plane[1], plane[2], plane[3], model.ComputeFaceArea(i));
switch(WeightingPolicy)
{
case MxWeighting.Angle:
{
for (int j = 0; j < 3; j++)
{
var quadJ = new MxQuadric3(quad);
quadJ *= model.ComputeCornerAngle(i, j);
quadrics[face[j]] += quadJ;
}
break;
}
case MxWeighting.Area:
{
quad *= quad.Area;
quadrics[face[0]] += quad;
quadrics[face[1]] += quad;
quadrics[face[2]] += quad;
break;
}
case MxWeighting.AreaAverage:
{
quad *= quad.Area;
quadrics[face[0]] += quad;
quadrics[face[1]] += quad;
quadrics[face[2]] += quad;
break;
}
default:
{
quadrics[face[0]] += quad;
quadrics[face[1]] += quad;
quadrics[face[2]] += quad;
break;
}
}
}
}
public static MxVector3 operator -(MxVector3 vec1)
{
var newVec = new MxVector3(0.0, 0.0, 0.0);
newVec[0] = -vec1[0];
newVec[1] = -vec1[1];
newVec[2] = -vec1[2];
return(newVec);
}
public static MxVector3 operator *(MxMatrix3 mat1, MxVector3 vec)
{
var ret = new MxVector3(0.0, 0.0, 0.0);
ret[0] = mat1[0] * vec;
ret[1] = mat1[1] * vec;
ret[2] = mat1[2] * vec;
return(ret);
}
internal static MxVector3 Cross(MxVector3 u, MxVector3 v)
{
var ret = new MxVector3(0.0, 0.0, 0.0);
ret[0] = u[1] * v[2] - v[1] * u[2];
ret[1] = v[0] * u[2] - u[0] * v[2];
ret[2] = u[0] * v[1] - v[0] * u[1];
return(ret);
}
public static MxVector3 operator +(MxVector3 vec1, MxVector3 vec2)
{
var newVec = new MxVector3(0.0, 0.0, 0.0);
newVec[0] = vec1[0] + vec2[0];
newVec[1] = vec1[1] + vec2[1];
newVec[2] = vec1[2] + vec2[2];
return(newVec);
}
public static MxVector3 operator *(MxVector3 vec, double scalar)
{
var newVec = new MxVector3(0.0, 0.0, 0.0);
newVec[0] = vec[0] * scalar;
newVec[1] = vec[1] * scalar;
newVec[2] = vec[2] * scalar;
return(newVec);
}
internal bool Optimize(ref MxVector3 vec)
{
var invMat = new MxMatrix3(0.0);
var det = MxMatrix3.Invert(Tensor, ref invMat);
if (det.IsSqCloseEnoughTo(0.0))
{
return(false);
}
vec = -(invMat * Vector);
return(true);
}
internal static MxMatrix3 OuterProduct(MxVector3 vec1, MxVector3 vec2)
{
var mat = new MxMatrix3(0.0);
for (var i = 0; i < 3; i++)
{
for (var j = 0; j < 3; j++)
{
mat[i, j] = vec1[i] * vec2[j];
}
}
return(mat);
}
internal bool Optimize(MxVector3 vec1, MxVector3 vec2, MxVector3 vec3, ref MxVector3 opt)
{
var d13 = vec1 - vec3;
var d23 = vec2 - vec3;
var A = Tensor;
var B = Vector;
var Ad13 = A * d13;
var Ad23 = A * d23;
var Av3 = A * vec3;
var d13D23 = (d13 * Ad23) + (d23 * Ad13);
var v3D13 = (d13 * Av3) + (vec3 * Ad13);
var v3D23 = (d23 * Av3) + (vec3 * Ad23);
var d23AD23 = d23 * Ad23;
var d13AD13 = d13 * Ad13;
var denom = d13AD13 * d23AD23 - 2.0 * d13D23;
if (denom.IsSqCloseEnoughTo(0.0))
{
return(false);
}
