/// <summary>
/// Calculating an intersection between a Face and a LineSegment
/// </summary>
/// <param name="F1">the Face3D</param>
/// <param name="LS">the Line Segment</param>
/// <param name="intPoint">the intersection point</param>
/// <returns></returns>
public static bool intersect(Face3D F1, LineSegment3D LS, out List <Point3D> intPoints)
{
intPoints = new List <Point3D>();
Point3D intPt = new Point3D();
// There are 2 possible cases: 1. Line punching the face, 2. Line lies on the same plane as the face
// Test whether the line is on the same plane
if (MathUtils.equalTol(Vector3D.DotProduct(F1.basePlane.normalVector, LS.baseLine.direction), 0.0, MathUtils.defaultTol))
{
// test whether at least one point of the segment is on the plane
if (!Plane3D.pointOnPlane(F1.basePlane, LS.startPoint))
{
return(false); // line is parallel with the plane, no intersection
}
LineSegmentIntersectEnum mode = LineSegmentIntersectEnum.Undefined;
for (int i = 0; i < F1.boundaries.Count; i++)
{
bool st = LineSegment3D.intersect(F1.boundaries[i], LS, out intPt, out mode);
if (st)
{
intPoints.Add(intPt);
}
}
if (intPoints.Count > 0)
{
return(true);
}
return(false);
}
else
{
bool res = Plane3D.PLintersect(F1.basePlane, LS, out intPt);
if (res == false)
{
return(false); // intersection occurs beyond the line segment
}
// There is intersection point, test whether the point in within (inside the boundary of the face boundaries
res = inside(F1, intPt);
if (res)
{
intPoints.Add(intPt);
return(true);
}
}
return(false);
}
/// <summary>
/// Test a point is inside a face
/// </summary>
/// <param name="F1"></param>
/// <param name="P1"></param>
/// <returns></returns>
public static bool inside(Face3D F1, Point3D P1)
{
if (!Plane3D.pointOnPlane(F1.basePlane, P1))
{
return(false); // Point is not on a plane
}
// test Point inside a Face
// Need to project the plane to 2D (XY-, YZ-, or XZ- plane). It should work well with convex face (esp. triangles and rectangles we will deal with mostly)
double maxDim = Double.MinValue;
int DimttoZero = 0;
// First test whether the plane is already axis-aligned (in this case we can just remove the appropriate axis)
if (MathUtils.equalTol(F1.basePlane.normalVector.Y, 0.0, MathUtils.defaultTol) && MathUtils.equalTol(F1.basePlane.normalVector.Z, 0.0, MathUtils.defaultTol))
{
DimttoZero = 0; // Ignore X, project to Y-Z plane
}
else if (MathUtils.equalTol(F1.basePlane.normalVector.X, 0.0, MathUtils.defaultTol) && MathUtils.equalTol(F1.basePlane.normalVector.Z, 0.0, MathUtils.defaultTol))
{
DimttoZero = 1; // Ignore Y, project to X-Z plane
}
else if (MathUtils.equalTol(F1.basePlane.normalVector.X, 0.0, MathUtils.defaultTol) && MathUtils.equalTol(F1.basePlane.normalVector.Y, 0.0, MathUtils.defaultTol))
{
DimttoZero = 2; // Ignore Z, project to X-Y plane
}
else
{
if (maxDim < Math.Abs(F1.basePlane.normalVector.X))
{
maxDim = Math.Abs(F1.basePlane.normalVector.X);
DimttoZero = 0;
}
if (maxDim < Math.Abs(F1.basePlane.normalVector.Y))
{
maxDim = Math.Abs(F1.basePlane.normalVector.Y);
DimttoZero = 1;
}
if (maxDim < Math.Abs(F1.basePlane.normalVector.Z))
{
maxDim = Math.Abs(F1.basePlane.normalVector.Z);
DimttoZero = 2;
}
}
// We ignore the largest component, which means the least impact to the projection plane
List <Point3D> projVert = new List <Point3D>();
Point3D projIntP = new Point3D(P1.X, P1.Y, P1.Z);
Point3D rayEndP = new Point3D(P1.X, P1.Y, P1.Z);
