/// <summary>
/// Attempts to encapsulate a cloud of points within a capsule. This may not produce an optimal or exact fit. The results
/// are approximate.
/// </summary>
/// <param name="points">The list of points with which to build an enclosing capsule.</param>
/// <param name="capsule">Returns the capsule containing all points.</param>
public static void Fit(IList <Vector3> points, out Capsule capsule)
{
capsule = new Capsule();
Vector3 axis, axisNeg;
GeometryHelper.ComputeMaxSpreadAxis(points, out axis);
Vector3.Negate(ref axis, out axisNeg);
if (axis.LengthSquared() < Constants.Epsilon)
{
return;
}
GeometryHelper.ComputeExtremePoint(points, ref axis, out capsule.P2);
GeometryHelper.ComputeExtremePoint(points, ref axisNeg, out capsule.P1);
Segment s = new Segment(capsule.P1, capsule.P2);
for (int i = 0; i < points.Count; i++)
{
var p = points[i];
float x = s.DistanceSquaredTo(ref p);
if (x > capsule.Radius)
{
capsule.Radius = x;
}
}
capsule.Radius = (float)Math.Sqrt(capsule.Radius);
Vector3.Multiply(ref axis, capsule.Radius, out axis);
Vector3.Negate(ref axis, out axisNeg);
Vector3.Add(ref capsule.P1, ref axis, out capsule.P1);
Vector3.Add(ref capsule.P2, ref axisNeg, out capsule.P2);
}
/// <summary>
/// Determines whether the specified point, when projected onto the face plane of the polyhedron, is within the face.
/// </summary>
/// <param name="faceIndex">The index of the face in which to check containment.</param>
/// <param name="p">The point in world-space that is either inside or outside the face.</param>
/// <param name="inclusive">Indicates whether points on the edge or vertices of a face should be considered within the face.</param>
/// <returns>Returns a value indicating whether the point is contained within the face.</returns>
public bool IsPointOnFace(int faceIndex, ref Vector3 p, bool inclusive)
{
int[] face = Face(faceIndex);
int low = 0, high = face.Length;
Vector3 normal;
FaceNormal(faceIndex, out normal);
Segment s;
Vector3 p0;
World(face[0], out p0);
do
{
int mid = (low + high) / 2;
Vector3 p1;
World(face[mid], out p1);
s = new Segment(p0, p1);
if ((mid == face.Length - 1 || mid == 1) &&
s.DistanceSquaredTo(ref p) < Constants.Epsilon)
{
return(inclusive);
}
if (GeometryHelper.IsTriangleCcw(ref normal, ref s.P1, ref s.P2, ref p))
{
low = mid;
}
else
{
high = mid;
}
}while (low + 1 < high);
if (low == 0 || high == face.Length)
{
return(false);
}
World(face[low], out s.P1);
World(face[high], out s.P2);
return(GeometryHelper.IsTriangleCcw(ref normal, ref s.P1, ref s.P2, ref p) ||
(inclusive && s.DistanceSquaredTo(ref p) < Constants.Epsilon));
}
/// <summary>
/// Attempts to encapsulate a cloud of points within a capsule. This may not produce an optimal or exact fit. The results
/// are approximate.
/// </summary>
/// <param name="points">The list of points with which to build an enclosing capsule.</param>
/// <param name="capsule">Returns the capsule containing all points.</param>
public static void Fit(IList<Vector3> points, out Capsule capsule)
{
capsule = new Capsule();
Vector3 axis, axisNeg;
GeometryHelper.ComputeMaxSpreadAxis(points, out axis);
Vector3.Negate(ref axis, out axisNeg);
if (axis.LengthSquared() < Constants.Epsilon)
return;
GeometryHelper.ComputeExtremePoint(points, ref axis, out capsule.P2);
GeometryHelper.ComputeExtremePoint(points, ref axisNeg, out capsule.P1);
Segment s = new Segment(capsule.P1, capsule.P2);
for (int i = 0; i < points.Count; i++)
{
var p = points[i];
float x = s.DistanceSquaredTo(ref p);
if (x > capsule.Radius)
{
capsule.Radius = x;
}
}
capsule.Radius = (float)Math.Sqrt(capsule.Radius);
Vector3.Multiply(ref axis, capsule.Radius, out axis);
Vector3.Negate(ref axis, out axisNeg);
Vector3.Add(ref capsule.P1, ref axis, out capsule.P1);
Vector3.Add(ref capsule.P2, ref axisNeg, out capsule.P2);
}
/// <summary>
/// Determines whether the specified point, when projected onto the face plane of the polyhedron, is within the face.
/// </summary>
/// <param name="faceIndex">The index of the face in which to check containment.</param>
/// <param name="p">The point in world-space that is either inside or outside the face.</param>
/// <param name="inclusive">Indicates whether points on the edge or vertices of a face should be considered within the face.</param>
/// <returns>Returns a value indicating whether the point is contained within the face.</returns>
public bool IsPointOnFace(int faceIndex, ref Vector3 p, bool inclusive)
{
int[] face = Face(faceIndex);
int low = 0, high = face.Length;
Vector3 normal;
FaceNormal(faceIndex, out normal);
Segment s;
Vector3 p0;
World(face[0], out p0);
do
{
int mid = (low + high) / 2;
Vector3 p1;
World(face[mid], out p1);
s = new Segment(p0, p1);
if ((mid == face.Length - 1 || mid == 1) &&
s.DistanceSquaredTo(ref p) < Constants.Epsilon)
{
return inclusive;
}
if (GeometryHelper.IsTriangleCcw(ref normal, ref s.P1, ref s.P2, ref p))
{
low = mid;
}
else
{
high = mid;
}
}
while (low + 1 < high);
if (low == 0 || high == face.Length) return false;
World(face[low], out s.P1);
World(face[high], out s.P2);
return GeometryHelper.IsTriangleCcw(ref normal, ref s.P1, ref s.P2, ref p) ||
(inclusive && s.DistanceSquaredTo(ref p) < Constants.Epsilon);
}
