private static bool CanFormConvexHull_3d(List <Vector3> points)
{
//First test of we can form a convex hull
//If fewer points, then we cant create a convex hull in 3d space
if (points.Count < 4)
{
Debug.Log("Too few points co calculate a convex hull");
return(false);
}
//Find the bounding box of the points
//If the spread is close to 0, then they are all at the same position, and we cant create a hull
AABB3 box = new AABB3(points);
if (!box.IsBoxABox())
{
Debug.Log("The points cant form a convex hull");
return(false);
}
return(true);
}
//Should return null if the mesh couldn't be cut because it doesn't intersect with the plane
//Otherwise it should return two new meshes
//meshTrans is needed so we can transform the cut plane to the mesh's local space
public static List <Mesh> CutMesh(Transform meshTrans, OrientedPlane3 orientedCutPlaneGlobal)
{
//Validate the input data
if (meshTrans == null)
{
Debug.Log("There's transform to cut");
return(null);
}
Mesh mesh = meshTrans.GetComponent <MeshFilter>().mesh;
if (mesh == null)
{
Debug.Log("There's no mesh to cut");
return(null);
}
//The plane with just a normal
Plane3 cutPlaneGlobal = orientedCutPlaneGlobal.Plane3;
//First check if the AABB of the mesh is intersecting with the plane
//Otherwise we can't cut the mesh, so its a waste of time
//To get the AABB in world space we need to use the mesh renderer
MeshRenderer mr = meshTrans.GetComponent <MeshRenderer>();
if (mr != null)
{
AABB3 aabb = new AABB3(mr.bounds);
//The corners of this box
HashSet <MyVector3> corners = aabb.GetCorners();
if (corners != null && corners.Count > 1)
{
//The points are in world space so use the plane in world space
if (ArePointsOnOneSideOfPlane(new List <MyVector3>(corners), cutPlaneGlobal))
{
Debug.Log("This mesh can't be cut because its AABB doesnt intersect with the plane");
return(null);
}
}
}
//The two meshes we might end up with after the cut
//One is in front of the plane and another is in back of the plane
HalfEdgeData3 newMeshO = new HalfEdgeData3();
HalfEdgeData3 newMeshI = new HalfEdgeData3();
//The data belonging to the original mesh
Vector3[] vertices = mesh.vertices;
int[] triangles = mesh.triangles;
Vector3[] normals = mesh.normals;
//Save the new edges we add when cutting triangles that intersects with the plane
//Need to be edges so we can later connect them with each other to fill the hole
//And to remove small triangles
HashSet <HalfEdge3> newEdgesO = new HashSet <HalfEdge3>();
HashSet <HalfEdge3> newEdgesI = new HashSet <HalfEdge3>();
//Transform the plane from global space to local space of the mesh
MyVector3 planePosLocal = meshTrans.InverseTransformPoint(cutPlaneGlobal.pos.ToVector3()).ToMyVector3();
MyVector3 planeNormalLocal = meshTrans.InverseTransformDirection(cutPlaneGlobal.normal.ToVector3()).ToMyVector3();
Plane3 cutPlane = new Plane3(planePosLocal, planeNormalLocal);
//Loop through all triangles in the original mesh
for (int i = 0; i < triangles.Length; i += 3)
{
//Get the triangle data we need
int triangleIndex1 = triangles[i + 0];
int triangleIndex2 = triangles[i + 1];
int triangleIndex3 = triangles[i + 2];
//Positions
Vector3 p1_unity = vertices[triangleIndex1];
Vector3 p2_unity = vertices[triangleIndex2];
Vector3 p3_unity = vertices[triangleIndex3];
MyVector3 p1 = p1_unity.ToMyVector3();
MyVector3 p2 = p2_unity.ToMyVector3();
MyVector3 p3 = p3_unity.ToMyVector3();
//Normals
MyVector3 n1 = normals[triangleIndex1].ToMyVector3();
MyVector3 n2 = normals[triangleIndex2].ToMyVector3();
MyVector3 n3 = normals[triangleIndex3].ToMyVector3();
//To make it easier to send data to methods
MyMeshVertex v1 = new MyMeshVertex(p1, n1);
MyMeshVertex v2 = new MyMeshVertex(p2, n2);
MyMeshVertex v3 = new MyMeshVertex(p3, n3);
//First check on which side of the plane these vertices are
//If they are all on one side we dont have to cut the triangle
bool is_p1_front = _Geometry.IsPointOutsidePlane(cutPlane, v1.position);
