public Similarity__x3t__(M4__x4t__ m, __ft__ epsilon = (__ft__)0.00001)
{
if (!(m.M30.IsTiny(epsilon) && m.M31.IsTiny(epsilon) && m.M32.IsTiny(epsilon)))
{
throw new ArgumentException("Matrix contains perspective components.");
}
if (m.M33.IsTiny(epsilon))
{
throw new ArgumentException("Matrix is not homogeneous.");
}
m /= m.M33; //normalize it
var m33 = (M3__x3t__)m;
var s0 = m33.C0.Norm2;
var s1 = m33.C1.Norm2;
var s2 = m33.C2.Norm2;
var s = (s0 * s1 * s2).Pow((__ft__)1.0 / 3); //geometric mean of scale
if (!((s0 / s - 1).IsTiny(epsilon) && (s1 / s - 1).IsTiny(epsilon) && (s2 / s - 1).IsTiny(epsilon)))
{
throw new ArgumentException("Matrix features non-uniform scaling");
}
m33 /= s;
Scale = s;
EuclideanTransformation = new Euclidean__x3t__(m33, m.C3.XYZ);
}
/// <summary>
/// Creates a similarity transformation from a rigid transformation <paramref name="euclideanTransformation"/> and an (subsequent) uniform scale by factor <paramref name="scale"/>.
/// </summary>
public Similarity__x3t__(Euclidean__x3t__ euclideanTransformation, __ft__ scale)
{
Scale = scale;
EuclideanTransformation = new Euclidean__x3t__(
euclideanTransformation.Rot,
scale * euclideanTransformation.Trans
);
}
/// <summary>
/// Creates a similarity transformation from an uniform scale by factor <paramref name="scale"/>, and a (subsequent) rigid transformation <paramref name="euclideanTransformation"/>.
/// </summary>
public Similarity__x3t__(__ft__ scale, Euclidean__x3t__ euclideanTransformation)
{
Scale = scale;
EuclideanTransformation = euclideanTransformation;
}
public static Similarity__x3t__ Parse(string s)
{
var x = s.NestedBracketSplitLevelOne().ToArray();
return(new Similarity__x3t__(__ft__.Parse(x[0]), Euclidean__x3t__.Parse(x[1])));
}
public static bool ApproxEqual(Similarity__x3t__ t0, Similarity__x3t__ t1, __ft__ angleTol, __ft__ posTol, __ft__ scaleTol)
{
return(t0.Scale.ApproximateEquals(t1.Scale, scaleTol) && Euclidean__x3t__.ApproxEqual(t0.EuclideanTransformation, t1.EuclideanTransformation, angleTol, posTol));
}
/// <summary>
/// Multiplies an Euclidean transformation by a Similarity transformation.
/// This concatenates the two transformations into a single one, first b is applied, then a.
/// Attention: Multiplication is NOT commutative!
/// </summary>
public static Similarity__x3t__ Multiply(Euclidean__x3t__ a, Similarity__x3t__ b)
{
return(Multiply((Similarity__x3t__)a, b));
}
/// <summary>
/// Multiplies a Similarity transformation by an Euclidean transformation.
/// This concatenates the two transformations into a single one, first b is applied, then a.
/// Attention: Multiplication is NOT commutative!
/// </summary>
public static Similarity__x3t__ Multiply(Similarity__x3t__ a, Euclidean__x3t__ b)
{
return(Multiply(a, (Similarity__x3t__)b));
}
