//If we have a forward and an up reference vector
//So this is not going to work if we have loops
//tangent is same as forward
public InterpolationTransform(MyVector3 position, MyVector3 tangent, MyVector3 up)
{
this.position = position;
MyVector3 biNormal = MyVector3.Normalize(MyVector3.Cross(up, tangent));
MyVector3 normal = MyVector3.Normalize(MyVector3.Cross(tangent, biNormal));
this.orientation = Quaternion.LookRotation(tangent.ToVector3(), normal.ToVector3());
}
//
// Quaternion operations
//
//Rotate a quaternion some degrees around some axis
public static MyQuaternion RotateQuaternion(MyQuaternion oldQuaternion, float angleInDegrees, MyVector3 rotationAxis)
{
Quaternion rotationQuaternion = Quaternion.AngleAxis(angleInDegrees, rotationAxis.ToVector3());
//To rotate a quaternion you just multiply it with the rotation quaternion
//Important that rotationQuaternion is first!
Quaternion newQuaternion = rotationQuaternion * oldQuaternion.unityQuaternion;
MyQuaternion myNewQuaternion = new MyQuaternion(newQuaternion);
return(myNewQuaternion);
}
//
// Get a Transform (includes position and orientation) at point t
//
public InterpolationTransform GetTransform(float t)
{
//Same as when we calculate t
MyVector3 interpolation_1_2 = _Interpolation.BezierQuadratic(posA, handleB, handleA, t);
MyVector3 interpolation_2_3 = _Interpolation.BezierQuadratic(posA, posB, handleB, t);
MyVector3 finalInterpolation = _Interpolation.BezierLinear(interpolation_1_2, interpolation_2_3, t);
//This direction is always tangent to the curve
MyVector3 forwardDir = MyVector3.Normalize(interpolation_2_3 - interpolation_1_2);
//A simple way to get the other directions is to use LookRotation with just forward dir as parameter
//Then the up direction will always be the world up direction, and it calculates the right direction
Quaternion orientation = Quaternion.LookRotation(forwardDir.ToVector3());
InterpolationTransform trans = new InterpolationTransform(finalInterpolation, orientation);
return(trans);
}
//Fill the hole (or holes) in the mesh
private static HashSet <Hole> FillHoles(HashSet <HalfEdge3> holeEdgesI, HashSet <HalfEdge3> holeEdgesO, OrientedPlane3 orientedCutPlane, Transform meshTrans, MyVector3 planeNormal)
{
if (holeEdgesI == null || holeEdgesI.Count == 0)
{
Debug.Log("This mesh has no hole");
return(null);
}
//Find all separate holes
HashSet <List <HalfEdge3> > allHoles = IdentifySeparateHoles(holeEdgesI);
if (allHoles.Count == 0)
{
Debug.LogWarning("Couldn't identify any holes even though we have hole edges");
return(null);
}
//Debug
//foreach (List<HalfEdge3> hole in allHoles)
//{
// foreach (HalfEdge3 e in hole)
// {
// Debug.DrawLine(meshTrans.TransformPoint(e.v.position.ToVector3()), Vector3.zero, Color.white, 5f);
// }
//}
//Fill the hole with a mesh
HashSet <Hole> holeMeshes = new HashSet <Hole>();
foreach (List <HalfEdge3> hole in allHoles)
{
HalfEdgeData3 holeMeshI = new HalfEdgeData3();
HalfEdgeData3 holeMeshO = new HalfEdgeData3();
//Transform vertices to local position of the cut plane to make it easier to triangulate with Ear Clipping
//Ear CLipping wants vertices in 2d
List <MyVector2> sortedEdges_2D = new List <MyVector2>();
Transform planeTrans = orientedCutPlane.planeTrans;
foreach (HalfEdge3 e in hole)
{
MyVector3 pMeshSpace = e.v.position;
//Mesh space to Global space
Vector3 pGlobalSpace = meshTrans.TransformPoint(pMeshSpace.ToVector3());
//Global space to Plane space
Vector3 pPlaneSpace = planeTrans.InverseTransformPoint(pGlobalSpace);
//Y is normal direction so should be 0
MyVector2 p2D = new MyVector2(pPlaneSpace.x, pPlaneSpace.z);
sortedEdges_2D.Add(p2D);
}
//Triangulate with Ear Clipping
