/// <summary>
/// constructs an affine manifold from a set of points
/// </summary>
/// <param name="pts">
/// points on the manifold;
/// 1st index: point index.
/// 2nd index: spatial dimension.
/// </param>
static public AffineManifold FromPoints(params double[][] pts) {
int D = pts.Length;
for (int i = 0; i < D; i++)
if (pts[i].Length != D)
throw new ArgumentException();
var ret = new AffineManifold(D);
switch (D) {
case 2:
ret.Normal[0] = -(pts[1][1] - pts[0][1]);
ret.Normal[1] = +(pts[1][0] - pts[0][0]);
break;
case 3:
double a_1 = pts[1][0] - pts[0][0];
double a_2 = pts[1][1] - pts[0][1];
double a_3 = pts[1][2] - pts[0][2];
double b_1 = pts[2][0] - pts[0][0];
double b_2 = pts[2][1] - pts[0][1];
double b_3 = pts[2][2] - pts[0][2];
ret.Normal[0] = a_2 * b_3 - a_3 * b_2;
ret.Normal[1] = a_3 * b_1 - a_1 * b_3;
ret.Normal[2] = a_1 * b_2 - a_2 * b_1;
break;
default:
throw new NotSupportedException();
}
ret.a = GenericBlas.InnerProd(ret.Normal, pts[0]);
return ret;
}
/// <summary>
/// Intersection of two 1D affine manifolds in 2D space
/// </summary>
static public Vector Intersect2D(AffineManifold A, AffineManifold B)
{
if (A.Normal.Dim != 2)
{
throw new ArgumentException();
}
if (B.Normal.Dim != 2)
{
throw new ArgumentException();
}
if (A.Normal.AbsSquare() <= 0.0)
{
throw new ArithmeticException();
}
if (B.Normal.AbsSquare() <= 0.0)
{
throw new ArithmeticException();
}
double n1x = A.Normal[0];
double n1y = A.Normal[1];
double a1 = A.a;
double n2x = B.Normal[0];
double n2y = B.Normal[1];
double a2 = B.a;
return(new Vector(
(-n1y * a2 + a1 * n2y) / (n1x * n2y - n2x * n1y),
-(-n1x * a2 + n2x * a1) / (n1x * n2y - n2x * n1y)
));
}
/// <summary>
/// constructs an affine manifold from a set of points
/// </summary>
/// <param name="pts">
/// points on the manifold;
/// 1st index: point index.
/// 2nd index: spatial dimension.
/// </param>
static public AffineManifold FromPoints(MultidimensionalArray pts) {
int D = pts.GetLength(1);
var ret = new AffineManifold(D);
switch (D) {
case 2:
ret.Normal[0] = -(pts[1, 1] - pts[0, 1]);
ret.Normal[1] = +(pts[1, 0] - pts[0, 0]);
break;
case 3:
double a_1 = pts[1, 0] - pts[0, 0];
double a_2 = pts[1, 1] - pts[0, 1];
double a_3 = pts[1, 2] - pts[0, 2];
double b_1 = pts[2, 0] - pts[0, 0];
double b_2 = pts[2, 1] - pts[0, 1];
double b_3 = pts[2, 2] - pts[0, 2];
ret.Normal[0] = a_2 * b_3 - a_3 * b_2;
ret.Normal[1] = a_3 * b_1 - a_1 * b_3;
ret.Normal[2] = a_1 * b_2 - a_2 * b_1;
break;
default:
throw new NotSupportedException();
}
double[] Offset = pts.ExtractSubArrayShallow(0, -1).To1DArray();
ret.a = GenericBlas.InnerProd(ret.Normal, Offset);
return ret;
}
/// <summary>
/// non-shallow cloning
/// </summary>
/// <returns></returns>
public object Clone()
{
var ret = new AffineManifold(this.Normal.Dim);
ret.Normal = this.Normal;
ret.a = this.a;
return(ret);
}
/// <summary>
/// constructs an affine manifold from a set of points
/// </summary>
/// <param name="pts">
/// points on the manifold;
/// 1st index: point index.
