/**
* Generate a mesh from the provided hull made of triangles
*/
private static Mesh CreateFrom(List <Triangle> hull)
{
int count = hull.Count;
if (count <= 0)
{
return(null);
}
Mesh newMesh = new Mesh();
Vector3[] newVertices = new Vector3[count * 3];
Vector2[] newUvs = new Vector2[count * 3];
int[] newIndices = new int[count * 3];
int addedCount = 0;
// fill our mesh arrays
for (int i = 0; i < count; i++)
{
Triangle newTri = hull[i];
int i0 = addedCount + 0;
int i1 = addedCount + 1;
int i2 = addedCount + 2;
newVertices[i0] = newTri.positionA;
newVertices[i1] = newTri.positionB;
newVertices[i2] = newTri.positionC;
newUvs[i0] = newTri.uvA;
newUvs[i1] = newTri.uvB;
newUvs[i2] = newTri.uvC;
// note -> this case could be optimized by having the order
// returned properly from the intersector
// -> note -> this is no longer required since triangles are added
// as clockwise from the intersector
/*if (newTri.IsCW()) {
* newIndices[i0] = i0;
* newIndices[i1] = i1;
* newIndices[i2] = i2;
* }
* else {
* newIndices[i0] = i0;
* newIndices[i1] = i2;
* newIndices[i2] = i1;
* }*/
newIndices[i0] = i0;
newIndices[i1] = i1;
newIndices[i2] = i2;
addedCount += 3;
}
// fill the mesh structure
newMesh.vertices = newVertices;
newMesh.uv = newUvs;
newMesh.triangles = newIndices;
// consider computing this array externally instead
newMesh.RecalculateNormals();
return(newMesh);
}
/**
* 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[] ve = sharedMesh.vertices;
Vector2[] uv = sharedMesh.uv;
int[] indices = sharedMesh.triangles;
int indicesCount = indices.Length;
// we reuse this object for all intersection tests
IntersectionResult result = new IntersectionResult();
// all our buffers, as Triangles
List <Triangle> upperHull = new List <Triangle>();
List <Triangle> lowerHull = new List <Triangle>();
List <Vector3> crossHull = new List <Vector3>();
// 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(ve[i0], ve[i1], ve[i2], uv[i0], uv[i1], uv[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++)
{
upperHull.Add(result.upperHull[i]);
}
for (int i = 0; i < lowerHullCount; i++)
{
lowerHull.Add(result.lowerHull[i]);
}
for (int i = 0; i < interHullCount; i++)
{
crossHull.Add(result.intersectionPoints[i]);
}
}
else
{
SideOfPlane side = pl.SideOf(ve[i0]);
if (side == SideOfPlane.UP || side == SideOfPlane.ON)
{
upperHull.Add(newTri);
}
else
{
lowerHull.Add(newTri);
}
}
}
// start creating our hulls
Mesh finalUpperHull = CreateFrom(upperHull);
Mesh finalLowerHull = CreateFrom(lowerHull);
// we need to generate the cross section if set
// NOTE -> This uses a MonotoneChain algorithm which will only work
// on cross sections which are Convex
if (genCrossSection)
{
Mesh[] crossSections = CreateFrom(crossHull, pl.normal);
if (crossSections != null)
{
return(new SlicedHull(finalUpperHull, finalLowerHull, crossSections[0], crossSections[1]));
}
}
return(new SlicedHull(finalUpperHull, finalLowerHull));
}
/**
* O(n log n) Convex Hull Algorithm.
