/**
* Perform an intersection between Plane and Line, storing intersection point
* in reference q. Function returns true if intersection has been found or
* false otherwise.
*/
public static bool Intersect(Plane pl, Line ln, out Vector3 q)
{
return(Intersector.Intersect(pl, ln.positionA, ln.positionB, out q));
}
/**
* Perform an intersection between Plane and Triangle. This is a comprehensive function
* which alwo builds a HULL Hirearchy useful for decimation projects. This obviously
* comes at the cost of more complex code and runtime checks, but the returned results
* are much more flexible.
* Results will be filled into the IntersectionResult reference. Check result.isValid()
* for the final results.
*/
public static void Intersect(Plane pl, Triangle tri, IntersectionResult result)
{
// clear the previous results from the IntersectionResult
result.Clear();
// grab local variables for easier access
Vector3 a = tri.positionA;
Vector3 b = tri.positionB;
Vector3 c = tri.positionC;
// check to see which side of the plane the points all
// lay in. SideOf operation is a simple dot product and some comparison
// operations, so these are a very quick checks
SideOfPlane sa = pl.SideOf(a);
SideOfPlane sb = pl.SideOf(b);
SideOfPlane sc = pl.SideOf(c);
// we cannot intersect if the triangle points all fall on the same side
// of the plane. This is an easy early out test as no intersections are possible.
if (sa == sb && sb == sc)
{
return;
}
// detect cases where two points lay straight on the plane, meaning
// that the plane is actually parralel with one of the edges of the triangle
else if ((sa == SideOfPlane.ON && sa == sb) ||
(sa == SideOfPlane.ON && sa == sc) ||
(sb == SideOfPlane.ON && sb == sc))
{
return;
}
// detect cases where one point is on the plane and the other two are on the same side
else if ((sa == SideOfPlane.ON && sb != SideOfPlane.ON && sb == sc) ||
(sb == SideOfPlane.ON && sa != SideOfPlane.ON && sa == sc) ||
(sc == SideOfPlane.ON && sa != SideOfPlane.ON && sa == sb))
{
return;
}
// keep in mind that intersection points are shared by both
// the upper HULL and lower HULL hence they lie perfectly
// on the plane that cut them
Vector3 qa;
Vector3 qb;
// check the cases where the points of the triangle actually lie on the plane itself
// in these cases, there is only going to be 2 triangles, one for the upper HULL and
// the other on the lower HULL
// we just need to figure out which points to accept into the upper or lower hulls.
if (sa == SideOfPlane.ON)
{
// if the point a is on the plane, test line b-c
if (Intersector.Intersect(pl, b, c, out qa))
{
// line b-c intersected, construct out triangles and return approprietly
result.AddIntersectionPoint(qa);
result.AddIntersectionPoint(a);
// our two generated triangles, we need to figure out which
// triangle goes into the UPPER hull and which goes into the LOWER hull
Triangle ta = new Triangle(a, b, qa);
Triangle tb = new Triangle(a, qa, c);
// generate UV coordinates if there is any
if (tri.hasUV)
{
// the computed UV coordinate if the intersection point
Vector2 pq = tri.GenerateUV(qa);
Vector2 pa = tri.uvA;
Vector2 pb = tri.uvB;
Vector2 pc = tri.uvC;
ta.SetUV(pa, pb, pq);
tb.SetUV(pa, pq, pc);
}
// generate Normal coordinates if there is any
if (tri.hasNormal)
{
// the computed Normal coordinate if the intersection point
Vector3 pq = tri.GenerateNormal(qa);
Vector3 pa = tri.normalA;
Vector3 pb = tri.normalB;
Vector3 pc = tri.normalC;
ta.SetNormal(pa, pb, pq);
tb.SetNormal(pa, pq, pc);
}
// generate Tangent coordinates if there is any
if (tri.hasTangent)
{
// the computed Tangent coordinate if the intersection point
Vector4 pq = tri.GenerateTangent(qa);
Vector4 pa = tri.tangentA;
Vector4 pb = tri.tangentB;
Vector4 pc = tri.tangentC;
ta.SetTangent(pa, pb, pq);
tb.SetTangent(pa, pq, pc);
}
// b point lies on the upside of the plane
if (sb == SideOfPlane.UP)
{
