public AlgPoly(TrigPoly f)
{
p = (Complex[])f.c.Clone();
}
/// <summary>
/// Constructing the curve which is approximating a polygon.
/// </summary>
/// <param name="polygon"> The polygon it approximates. </param>
/// <param name="N"> The last index of the coefficients. </param>
public FourierCurve(Polygon polygon, int N = 10)
{
LastInd = N;
x = new TrigPoly(N);
y = new TrigPoly(N);
List <Vector2> vertices = new List <Vector2>();
List <float> t = new List <float>();
float length = 0;
t.Add(0);
vertices.Add(polygon[0]);
int n = 1;
for (int i = 1; i < polygon.Count; i++)
{
float d = Vector2.Distance(polygon[i], vertices[n - 1]);
if (d > Mathf.Epsilon)
{
length += d;
t.Add(2 * Mathf.PI * length);
vertices.Add(polygon[i]);
n++;
}
}
t[0] /= length;
for (int i = 1; i < n; i++)
{
t[i] /= length;
x.a[0] += (t[i] - t[i - 1]) * (vertices[i].x + vertices[i - 1].x) / (4 * Mathf.PI);
y.a[0] += (t[i] - t[i - 1]) * (vertices[i].y + vertices[i - 1].y) / (4 * Mathf.PI);
}
for (int k = 1; k <= N; k++)
{
x.a[k] = x.b[k] = y.a[k] = y.b[k] = 0;
float denom = (k * k * Mathf.PI);
float dt, dx, dy, dCos, dSin;
for (int i = 0; i < n - 1; i++)
{
dt = t[i + 1] - t[i];
dx = vertices[i + 1].x - vertices[i].x;
dy = vertices[i + 1].y - vertices[i].y;
dCos = Mathf.Cos(k * t[i + 1]) - Mathf.Cos(k * t[i]);
dSin = Mathf.Sin(k * t[i + 1]) - Mathf.Sin(k * t[i]);
x.a[k] += (dx / dt) * dCos / denom;
x.b[k] += (dx / dt) * dSin / denom;
y.a[k] += (dy / dt) * dCos / denom;
y.b[k] += (dy / dt) * dSin / denom;
}
}
x.ComputeComplexCoeffs();
y.ComputeComplexCoeffs();
transform = new Transform2D(new Vector2(0, 0), 1, 0);
AABB = polygon.AABB;
}