/**
* 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, ref 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;
}
// 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);
}
}
}
/**
* Slice the gameobject mesh (if any) using the Plane, which will generate
* a maximum of 2 other Meshes.
* This function will recalculate new UV coordinates to ensure textures are applied
* properly.
* Returns null if no intersection has been found or the GameObject does not contain
* a valid mesh to cut.
*/
public static SlicedHull Slice(Mesh sharedMesh, Plane pl, bool genCrossSection = true)
{
if (sharedMesh == null)
{
return(null);
}
Vector3[] verts = sharedMesh.vertices;
Vector2[] uv = sharedMesh.uv;
Vector3[] norm = sharedMesh.normals;
Vector4[] tan = sharedMesh.tangents;
int submeshCount = sharedMesh.subMeshCount;
// each submesh will be sliced and placed in its own array structure
SlicedSubmesh[] slices = new SlicedSubmesh[submeshCount];
// the cross section hull is common across all submeshes
List <Vector3> crossHull = new List <Vector3>();
// we reuse this object for all intersection tests
IntersectionResult result = new IntersectionResult();
// see if we would like to split the mesh using uv, normals and tangents
bool genUV = verts.Length == uv.Length;
bool genNorm = verts.Length == norm.Length;
bool genTan = verts.Length == tan.Length;
// iterate over all the submeshes individually. vertices and indices
// are all shared within the submesh
for (int submesh = 0; submesh < submeshCount; submesh++)
{
int[] indices = sharedMesh.GetTriangles(submesh);
int indicesCount = indices.Length;
SlicedSubmesh mesh = new SlicedSubmesh();
// loop through all the mesh vertices, generating upper and lower hulls
// and all intersection points
for (int index = 0; index < indicesCount; index += 3)
{
int i0 = indices[index + 0];
int i1 = indices[index + 1];
int i2 = indices[index + 2];
Triangle newTri = new Triangle(verts[i0], verts[i1], verts[i2]);
// generate UV if available
if (genUV)
{
newTri.SetUV(uv[i0], uv[i1], uv[i2]);
}
// generate normals if available
if (genNorm)
{
newTri.SetNormal(norm[i0], norm[i1], norm[i2]);
}
// generate tangents if available
if (genTan)
{
newTri.SetTangent(tan[i0], tan[i1], tan[i2]);
}
// slice this particular triangle with the provided
// plane
if (newTri.Split(pl, result))
{
int upperHullCount = result.upperHullCount;
int lowerHullCount = result.lowerHullCount;
int interHullCount = result.intersectionPointCount;
for (int i = 0; i < upperHullCount; i++)
{
mesh.upperHull.Add(result.upperHull[i]);
}
for (int i = 0; i < lowerHullCount; i++)
{
mesh.lowerHull.Add(result.lowerHull[i]);
}
for (int i = 0; i < interHullCount; i++)
{
crossHull.Add(result.intersectionPoints[i]);
}
}
else
{
SideOfPlane side = pl.SideOf(verts[i0]);
if (side == SideOfPlane.UP || side == SideOfPlane.ON)
{
mesh.upperHull.Add(newTri);
}
else
{
mesh.lowerHull.Add(newTri);
}
}
}
// register into the index
slices[submesh] = mesh;
}
return(CreateFrom(slices, CreateFrom(crossHull, pl.normal)));
}
/**
* Slice the gameobject mesh (if any) using the Plane, which will generate
* a maximum of 2 other Meshes.
* This function will recalculate new UV coordinates to ensure textures are applied
* properly.
* Returns null if no intersection has been found or the GameObject does not contain
* a valid mesh to cut.
*/
public static SlicedHull Slice(Mesh sharedMesh, Plane pl, TextureRegion region, int crossIndex)
{
if (sharedMesh == null)
{
return(null);
}
Vector3[] verts = sharedMesh.vertices;
Vector2[] uv = sharedMesh.uv;
Vector3[] norm = sharedMesh.normals;
Vector4[] tan = sharedMesh.tangents;
int submeshCount = sharedMesh.subMeshCount;
// each submesh will be sliced and placed in its own array structure
SlicedSubmesh[] slices = new SlicedSubmesh[submeshCount];
// the cross section hull is common across all submeshes
List <Vector3> crossHull = new List <Vector3>();
// we reuse this object for all intersection tests
IntersectionResult result = new IntersectionResult();
// see if we would like to split the mesh using uv, normals and tangents
bool genUV = verts.Length == uv.Length;
bool genNorm = verts.Length == norm.Length;
bool genTan = verts.Length == tan.Length;
// iterate over all the submeshes individually. vertices and indices
// are all shared within the submesh
for (int submesh = 0; submesh < submeshCount; submesh++)
{
int[] indices = sharedMesh.GetTriangles(submesh);
int indicesCount = indices.Length;
SlicedSubmesh mesh = new SlicedSubmesh();
// loop through all the mesh vertices, generating upper and lower hulls
// and all intersection points
for (int index = 0; index < indicesCount; index += 3)
{
int i0 = indices[index + 0];
int i1 = indices[index + 1];
int i2 = indices[index + 2];
Triangle newTri = new Triangle(verts[i0], verts[i1], verts[i2]);
// generate UV if available
if (genUV)
{
newTri.SetUV(uv[i0], uv[i1], uv[i2]);
}
// generate normals if available
if (genNorm)
{
newTri.SetNormal(norm[i0], norm[i1], norm[i2]);
}
// generate tangents if available
if (genTan)
{
newTri.SetTangent(tan[i0], tan[i1], tan[i2]);
}
// slice this particular triangle with the provided
// plane
if (newTri.Split(pl, result))
{
int upperHullCount = result.upperHullCount;
int lowerHullCount = result.lowerHullCount;
int interHullCount = result.intersectionPointCount;
for (int i = 0; i < upperHullCount; i++)
{
mesh.upperHull.Add(result.upperHull[i]);
}
for (int i = 0; i < lowerHullCount; i++)
{
mesh.lowerHull.Add(result.lowerHull[i]);
}
for (int i = 0; i < interHullCount; i++)
{
crossHull.Add(result.intersectionPoints[i]);
}
}
else
{
SideOfPlane sa = pl.SideOf(verts[i0]);
SideOfPlane sb = pl.SideOf(verts[i1]);
SideOfPlane sc = pl.SideOf(verts[i2]);
SideOfPlane side = SideOfPlane.ON;
if (sa != SideOfPlane.ON)
{
side = sa;
}
if (sb != SideOfPlane.ON)
{
Debug.Assert(side == SideOfPlane.ON || side == sb);
side = sb;
}
if (sc != SideOfPlane.ON)
{
Debug.Assert(side == SideOfPlane.ON || side == sc);
side = sc;
}
if (side == SideOfPlane.UP || side == SideOfPlane.ON)
{
mesh.upperHull.Add(newTri);
}
else
{
mesh.lowerHull.Add(newTri);
}
}
}
// register into the index
slices[submesh] = mesh;
}
// check if slicing actually occured
for (int i = 0; i < slices.Length; i++)
{
// check if at least one of the submeshes was sliced. If so, stop checking
// because we need to go through the generation step
if (slices[i] != null && slices[i].isValid)
{
return(CreateFrom(slices, CreateFrom(crossHull, pl.normal, region), crossIndex));
}
}
// no slicing occured, just return null to signify
return(null);
}