var a = ((d23AD23 * (2.0 * (B * d13) + v3D13)) -
(d13D23 * (2.0 * (B * d23) + v3D23))) / -denom;
var b = ((d13AD13 * (2.0 * (B * d13) + v3D23)) - (d13D23 * (2.0 * (B * d13) + v3D13))) / -denom;
if (a < 0.0)
{
a = 0.0;
}
else if (a > 1.0)
{
a = 1.0;
}
if (b < 0.0)
{
b = 0.0;
}
else if (b > 1.0)
{
b = 1.0;
}
opt = a * d13 + b * d23 + vec3;
return(true);
}
public static MxVector3 operator /(MxVector3 vec, double scalar)
{
if (scalar.IsCloseEnoughTo(0.0))
{
return(vec);
}
var invScalar = 1.0 / scalar;
var newVec = new MxVector3(0.0, 0.0, 0.0);
newVec[0] = vec[0] * invScalar;
newVec[1] = vec[1] * invScalar;
newVec[2] = vec[2] * invScalar;
return(newVec);
}
internal bool Optimize(ref double x, ref double y, ref double z)
{
var vec = new MxVector3(0.0, 0.0, 0.0);
var success = Optimize(ref vec);
if (!success)
{
return(false);
}
x = vec[0];
y = vec[1];
z = vec[2];
return(true);
}
internal static void Unitize(ref MxVector3 vec)
{
var denom = vec[0] * vec[0] + vec[1] * vec[1] + vec[2] * vec[2];
if (denom.IsSqCloseEnoughTo(0.0))
{
return;
}
denom = Math.Sqrt(denom);
var invDenom = 1.0 / denom;
vec[0] *= invDenom;
vec[1] *= invDenom;
vec[2] *= invDenom;
}
internal static MxMatrix3 OuterProduct(MxVector3 vec)
{
var mat = new MxMatrix3(0.0);
var x = vec[0];
var y = vec[1];
var z = vec[2];
mat[0, 0] = x * x;
mat[0, 1] = x * y;
mat[0, 2] = x * z;
mat[1, 0] = mat[0, 1];
mat[1, 1] = y * y;
mat[1, 2] = y * z;
mat[2, 0] = mat[0, 2];
mat[2, 1] = mat[1, 2];
mat[2, 2] = z * z;
return(mat);
}
internal static MxMatrix4 RotationMatrixRad(double theta, MxVector3 axis)
{
var cos = Math.Cos(theta);
var sin = Math.Sin(theta);
var xx = axis[0] * axis[0];
var xy = axis[0] * axis[1];
var xz = axis[0] * axis[2];
var yy = axis[1] * axis[1];
var yz = axis[1] * axis[2];
var zz = axis[2] * axis[2];
var xs = axis[0] * sin;
var ys = axis[1] * sin;
var zs = axis[2] * sin;
return(new MxMatrix4(new MxVector4(xx * (1 - cos) + cos, xy * (1 - cos) - zs, xz * (1 - cos) + ys, 0.0),
new MxVector4(xy * (1 - cos) + zs, yy * (1 - cos) + cos, yz * (1 - cos) - xs, 0.0),
new MxVector4(xz * (1 - cos) - ys, yz * (1 - cos) + xs, zz * (1 - cos) - cos, 0.0),
new MxVector4(0.0, 0.0, 0.0, 1.0)));
}
internal static MxMatrix4 LookAtMatrix(MxVector3 from, MxVector3 at, MxVector3 up)
{
var vUp = new MxVector3(up[0], up[1], up[2]);
MxVector3.Unitize(ref vUp);
var f = at - from;
MxVector3.Unitize(ref f);
var s = f ^ vUp;
MxVector3.Unitize(ref s);
var u = s ^ f;
MxVector3.Unitize(ref u);
var mat = new MxMatrix4(new MxVector4(s, 0.0), new MxVector4(u, 0.0), new MxVector4(-f, 0.0),
new MxVector4(0.0, 0.0, 0.0, 1.0));
return(mat * TranslationMatrix(-from));
}