/// </param>
static public AffineManifold FromPoints(params Vector[] pts)
{
int D = pts.Length;
if (D <= 1)
{
throw new ArgumentException("1D or lower is not supported");
}
for (int i = 0; i < D; i++)
{
if (pts[i].Dim != D)
{
throw new ArgumentException();
}
}
var ret = new AffineManifold(D);
switch (D)
{
case 2:
ret.Normal[0] = -(pts[1][1] - pts[0][1]);
ret.Normal[1] = +(pts[1][0] - pts[0][0]);
break;
case 3:
double a_1 = pts[1][0] - pts[0][0];
double a_2 = pts[1][1] - pts[0][1];
double a_3 = pts[1][2] - pts[0][2];
double b_1 = pts[2][0] - pts[0][0];
double b_2 = pts[2][1] - pts[0][1];
double b_3 = pts[2][2] - pts[0][2];
ret.Normal[0] = a_2 * b_3 - a_3 * b_2;
ret.Normal[1] = a_3 * b_1 - a_1 * b_3;
ret.Normal[2] = a_1 * b_2 - a_2 * b_1;
break;
default:
throw new NotSupportedException();
}
ret.a = ret.Normal * pts[0];
if (ret.Normal.AbsSquare() <= 0.0)
{
throw new ArithmeticException();
}
return(ret);
}
/// <summary>
/// Intersection of two 1D affine manifolds in 2D space
/// </summary>
static public double[] Intersect2D(AffineManifold A, AffineManifold B) {
if (A.Normal.Length != 2)
throw new ArgumentException();
if (B.Normal.Length != 2)
throw new ArgumentException();
double[] ret = new double[2];
double n1x = A.Normal[0];
double n1y = A.Normal[1];
double a1 = A.a;
double n2x = B.Normal[0];
double n2y = B.Normal[1];
double a2 = B.a;
ret[0] = (-n1y*a2+a1*n2y)/(n1x*n2y-n2x*n1y);
ret[1] = -(-n1x*a2+n2x*a1)/(n1x*n2y-n2x*n1y);
return ret;
}
/// <summary>
/// constructs an affine manifold from a set of points
/// </summary>
/// <param name="pts">
/// points on the manifold;
/// 1st index: point index.
/// 2nd index: spatial dimension.
/// </param>
static public AffineManifold FromPoints(MultidimensionalArray pts)
{
int D = pts.GetLength(1);
var ret = new AffineManifold(D);
switch (D)
{
case 2:
ret.Normal[0] = -(pts[1, 1] - pts[0, 1]);
ret.Normal[1] = +(pts[1, 0] - pts[0, 0]);
break;
case 3:
double a_1 = pts[1, 0] - pts[0, 0];
double a_2 = pts[1, 1] - pts[0, 1];
double a_3 = pts[1, 2] - pts[0, 2];
double b_1 = pts[2, 0] - pts[0, 0];
double b_2 = pts[2, 1] - pts[0, 1];
double b_3 = pts[2, 2] - pts[0, 2];
ret.Normal[0] = a_2 * b_3 - a_3 * b_2;
ret.Normal[1] = a_3 * b_1 - a_1 * b_3;
ret.Normal[2] = a_1 * b_2 - a_2 * b_1;
break;
default:
throw new NotSupportedException();
}
double[] Offset = pts.ExtractSubArrayShallow(0, -1).To1DArray();
ret.a = ret.Normal * (new Vector(Offset));
if (ret.Normal.AbsSquare() <= 0.0)
{
throw new ArithmeticException();
}
return(ret);
}
/// <summary>
/// non-shallow cloning
/// </summary>
/// <returns></returns>
public object Clone() {
var ret = new AffineManifold(this.Normal.Length);
Array.Copy(this.Normal, ret.Normal, this.Normal.Length);
ret.a = this.a;
return ret;
}
