private static bool EdgeOkUHS(H3.Cell.Edge edge, Circle region)
{
if (Tolerance.GreaterThan(edge.Start.Abs(), region.Radius) ||
Tolerance.GreaterThan(edge.End.Abs(), region.Radius))
{
return(false);
}
return(EdgeOk(edge, m_params.UhsCutoff));
}
private static bool TetOk(Tet tet)
{
double cutoff = 0.95;
foreach (Vector3D v in tet.Verts)
{
if (Tolerance.GreaterThan(v.Z, 0) ||
v.Abs() > cutoff)
{
return(false);
}
}
return(true);
}
/// <summary>
/// Checks to see if two segments intersect.
/// This does not actually calculate the intersection point.
/// It uses information from the following paper:
/// http://www.geometrictools.com/Documentation/DistanceLine3Line3.pdf
/// </summary>
public static bool DoSegmentsIntersect(Vector3D a1, Vector3D a2, Vector3D b1, Vector3D b2)
{
/* Our approach.
* (1) Check if endpoints are on other segment. Note that this also checks if A endpoints equal B endpoints.
* (2) Calc line-line distance. If > 0, we don't intersect.
* (3) At this point, we only have to deal with non-parallel case in the paper, and only
* need to determine if we are in "region 0" (we intersect) or not (we don't)
*/
// (1)
if (PointOnSegment(a1, a2, b1) ||
PointOnSegment(a1, a2, b2) ||
PointOnSegment(b1, b2, a1) ||
PointOnSegment(b1, b2, a2))
{
return(true);
}
// (2)
Vector3D ma = a2 - a1;
Vector3D mb = b2 - b1;
if (Tolerance.GreaterThan(DistanceLineLine(ma, a1, mb, b1), 0))
{
return(false);
}
// (3)
Vector3D D = a1 - b1;
double a = ma.Dot(ma);
double b = -ma.Dot(mb);
double c = mb.Dot(mb);
double d = ma.Dot(D);
double e = -mb.Dot(D);
double det = a * c - b * b;
double s = b * e - c * d;
double t = b * d - a * e;
if (s >= 0 && s <= det &&
t >= 0 && t <= det)
{
return(true);
}
return(false);
}
public static Geometry GetGeometry(int p, int q, int r)
{
double t1 = Math.Sin(PiOverNSafe(p)) * Math.Sin(PiOverNSafe(r));
double t2 = Math.Cos(PiOverNSafe(q));
if (Tolerance.Equal(t1, t2))
{
return(Geometry.Euclidean);
}
if (Tolerance.GreaterThan(t1, t2))
{
return(Geometry.Spherical);
}
return(Geometry.Hyperbolic);
}
public int Compare(Vector3D v1, Vector3D v2)
{
const int less = -1;
const int greater = 1;
if (Tolerance.LessThan(v1.X, v2.X))
{
return(less);
}
if (Tolerance.GreaterThan(v1.X, v2.X))
{
return(greater);
}
if (Tolerance.LessThan(v1.Y, v2.Y))
{
return(less);
}
if (Tolerance.GreaterThan(v1.Y, v2.Y))
{
return(greater);
}
if (Tolerance.LessThan(v1.Z, v2.Z))
{
return(less);
}
if (Tolerance.GreaterThan(v1.Z, v2.Z))
{
return(greater);
}
if (Tolerance.LessThan(v1.W, v2.W))
{
return(less);
}
if (Tolerance.GreaterThan(v1.W, v2.W))
{
return(greater);
}
// Making it here means we are equal.
return(0);
}
public static int IntersectionCircleCircle(Circle c1, Circle c2, out Vector3D p1, out Vector3D p2)
{
p1 = new Vector3D();
p2 = new Vector3D();
// A useful page describing the cases in this function is:
// http://ozviz.wasp.uwa.edu.au/~pbourke/geometry/2circle/
p1.Empty();
p2.Empty();
// Vector and distance between the centers.
Vector3D v = c2.Center - c1.Center;
double d = v.Abs();
double r1 = c1.Radius;
double r2 = c2.Radius;
// Circle centers coincident.
if (Tolerance.Zero(d))
{
if (Tolerance.Equal(r1, r2))
{
return(-1);
}
else
{
return(0);
}
}
// We should be able to normalize at this point.
if (!v.Normalize())
{
Debug.Assert(false);
return(0);
}
// No intersection points.
// First case is disjoint circles.
// Second case is where one circle contains the other.
if (Tolerance.GreaterThan(d, r1 + r2) ||
Tolerance.LessThan(d, Math.Abs(r1 - r2)))
{
return(0);
}
// One intersection point.
if (Tolerance.Equal(d, r1 + r2) ||
Tolerance.Equal(d, Math.Abs(r1 - r2)))
{
p1 = c1.Center + v * r1;
return(1);
}
// There must be two intersection points.
p1 = p2 = v * r1;
double temp = (r1 * r1 - r2 * r2 + d * d) / (2 * d);
double angle = Math.Acos(temp / r1);
Debug.Assert(!Tolerance.Zero(angle) && !Tolerance.Equal(angle, Math.PI));
p1.RotateXY(angle);
p2.RotateXY(-angle);
p1 += c1.Center;
p2 += c1.Center;
return(2);
}
/// <summary>
/// Returns intersection points between a circle and a great circle.
/// There may be 0, 1, or 2 intersection points.
/// Returns false if the circle is the same as gc.
/// </summary>
static bool IntersectionCircleGC(Circle3D c, Vector3D gc, List <Vector3D> iPoints)
{
double radiusCosAngle = CosAngle(c.Normal, c.PointOnCircle);
double radiusAngle = Math.Acos(radiusCosAngle);
double radius = radiusAngle; // Since sphere radius is 1.
// Find the great circle perpendicular to gc, and through the circle center.
Vector3D gcPerp = c.Normal.Cross(gc);
if (!gcPerp.Normalize())
{
// Circles are parallel => Zero or infinity intersections.
if (Tolerance.Equal(radius, Math.PI / 2))
{
return(false);
}
return(true);
}
// Calculate the offset angle from the circle normal to the gc normal.
double offsetAngle = c.Normal.AngleTo(gc);
if (Tolerance.GreaterThan(offsetAngle, Math.PI / 2))
{
gc *= -1;
offsetAngle = c.Normal.AngleTo(gc);
}
double coAngle = Math.PI / 2 - offsetAngle;
// No intersections.
if (radiusAngle < coAngle)
{
return(true);
}
// Here is the perpendicular point on the great circle.
Vector3D pointOnGC = c.Normal;
pointOnGC.RotateAboutAxis(gcPerp, coAngle);
// 1 intersection.
if (Tolerance.Equal(radiusAngle, coAngle))
{
iPoints.Add(pointOnGC);
return(true);
}
// 2 intersections.
// Spherical pythagorean theorem
// http://en.wikipedia.org/wiki/Pythagorean_theorem#Spherical_geometry
// We know the hypotenuse and one side. We need the third leg.
// We do this calculation on a unit sphere, to get the result as a normalized cosine of an angle.
double sideCosA = radiusCosAngle / Math.Cos(coAngle);
double rot = Math.Acos(sideCosA);
Vector3D i1 = pointOnGC, i2 = pointOnGC;
i1.RotateAboutAxis(gc, rot);
i2.RotateAboutAxis(gc, -rot);
iPoints.Add(i1);
iPoints.Add(i2);
Circle3D test = new Circle3D {
Normal = gc, Center = new Vector3D(), Radius = 1
};
return(true);
}