/// <summary>
/// Calculate basePoints along a circle defined by a center on the z axis, and going through the point (0,0,1).
/// .5 is horosphere, 1 is geodesic
/// Result is in UHS model
/// </summary>
private static Vector3D[] BasePointsCircle(double centerUHS)
{
if (centerUHS > 1)
{
centerUHS = 1;
}
if (centerUHS < 0)
{
centerUHS = 0;
}
if (centerUHS == 0)
{
return new Vector3D[] { new Vector3D() }
}
;
bool hyperbolicOffsets = true;
if (hyperbolicOffsets)
{
// h-distance between each point.
double d = 0.1;
// We need to work in 2D first, then we'll switch to xz plane.
Circle circle = new Circle(new Vector3D(0, 1), new Vector3D(0, 1 - 2 * centerUHS), new Vector3D(centerUHS, 1 - centerUHS));
// XXX - check to make sure total distance won't wrap around the circle.
List <Vector3D> points = new List <Vector3D>();
int count = 75;
for (int i = -count; i <= count; i++)
{
double currentD = d * i;
// Angle t around a circle with center c and radius r to get an h-distance.
// https://en.wikipedia.org/wiki/Poincar%C3%A9_half-plane_model
// http://www.wolframalpha.com/input/?i=d+%3D+arcosh%281%2B%28%28r*sin%28t%29%29%5E2%2B%28r*cos%28t%29-r%29%5E2%29%2F%282*%28c%2Br%29*%28c%2Br*cos%28t%29%29%29%29%2C+solve+for+t
double c = circle.Center.Y;
double r = circle.Radius;
double coshd = DonHatch.cosh(currentD);
double numerator = c * c - c * (c + r) * coshd + c * r + r * r;
double denominator = r * ((c + r) * coshd - c);
double angle = Math.Acos(numerator / denominator);
if (i < 0)
{
angle *= -1;
}
points.Add(new Vector3D(r * Math.Sin(angle), 0, c + r * Math.Cos(angle)));
/*
* // XXX - This was my first attempt, but this code only works for geodesics, not general arcs!
* // Equidistant lines in UHS will all be lines through the origin.
* // In the following formula, x is the angle to use to get h-spaced equidistant line a distance d away.
* // http://www.wolframalpha.com/input/?i=d+%3D+arccosh%28sec%28x%29%29%2C+solve+for+x
* double angle = Math.Acos( 1.0 / DonHatch.cosh( currentD ) );
* angle = Math.PI/2 - angle;
* if( i < 0 )
* angle *= -1;
*
* Vector3D p1, p2;
* Euclidean2D.IntersectionLineCircle( new Vector3D(), new Vector3D( Math.Cos(angle), Math.Sin(angle) ), circle, out p1, out p2 );
* Vector3D highest = p1.Y > p2.Y ? p1 : p2;
* points.Add( new Vector3D( highest.X, 0, highest.Y ) );
*/
}
return(points.ToArray());
}
else
{
// equal euclidean spacing.
Circle3D c = new Circle3D(new Vector3D(0, 0, 1), new Vector3D(0, 0, 1 - 2 * centerUHS), new Vector3D(centerUHS, 0, 1 - centerUHS));
return(c.Subdivide(125));
}
}