public static bool DecomposeIntoRotationAndScale(Matrix source, out Matrix rotation, out Vector scale)
{
source.OffsetX = 0.0;
source.OffsetY = 0.0;
Matrix U;
Vector S;
Matrix VTranspose;
bool flag = Matrix3DOperations.SVD(source, out U, out S, out VTranspose);
Matrix matrix1 = Matrix3DOperations.Transpose(VTranspose);
Matrix matrix2 = new Matrix()
{
M11 = S.X,
M22 = S.Y
};
rotation = U * matrix1;
Matrix matrix3 = rotation;
matrix3.Invert();
Matrix matrix4 = source * matrix3;
Matrix matrix5 = matrix3 * source;
double tolerance = 1E-13;
scale = !Matrix3DOperations.IsDiagonal(matrix4, tolerance) ? new Vector(matrix5.M11, matrix5.M22) : new Vector(matrix4.M11, matrix4.M22);
return(flag);
}
public static bool DecomposeIntoRotationAndScale(Matrix3D source, out Matrix3D rotation, out Vector3D scale)
{
source.OffsetX = 0.0;
source.OffsetY = 0.0;
source.OffsetZ = 0.0;
Matrix3D U;
Vector3D S;
Matrix3D VTranspose;
bool flag = Matrix3DOperations.SVD(source, out U, out S, out VTranspose);
Matrix3D matrix3D1 = Matrix3DOperations.Transpose(VTranspose);
Matrix3D matrix3D2 = new Matrix3D()
{
M11 = S.X,
M22 = S.Y,
M33 = S.Z,
M44 = 1.0
};
rotation = U * matrix3D1;
Matrix3D matrix3D3 = rotation;
matrix3D3.Invert();
Matrix3D matrix = source * matrix3D3;
Matrix3D matrix3D4 = matrix3D3 * source;
double tolerance = 1E-13;
scale = !Matrix3DOperations.IsDiagonal(matrix, tolerance) ? new Vector3D(matrix3D4.M11, matrix3D4.M22, matrix3D4.M33) : new Vector3D(matrix.M11, matrix.M22, matrix.M33);
return(flag);
}
public static bool SVD(Matrix original, out Matrix U, out Vector S, out Matrix VTranspose)
{
double[,] U1;
double[] S1;
double[,] V;
bool flag = Matrix3DOperations.Svd(Matrix3DOperations.CreateMatrix2x2(original), out U1, out S1, out V);
U = Matrix3DOperations.CreateMatrix(U1);
VTranspose = Matrix3DOperations.CreateMatrix(V);
S = Matrix3DOperations.CreateVector(S1);
return(flag);
}
private void ConvertGenericTransform(Transform3D transform)
{
Point3D point3D1 = new Point3D(0.0, 0.0, 0.0);
this.Initialize();
ScaleTransform3D scaleTransform3D = transform as ScaleTransform3D;
if (scaleTransform3D != null)
{
this.scale = new Vector3D(scaleTransform3D.ScaleX, scaleTransform3D.ScaleY, scaleTransform3D.ScaleZ);
this.center = new Point3D(scaleTransform3D.CenterX, scaleTransform3D.CenterY, scaleTransform3D.CenterZ);
}
else
{
Point3D point3D2 = point3D1 * transform.Value;
this.translation = new Vector3D(point3D2.X, point3D2.Y, point3D2.Z);
Matrix3D rotation;
Vector3D scale;
Matrix3DOperations.DecomposeIntoRotationAndScale(transform.Value, out rotation, out scale);
this.scale = scale;
this.RotationAngles = Helper3D.EulerAnglesFromQuaternion(this.MatrixToQuaternion(rotation));
}
this.InitializeTransformGroup();
}
internal static bool Svd(double[,] M, out double[,] U, out double[] S, out double[,] V)
{
double val1 = 0.0;
double num1 = 0.0;
double num2 = 0.0;
int index1 = 0;
int index2 = 0;
int length = M.Length == 4 ? 2 : 3;
double[] numArray = new double[length];
U = new double[length, length];
V = new double[length, length];
S = new double[length];
for (int index3 = 0; index3 < length; ++index3)
{
for (int index4 = 0; index4 < length; ++index4)
