public static Vector3 LeftIntersection(this IArc arc, Sweepline sweepline)
{
var p = arc.LeftNeighbour.Position;
var q = arc.Site.Position;
var Z = sweepline.Z;
if (Vector.AlmostEqual(p, q))
{
return(AngleUtilities.EquatorialDirection(p));
}
if (Number.AlmostEqual(Z, p.Z) && Number.AlmostEqual(Z, q.Z))
{
return(AngleUtilities.EquatorialMidpoint(p, q));
}
var A = p.X * (Z - q.Z) - q.X * (Z - p.Z);
var B = p.Y * (Z - q.Z) - q.Y * (Z - p.Z);
var C = (p.Z - q.Z) * Math.Sign(sweepline.Priority) * Math.Sqrt(1 - Z * Z);
var A2PlusB2MinusC2 = Math.Max(A * A + B * B - C * C, 0);
var x = (A * C + B * Math.Sqrt(A2PlusB2MinusC2)) / (A * A + B * B);
var y = (B * C - A * Math.Sqrt(A2PlusB2MinusC2)) / (A * A + B * B);
return(new Vector3(x, y, 0));
}
public static Vector3 PointAt(Vector3 focus, Vector3 vector, Sweepline sweepline)
{
var p = focus;
var n = AngleUtilities.EquatorialDirection(vector);
var Z = sweepline.Z;
if (Number.AlmostEqual(p.Z, Z) && Vector.AlmostEqual(AngleUtilities.EquatorialDirection(p), n))
{
return(p);
}
if (Number.AlmostEqual(p.Z, Z))
{
return(new Vector3(0, 0, 1));
}
var tanOfColatitude = (Z - p.Z) / (p.ScalarMultiply(n) - Math.Sign(sweepline.Priority) * Math.Sqrt(1 - Z * Z));
var x = n.X * Math.Abs(tanOfColatitude / Math.Sqrt(1 + tanOfColatitude * tanOfColatitude));
var y = n.Y * Math.Abs(tanOfColatitude / Math.Sqrt(1 + tanOfColatitude * tanOfColatitude));
var z = Math.Sign(tanOfColatitude) / Math.Sqrt(1 + tanOfColatitude * tanOfColatitude);
return(new Vector3(x, y, z));
}