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Using matrix transforms for ellipse arcs.
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public static DVec.Vector2[] EllipseFullMtxSweep(double semiMaj, double eccentricity, double tilt, double start, | |
double sweep, int numPoints) | |
{ | |
//convert ellipse angles to circle angles. | |
double b = semiMaj * Math.Sqrt(1 - eccentricity * eccentricity); | |
start = Math.Atan(semiMaj / b * Math.Tan(start)); | |
sweep = Math.Atan(semiMaj / b * Math.Tan(sweep)); | |
double end = start + sweep; | |
double Δθ = 2 * Math.PI / (numPoints - 1) * Math.Sign(sweep); //arc increment for a whole circle | |
numPoints = (int)Math.Abs(sweep / Δθ); //numpoints for just the arc | |
DVec.Vector2[] points = new DVec.Vector2[numPoints + 1]; | |
double linEcc = Math.Sqrt(semiMaj * semiMaj - b * b); | |
double θ = 0; | |
double x = 0; | |
double y = 0; | |
for (int i = 0; i < numPoints; i++) | |
{ | |
θ = start + Δθ * i; | |
x = semiMaj * Math.Cos(θ); | |
y = semiMaj * Math.Sin(θ); | |
points[i] = new DVec.Vector2(x, y); | |
} | |
x = semiMaj * Math.Cos(end); | |
y = semiMaj * Math.Sin(end); | |
points[numPoints] = new DVec.Vector2(x, y); | |
Matrix mirMtx = Matrix.IDMirror(true, false); | |
Matrix scalemtx = Matrix.IDScale(1, 1 - eccentricity); | |
Matrix moveMtx = Matrix.IDTranslate(-linEcc, 0); | |
Matrix rotMtx = Matrix.IDRotate(tilt); | |
Matrix endMtx = mirMtx * moveMtx * scalemtx * rotMtx; | |
points = endMtx.Transform(points); | |
return points; | |
} |
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