{
U[index3, index4] = M[index3, index4];
}
S[index3] = 0.0;
}
for (int index3 = 0; index3 < length; ++index3)
{
index1 = index3 + 1;
numArray[index3] = num2 * num1;
double num3;
double num4 = num3 = 0.0;
double d1 = num3;
double num5 = num3;
for (int index4 = index3; index4 < length; ++index4)
{
num4 += Math.Abs(U[index4, index3]);
}
if (num4 != 0.0)
{
for (int index4 = index3; index4 < length; ++index4)
{
U[index4, index3] /= num4;
d1 += U[index4, index3] * U[index4, index3];
}
double num6 = U[index3, index3];
num5 = num6 >= 0.0 ? -Math.Sqrt(d1) : Math.Sqrt(d1);
double num7 = num6 * num5 - d1;
U[index3, index3] = num6 - num5;
for (int index4 = index1; index4 < length; ++index4)
{
double num8 = 0.0;
for (int index5 = index3; index5 < length; ++index5)
{
num8 += U[index5, index3] * U[index5, index4];
}
double num9 = num8 / num7;
for (int index5 = index3; index5 < length; ++index5)
{
U[index5, index4] += num9 * U[index5, index3];
}
}
for (int index4 = index3; index4 < length; ++index4)
{
U[index4, index3] *= num4;
}
}
S[index3] = num4 * num5;
double num10;
num2 = num10 = 0.0;
double d2 = num10;
num1 = num10;
for (int index4 = index1; index4 < length; ++index4)
{
num2 += Math.Abs(U[index3, index4]);
}
if (num2 != 0.0)
{
for (int index4 = index1; index4 < length; ++index4)
{
U[index3, index4] /= num2;
d2 += U[index3, index4] * U[index3, index4];
}
double num6 = U[index3, index1];
num1 = num6 >= 0.0 ? -Math.Sqrt(d2) : Math.Sqrt(d2);
double num7 = num6 * num1 - d2;
U[index3, index1] = num6 - num1;
for (int index4 = index1; index4 < length; ++index4)
{
numArray[index4] = U[index3, index4] / num7;
}
for (int index4 = index1; index4 < length; ++index4)
{
double num8 = 0.0;
for (int index5 = index1; index5 < length; ++index5)
{
num8 += U[index4, index5] * U[index3, index5];
}
for (int index5 = index1; index5 < length; ++index5)
{
U[index4, index5] += num8 * numArray[index5];
}
}
for (int index4 = index1; index4 < length; ++index4)
{
U[index3, index4] *= num2;
}
}
val1 = Math.Max(val1, Math.Abs(S[index3]) + Math.Abs(numArray[index3]));
}
int index6 = length;
while (--index6 >= 0)
{
if (num1 != 0.0)
{
for (int index3 = index1; index3 < length; ++index3)
{
V[index3, index6] = U[index6, index3] / U[index6, index1] / num1;
}
for (int index3 = index1; index3 < length; ++index3)
{
double num3 = 0.0;
for (int index4 = index1; index4 < length; ++index4)
{
num3 += U[index6, index4] * V[index4, index3];
}
for (int index4 = index1; index4 < length; ++index4)
{
V[index4, index3] += num3 * V[index4, index6];
}
}
}
for (int index3 = index1; index3 < length; ++index3)
{
V[index6, index3] = V[index3, index6] = 0.0;
}
V[index6, index6] = 1.0;
num1 = numArray[index6];
index1 = index6;
}
int index7 = length;
while (--index7 >= 0)
{
int num3 = index7 + 1;
double num4 = S[index7];
for (int index3 = num3; index3 < length; ++index3)
{
U[index7, index3] = 0.0;
}
if (num4 != 0.0)
{
double num5 = 1.0 / num4;
for (int index3 = num3; index3 < length; ++index3)
{
double num6 = 0.0;
for (int index4 = num3; index4 < length; ++index4)
{
num6 += U[index4, index7] * U[index4, index3];
}
double num7 = num6 / U[index7, index7] * num5;