internal static double TriangleArea(MxVector3 v1, MxVector3 v2, MxVector3 v3)
{
var vec = TriangleRawNormal(v1, v2, v3);
return 0.5*(MxVector3.Norm(vec));
}
internal static MxMatrix4 TranslationMatrix(MxVector3 delta)
{
return new MxMatrix4(new MxVector4(1.0, 0.0, 0.0, delta[0]),
new MxVector4(0.0, 1.0, 0.0, delta[1]),
new MxVector4(0.0, 0.0, 1.0, delta[2]),
new MxVector4(0.0, 0.0, 0.0, 1.0));
}
internal MxQuadric3(MxVector3 vec, double d, double area = 1.0)
: this(vec[0], vec[1], vec[2], d, area)
{
}
internal bool Optimize(MxVector3 vec1, MxVector3 vec2, MxVector3 vec3, ref MxVector3 opt)
{
var d13 = vec1 - vec3;
var d23 = vec2 - vec3;
var A = Tensor;
var B = Vector;
var Ad13 = A*d13;
var Ad23 = A*d23;
var Av3 = A*vec3;
var d13D23 = (d13*Ad23) + (d23*Ad13);
var v3D13 = (d13*Av3) + (vec3*Ad13);
var v3D23 = (d23*Av3) + (vec3*Ad23);
var d23AD23 = d23*Ad23;
var d13AD13 = d13*Ad13;
var denom = d13AD13*d23AD23 - 2.0*d13D23;
if (denom.IsSqCloseEnoughTo(0.0)) return false;
var a = ((d23AD23*(2.0*(B*d13) + v3D13)) -
(d13D23*(2.0*(B*d23) + v3D23)))/-denom;
var b = ((d13AD13*(2.0*(B*d13) + v3D23)) - (d13D23*(2.0*(B*d13) + v3D13)))/-denom;
if (a < 0.0) a = 0.0;
else if (a > 1.0) a = 1.0;
if (b < 0.0) b = 0.0;
else if (b > 1.0) b = 1.0;
opt = a*d13 + b*d23 + vec3;
return true;
}
internal static MxVector3 TriangleRawNormal(MxVector3 v1, MxVector3 v2, MxVector3 v3)
{
return MxVector3.Cross(v2 - v1, v3 - v1);
}
internal void ComputeTargetPlacement(MxQSlimEdge info)
{
var i = info.V1;
var j = info.V2;
var Qi = quadrics[i];
var Qj = quadrics[j];
var Q = Qi + Qj;
var eMin = 0.0;
if (PlacementPolicy == MxPlacement.Optimal
&& Q.Optimize(ref info.vNew[0], ref info.vNew[1], ref info.vNew[2]))
{
eMin = Q.Evaluate(info.vNew);
}
else
{
var vi = new MxVector3(model.Vertex(i));
var vj = new MxVector3(model.Vertex(j));
var best = new MxVector3(0.0, 0.0, 0.0);
if (PlacementPolicy == MxPlacement.Line && Q.Optimize(vi, vj, ref best))
{
eMin = Q.Evaluate(best);
}
else
{
var ei = Q.Evaluate(vi);
var ej = Q.Evaluate(vj);
if (ei < ej)
{
eMin = ei;
best = vi;
}
else
{
eMin = ej;
best = vj;
}
if (PlacementPolicy == MxPlacement.EndOrMid)
{
var mid = (vi + vj)*0.5;
var eMid = Q.Evaluate(mid);
if (eMid < eMin)
{
eMin = eMid;
best = mid;
}
}
}
info.vNew[0] = best[0];
info.vNew[1] = best[1];
info.vNew[2] = best[2];
}
if (WeightingPolicy == MxWeighting.AreaAverage)
{
eMin /= Q.Area;
}
info.HeapKey = (float)(-eMin);
}
internal void ComputeFaceInfo(int faceId)
{
var info = faceInfo[faceId];
info.FaceId = faceId;
var i = model.Face(faceId)[0];
var j = model.Face(faceId)[1];
var k = model.Face(faceId)[2];
var Qi = quadrics[i];
