| public static IntersectionLineLine ( Vector3D p1, Vector3D p2, Vector3D p3, Vector3D p4, Vector3D &intersection ) : int | ||
| p1 | Vector3D | |
| p2 | Vector3D | |
| p3 | Vector3D | |
| p4 | Vector3D | |
| intersection | Vector3D | |
| Résultat | int | |
/// <summary>
/// Construct a circle from 3 points
/// </summary>
/// <returns>false if the construction failed (if we are a line).</returns>
public bool From3Points(Vector3D p1, Vector3D p2, Vector3D p3)
{
Reset();
// Check for any infinite points, in which case we are a line.
// I'm not sure these checks are smart, since our IsInfinite check is so inclusive,
// but Big Chop puzzle doesn't work if we don't do this.
// ZZZ - Still, I need to think on this more.
if (Infinity.IsInfinite(p1))
{
this.From2Points(p2, p3);
return(false);
}
else if (Infinity.IsInfinite(p2))
{
this.From2Points(p1, p3);
return(false);
}
else if (Infinity.IsInfinite(p3))
{
this.From2Points(p1, p2);
return(false);
}
/* Some links
* http://mathforum.org/library/drmath/view/54323.html
* http://delphiforfun.org/Programs/Math_Topics/circle_from_3_points.htm
* There is lots of info out there about solving via equations,
* but as with other code in this project, I wanted to use geometrical constructions. */
// Midpoints.
Vector3D m1 = (p1 + p2) / 2;
Vector3D m2 = (p1 + p3) / 2;
// Perpendicular bisectors.
Vector3D b1 = (p2 - p1) / 2;
Vector3D b2 = (p3 - p1) / 2;
b1.Normalize();
b2.Normalize();
b1.Rotate90();
b2.Rotate90();
Vector3D newCenter;
int found = Euclidean2D.IntersectionLineLine(m1, m1 + b1, m2, m2 + b2, out newCenter);
Center = newCenter;
if (0 == found)
{
// The points are collinear, so we are a line.
From2Points(p1, p2);
return(false);
}
Radius = (p1 - Center).Abs();
Debug.Assert(Tolerance.Equal(Radius, (p2 - Center).Abs()));
Debug.Assert(Tolerance.Equal(Radius, (p3 - Center).Abs()));
return(true);
}
public bool Intersects(Segment s)
{
Vector3D i1 = Vector3D.DneVector(), i2 = Vector3D.DneVector();
int numInt = 0;
if (SegmentType.Arc == Type)
{
if (SegmentType.Arc == s.Type)
{
numInt = Euclidean2D.IntersectionCircleCircle(Circle, s.Circle, out i1, out i2);
}
else
{
numInt = Euclidean2D.IntersectionLineCircle(P1, P2, s.Circle, out i1, out i2);
}
}
else
{
if (SegmentType.Arc == s.Type)
{
numInt = Euclidean2D.IntersectionLineCircle(s.P1, s.P2, Circle, out i1, out i2);
}
else
{
numInt = Euclidean2D.IntersectionLineLine(P1, P2, s.P1, s.P2, out i1);
}
}
// -1 can denote conincident segments (I'm not consistent in the impls above :/),
// and we are not going to include those for now.
if (numInt <= 0)
{
return(false);
}
if (numInt > 0)
{
if (IsPointOn(i1) && s.IsPointOn(i1))
{
return(true);
}
}
if (numInt > 1)
{
if (IsPointOn(i2) && s.IsPointOn(i2))
{
return(true);
}
}
return(false);
}
// Get the intersection points with a segment.