HashSet <Triangle2> triangles = _EarClipping.Triangulate(sortedEdges_2D, null, optimizeTriangles: false);
//Debug.Log($"Number of triangles from Ear Clipping: {triangles.Count}");
//Transform vertices to mesh space and half-edge data structure
foreach (Triangle2 t in triangles)
{
//3d space
Vector3 p1 = new Vector3(t.p1.x, 0f, t.p1.y);
Vector3 p2 = new Vector3(t.p2.x, 0f, t.p2.y);
Vector3 p3 = new Vector3(t.p3.x, 0f, t.p3.y);
//Plane space to Global space
Vector3 p1Global = planeTrans.TransformPoint(p1);
Vector3 p2Global = planeTrans.TransformPoint(p2);
Vector3 p3Global = planeTrans.TransformPoint(p3);
//Global space to Mesh space
Vector3 p1Mesh = meshTrans.InverseTransformPoint(p1Global);
Vector3 p2Mesh = meshTrans.InverseTransformPoint(p2Global);
Vector3 p3Mesh = meshTrans.InverseTransformPoint(p3Global);
//For inside mesh
MyMeshVertex v1_I = new MyMeshVertex(p1Mesh.ToMyVector3(), planeNormal);
MyMeshVertex v2_I = new MyMeshVertex(p2Mesh.ToMyVector3(), planeNormal);
MyMeshVertex v3_I = new MyMeshVertex(p3Mesh.ToMyVector3(), planeNormal);
//For inside mesh
MyMeshVertex v1_O = new MyMeshVertex(p1Mesh.ToMyVector3(), -planeNormal);
MyMeshVertex v2_O = new MyMeshVertex(p2Mesh.ToMyVector3(), -planeNormal);
MyMeshVertex v3_O = new MyMeshVertex(p3Mesh.ToMyVector3(), -planeNormal);
//Now we can finally add this triangle to the half-edge data structure
AddTriangleToMesh(v1_I, v2_I, v3_I, holeMeshI, null);
AddTriangleToMesh(v1_O, v3_O, v2_O, holeMeshO, null);
}
//We also need an edge belonging to the mesh (not hole mesh) to easier merge mesh with hole
//The hole edges were generated for the Inside mesh
HalfEdge3 holeEdgeI = hole[0];
//But we also need an edge for the Outside mesh
bool foundCorrespondingEdge = false;
MyVector3 eGoingTo = holeEdgeI.v.position;
MyVector3 eGoingFrom = holeEdgeI.prevEdge.v.position;
foreach (HalfEdge3 holeEdgeO in holeEdgesO)
{
MyVector3 eOppsiteGoingTo = holeEdgeO.v.position;
MyVector3 eOppsiteGoingFrom = holeEdgeO.prevEdge.v.position;
if (eOppsiteGoingTo.Equals(eGoingFrom) && eOppsiteGoingFrom.Equals(eGoingTo))
{
Hole newHoleMesh = new Hole(holeMeshI, holeMeshO, holeEdgeI, holeEdgeO);
holeMeshes.Add(newHoleMesh);
foundCorrespondingEdge = true;
break;
}
}
if (!foundCorrespondingEdge)
{
Debug.Log("Couldnt find opposite edge in hole, so no hole was added");
}
}
return(holeMeshes);
}
//Remove flat tetrahedrons (a vertex in a triangle)
private static bool RemoveFlatTetrahedrons(HalfEdgeData3 meshData, Normalizer3 normalizer = null)
{
HashSet <HalfEdgeVertex3> vertices = meshData.verts;
bool foundFlatTetrahedron = false;
foreach (HalfEdgeVertex3 vertex in vertices)
{
HashSet <HalfEdge3> edgesGoingToVertex = vertex.GetEdgesPointingToVertex(meshData);
if (edgesGoingToVertex.Count == 3)
{
//Find the vertices of the triangle covering this vertex clock-wise
HalfEdgeVertex3 v1 = vertex.edge.v;
HalfEdgeVertex3 v2 = vertex.edge.prevEdge.oppositeEdge.v;
HalfEdgeVertex3 v3 = vertex.edge.oppositeEdge.nextEdge.v;
//Build a plane
MyVector3 normal = MyVector3.Normalize(MyVector3.Cross(v3.position - v2.position, v1.position - v2.position));
Plane3 plane = new Plane3(v1.position, normal);
//Find the distance from the vertex to the plane
float distance = _Geometry.GetSignedDistanceFromPointToPlane(vertex.position, plane);
distance = Mathf.Abs(distance);
if (distance < FLAT_TETRAHEDRON_DISTANCE)
{
//Debug.Log("Found flat tetrahedron");
Vector3 p1 = normalizer.UnNormalize(v1.position).ToVector3();
Vector3 p2 = normalizer.UnNormalize(v2.position).ToVector3();
Vector3 p3 = normalizer.UnNormalize(v3.position).ToVector3();
TestAlgorithmsHelpMethods.DebugDrawTriangle(p1, p2, p3, normal.ToVector3(), Color.blue, Color.red);
foundFlatTetrahedron = true;
//Save the opposite edges