var Qj = quadrics[j];
var Qk = quadrics[k];
var Q = Qi + Qj + Qk;
if (PlacementPolicy == MxPlacement.Optimal &&
Q.Optimize(ref info.vNew[0], ref info.vNew[1], ref info.vNew[2]))
{
info.HeapKey = (float)-Q.Evaluate(info.vNew);
}
else
{
var v1 = new MxVector3(model.Vertex(i));
var v2 = new MxVector3(model.Vertex(j));
var v3 = new MxVector3(model.Vertex(k));
var e1 = Q.Evaluate(v1);
var e2 = Q.Evaluate(v2);
var e3 = Q.Evaluate(v3);
MxVector3 best;
double eMin;
if (e1 <= e2 && e1 <= e3)
{
eMin = e1;
best = v1;
}
else if (e2 <= e1 && e2 <= e3)
{
eMin = e2;
best = v2;
}
else
{
eMin = e3;
best = v3;
}
info.vNew[0] = best[0];
info.vNew[1] = best[1];
info.vNew[2] = best[2];
info.HeapKey = (float)(-eMin);
}
if (WeightingPolicy == MxWeighting.AreaAverage)
{
info.HeapKey = (float)(info.HeapKey/Q.Area);
}
if (info.IsInHeap) heap.Update(info);
else heap.Insert(info);
}
internal static MxMatrix4 RotationMatrixDeg(double theta, MxVector3 axis)
{
return RotationMatrixRad(theta*Math.PI/180.0, axis);
}
internal static void Unitize(ref MxVector3 vec)
{
var denom = vec[0]*vec[0] + vec[1]*vec[1] + vec[2]*vec[2];
if (denom.IsSqCloseEnoughTo(0.0)) return;
denom = Math.Sqrt(denom);
var invDenom = 1.0 / denom;
vec[0] *= invDenom;
vec[1] *= invDenom;
vec[2] *= invDenom;
}
internal static double Norm(MxVector3 u)
{
return Math.Sqrt(NormSquared(u));
}
public static MxVector3 operator /(MxVector3 vec, double scalar)
{
if (scalar.IsCloseEnoughTo(0.0)) return vec;
var invScalar = 1.0/scalar;
var newVec = new MxVector3(0.0, 0.0, 0.0);
newVec[0] = vec[0]*invScalar;
newVec[1] = vec[1]*invScalar;
newVec[2] = vec[2]*invScalar;
return newVec;
}
internal static MxVector3 TriangleNormal(MxVector3 v1, MxVector3 v2, MxVector3 v3)
{
var n = TriangleRawNormal(v1, v2, v3);
MxVector3.Unitize(ref n);
return n;
}
internal MxMatrix3(MxVector3 row0, MxVector3 row1, MxVector3 row2)
{
rows[0] = row0;
rows[1] = row1;
rows[2] = row2;
}
internal static double NormSquared(MxVector3 u)
{
return(u * u);
}
internal static double Norm(MxVector3 u)
{
return(Math.Sqrt(NormSquared(u)));
}
internal static MxMatrix4 LookAtMatrix(MxVector3 from, MxVector3 at, MxVector3 up)
{
var vUp = new MxVector3(up[0], up[1], up[2]);
MxVector3.Unitize(ref vUp);
var f = at - from;
MxVector3.Unitize(ref f);
var s = f ^ vUp;
MxVector3.Unitize(ref s);
var u = s ^ f;
MxVector3.Unitize(ref u);
var mat = new MxMatrix4(new MxVector4(s, 0.0), new MxVector4(u, 0.0), new MxVector4(-f, 0.0),
new MxVector4(0.0, 0.0, 0.0, 1.0));
return (mat*TranslationMatrix(-from));
}
public MxVector4(MxVector3 vec3, double w)
: this(vec3[0], vec3[1], vec3[2], w)
{
}
