public static Inclusions EllipticalArcContainsPoint1(
double cX, double cY,
double r1, double r2,
double cosT, double sinT,
double startCosT, double startSinT,
double sweepCosT, double sweepSinT,
double pX, double pY,
double epsilon = Epsilon)
{
// If the ellipse is empty it can't contain anything.
if (r1 <= 0d || r2 <= 0d)
{
return(Inclusions.Outside);
}
// If the Sweep angle is Tau, the EllipticalArc must be an Ellipse.
if (Abs(sweepCosT - 1d) < epsilon && Abs(sweepSinT) < epsilon)
{
return(EllipseWithVectorAngleContainsPointTests.EllipseContainsPoint(cX, cY, r1, r2, sinT, cosT, pX, pY));
}
var endSinT = (sweepSinT * startCosT) + (sweepCosT * startSinT);
var endCosT = (sweepCosT * startCosT) - (sweepSinT * startSinT);
// Find the start and end angles.
var sa = EllipticalPolarVectorTests.EllipticalPolarVector(startCosT, startSinT, r1, r2);
var ea = EllipticalPolarVectorTests.EllipticalPolarVector(endCosT, endSinT, r1, r2);
// Ellipse equation for an ellipse at origin for the chord end points.
var u1 = r1 * sa.cosT;
var v1 = -(r2 * sa.sinT);
var u2 = r1 * ea.cosT;
var v2 = -(r2 * ea.sinT);
// Find the points of the chord.
var sX = cX + ((u1 * cosT) + (v1 * sinT));
var sY = cY + ((u1 * sinT) - (v1 * cosT));
var eX = cX + ((u2 * cosT) + (v2 * sinT));
var eY = cY + ((u2 * sinT) - (v2 * cosT));
// Find the determinant of the chord.
var determinant = ((sX - pX) * (eY - pY)) - ((eX - pX) * (sY - pY));
// Check whether the point is on the same side of the chord as the center.
if (Sign(-determinant) == Sign(sweepSinT * sweepCosT))
{
return(Inclusions.Outside);
}
// Translate point to origin.
var u0 = pX - cX;
var v0 = pY - cY;
// Apply the rotation transformation to the point at the origin.
var a = (u0 * cosT) + (v0 * sinT);
var b = (u0 * sinT) - (v0 * cosT);
// Normalize the radius.
var normalizedRadius
= (a * a / (r1 * r1))
+ (b * b / (r2 * r2));
return((normalizedRadius <= 1d)
? ((Abs(normalizedRadius - 1d) < epsilon)
? Inclusions.Boundary : Inclusions.Inside) : Inclusions.Outside);
}
public static double EllipticalPolarAngle1(double angle, double rx, double ry)
{
var(cosT, sinT) = EllipticalPolarVectorTests.EllipticalPolarVector(Cos(angle), Sin(angle), rx, ry);
return(Atan2(sinT, cosT));
}
