public InterpolationTransform(MyVector3 position, MyQuaternion orientation)
{
this.position = position;
this.orientation = orientation;
}
public static float SqrMagnitude(MyVector3 a)
{
float sqrMagnitude = (a.x * a.x) + (a.y * a.y) + (a.z * a.z);
return(sqrMagnitude);
}
public static float SqrDistance(MyVector3 a, MyVector3 b)
{
float distance = SqrMagnitude(a - b);
return(distance);
}
public MyQuaternion(MyVector3 forward, MyVector3 up)
{
this.unityQuaternion = Quaternion.LookRotation(forward.ToVector3(), up.ToVector3());
}
public static float Magnitude(MyVector3 a)
{
float magnitude = Mathf.Sqrt(SqrMagnitude(a));
return(magnitude);
}
//
// Transform between coordinate systems
//
//Transform a position from local to world
//If input is MyVector3.Right * 2f then we should get a point in world space on the curve
//at this position moved along the local x-axis 2m
public MyVector3 LocalToWorld_Pos(MyVector3 localPos)
{
MyVector3 worldPos = position + MyQuaternion.RotateVector(orientation, localPos);
return(worldPos);
}
public static InterpolationTransform GetTransform_UpRef(_Curve curve, float t, MyVector3 upRef)
{
//Position on the curve at point t
MyVector3 pos = curve.GetPosition(t);
//Forward direction (tangent) on the curve at point t
MyVector3 forwardDir = curve.GetTangent(t);
//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
//This idea is not working for all possible curve orientations
//MyQuaternion orientation = new MyQuaternion(forwardDir);
//Your own reference up vector
MyQuaternion orientation = InterpolationTransform.GetOrientation_UpRef(forwardDir, upRef);
InterpolationTransform trans = new InterpolationTransform(pos, orientation);
return(trans);
}
public HalfEdgeVertex3(MyVector3 position, MyVector3 normal)
{
this.position = position;
this.normal = normal;
}
public Plane3(MyVector3 pos, MyVector3 normal)
{
this.pos = pos;
this.normal = normal;
}
//
// Contract an edge if we know we are dealing only with triangles
//
//Returns all edge pointing to the new vertex
public HashSet <HalfEdge3> ContractTriangleHalfEdge(HalfEdge3 e, MyVector3 mergePos, System.Diagnostics.Stopwatch timer = null)
{
//Step 1. Get all edges pointing to the vertices we will merge
//And edge is going TO a vertex, so this edge goes from v1 to v2
HalfEdgeVertex3 v1 = e.prevEdge.v;
HalfEdgeVertex3 v2 = e.v;
//timer.Start();
//It's better to get these before we remove triangles because then we will get a messed up half-edge system?
HashSet <HalfEdge3> edgesGoingToVertex_v1 = v1.GetEdgesPointingToVertex(this);
HashSet <HalfEdge3> edgesGoingToVertex_v2 = v2.GetEdgesPointingToVertex(this);
//timer.Stop();
//Step 2. Remove the triangles, which will create a hole,
//and the edges on the opposite sides of the hole are connected
RemoveTriangleAndConnectOppositeSides(e);
//We might also have an opposite triangle, so we may have to delete a total of two triangles
if (e.oppositeEdge != null)
{
RemoveTriangleAndConnectOppositeSides(e.oppositeEdge);
}
//Step 3. Move the vertices to the merge position
//Some of these edges belong to the triangles we removed, but it doesnt matter because this operation is fast
//We can at the same time find the edges pointing to the new vertex
HashSet <HalfEdge3> edgesPointingToVertex = new HashSet <HalfEdge3>();
if (edgesGoingToVertex_v1 != null)
{
foreach (HalfEdge3 edgeToV in edgesGoingToVertex_v1)
{
//This edge belonged to one of the faces we removed
if (edgeToV.face == null)
{
continue;
}
edgeToV.v.position = mergePos;
edgesPointingToVertex.Add(edgeToV);
}
}
if (edgesGoingToVertex_v2 != null)
{
foreach (HalfEdge3 edgeToV in edgesGoingToVertex_v2)
{
//This edge belonged to one of the faces we removed
if (edgeToV.face == null)
{
continue;
}
edgeToV.v.position = mergePos;
edgesPointingToVertex.Add(edgeToV);
}
}
return(edgesPointingToVertex);
}
public HalfEdgeVertex3(MyVector3 position)
{
this.position = position;
}
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());
}
//
// 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);
}
//
// Alternative 3. Rotation Minimising Frame (also known as "Parallel Transport Frame" or "Bishop Frame")