result.AddUpperHull(ta).AddLowerHull(tb);
}
// b point lies on the downside of the plane
else if (sb == SideOfPlane.DOWN)
{
result.AddUpperHull(tb).AddLowerHull(ta);
}
}
}
// test the case where the b point lies on the plane itself
else if (sb == SideOfPlane.ON)
{
// if the point b is on the plane, test line a-c
if (Intersector.Intersect(pl, a, c, out qa))
{
// line a-c intersected, construct out triangles and return approprietly
result.AddIntersectionPoint(qa);
result.AddIntersectionPoint(b);
// our two generated triangles, we need to figure out which
// triangle goes into the UPPER hull and which goes into the LOWER hull
Triangle ta = new Triangle(a, b, qa);
Triangle tb = new Triangle(qa, b, c);
// generate UV coordinates if there is any
if (tri.hasUV)
{
// the computed UV coordinate if the intersection point
Vector2 pq = tri.GenerateUV(qa);
Vector2 pa = tri.uvA;
Vector2 pb = tri.uvB;
Vector2 pc = tri.uvC;
ta.SetUV(pa, pb, pq);
tb.SetUV(pq, pb, pc);
}
// generate Normal coordinates if there is any
if (tri.hasNormal)
{
// the computed Normal coordinate if the intersection point
Vector3 pq = tri.GenerateNormal(qa);
Vector3 pa = tri.normalA;
Vector3 pb = tri.normalB;
Vector3 pc = tri.normalC;
ta.SetNormal(pa, pb, pq);
tb.SetNormal(pq, pb, pc);
}
// generate Tangent coordinates if there is any
if (tri.hasTangent)
{
// the computed Tangent coordinate if the intersection point
Vector4 pq = tri.GenerateTangent(qa);
Vector4 pa = tri.tangentA;
Vector4 pb = tri.tangentB;
Vector4 pc = tri.tangentC;
ta.SetTangent(pa, pb, pq);
tb.SetTangent(pq, pb, pc);
}
// a point lies on the upside of the plane
if (sa == SideOfPlane.UP)
{
result.AddUpperHull(ta).AddLowerHull(tb);
}
// a point lies on the downside of the plane
else if (sa == SideOfPlane.DOWN)
{
result.AddUpperHull(tb).AddLowerHull(ta);
}
}
}
// test the case where the c point lies on the plane itself
else if (sc == SideOfPlane.ON)
{
// if the point c is on the plane, test line a-b
if (Intersector.Intersect(pl, a, b, out qa))
{
// line a-c intersected, construct out triangles and return approprietly
result.AddIntersectionPoint(qa);
result.AddIntersectionPoint(c);
// our two generated triangles, we need to figure out which
// triangle goes into the UPPER hull and which goes into the LOWER hull
Triangle ta = new Triangle(a, qa, c);
Triangle tb = new Triangle(qa, b, c);
// generate UV coordinates if there is any
if (tri.hasUV)
{
// the computed UV coordinate if the intersection point
Vector2 pq = tri.GenerateUV(qa);
Vector2 pa = tri.uvA;
Vector2 pb = tri.uvB;
Vector2 pc = tri.uvC;
ta.SetUV(pa, pq, pc);
tb.SetUV(pq, pb, pc);
}
// generate Normal coordinates if there is any
if (tri.hasNormal)
{
// the computed Normal coordinate if the intersection point
Vector3 pq = tri.GenerateNormal(qa);
Vector3 pa = tri.normalA;
Vector3 pb = tri.normalB;
Vector3 pc = tri.normalC;
ta.SetNormal(pa, pq, pc);
tb.SetNormal(pq, pb, pc);
}
// generate Tangent coordinates if there is any
if (tri.hasTangent)
{
// the computed Tangent coordinate if the intersection point
Vector4 pq = tri.GenerateTangent(qa);
Vector4 pa = tri.tangentA;
Vector4 pb = tri.tangentB;
Vector4 pc = tri.tangentC;
ta.SetTangent(pa, pq, pc);
tb.SetTangent(pq, pb, pc);
}
// a point lies on the upside of the plane
if (sa == SideOfPlane.UP)
{
result.AddUpperHull(ta).AddLowerHull(tb);
}
// a point lies on the downside of the plane
else if (sa == SideOfPlane.DOWN)
{
result.AddUpperHull(tb).AddLowerHull(ta);
}
}
}
// at this point, all edge cases have been tested and failed, we need to perform
// full intersection tests against the lines. From this point onwards we will generate
// 3 triangles
else if (sa != sb && Intersector.Intersect(pl, a, b, out qa))
{
// intersection found against a - b
result.AddIntersectionPoint(qa);
// since intersection was found against a - b, we need to check which other
// lines to check (we only need to check one more line) for intersection.
