/// <summary>
/// Testing a point inside a polyhedron is similar with the 2D version of a point inside a polygon by testing intersection between a ray starting from the point.
/// If the number of intersection is odd the point is inside. In 3D the intersection is against the Faces
/// </summary>
/// <param name="polyH"></param>
/// <param name="aPoint"></param>
/// <returns></returns>
public static bool inside(Polyhedron polyH, Point3D aPoint)
{
double extent = 0;
if (Octree.WorldBB == null)
{
extent = Point3D.distance(polyH.boundingBox.LLB, polyH.boundingBox.URT);
}
else
{
extent = Octree.WorldBB.extent;
}
// define a ray using linesegment from the point toward and along +X-axis with 2*the extent of the World BB to ensure ray is always long enough
LineSegment3D ray = new LineSegment3D(aPoint, new Point3D(aPoint.X + 2 * extent, aPoint.Y, aPoint.Z));
List <Face3D> reducedList = Face3D.inclFacesBeyondAxis(polyH.Faces, new Plane3D(aPoint, new Vector3D(1.0, 0.0, 0.0))); // beyond YZ plane
List <Point3D> corners = new List <Point3D>();
corners.Add(aPoint);
corners.Add(aPoint);
BoundingBox3D bound = new BoundingBox3D(corners);
if (reducedList.Count > 0)
{
reducedList = Face3D.exclFacesOutsideOfBound(reducedList, bound, 0x011); // reduce list on Y and Z both direction
}
if (reducedList.Count == 0)
{
return(false); // no faces left, either they are all on the left or they are all on the right
}
int iCount = 0;
for (int i = 0; i < reducedList.Count; i++)
{
List <Point3D> intPts = new List <Point3D>();
if (Face3D.intersect(reducedList[i], ray, out intPts))
{
iCount++;
}
}
if ((iCount % 2) == 1)
{
return(true);
}
return(false);
}
/// <summary>
/// To determine that a line segment is inside (completely inside) of a polyhedron, it must satisfy the following:
/// 1. both end points are inside the polyhedron
/// 2. There no intersection between the segment and the polyhedron
/// </summary>
/// <param name="polyH"></param>
/// <param name="lineS"></param>
/// <returns></returns>
public static bool inside(Polyhedron polyH, LineSegment3D lineS)
{
// reducing the face candidate list is less expensive than inside test, do it first
Point3D leftX = new Point3D();
Point3D rightX = new Point3D();
leftX.X = lineS.startPoint.X < lineS.endPoint.X ? lineS.startPoint.X : lineS.endPoint.X;
rightX.X = lineS.startPoint.X < lineS.endPoint.X ? lineS.endPoint.X : lineS.startPoint.X;
List <Face3D> reducedList = Face3D.inclFacesBeyondAxis(polyH.Faces, new Plane3D(leftX, new Vector3D(1.0, 0.0, 0.0)));
// reducedList = Face3D.exclFacesBeyondAxis(reducedList, rightX); // cannot remove this otherwise inside test for StartPoint may not be correct!!!
List <Point3D> corners = new List <Point3D>();
corners.Add(lineS.startPoint);
corners.Add(lineS.endPoint);
BoundingBox3D bound = new BoundingBox3D(corners);
if (reducedList.Count > 0)
{
reducedList = Face3D.exclFacesOutsideOfBound(reducedList, bound, 0x011); // reduce list on Y and Z both direction
}
if (reducedList.Count == 0)
{
return(false); // no faces left, either they are all on the left or they are all on the right
}
// inside test for both segment ends. Test one by one so that we can exit when any one of them are not inside
if (!inside(polyH, lineS.startPoint))
{
return(false);
}
if (!inside(polyH, lineS.endPoint))
{
return(false);
}
// Now test whether there is any intersection. If there is, the segment is not completely inside
for (int i = 0; i < reducedList.Count; i++)
{
List <Point3D> iPoints = new List <Point3D>();
if (Face3D.intersect(reducedList[i], lineS, out iPoints))
{
return(false);
}
}
return(true);
}
