public Ellipsoid(EllipsoidQuadraticForm ellipsoidQuadraticForm)
{
Requires.NotNull(ellipsoidQuadraticForm, "ellipsoidQuadraticForm");
_quadraticForm = ellipsoidQuadraticForm;
_parametricForm = ellipsoidQuadraticForm.EllipsoidParametricForm;
XRadius = _parametricForm.XRadius;
YRadius = _parametricForm.YRadius;
ZRadius = _parametricForm.ZRadius;
Xmax = _parametricForm.GetXmax();
Ymax = _parametricForm.GetYmax();
Zmax = _parametricForm.GetZmax();
InverseTransform = _quadraticForm.AffineTransform;
Poles = _parametricForm.GetPoles();
}
public EllipsoidQuadraticForm(double A, double B, double C, double D, double E, double F, double G, double H, double I, double J)
{
var doubleUtils = new DoubleUtils(1e-12);
if (doubleUtils.Sign(A) < 0)
{
A = -A;
B = -B;
C = -C;
D = -D;
E = -E;
F = -F;
G = -G;
H = -H;
I = -I;
J = -J;
}
Requires.Positive(doubleUtils.Sign(A), "A");
Requires.Positive(doubleUtils.Sign(B), "B");
Requires.Positive(doubleUtils.Sign(C), "C");
Requires.Positive(doubleUtils.Sign(A * B - D * D), "A * B - D * D");
Requires.Positive(doubleUtils.Sign(A * C - E * E), "A * C - E * E");
Requires.Positive(doubleUtils.Sign(B * C - F * F), "B * C - F * F");
_coefficients = new[] { A, B, C, D, E, F, G, H, I, J };
QuadraticFrom = new[, ] {
{ A, D, E },
{ D, B, F },
{ E, F, C }
};
Offset = new[] { G, H, I, };
var b = QuadraticFrom.Inverse().Multiply(Offset.Multiply(-1));
var eigenDecomposition = new EigenvalueDecomposition(QuadraticFrom);
var axisNumerator = b.ElementwiseMultiply(QuadraticFrom.Multiply(b)).Sum() - J;
var xradius = System.Math.Sqrt(axisNumerator / eigenDecomposition.RealEigenvalues[0]);
var yradius = System.Math.Sqrt(axisNumerator / eigenDecomposition.RealEigenvalues[1]);
var zradius = System.Math.Sqrt(axisNumerator / eigenDecomposition.RealEigenvalues[2]);
var rotation = eigenDecomposition.Eigenvectors;
EllipsoidParametricForm = new EllipsoidParametricForm(xradius, yradius, zradius, new Point3D(b[0], b[1], b[2]), rotation);
var sqrt = rotation.Multiply(eigenDecomposition.DiagonalMatrix.Sqrt().Multiply(rotation.Inverse()));
AffineTransform = sqrt.Multiply(1.0 / System.Math.Sqrt(axisNumerator));
}
public EllipsoidQuadraticForm(double A, double B, double C, double D, double E, double F, double G, double H, double I, double J)
{
var doubleUtils = new DoubleUtils(1e-12);
if (doubleUtils.Sign(A) < 0) {
A = -A;
B = -B;
C = -C;
D = -D;
E = -E;
F = -F;
G = -G;
H = -H;
I = -I;
J = -J;
}
Requires.Positive(doubleUtils.Sign(A), "A");
Requires.Positive(doubleUtils.Sign(B), "B");
Requires.Positive(doubleUtils.Sign(C), "C");
Requires.Positive(doubleUtils.Sign(A * B - D * D), "A * B - D * D");
Requires.Positive(doubleUtils.Sign(A * C - E * E), "A * C - E * E");
Requires.Positive(doubleUtils.Sign(B * C - F * F), "B * C - F * F");
_coefficients = new[] { A, B, C, D, E, F, G, H, I, J };
QuadraticFrom = new[,] {
{ A, D, E },
{ D, B, F },
{ E, F, C }
};
Offset = new[] { G, H, I, };
var b = QuadraticFrom.Inverse().Multiply(Offset.Multiply(-1));
var eigenDecomposition = new EigenvalueDecomposition(QuadraticFrom);
var axisNumerator = b.ElementwiseMultiply(QuadraticFrom.Multiply(b)).Sum() - J;
var xradius = System.Math.Sqrt(axisNumerator / eigenDecomposition.RealEigenvalues[0]);
var yradius = System.Math.Sqrt(axisNumerator / eigenDecomposition.RealEigenvalues[1]);
var zradius = System.Math.Sqrt(axisNumerator / eigenDecomposition.RealEigenvalues[2]);
var rotation = eigenDecomposition.Eigenvectors;
EllipsoidParametricForm = new EllipsoidParametricForm(xradius, yradius, zradius, new Point3D(b[0], b[1], b[2]), rotation);
var sqrt = rotation.Multiply(eigenDecomposition.DiagonalMatrix.Sqrt().Multiply(rotation.Inverse()));
AffineTransform = sqrt.Multiply(1.0 / System.Math.Sqrt(axisNumerator));
}