// the line we check against will be the line against the point which lies on
// the other side of the plane.
if (sa == sc)
{
// we likely have an intersection against line b-c which will complete this loop
if (Intersector.Intersect(pl, b, c, out qb))
{
result.AddIntersectionPoint(qb);
// our three generated triangles. Two of these triangles will end
// up on either the UPPER or LOWER hulls.
Triangle ta = new Triangle(qa, b, qb);
Triangle tb = new Triangle(a, qa, qb);
Triangle tc = new Triangle(a, qb, c);
// generate UV coordinates if there is any
if (tri.hasUV)
{
// the computed UV coordinate if the intersection point
Vector2 pqa = tri.GenerateUV(qa);
Vector2 pqb = tri.GenerateUV(qb);
Vector2 pa = tri.uvA;
Vector2 pb = tri.uvB;
Vector2 pc = tri.uvC;
ta.SetUV(pqa, pb, pqb);
tb.SetUV(pa, pqa, pqb);
tc.SetUV(pa, pqb, pc);
}
// generate Normal coordinates if there is any
if (tri.hasNormal)
{
// the computed Normal coordinate if the intersection point
Vector3 pqa = tri.GenerateNormal(qa);
Vector3 pqb = tri.GenerateNormal(qb);
Vector3 pa = tri.normalA;
Vector3 pb = tri.normalB;
Vector3 pc = tri.normalC;
ta.SetNormal(pqa, pb, pqb);
tb.SetNormal(pa, pqa, pqb);
tc.SetNormal(pa, pqb, pc);
}
// generate Tangent coordinates if there is any
if (tri.hasTangent)
{
// the computed Tangent coordinate if the intersection point
Vector4 pqa = tri.GenerateTangent(qa);
Vector4 pqb = tri.GenerateTangent(qb);
Vector4 pa = tri.tangentA;
Vector4 pb = tri.tangentB;
Vector4 pc = tri.tangentC;
ta.SetTangent(pqa, pb, pqb);
tb.SetTangent(pa, pqa, pqb);
tc.SetTangent(pa, pqb, pc);
}
if (sa == SideOfPlane.UP)
{
result.AddUpperHull(tb).AddUpperHull(tc).AddLowerHull(ta);
}
else
{
result.AddLowerHull(tb).AddLowerHull(tc).AddUpperHull(ta);
}
}
}
else
{
// in this scenario, the point a is a "lone" point which lies in either upper
// or lower HULL. We need to perform another intersection to find the last point
if (Intersector.Intersect(pl, a, c, out qb))
{
result.AddIntersectionPoint(qb);
// our three generated triangles. Two of these triangles will end
// up on either the UPPER or LOWER hulls.