if (DimttoZero == 0)
{
for (int i = 0; i < F1.vertices.Count; i++)
{
projVert.Add(new Point3D(0.0, F1.vertices[i].Y, F1.vertices[i].Z));
}
projIntP.X = 0.0;
rayEndP.X = 0.0;
if (Octree.WorldBB == null)
{
rayEndP.Y += Point3D.distance(F1.containingBB.URT, F1.containingBB.LLB) * 1000;
}
else
{
rayEndP.Y += Octree.WorldBB.extent * 2;
}
}
else if (DimttoZero == 1)
{
for (int i = 0; i < F1.vertices.Count; i++)
{
projVert.Add(new Point3D(F1.vertices[i].X, 0.0, F1.vertices[i].Z));
}
projIntP.Y = 0.0;
rayEndP.Y = 0.0;
//rayEndP.Z += Point3D.distance(F1.containingBB.URT, F1.containingBB.LLB) * 2;
if (Octree.WorldBB == null)
{
rayEndP.X += Point3D.distance(F1.containingBB.URT, F1.containingBB.LLB) * 2; // Use X axis for the ray
}
else
{
rayEndP.X += Octree.WorldBB.extent * 2;
}
}
else if (DimttoZero == 2)
{
for (int i = 0; i < F1.vertices.Count; i++)
{
projVert.Add(new Point3D(F1.vertices[i].X, F1.vertices[i].Y, 0.0));
}
projIntP.Z = 0.0;
rayEndP.Z = 0.0;
if (Octree.WorldBB == null)
{
rayEndP.X += Point3D.distance(F1.containingBB.URT, F1.containingBB.LLB) * 2;
}
else
{
rayEndP.X += Octree.WorldBB.extent * 2;
}
}
Face3D projFace = new Face3D(projVert);
// define a ray from the intersection point along the X-axis of the projected plane by using long enough line segment beginning from the point, using
// max extent of the face containingBB *2
LineSegment3D ray = new LineSegment3D(projIntP, rayEndP);
// Now do intersection between the ray and all the segments of the face. Odd number indicates the point is inside
// 4 rules to follow:
// 1. If the segment is upward, exclude the endpoint for intersection (only consider the startpoint)
// 2. If the segment is downward, exclude the startpoint for intersection (only considers the end point)
// 3. Ignore the segment that is horizontal (parallel to the ray)
// 4. ray is always strictly to the right of the Point
int intCount = 0;
Point3D iP = new Point3D();
LineSegmentIntersectEnum mod = LineSegmentIntersectEnum.Undefined;
for (int i = 0; i < projFace.boundaries.Count; i++)
{
if (ray.baseLine.direction == projFace.boundaries[i].baseLine.direction)
{
continue; //ignore segment that is parallel to the ray (rule #3)
}
Point3D pointToExclude = new Point3D();
if (DimttoZero == 0 || DimttoZero == 1)
{
// for both X-Z and Y-Z plane (Z as vertical axis)
if (projFace.boundaries[i].startPoint.Z <= ray.startPoint.Z && projFace.boundaries[i].endPoint.Z > ray.startPoint.Z)
{
pointToExclude = projFace.boundaries[i].endPoint; // Rule #1
}
else if (projFace.boundaries[i].startPoint.Z > ray.startPoint.Z && projFace.boundaries[i].endPoint.Z <= ray.startPoint.Z)
{
pointToExclude = projFace.boundaries[i].startPoint; // Rule #2
}
}
else
{
// for X-Y plane (Y as vertical axis)
if (projFace.boundaries[i].startPoint.Y <= ray.startPoint.Y && projFace.boundaries[i].endPoint.Y > ray.startPoint.Y)
{
pointToExclude = projFace.boundaries[i].endPoint; // Rule #1
}
else if (projFace.boundaries[i].startPoint.Y > ray.startPoint.Y && projFace.boundaries[i].endPoint.Y <= ray.startPoint.Y)
{
pointToExclude = projFace.boundaries[i].startPoint; // Rule #2
}
}
// In the evaluation of the number of intersection between a ray and a face, we will ignore the intersection point that is equal to the rule #2 or #3
if (LineSegment3D.intersect(ray, projFace.boundaries[i], out iP, out mod) && (iP != pointToExclude))
{
intCount++;
}
}
if (intCount % 2 == 1)
{
return(true);
}
return(false);
}