bool is_p2_front = _Geometry.IsPointOutsidePlane(cutPlane, v2.position);
bool is_p3_front = _Geometry.IsPointOutsidePlane(cutPlane, v3.position);
//Build triangles belonging to respective mesh
//All are outside the plane
if (is_p1_front && is_p2_front && is_p3_front)
{
AddTriangleToMesh(v1, v2, v3, newMeshO, newEdges: null);
}
//All are inside the plane
else if (!is_p1_front && !is_p2_front && !is_p3_front)
{
AddTriangleToMesh(v1, v2, v3, newMeshI, newEdges: null);
}
//The vertices are on different sides of the plane, so we need to cut the triangle into 3 new triangles
else
{
//We get 6 cases where each vertex is on its own in front or in the back of the plane
//p1 is outside
if (is_p1_front && !is_p2_front && !is_p3_front)
{
CutTriangleOneOutside(v1, v2, v3, newMeshO, newMeshI, newEdgesI, newEdgesO, cutPlane);
}
//p1 is inside
else if (!is_p1_front && is_p2_front && is_p3_front)
{
CutTriangleTwoOutside(v2, v3, v1, newMeshO, newMeshI, newEdgesI, newEdgesO, cutPlane);
}
//p2 is outside
else if (!is_p1_front && is_p2_front && !is_p3_front)
{
CutTriangleOneOutside(v2, v3, v1, newMeshO, newMeshI, newEdgesI, newEdgesO, cutPlane);
}
//p2 is inside
else if (is_p1_front && !is_p2_front && is_p3_front)
{
CutTriangleTwoOutside(v3, v1, v2, newMeshO, newMeshI, newEdgesI, newEdgesO, cutPlane);
}
//p3 is outside
else if (!is_p1_front && !is_p2_front && is_p3_front)
{
CutTriangleOneOutside(v3, v1, v2, newMeshO, newMeshI, newEdgesI, newEdgesO, cutPlane);
}
//p3 is inside
else if (is_p1_front && is_p2_front && !is_p3_front)
{
CutTriangleTwoOutside(v1, v2, v3, newMeshO, newMeshI, newEdgesI, newEdgesO, cutPlane);
}
//Something is strange if we end up here...
else
{
Debug.Log("No case was gound where we split triangle into 3 new triangles");
}
}
}
//Generate the new meshes only needed the old mesh intersected with the plane
if (newMeshO.verts.Count == 0 || newMeshI.verts.Count == 0)
{
return(null);
}
//Find opposite edges to each edge
//This is a slow process, so should be done only if the mesh is intersecting with the plane
newMeshO.ConnectAllEdges();
newMeshI.ConnectAllEdges();
//Display all edges which have no opposite
DebugHalfEdge.DisplayEdgesWithNoOpposite(newMeshO.edges, meshTrans, Color.white);
DebugHalfEdge.DisplayEdgesWithNoOpposite(newMeshI.edges, meshTrans, Color.white);
//Remove small triangles at the seam where we did the cut because they will cause shading issues if the surface is smooth
//RemoveSmallTriangles(F_Mesh, newEdges);
//Split each mesh into separate meshes if the original mesh is not connected, meaning it has islands
HashSet <HalfEdgeData3> newMeshesO = SeparateMeshIslands(newMeshO);
HashSet <HalfEdgeData3> newMeshesI = SeparateMeshIslands(newMeshI);
//Fill the holes in the mesh
HashSet <Hole> allHoles = FillHoles(newEdgesI, newEdgesO, orientedCutPlaneGlobal, meshTrans, planeNormalLocal);
//Connect the holes with respective mesh
AddHolesToMeshes(newMeshesO, newMeshesI, allHoles);
//Finally generate standardized Unity meshes
List <Mesh> cuttedUnityMeshes = new List <Mesh>();
foreach (HalfEdgeData3 meshData in newMeshesO)
{
Mesh unityMesh = meshData.ConvertToUnityMesh("Outside mesh", shareVertices: true, generateNormals: false);
cuttedUnityMeshes.Add(unityMesh);
}
foreach (HalfEdgeData3 meshData in newMeshesI)
{
Mesh unityMesh = meshData.ConvertToUnityMesh("Inside mesh", shareVertices: true, generateNormals: false);
cuttedUnityMeshes.Add(unityMesh);
}
return(cuttedUnityMeshes);
}
//From "A fast algorithm for constructing Delaunay triangulations in the plane" by Sloan
//boundingBox is the rectangle that covers all original points before normalization
public float CalculateDMax(AABB3 aabb)
{
float dMax = Mathf.Max(aabb.max.x - aabb.min.x, Mathf.Max(aabb.max.y - aabb.min.y, aabb.max.z - aabb.min.z));
return(dMax);
}
public Normalizer3(List <MyVector3> points)
{
this.boundingBox = new AABB3(points);
this.dMax = CalculateDMax(this.boundingBox);
}