* Accepts a list of vertices as Vector3 and triangulates them according to a projection
* plane defined as planeNormal. Algorithm will output vertices, indices and UV coordinates
* as arrays
*/
public static bool MonotoneChain(List <Vector3> vertices, Vector3 normal, out List <Triangle> tri, TextureRegion texRegion)
{
int count = vertices.Count;
// we cannot triangulate less than 3 points. Use minimum of 3 points
if (count < 3)
{
tri = null;
return(false);
}
// first, we map from 3D points into a 2D plane represented by the provided normal
Vector3 u = Vector3.Normalize(Vector3.Cross(normal, Vector3.up));
if (Vector3.zero == u)
{
u = Vector3.Normalize(Vector3.Cross(normal, Vector3.forward));
}
Vector3 v = Vector3.Cross(u, normal);
// generate an array of mapped values
Mapped2D[] mapped = new Mapped2D[count];
// these values will be used to generate new UV coordinates later on
float maxDivX = float.MinValue;
float maxDivY = float.MinValue;
float minDivX = float.MaxValue;
float minDivY = float.MaxValue;
// map the 3D vertices into the 2D mapped values
for (int i = 0; i < count; i++)
{
Vector3 vertToAdd = vertices[i];
Mapped2D newMappedValue = new Mapped2D(vertToAdd, u, v);
Vector2 mapVal = newMappedValue.mappedValue;
// grab our maximal values so we can map UV's in a proper range
maxDivX = Mathf.Max(maxDivX, mapVal.x);
maxDivY = Mathf.Max(maxDivY, mapVal.y);
minDivX = Mathf.Min(minDivX, mapVal.x);
minDivY = Mathf.Min(minDivY, mapVal.y);
mapped[i] = newMappedValue;
}
// sort our newly generated array values
Array.Sort <Mapped2D>(mapped, (a, b) => {
Vector2 x = a.mappedValue;
Vector2 p = b.mappedValue;
return((x.x < p.x || (x.x == p.x && x.y < p.y)) ? -1 : 1);
});
// our final hull mappings will end up in herew
Mapped2D[] hulls = new Mapped2D[count + 1];
int k = 0;
// build the lower hull of the chain
for (int i = 0; i < count; i++)
{
while (k >= 2)
{
Vector2 mA = hulls[k - 2].mappedValue;
Vector2 mB = hulls[k - 1].mappedValue;
Vector2 mC = mapped[i].mappedValue;
if (Intersector.TriArea2D(mA.x, mA.y, mB.x, mB.y, mC.x, mC.y) > 0.0f)
{
break;
}
k--;
}
hulls[k++] = mapped[i];
}
// build the upper hull of the chain
for (int i = count - 2, t = k + 1; i >= 0; i--)
{
while (k >= t)
{
Vector2 mA = hulls[k - 2].mappedValue;
Vector2 mB = hulls[k - 1].mappedValue;
Vector2 mC = mapped[i].mappedValue;
if (Intersector.TriArea2D(mA.x, mA.y, mB.x, mB.y, mC.x, mC.y) > 0.0f)
{
break;
}
k--;
}
hulls[k++] = mapped[i];
}
// finally we can build our mesh, generate all the variables
// and fill them up
int vertCount = k - 1;
int triCount = (vertCount - 2) * 3;
// this should not happen, but here just in case
if (vertCount < 3)
{
tri = null;
return(false);
}
// ensure List does not dynamically grow, performing copy ops each time!
tri = new List <Triangle>(triCount / 3);
float width = maxDivX - minDivX;
float height = maxDivY - minDivY;
int indexCount = 1;
// generate both the vertices and uv's in this loop
for (int i = 0; i < triCount; i += 3)
{
// the Vertices in our triangle
Mapped2D posA = hulls[0];
Mapped2D posB = hulls[indexCount];
Mapped2D posC = hulls[indexCount + 1];
// generate UV Maps
Vector2 uvA = posA.mappedValue;
Vector2 uvB = posB.mappedValue;
Vector2 uvC = posC.mappedValue;
uvA.x = (uvA.x - minDivX) / width;
uvA.y = (uvA.y - minDivY) / height;
uvB.x = (uvB.x - minDivX) / width;
uvB.y = (uvB.y - minDivY) / height;
uvC.x = (uvC.x - minDivX) / width;
uvC.y = (uvC.y - minDivY) / height;
Triangle newTriangle = new Triangle(posA.originalValue, posB.originalValue, posC.originalValue);
// ensure our UV coordinates are mapped into the requested TextureRegion
newTriangle.SetUV(texRegion.Map(uvA), texRegion.Map(uvB), texRegion.Map(uvC));
// the normals is the same for all vertices since the final mesh is completly flat
newTriangle.SetNormal(normal, normal, normal);
newTriangle.ComputeTangents();
tri.Add(newTriangle);
indexCount++;
}
return(true);
}