internal double CheckLocalInversion(int vertId, double[] vNew)
{
var nMin = 1.0;
var n1 = model.Neighbors(vertId);
foreach (var faceId in n1)
{
if (!model.FaceIsValid(faceId)) continue;
var face = model.Face(faceId);
var nml = new double[3];
model.ComputeFaceNormal(faceId, ref nml);
var nBefore = new MxVector3(nml);
var fAfter = new MxVector3[3];
for (var i = 0; i < 3; i++)
{
fAfter[i] = (face[i] == vertId)
? new MxVector3(vNew)
: new MxVector3(model.Vertex(face[i]));
}
var newNml = MxGeom3d.TriangleNormal(fAfter[0], fAfter[1], fAfter[2]);
var delta = nBefore*newNml;
if (delta < nMin) nMin = delta;
}
return nMin;
}
internal bool Optimize(MxVector3 vec1, MxVector3 vec2, ref MxVector3 opt)
{
var diff = vec1 - vec2;
var tens = Tensor;
var tV2 = tens*vec2;
var tDiff = tens*diff;
var denom = 2.0*diff*tDiff;
if (denom.IsSqCloseEnoughTo(0.0)) return false;
var a = (-2.0*(Vector*diff) - (diff*tV2) - (vec2*tDiff))/(2.0*(diff*tDiff));
if (a < 0.0) a = 0.0;
else if (a > 1.0) a = 1.0;
opt = a*diff + vec2;
return true;
}
internal static MxVector4 TriangleRawPlane(MxVector3 v1, MxVector3 v2, MxVector3 v3)
{
var n = TriangleRawNormal(v1, v2, v3);
return new MxVector4(n, -(n*v1));
}
internal static MxVector3 Cross(MxVector3 u, MxVector3 v)
{
var ret = new MxVector3(0.0, 0.0, 0.0);
ret[0] = u[1] * v[2] - v[1] * u[2];
ret[1] = v[0] * u[2] - u[0] * v[2];
ret[2] = u[0] * v[1] - v[0] * u[1];
return ret;
}
internal static MxMatrix4 ScalingMatrix(MxVector3 scale)
{
return new MxMatrix4(new MxVector4(scale[0], 0.0, 0.0, 0.0),
new MxVector4(0.0, scale[1], 0.0, 0.0),
new MxVector4(0.0, 0.0, scale[2], 0.0),
new MxVector4(0.0, 0.0, 0.0, 1.0));
}
internal static double NormSquared(MxVector3 u)
{
return (u*u);
}
internal double Evaluate(MxVector3 vec)
{
return Evaluate(vec[0], vec[1], vec[2]);
}
internal static MxMatrix4 RotationMatrixRad(double theta, MxVector3 axis)
{
var cos = Math.Cos(theta);
var sin = Math.Sin(theta);
var xx = axis[0]*axis[0];
var xy = axis[0]*axis[1];
var xz = axis[0]*axis[2];
var yy = axis[1]*axis[1];
var yz = axis[1]*axis[2];
var zz = axis[2]*axis[2];
var xs = axis[0]*sin;
var ys = axis[1]*sin;
var zs = axis[2]*sin;
return new MxMatrix4(new MxVector4(xx*(1 - cos) + cos, xy*(1 - cos) - zs, xz*(1 - cos) + ys, 0.0),
new MxVector4(xy*(1 - cos) + zs, yy*(1 - cos) + cos, yz*(1 - cos) - xs, 0.0),
new MxVector4(xz*(1 - cos) - ys, yz*(1 - cos) + xs, zz*(1 - cos) - cos, 0.0),
new MxVector4(0.0, 0.0, 0.0, 1.0));
}
internal bool Optimize(ref MxVector3 vec)
{
var invMat = new MxMatrix3(0.0);
var det = MxMatrix3.Invert(Tensor, ref invMat);
if (det.IsSqCloseEnoughTo(0.0)) return false;
vec = -(invMat*Vector);
return true;
