public static List <NI2dPoint> unwindingmacroParabola(double alpha, NI2dPoint F, double r, NI2dPoint P, double phi_start, double phi_end, double phi_step)
{
List <NI2dPoint> parabolaPts = new List <NI2dPoint>();
NI2dVector v1 = new NI2dVector(P, F);
NI2dVector v2 = new NI2dVector(Math.Cos(alpha), Math.Sin(alpha));
double phiP = v1.AngleBetween(v2) - Math.Asin(r / NI2dPoint.DistanceBetweenPoints(P, F));
if (phiP < 0.0)
{
phiP = 2 * Math.PI + phiP;
}
double t1 = Math.Sqrt((NI2dPoint.DistanceBetweenPoints(P, F) * NI2dPoint.DistanceBetweenPoints(P, F)) - (r * r));
double t2 = (1 - Math.Cos(phiP));
double t3 = (1 - phiP + Math.Sin(phiP));
double K = (t1 * t2) + (r * t3);
for (double phi = phi_start; phi < phi_end + phi_step; phi += phi_step)
{
NI2dPoint pt1 = new NI2dPoint(-1 * Math.Sin(phi + alpha), Math.Cos(phi + alpha));
NI2dPoint pt2 = new NI2dPoint(Math.Cos(phi + alpha), Math.Sin(phi + alpha));
double c1 = (K + r * (phi - 1 - Math.Sin(phi))) / (1 - Math.Cos(phi));
NI2dPoint parabpoint = (r * pt1) + (c1 * pt2) + F;
parabolaPts.Add(parabpoint);
}
return(parabolaPts);
}
public static List <NI2dPoint> unwindingmacroEllipse(NI2dPoint F, double r, NI2dPoint G, NI2dPoint P, double phi_start, double phi_end, double phi_step)
{
List <NI2dPoint> ellipsepts = new List <NI2dPoint>();
double distanceFP = NI2dPoint.DistanceBetweenPoints(F, P);
double f = NI2dPoint.DistanceBetweenPoints(F, G);
double alpha = new NI2dVector(G, F).AngleH();
NI2dVector v1 = new NI2dVector(Math.Cos(alpha), Math.Sin(alpha));
NI2dVector v2 = new NI2dVector(P, F);
double phiP = v2.AngleBetween(v1) - Math.Asin(r / distanceFP);
if (phiP < 0)
{
phiP = phiP + 2 * Math.PI;
}
double tp = Math.Sqrt((distanceFP * distanceFP) - (r * r));
double K = tp - (r * phiP) + Math.Sqrt((f * f) + (r * r) + (tp * tp) - (2 * f * ((tp * Math.Cos(phiP)) - (r * Math.Sin(phiP)))));
for (double phi = phi_start; phi < phi_end + phi_step; phi += phi_step)
{
NI2dPoint pt1 = new NI2dPoint(-1 * Math.Sin(phi + alpha), Math.Cos(phi + alpha));
NI2dPoint pt2 = new NI2dPoint(Math.Cos(phi + alpha), Math.Sin(phi + alpha));
double c1numerator = ((K + r * phi) * (K + r * phi)) - 2 * f * r * Math.Sin(phi) - (f * f) - (r * r);
double c1denominator = 2 * (K + (r * phi) - (f * Math.Cos(phi)));
double c1 = c1numerator / c1denominator;
NI2dPoint ellipsePoint = (r * pt1) + (c1 * pt2) + F;
ellipsepts.Add(ellipsePoint);
}
return(ellipsepts);
}
public static double PlaneAngleBetween(NI2dVector v1, NI2dVector v2)
{
if (((v2.x1 * v1.x2) - (v2.x2 * v1.x1)) >= 0)
{
return(NI2dVector.AngleBetween(v1, v2));
}
else
{
return((2 * Math.PI) - NI2dVector.AngleBetween(v1, v2));
}
}
public static List <NI2dPoint> cartesianOvalParallel(NI2dPoint F, double n1, double n2, NI2dPoint P, double alpha, double phi_start, double phi_end, double phi_step)
{
List <NI2dPoint> ovalpts = new List <NI2dPoint>();
double distanceFP = NI2dPoint.DistanceBetweenPoints(F, P);
NI2dVector v1 = new NI2dVector(P, F);
NI2dVector v2 = new NI2dVector(Math.Cos(alpha), Math.Sin(alpha));
double phiP = v1.AngleBetween(v2);
for (double phi = phi_start; phi < phi_end + phi_step; phi += phi_step)
{
NI2dPoint pt1 = new NI2dPoint(Math.Cos(phi + alpha), Math.Sin(phi + alpha));
double c1 = (distanceFP * (n1 - (n2 * Math.Cos(phiP)))) / (n1 - (n2 * Math.Cos(phi)));
NI2dPoint ovalPoint = (c1 * pt1) + F;
ovalpts.Add(ovalPoint);
}
return(ovalpts);
}
public static List <NI2dPoint> cartesianOvalDiverge(NI2dPoint F, double n1, NI2dPoint G, double n2, NI2dPoint P, double phi_start, double phi_end, double phi_step)
{
List <NI2dPoint> ovalpts = new List <NI2dPoint>();
double distanceFP = NI2dPoint.DistanceBetweenPoints(F, P);
double distancePG = NI2dPoint.DistanceBetweenPoints(P, G);
double K = (n1 * distanceFP) - (n2 * distancePG);
double f = NI2dPoint.DistanceBetweenPoints(F, G);
double phiC = 0;
if (Math.Abs(K) <= n1 * f)
{
phiC = Math.Acos(K / (f * n1));
}
else if (Math.Abs(K) > n1 * f)
{
phiC = 0;
}
NI2dVector v1 = new NI2dVector(P, F);
NI2dVector v2 = new NI2dVector(G, F);
if (K > -1 * n2 * f && v1.AngleBetween(v2) >= phiC)
{
for (double phi = phi_start; phi < phi_end + phi_step; phi += phi_step)
{
double D = (f * n1 - K * Math.Cos(phi)) * (f * n1 - K * Math.Cos(phi)) + (K * K - f * f * n2 * n2) * Math.Sin(phi) * Math.Sin(phi);
double alpha = new NI2dVector(G, F).AngleH();
double c1numerator = K * n1 - f * n2 * n2 * Math.Cos(phi) + n2 * Math.Sqrt(D);
double c1denominator = n1 * n1 - n2 * n2;
double c1 = c1numerator / c1denominator;
NI2dPoint pt1 = new NI2dPoint(Math.Cos(phi + alpha), Math.Sin(phi + alpha));
NI2dPoint ovalPoint = (c1 * pt1) + F;
ovalpts.Add(ovalPoint);
}
}
return(ovalpts);
}