public static V2f Multiply(Rot2f rot, V2f vec)
{
float a = (float)System.Math.Cos(rot.Angle);
float b = (float)System.Math.Sin(rot.Angle);
return(new V2f(a * vec.X + b * vec.Y,
-b * vec.X + a * vec.Y));
}
/// <summary>
/// Calculates the centroid for a given set of V2fs.
/// </summary>
public static V2f ComputeCentroid(this V2f[] vectors, int[] indices)
{
V2f sum = V2f.Zero;
for (var i = 0; i < indices.Length; i++)
{
sum += vectors[indices[i]];
}
return(sum / (float)indices.Length);
}
/// <summary>
/// Calculates the sum for a given set of V2fs.
/// </summary>
public static V2f Sum(this V2f[] vectors)
{
V2f sum = V2f.Zero;
for (var i = 0; i < vectors.Length; i++)
{
sum += vectors[i];
}
return(sum);
}
/// <summary>
/// Calculates the centroid for a given set of V2fs.
/// </summary>
public static V2f ComputeCentroid(this V2f[] vectors)
{
V2f sum = V2f.Zero;
for (var i = 0; i < vectors.Length; i++)
{
sum += vectors[i];
}
return(sum / (float)vectors.Length);
}
/// <summary>
/// Calculates the sum for a given set of V2fs.
/// </summary>
public static V2f Sum(this IEnumerable <V2f> vectors)
{
V2f sum = V2f.Zero;
foreach (var e in vectors)
{
sum += e;
}
return(sum);
}
/// <summary>
/// Calculates the centroid for a given set of V2fs.
/// </summary>
public static V2f ComputeCentroid(this IEnumerable <V2f> vectors)
{
V2f sum = V2f.Zero;
int count = 0;
foreach (var e in vectors)
{
sum += e;
count++;
}
return(sum / (float)count);
}
/// <summary>
/// Calculates a weighted centroid for a given array of V2fs.
/// </summary>
public static V2f ComputeCentroid(this V2f[] vectors, float[] weights)
{
V2f sum = V2f.Zero;
float weightSum = 0;
for (int i = 0; i < vectors.Length; i++)
{
sum += weights[i] * vectors[i];
weightSum += weights[i];
}
return(sum / weightSum);
}
/// <summary>
/// Calculates a weighted centroid for vectors and weights given by indices.
/// Sum(vectors[indices[i]] * weights[indices[i]]) / Sum(weights[indices[i]].
/// </summary>
public static V2f ComputeCentroid(this V2f[] vectors, float[] weights, int[] indices)
{
V2f sum = V2f.Zero;
float weightSum = 0;
for (int i = 0; i < indices.Length; i++)
{
var w = weights[indices[i]];
sum += w * vectors[indices[i]];
weightSum += w;
}
return(sum / weightSum);
}
/// <summary>
/// Provides perspective projection matrix.
/// The parameters describe the dimensions of the view volume.
/// </summary>
public static M44f PerspectiveProjectionTransformRH(V2f size, float n, float f)
{
float w = size.X;
float h = size.Y;
// Fx 0 0 0
// 0 Fy 0 0
// 0 0 A B
// 0 0 -1 0
float Fx = 2 * n / w;
float Fy = 2 * n / h;
float A = f / (n - f);
float B = n * f / (n - f);
M44f P = new M44f(
Fx, 0, 0, 0,
0, Fy, 0, 0,
0, 0, A, B,
0, 0, -1, 0);
return(P);
}
/// <summary>
/// Creates a rigid transformation from a rotation <paramref name="rot"/> and a (subsequent) translation <paramref name="trans"/>.
/// </summary>
public Euclidean2f(Rot2f rot, V2f trans)
{
Rot = rot;
Trans = trans;
}
public static bool ApproxEqual(Euclidean2f r0, Euclidean2f r1, float angleTol, float posTol)
{
return(V2f.ApproxEqual(r0.Trans, r1.Trans, posTol) && Rot2f.ApproxEqual(r0.Rot, r1.Rot, angleTol));
}
/// <summary>
/// Inverts this rigid transformation (multiplicative inverse).