Triangle ta = new Triangle(a, qa, qb);
Triangle tb = new Triangle(qa, b, c);
Triangle tc = new Triangle(qb, qa, c);
// generate UV coordinates if there is any
if (tri.hasUV)
{
// the computed UV coordinate if the intersection point
Vector2 pqa = tri.GenerateUV(qa);
Vector2 pqb = tri.GenerateUV(qb);
Vector2 pa = tri.uvA;
Vector2 pb = tri.uvB;
Vector2 pc = tri.uvC;
ta.SetUV(pa, pqa, pqb);
tb.SetUV(pqa, pb, pc);
tc.SetUV(pqb, pqa, pc);
}
// generate Normal coordinates if there is any
if (tri.hasNormal)
{
// the computed Normal coordinate if the intersection point
Vector3 pqa = tri.GenerateNormal(qa);
Vector3 pqb = tri.GenerateNormal(qb);
Vector3 pa = tri.normalA;
Vector3 pb = tri.normalB;
Vector3 pc = tri.normalC;
ta.SetNormal(pa, pqa, pqb);
tb.SetNormal(pqa, pb, pc);
tc.SetNormal(pqb, pqa, pc);
}
// generate Tangent coordinates if there is any
if (tri.hasTangent)
{
// the computed Tangent coordinate if the intersection point
Vector4 pqa = tri.GenerateTangent(qa);
Vector4 pqb = tri.GenerateTangent(qb);
Vector4 pa = tri.tangentA;
Vector4 pb = tri.tangentB;
Vector4 pc = tri.tangentC;
ta.SetTangent(pa, pqa, pqb);
tb.SetTangent(pqa, pb, pc);
tc.SetTangent(pqb, pqa, pc);
}
if (sa == SideOfPlane.UP)
{
result.AddUpperHull(ta).AddLowerHull(tb).AddLowerHull(tc);
}
else
{
result.AddLowerHull(ta).AddUpperHull(tb).AddUpperHull(tc);
}
}
}
}
// if line a-b did not intersect (or the lie on the same side of the plane)
// this simplifies the problem a fair bit. This means we have an intersection
// in line a-c and b-c, which we can use to build a new UPPER and LOWER hulls
// we are expecting both of these intersection tests to pass, otherwise something
// went wrong (float errors? missed a checked case?)
else if (Intersector.Intersect(pl, c, a, out qa) && Intersector.Intersect(pl, c, b, out qb))
{
// in here we know that line a-b actually lie on the same side of the plane, this will
// simplify the rest of the logic. We also have our intersection points
// the computed UV coordinate of the intersection point
result.AddIntersectionPoint(qa);
result.AddIntersectionPoint(qb);
// our three generated triangles. Two of these triangles will end
// up on either the UPPER or LOWER hulls.
Triangle ta = new Triangle(qa, qb, c);
Triangle tb = new Triangle(a, qb, qa);
Triangle tc = new Triangle(a, b, qb);
// generate UV coordinates if there is any
if (tri.hasUV)
{
// the computed UV coordinate if the intersection point
Vector2 pqa = tri.GenerateUV(qa);
Vector2 pqb = tri.GenerateUV(qb);
Vector2 pa = tri.uvA;
Vector2 pb = tri.uvB;
Vector2 pc = tri.uvC;
ta.SetUV(pqa, pqb, pc);
tb.SetUV(pa, pqb, pqa);
tc.SetUV(pa, pb, pqb);
}
// generate Normal coordinates if there is any
if (tri.hasNormal)
{
// the computed Normal coordinate if the intersection point
Vector3 pqa = tri.GenerateNormal(qa);
Vector3 pqb = tri.GenerateNormal(qb);
Vector3 pa = tri.normalA;
Vector3 pb = tri.normalB;
Vector3 pc = tri.normalC;
ta.SetNormal(pqa, pqb, pc);
tb.SetNormal(pa, pqb, pqa);
tc.SetNormal(pa, pb, pqb);
}
// generate Tangent coordinates if there is any
if (tri.hasTangent)
{
// the computed Tangent coordinate if the intersection point
Vector4 pqa = tri.GenerateTangent(qa);
Vector4 pqb = tri.GenerateTangent(qb);
Vector4 pa = tri.tangentA;
Vector4 pb = tri.tangentB;
Vector4 pc = tri.tangentC;
ta.SetTangent(pqa, pqb, pc);
tb.SetTangent(pa, pqb, pqa);
tc.SetTangent(pa, pb, pqb);
}
if (sa == SideOfPlane.UP)
{
result.AddUpperHull(tb).AddUpperHull(tc).AddLowerHull(ta);
}
else
{
result.AddLowerHull(tb).AddLowerHull(tc).AddUpperHull(ta);
}
}
}
/**
* Helper function to split this triangle by the provided plane and store
* the results inside the IntersectionResult structure.
* Returns true on success or false otherwise
*/
public bool Split(Plane pl, IntersectionResult result)
{
Intersector.Intersect(pl, this, result);
return(result.isValid);
}