for (int index4 = index7; index4 < length; ++index4)
{
U[index4, index3] += num7 * U[index4, index7];
}
}
for (int index3 = index7; index3 < length; ++index3)
{
U[index3, index7] *= num5;
}
}
else
{
for (int index3 = index7; index3 < length; ++index3)
{
U[index3, index7] = 0.0;
}
}
++U[index7, index7];
}
int index8 = length;
while (--index8 >= 0)
{
for (int index3 = 1; index3 <= 30; ++index3)
{
bool flag = true;
int index4;
for (index4 = index8; index4 >= 0; --index4)
{
index2 = index4 - 1;
if (Math.Abs(numArray[index4]) + val1 == val1)
{
flag = false;
break;
}
if (index2 < 0)
{
return(false);
}
if (Math.Abs(S[index2]) + val1 == val1)
{
break;
}
}
if (flag)
{
double num3 = 0.0;
double num4 = 1.0;
for (int index5 = index4; index5 <= index8; ++index5)
{
double a = num4 * numArray[index5];
numArray[index5] *= num3;
if (Math.Abs(a) + val1 != val1)
{
double b = S[index5];
double num5 = Matrix3DOperations.Hypotenuse(a, b);
S[index5] = num5;
double num6 = 1.0 / num5;
num3 = b * num6;
num4 = -a * num6;
for (int index9 = 0; index9 < length; ++index9)
{
double num7 = U[index9, index2];
double num8 = U[index9, index5];
U[index9, index2] = num7 * num3 + num8 * num4;
U[index9, index5] = num8 * num3 - num7 * num4;
}
}
else
{
break;
}
}
}
double num9 = S[index8];
if (index4 == index8)
{
if (num9 < 0.0)
{
S[index8] = -num9;
for (int index5 = 0; index5 < length; ++index5)
{
V[index5, index8] = -V[index5, index8];
}
break;
}
break;
}
if (index3 == 30)
{
return(false);
}
double num10 = S[index4];
index2 = index8 - 1;
double num11 = S[index2];
double num12 = numArray[index2];
double num13 = numArray[index8];
double a1 = ((num11 - num9) * (num11 + num9) + (num12 - num13) * (num12 + num13)) / (2.0 * num13 * num11);
double num14 = Matrix3DOperations.Hypotenuse(a1, 1.0);
double a2 = ((num10 - num9) * (num10 + num9) + num13 * (num11 / (a1 + (a1 >= 0.0 ? num14 : -num14)) - num13)) / num10;
double num15;
double num16 = num15 = 1.0;
for (int index5 = index4; index5 <= index2; ++index5)
{
int index9 = index5 + 1;
double num3 = numArray[index9];
double num4 = S[index9];
double b1 = num15 * num3;
double num5 = num16 * num3;
double num6 = Matrix3DOperations.Hypotenuse(a2, b1);
numArray[index5] = num6;
num16 = a2 / num6;
num15 = b1 / num6;
double a3 = num10 * num16 + num5 * num15;
double num7 = num5 * num16 - num10 * num15;
double b2 = num4 * num15;
double num8 = num4 * num16;
for (int index10 = 0; index10 < length; ++index10)
{
double num17 = V[index10, index5];
double num18 = V[index10, index9];
V[index10, index5] = num17 * num16 + num18 * num15;
V[index10, index9] = num18 * num16 - num17 * num15;
}
double num19 = Matrix3DOperations.Hypotenuse(a3, b2);
S[index5] = num19;
if (num19 != 0.0)
{
double num17 = 1.0 / num19;
num16 = a3 * num17;
num15 = b2 * num17;
}
a2 = num16 * num7 + num15 * num8;
num10 = num16 * num8 - num15 * num7;
for (int index10 = 0; index10 < length; ++index10)
{
double num17 = U[index10, index5];
double num18 = U[index10, index9];
U[index10, index5] = num17 * num16 + num18 * num15;
U[index10, index9] = num18 * num16 - num17 * num15;
}
}
numArray[index4] = 0.0;
numArray[index8] = a2;
S[index8] = num10;
}
}
return(true);
}