/// <summary>
/// Testing intersection between a line segment and a polyhedron and return ALL intersection points
/// </summary>
/// <param name="polyH">Polyhedron</param>
/// <param name="lineS">Line segment</param>
/// <param name="intPoints">List of intersection points</param>
/// <returns></returns>
public static bool intersect(Polyhedron polyH, LineSegment3D lineS, out List <Point3D> intPoints)
{
List <Point3D> iPoints = new List <Point3D>();
intPoints = iPoints;
List <Point3D> corners = new List <Point3D>();
corners.Add(lineS.startPoint);
corners.Add(lineS.endPoint);
BoundingBox3D bound = new BoundingBox3D(corners);
List <Face3D> reducedList = Face3D.exclFacesOutsideOfBound(polyH.Faces, bound, 0x111);
if (reducedList.Count == 0)
{
return(false); // no faces left, either they are all on the left or they are all on the right
}
// Now test whether there is any intersection. It needs to complete the test with entire faces to collect the intersection points
for (int i = 0; i < reducedList.Count; i++)
{
List <Point3D> iPts = new List <Point3D>();
if (Face3D.intersect(reducedList[i], lineS, out iPts))
{
for (int j = 0; j < iPts.Count; j++)
{
iPoints.Add(iPts[j]);
}
}
}
if (iPoints.Count > 0)
{
return(true);
}
return(false);
}
/// <summary>
/// Touch check between 2 faces. Currently only returns true/false. Should be improved with a new face that overlap between the 2 input faces
/// </summary>
/// <param name="F1">Face 1</param>
/// <param name="F2">Face 2</param>
/// <returns></returns>
public static bool touch(Face3D F1, Face3D F2)
{
if (Vector3D.Parallels(F1._basePlane.normalVector, F2._basePlane.normalVector))
{
// test for any point inside another face
for (int i = 0; i < F2._vertices.Count; i++)
{
if (Face3D.inside(F1, F2._vertices[i]))
{
return(true);
}
}
for (int i = 0; i < F1._vertices.Count; i++)
{
if (Face3D.inside(F2, F1._vertices[i]))
{
return(true);
}
}
// if still not returning true, test whether the edges intersect
List <Point3D> intPoints = new List <Point3D>();
for (int i = 0; i < F2.boundaries.Count; ++i)
{
if (Face3D.intersect(F1, F2.boundaries[i], out intPoints))
{
return(true);
}
}
}
return(false);
}
/// <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);
}
/// <summary>
/// Test whether a Face (bounded plane) intersects with a plane
/// </summary>
/// <param name="P1">Plane</param>
/// <param name="F1">Face</param>
/// <param name="intersectingLine">Resulting intercting linesegment (bounded)</param>
/// <returns></returns>
public static bool PPintersect(Plane3D P1, Face3D F1, out LineSegment3D intersectingLine)
{
Line3D intLine = new Line3D();
LineSegment3D ls = new LineSegment3D(new Point3D(0.0, 0.0, 0.0), new Point3D(1.0, 1.0, 1.0));
intersectingLine = ls;
// Intersect operation: get the intersection (unbounded) line
if (!PPintersect(P1, F1.basePlane, out intLine))
{
return(false);
}
// Now needs to check get the segment by getting intersecting points between the line and the Face boundaries
List <Point3D> intPts = new List <Point3D>();
// Use line segment that is large enough to ensure it covers the extent of the face
//double extent = Point3D.distance(F1.boundingBox.LLB, F1.boundingBox.URT) * 10; // Bug: NOT big enough for some cases!, use worldBB extent
double extent;
if (Octree.WorldBB == null)
{
extent = 1000000000;
}
else
{
extent = Octree.WorldBB.extent * 10;
}
LineSegment3D intLS = new LineSegment3D(new Point3D(intLine.point - (intLine.direction * extent)), new Point3D(intLine.point + (intLine.direction * extent)));
bool res = Face3D.intersect(F1, intLS, out intPts);
if (res)
{
intersectingLine.startPoint = intPts[0];
intersectingLine.endPoint = intPts[intPts.Count - 1];
return(true);
}
return(false);
}
/// <summary>
/// Test intersection between a polyhedron and a face. There is optmization applied for axis-aligned face (useful for Octree cells as they are all axis aligned)
/// </summary>
/// <param name="polyH">The Polyhedron</param>
/// <param name="face">The face to test the intersection</param>
/// <returns>true=intersected; false otherwise</returns>
public static bool intersect(Polyhedron polyH, Face3D face)
{
List <Face3D> faceList = new List <Face3D>();
BoundingBox3D bound = new BoundingBox3D(face.vertices);
faceList = Face3D.exclFacesOutsideOfBound(polyH.Faces, bound, 0x111);
if (faceList.Count == 0)
{
return(false); // There is no face remaining to test, return false
}
for (int i = 0; i < faceList.Count; i++)
{
FaceIntersectEnum mode;
LineSegment3D intL = new LineSegment3D(new Point3D(), new Point3D());
bool status = Face3D.intersect(face, faceList[i], out intL, out mode);
if (status == true)
{
return(true); // return true as soon as an intersection is detected
}
}
return(false);
}
/// <summary>
/// Testing intersection between a line segment and a polyhedron only. It stops at the first intersection
/// </summary>
/// <param name="polyH">polyhedron</param>
/// <param name="lineS">Line segment</param>
/// <returns></returns>
public static bool intersect(Polyhedron polyH, LineSegment3D lineS)
{
List <Point3D> corners = new List <Point3D>();
corners.Add(lineS.startPoint);
corners.Add(lineS.endPoint);
BoundingBox3D bound = new BoundingBox3D(corners);
List <Face3D> reducedList = Face3D.exclFacesOutsideOfBound(polyH.Faces, bound, 0x111);
if (reducedList.Count == 0)
{
return(false); // no faces left, either they are all on the left or they are all on the right
}
// Now test whether there is any intersection.
for (int i = 0; i < reducedList.Count; i++)
{
List <Point3D> iPoints = new List <Point3D>();
if (Face3D.intersect(reducedList[i], lineS, out iPoints))
{
return(true);
}
}
return(false);
}