/// this = [Rot^T,-Rot^T Trans]
/// </summary>
public void Invert()
{
Rot.Invert();
Trans = -Rot.TransformDir(Trans);
}
/// <summary>
/// Transforms point p (p.w is presumed 1.0) by the inverse of this rigid transformation.
/// </summary>
public V2f InvTransformPos(V2f p)
{
return(InvTransformPos(this, p));
}
/// <summary>
/// Transforms direction vector v (v.w is presumed 0.0) by the inverse of this rigid transformation.
/// Actually, only the rotation is used.
/// </summary>
public V2f InvTransformDir(V2f v)
{
return(InvTransformDir(this, v));
}
/// <summary>
/// Transforms point p (p.w is presumed 1.0) by this rigid transformation.
/// </summary>
public V2f TransformPos(V2f p)
{
return(TransformPos(this, p));
}
/// <summary>
/// Transforms direction vector v (v.w is presumed 0.0) by this rigid transformation.
/// Actually, only the rotation is used.
/// </summary>
public V2f TransformDir(V2f v)
{
return(TransformDir(this, v));
}
/// <summary>
/// Transforms a position vector.
/// </summary>
public static V2f TransformPos(Rot2f rot, V2f v)
{
return((M22f)rot * v);
}
/// <summary>
/// Creates a rigid transformation from a trafo <paramref name="trafo"/>.
/// </summary>
public Euclidean2f(Trafo2d trafo)
{
Rot = Rot2f.FromM22f((M22f)trafo.Forward);
Trans = (V2f)trafo.Forward.C2.XY;
}
public static Euclidean2f Parse(string s)
{
var x = s.NestedBracketSplitLevelOne().ToArray();
return(new Euclidean2f(Rot2f.Parse(x[0]), V2f.Parse(x[1])));
}
/// <summary>
/// Transforms a position vector.
/// </summary>
public static V2f InvTransformPos(Rot2f rot, V2f v)
{
return((M22f)Rot2f.Negate(rot) * v);
}
/// <summary>
/// Transforms a position vector.
/// </summary>
public V2f InvTransformPos(V2f v)
{
return(Rot2f.InvTransformPos(this, v));
}
/// <summary>
/// Creates a rigid transformation from a rotation matrix <paramref name="rot"/> and a (subsequent) translation <paramref name="trans"/>.
/// </summary>
public Euclidean2f(M22f rot, V2f trans)
{
Rot = Rot2f.FromM22f(rot);
Trans = trans;
}
/// <summary>
/// Returns the outer product (tensor-product) of v1 * v2^T as a 3x3 Matrix.
/// </summary>
public static M22f OuterProduct(this V2f v1, V2f v2)
{
return(new M22f(
v2.X * v1.X, v2.Y * v1.X,
v2.X * v1.Y, v2.Y * v1.Y));
}
/// <summary>
/// Transforms direction vector v (v.w is presumed 0.0) by rigid transformation r.
/// Actually, only the rotation is used.
/// </summary>
public static V2f TransformDir(Euclidean2f r, V2f v)
{
return(r.Rot.TransformDir(v));
}
/// <summary>
/// Transforms point p (p.w is presumed 1.0) by rigid transformation r.
/// </summary>
public static V2f TransformPos(Euclidean2f r, V2f p)
{
return(r.Rot.TransformPos(p) + r.Trans);
}
/// <summary>
/// Multiplacation of a <see cref="Scale3f"/> with a <see cref="V2f"/>.
/// </summary>
public static V2f Multiply(Scale3f scale, V2f v)
{
return(new V2f(v.X * scale.X, v.Y * scale.Y));
}
/// <summary>
/// Transforms point p (p.w is presumed 1.0) by the inverse of the rigid transformation r.
/// </summary>
public static V2f InvTransformPos(Euclidean2f r, V2f p)
{
return(r.Rot.InvTransformPos(p - r.Trans));
}