HashSet <HalfEdge3> oppositeEdges = new HashSet <HalfEdge3>();
oppositeEdges.Add(v1.edge.oppositeEdge);
oppositeEdges.Add(v2.edge.oppositeEdge);
oppositeEdges.Add(v3.edge.oppositeEdge);
//Remove the three triangles
foreach (HalfEdge3 e in edgesGoingToVertex)
{
meshData.DeleteFace(e.face);
}
//Add the new triangle (could maybe connect it ourselves)
HalfEdgeFace3 newTriangle = meshData.AddTriangle(v1.position, v2.position, v3.position, findOppositeEdge: false);
meshData.TryFindOppositeEdge(newTriangle.edge, oppositeEdges);
meshData.TryFindOppositeEdge(newTriangle.edge.nextEdge, oppositeEdges);
meshData.TryFindOppositeEdge(newTriangle.edge.nextEdge.nextEdge, oppositeEdges);
break;
}
}
}
return(foundFlatTetrahedron);
}
//Generate a mesh
public static Mesh GenerateMesh(List <InterpolationTransform> transforms, MeshProfile profile, float profileScale)
{
if (profile == null)
{
Debug.Log("You need to assign a mesh profile");
return(null);
}
if (transforms == null || transforms.Count <= 1)
{
Debug.Log("You need more transforms");
return(null);
}
//Test that the profile is correct
//InterpolationTransform testTrans = transforms[1];
//DisplayMeshProfile(profile, testTrans, profileScale);
//Vertices
List <Vector3> vertices = new List <Vector3>();
//Normals
List <Vector3> normals = new List <Vector3>();
for (int step = 0; step < transforms.Count; step++)
{
InterpolationTransform thisTransform = transforms[step];
for (int i = 0; i < profile.vertices.Length; i++)
{
MyVector2 localPos2d = profile.vertices[i].point;
MyVector3 localPos = new MyVector3(localPos2d.x, localPos2d.y, 0f);
MyVector3 pos = thisTransform.LocalToWorld_Pos(localPos * profileScale);
vertices.Add(pos.ToVector3());
//Normals
MyVector2 localNormal2d = profile.vertices[i].normal;
MyVector3 localNormal = new MyVector3(localNormal2d.x, localNormal2d.y, 0f);
MyVector3 normal = thisTransform.LocalToWorld_Dir(localNormal);
normals.Add(normal.ToVector3());
}
}
//Triangles
List <int> triangles = new List <int>();
//We connect the first transform with the next transform, ignoring the last transform because it doesnt have a next
for (int step = 0; step < transforms.Count - 1; step++)
{
//The index where this profile starts in the list of all vertices in the entire mesh
int profileIndexThis = step * profile.vertices.Length;
//The index where the next profile starts
int profileIndexNext = (step + 1) * profile.vertices.Length;
//Each line has 2 points
for (int line = 0; line < profile.lineIndices.Length; line++)
{
int lineIndexA = profile.lineIndices[line].x;
int lineIndexB = profile.lineIndices[line].y;
//Now we can identify the vertex we need in the list of all vertices in the entire mesh
//The current profile
int thisA = profileIndexThis + lineIndexA;
int thisB = profileIndexThis + lineIndexB;
//The next profile
int nextA = profileIndexNext + lineIndexA;
int nextB = profileIndexNext + lineIndexB;
//Build two triangles
triangles.Add(thisA);
triangles.Add(nextA);
triangles.Add(nextB);
triangles.Add(thisB);
triangles.Add(thisA);
triangles.Add(nextB);
}
}
Mesh mesh = new Mesh();
mesh.vertices = vertices.ToArray();
mesh.triangles = triangles.ToArray();
mesh.normals = normals.ToArray();
//mesh.RecalculateNormals();
return(mesh);
}
public MyVector3 RotateVector(MyVector3 vec)
{
Vector3 rotatedVec = unityQuaternion * vec.ToVector3();
return(rotatedVec.ToMyVector3());
}
//Rotate a vector by using a quaternion
public static MyVector3 RotateVector(MyQuaternion quat, MyVector3 vec)
{
Vector3 rotatedVec = quat.unityQuaternion * vec.ToVector3();
return(rotatedVec.ToMyVector3());
}
public MyQuaternion(MyVector3 forward, MyVector3 up)
{
this.unityQuaternion = Quaternion.LookRotation(forward.ToVector3(), up.ToVector3());
}