// creates an arbitrary Caresian coordinate system with given plane xy
public static RotoTranslation3 CoordinateSystemWithPlaneXY(Plane plane)
{
var x = Vector3Utils.VectorOrthogonalTo(plane.Normal);
var y = plane.Normal.Cross(x);
return(new RotoTranslation3(Rotation3Utils.GramSchmidt(x, y), plane.ProjectOrigin()));
}
public void VectorOrthogonalTo_returns_Vector3_orthogonal_to_input_Vector3_which_is_not_zero_when_input_Vector3_is_not_zero
([ValueSource("VectorOrthogonalTo_TestCases")] Vector3 v)
{
var result = Vector3Utils.VectorOrthogonalTo(v);
Expect(v * result, Is.EqualTo(0).Within(_tolerance));
Expect(result.Norm, Is.GreaterThan(0.8 * v.Norm));
}
private static Vector3 Eigenvector(this SymmetricMatrix3 @this, double eigenvalue)
{
var rowX = new Vector3(@this.XX - eigenvalue, @this.XY, @this.ZX);
var rowY = new Vector3(@this.XY, @this.YY - eigenvalue, @this.YZ);
var rowZ = new Vector3(@this.ZX, @this.YZ, @this.ZZ - eigenvalue);
var normX2 = rowX.Norm2;
var normY2 = rowY.Norm2;
var normZ2 = rowZ.Norm2;
Vector3 row1, row2, row3;
if (normX2 > normY2)
{
if (normX2 > normZ2)
{
row1 = rowX / Math.Sqrt(normX2);
row2 = rowY;
row3 = rowZ;
}
else
{
row1 = rowZ / Math.Sqrt(normZ2);
row2 = rowX;
row3 = rowY;
}
}
else
{
if (normY2 > normZ2)
{
row1 = rowY / Math.Sqrt(normY2);
row2 = rowX;
row3 = rowZ;
}
else
{
row1 = rowZ / Math.Sqrt(normZ2);
row2 = rowY;
row3 = rowX;
}
}
var cross2 = row1.Cross(row2);
var cross3 = row1.Cross(row3);
var norm22 = cross2.Norm2;
var norm32 = cross3.Norm2;
if (norm22 > norm32)
{
if (norm22 > BasicMath.Epsilon)
{
return(cross2 / Math.Sqrt(norm22));
}
else
{
return(Vector3Utils.VectorOrthogonalTo(row1).Normalized);
}
}
else
{
if (norm32 > BasicMath.Epsilon)
{
return(cross3 / Math.Sqrt(norm32));
}
else
{
return(Vector3Utils.VectorOrthogonalTo(row1).Normalized);
}
}
}
