//Initialize by making 2 triangles by using three points, so its a flat triangle with a face on each side
//We could use the ideas from Quickhull to make the start triangle as big as possible
//Then find a point which is the furthest away as possible from these triangles
//Add that point and you have a tetrahedron (triangular pyramid)
public static void BuildFirstTetrahedron(HashSet <Vector3> points, HalfEdgeData3 convexHull)
{
//Of all points, find the two points that are furthes away from each other
Edge3 eFurthestApart = FindEdgeFurthestApart(points);
//Remove the two points we found
points.Remove(eFurthestApart.p1);
points.Remove(eFurthestApart.p2);
//Find a point which is the furthest away from this edge
//TODO: Is this point also on the AABB? So we don't have to search all remaining points...
Vector3 pointFurthestAway = FindPointFurthestFromEdge(eFurthestApart, points);
//Remove the point
points.Remove(pointFurthestAway);
//Display the triangle
//Debug.DrawLine(eFurthestApart.p1.ToVector3(), eFurthestApart.p2.ToVector3(), Color.white, 1f);
//Debug.DrawLine(eFurthestApart.p1.ToVector3(), pointFurthestAway.ToVector3(), Color.blue, 1f);
//Debug.DrawLine(eFurthestApart.p2.ToVector3(), pointFurthestAway.ToVector3(), Color.blue, 1f);
//Now we can build two triangles
//It doesnt matter how we build these triangles as long as they are opposite
//But the normal matters, so make sure it is calculated so the triangles are ordered clock-wise while the normal is pointing out
Vector3 p1 = eFurthestApart.p1;
Vector3 p2 = eFurthestApart.p2;
Vector3 p3 = pointFurthestAway;
convexHull.AddTriangle(p1, p2, p3);
convexHull.AddTriangle(p1, p3, p2);
//Debug.Log(convexHull.faces.Count);
/*
* foreach (HalfEdgeFace3 f in convexHull.faces)
* {
* TestAlgorithmsHelpMethods.DebugDrawTriangle(f, Color.white, Color.red);
* }
*/
//Find the point which is furthest away from the triangle (this point cant be co-planar)
List <HalfEdgeFace3> triangles = new List <HalfEdgeFace3>(convexHull.faces);
//Just pick one of the triangles
HalfEdgeFace3 triangle = triangles[0];
//Build a plane
Plane3 plane = new Plane3(triangle.edge.v.position, triangle.edge.v.normal);
//Find the point furthest away from the plane
Vector3 p4 = FindPointFurthestAwayFromPlane(points, plane);
//Remove the point
points.Remove(p4);
//Debug.DrawLine(p1.ToVector3(), p4.ToVector3(), Color.green, 1f);
//Debug.DrawLine(p2.ToVector3(), p4.ToVector3(), Color.green, 1f);
//Debug.DrawLine(p3.ToVector3(), p4.ToVector3(), Color.green, 1f);
//Now we have to remove one of the triangles == the triangle the point is outside of
HalfEdgeFace3 triangleToRemove = triangles[0];
HalfEdgeFace3 triangleToKeep = triangles[1];
//This means the point is inside the triangle-plane, so we have to switch
//We used triangle #0 to generate the plane
if (_Geometry.GetSignedDistanceFromPointToPlane(p4, plane) < 0f)
{
triangleToRemove = triangles[1];
triangleToKeep = triangles[0];
}
//Delete the triangle
convexHull.DeleteFace(triangleToRemove);
//Build three new triangles
//The triangle we keep is ordered clock-wise:
Vector3 p1_opposite = triangleToKeep.edge.v.position;
Vector3 p2_opposite = triangleToKeep.edge.nextEdge.v.position;
Vector3 p3_opposite = triangleToKeep.edge.nextEdge.nextEdge.v.position;
//But we are looking at it from the back-side,
//so we add those vertices counter-clock-wise to make the new triangles clock-wise
convexHull.AddTriangle(p1_opposite, p3_opposite, p4);
convexHull.AddTriangle(p3_opposite, p2_opposite, p4);
convexHull.AddTriangle(p2_opposite, p1_opposite, p4);
//Make sure all opposite edges are connected
convexHull.ConnectAllEdgesSlow();
//Debug.Log(convexHull.faces.Count);
//Display what weve got so far
//foreach (HalfEdgeFace3 f in convexHull.faces)
//{
// TestAlgorithmsHelpMethods.DebugDrawTriangle(f, Color.white, Color.red);
//}
/*
* //Now we might as well remove all the points that are within the tetrahedron because they are not on the hull
* //But this is slow if we have many points and none of them are inside
* HashSet<MyVector3> pointsToRemove = new HashSet<MyVector3>();
*
* foreach (MyVector3 p in points)
* {
* bool isWithinConvexHull = _Intersections.PointWithinConvexHull(p, convexHull);
*
* if (isWithinConvexHull)
* {
* pointsToRemove.Add(p);
* }
* }
*
* Debug.Log($"Removed {pointsToRemove.Count} points because they were within the tetrahedron");
*
* foreach (MyVector3 p in pointsToRemove)
* {
* points.Remove(p);
* }
*/
}
//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(v1.position, cutPlane);
bool is_p2_front = _Geometry.IsPointOutsidePlane(v2.position, cutPlane);
bool is_p3_front = _Geometry.IsPointOutsidePlane(v3.position, cutPlane);
//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.ConnectAllEdgesSlow();
newMeshI.ConnectAllEdgesSlow();
//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)
{
MyMesh myMesh = meshData.ConvertToMyMesh("Outside mesh", MyMesh.MeshStyle.HardAndSoftEdges);
Mesh unityMesh = myMesh.ConvertToUnityMesh(generateNormals: false);
cuttedUnityMeshes.Add(unityMesh);
}
foreach (HalfEdgeData3 meshData in newMeshesI)
{
MyMesh myMesh = meshData.ConvertToMyMesh("Inside mesh", MyMesh.MeshStyle.HardAndSoftEdges);
Mesh unityMesh = myMesh.ConvertToUnityMesh(generateNormals: false);
cuttedUnityMeshes.Add(unityMesh);
}
return(cuttedUnityMeshes);
}