}
public static MxVector3 operator -(MxVector3 vec1)
{
var newVec = new MxVector3(0.0, 0.0, 0.0);
newVec[0] = -vec1[0];
newVec[1] = -vec1[1];
newVec[2] = -vec1[2];
return newVec;
}
internal bool Optimize(ref double x, ref double y, ref double z)
{
var vec = new MxVector3(0.0, 0.0, 0.0);
var success = Optimize(ref vec);
if (!success) return false;
x = vec[0];
y = vec[1];
z = vec[2];
return true;
}
internal MxMatrix3(MxMatrix3 mat3)
{
rows[0] = new MxVector3((mat3[0])[0], (mat3[0])[1], (mat3[0])[2]);
rows[1] = new MxVector3((mat3[1])[0], (mat3[1])[1], (mat3[1])[2]);
rows[2] = new MxVector3((mat3[2])[0], (mat3[2])[1], (mat3[2])[2]);
}
internal double CheckLocalCompactness(int vertId, double[] vNew)
{
var n1 = model.Neighbors(vertId);
var cMin = 1.0;
foreach (var faceId in n1)
{
if (!model.FaceIsValid(faceId)) continue;
var face = model.Face(faceId);
MxVector3[] fAfter = new MxVector3[3];
for (var i = 0; i < 3; i++)
{
fAfter[i] = (face[i] == vertId)
? new MxVector3(vNew)
: new MxVector3(model.Vertex(face[i]));
}
var c = MxGeom3d.TriangleCompactness(fAfter[0], fAfter[1], fAfter[2]);
if (c < cMin) cMin = c;
}
return cMin;
}
internal static MxMatrix4 RotationMatrixDeg(double theta, MxVector3 axis)
{
return(RotationMatrixRad(theta * Math.PI / 180.0, axis));
}
internal static MxMatrix3 RowExtend(MxVector3 vec)
{
return(new MxMatrix3(vec, vec, vec));
}
internal void ComputeFaceInfo(int faceId)
{
var info = faceInfo[faceId];
info.FaceId = faceId;
var i = model.Face(faceId)[0];
var j = model.Face(faceId)[1];
var k = model.Face(faceId)[2];
var Qi = quadrics[i];
var Qj = quadrics[j];
var Qk = quadrics[k];
var Q = Qi + Qj + Qk;
if (PlacementPolicy == MxPlacement.Optimal &&
Q.Optimize(ref info.vNew[0], ref info.vNew[1], ref info.vNew[2]))
{
info.HeapKey = (float)-Q.Evaluate(info.vNew);
}
else
{
var v1 = new MxVector3(model.Vertex(i));
var v2 = new MxVector3(model.Vertex(j));
var v3 = new MxVector3(model.Vertex(k));
var e1 = Q.Evaluate(v1);
var e2 = Q.Evaluate(v2);
var e3 = Q.Evaluate(v3);
MxVector3 best;
double eMin;
if (e1 <= e2 && e1 <= e3)
{
eMin = e1;
best = v1;
}
else if (e2 <= e1 && e2 <= e3)
{
eMin = e2;
best = v2;
}
else
{
eMin = e3;
best = v3;
}
info.vNew[0] = best[0];
info.vNew[1] = best[1];
info.vNew[2] = best[2];
info.HeapKey = (float)(-eMin);
}
if (WeightingPolicy == MxWeighting.AreaAverage)
{
info.HeapKey = (float)(info.HeapKey / Q.Area);
}
if (info.IsInHeap)
{
heap.Update(info);
}
else
{
heap.Insert(info);
}
}
internal static MxMatrix3 Diag(MxVector3 vec)
{
return(new MxMatrix3(new MxVector3(vec[0], 0.0, 0.0),
new MxVector3(0.0, vec[1], 0.0),
new MxVector3(0.0, 0.0, vec[2])));
}