// Returns null if the segment is an arc coincident with the circle (infinite number of intersection points).
public Vector3D[] GetIntersectionPoints(Segment segment)
{
Vector3D p1, p2;
int result;
// Are we a line?
if (this.IsLine)
{
if (SegmentType.Arc == segment.Type)
{
Circle tempCircle = segment.Circle;
result = Euclidean2D.IntersectionLineCircle(this.P1, this.P2, tempCircle, out p1, out p2);
}
else
{
result = Euclidean2D.IntersectionLineLine(this.P1, this.P2, segment.P1, segment.P2, out p1);
p2 = Vector3D.DneVector();
}
}
else
{
if (SegmentType.Arc == segment.Type)
{
Circle tempCircle = segment.Circle;
result = Euclidean2D.IntersectionCircleCircle(tempCircle, this, out p1, out p2);
}
else
{
result = Euclidean2D.IntersectionLineCircle(segment.P1, segment.P2, this, out p1, out p2);
}
}
if (-1 == result)
{
return(null);
}
List <Vector3D> ret = new List <Vector3D>();
if (result >= 1 && segment.IsPointOn(p1))
{
ret.Add(p1);
}
if (result >= 2 && segment.IsPointOn(p2))
{
ret.Add(p2);
}
return(ret.ToArray());
}
/// <summary>
/// Returns the 6 simplex edges in the UHS model.
/// </summary>
public static H3.Cell.Edge[] SimplexEdgesUHS(int p, int q, int r)
{
// Only implemented for honeycombs with hyperideal cells right now.
if (!(Geometry2D.GetGeometry(p, q) == Geometry.Hyperbolic))
{
throw new System.NotImplementedException();
}
Sphere[] simplex = SimplexCalcs.Mirrors(p, q, r, moveToBall: false);
Circle[] circles = simplex.Select(s => H3Models.UHS.IdealCircle(s)).ToArray();
Vector3D[] defPoints = new Vector3D[6];
Vector3D dummy;
Euclidean2D.IntersectionLineCircle(circles[1].P1, circles[1].P2, circles[0], out defPoints[0], out dummy);
Euclidean2D.IntersectionLineCircle(circles[2].P1, circles[2].P2, circles[0], out defPoints[1], out dummy);
Euclidean2D.IntersectionLineCircle(circles[1].P1, circles[1].P2, circles[3], out defPoints[2], out dummy);
Euclidean2D.IntersectionLineCircle(circles[2].P1, circles[2].P2, circles[3], out defPoints[3], out dummy);
Circle3D c = simplex[0].Intersection(simplex[3]);
Vector3D normal = c.Normal;
normal.RotateXY(Math.PI / 2);
Vector3D intersection;
double height, off;
Euclidean2D.IntersectionLineLine(c.Center, c.Center + normal, circles[1].P1, circles[1].P2, out intersection);
off = (intersection - c.Center).Abs();
height = Math.Sqrt(c.Radius * c.Radius - off * off);
intersection.Z = height;
defPoints[4] = intersection;
Euclidean2D.IntersectionLineLine(c.Center, c.Center + normal, circles[2].P1, circles[2].P2, out intersection);
off = (intersection - c.Center).Abs();
height = Math.Sqrt(c.Radius * c.Radius - off * off);
intersection.Z = height;
defPoints[5] = intersection;
// Hyperideal vertex too?
bool order = false;
H3.Cell.Edge[] edges = null;
if (Geometry2D.GetGeometry(q, r) == Geometry.Hyperbolic)
{
edges = new H3.Cell.Edge[]
{
new H3.Cell.Edge(new Vector3D(), new Vector3D(0, 0, 10)),
new H3.Cell.Edge(defPoints[4], defPoints[5], order),
new H3.Cell.Edge(defPoints[0], defPoints[4], order),
new H3.Cell.Edge(defPoints[1], defPoints[5], order),
new H3.Cell.Edge(defPoints[2], defPoints[4], order),
new H3.Cell.Edge(defPoints[3], defPoints[5], order),
};
}
else
{
Vector3D vPointUHS = H3Models.BallToUHS(VertexPointBall(p, q, r));
defPoints[0] = defPoints[1] = vPointUHS;
edges = new H3.Cell.Edge[]
{
new H3.Cell.Edge(vPointUHS, new Vector3D(0, 0, 10)),
new H3.Cell.Edge(defPoints[4], defPoints[5], order),
new H3.Cell.Edge(defPoints[0], defPoints[4], order),
new H3.Cell.Edge(defPoints[1], defPoints[5], order),
new H3.Cell.Edge(defPoints[2], defPoints[4], order),
new H3.Cell.Edge(defPoints[3], defPoints[5], order),
};
}
return(edges);
}