//
//Gets its stability by incrementally rotating a coordinate system (= frame) as it is translate along the curve
//Has to be computed for the entire curve because we need the previous frame (previousTransform) belonging to a point before this point
//Is initalized by using "Fixed Up" or "Frenet Normal"
public static MyQuaternion GetOrientation_RotationFrame(MyVector3 position, MyVector3 tangent, InterpolationTransform previousTransform)
{
/*
* //This version is from https://pomax.github.io/bezierinfo/#pointvectors3d
* //Reflect the known frame onto the next point, by treating the plane through the curve at the point exactly between the next and previous points as a "mirror"
* MyVector3 v1 = position - previousTransform.position;
*
* float c1 = MyVector3.Dot(v1, v1);
*
* MyVector3 riL = previousTransform.Right - v1 * (2f / c1) * MyVector3.Dot(v1, previousTransform.Right);
*
* MyVector3 tiL = previousTransform.Forward - v1 * (2f / c1) * MyVector3.Dot(v1, previousTransform.Forward);
*
* //This gives the next point a tangent vector that's essentially pointing in the opposite direction of what it should be, and a normal that's slightly off-kilter
* //reflect the vectors of our "mirrored frame" a second time, but this time using the plane through the "next point" itself as "mirror".
* MyVector3 v2 = tangent - tiL;
*
* float c2 = MyVector3.Dot(v2, v2);
*
* //Now we can calculate the normal and right vector belonging to this orientation
* MyVector3 right = riL - v2 * (2f / c2) * MyVector3.Dot(v2, riL);
*
* //The source has right x tangent, but then every second normal is flipped
* MyVector3 normal = MyVector3.Cross(tangent, right);
*
* MyQuaternion orientation = new MyQuaternion(tangent, normal);
*/
//This version is from Game Programming Gems 2: The Parallel Transport Frame
//They generate the same result and this one is easier to understand
//The two tangents
MyVector3 T1 = previousTransform.Forward;
MyVector3 T2 = tangent;
//You move T1 to the new position, so A is a vector going from the new position
MyVector3 A = MyVector3.Cross(T1, T2);
//This is the angle between T1 and T2
float alpha = Mathf.Acos(MyVector3.Dot(T1, T2) / (MyVector3.Magnitude(T1) * MyVector3.Magnitude(T2)));
//Now rotate the previous frame around axis A with angle alpha
MyQuaternion F1 = previousTransform.orientation;
MyQuaternion F2 = MyQuaternion.RotateQuaternion(F1, alpha * Mathf.Rad2Deg, A);
MyQuaternion orientation = F2;
return(orientation);
}
//Is this edge intersecting with another edge?
//public bool isIntersecting = false;
public Edge3(MyVector3 p1, MyVector3 p2)
{
this.p1 = p1;
this.p2 = p2;
}
//Not defined for a single point, you always need a previous transform
//public static InterpolationTransform InterpolationTransform GetTransform_RotationMinimisingFrame()
//{
//}
public static List <InterpolationTransform> GetTransforms_RotationMinimisingFrame(_Curve curve, List <float> tValues, MyVector3 upRef)
{
List <InterpolationTransform> transforms = new List <InterpolationTransform>();
for (int i = 0; i < tValues.Count; i++)
{
float t = tValues[i];
//Position on the curve at point t
MyVector3 position = curve.GetPosition(t);
//Forward direction (tangent) on the curve at point t
MyVector3 tangent = curve.GetTangent(t);
//At first pos we dont have a previous transform
if (i == 0)
{
//Just use one of the other algorithms available to generate a transform at a single position
MyQuaternion orientation = InterpolationTransform.GetOrientation_UpRef(tangent, upRef);
InterpolationTransform transform = new InterpolationTransform(position, orientation);
transforms.Add(transform);
}
else
{
//To calculate the orientation for this point, we need data from the previous point on the curve
InterpolationTransform previousTransform = transforms[i - 1];
MyQuaternion orientation = InterpolationTransform.GetOrientation_RotationFrame(position, tangent, previousTransform);
InterpolationTransform transform = new InterpolationTransform(position, orientation);
transforms.Add(transform);
}
}
return(transforms);
}
//
// Triangle to Unity mesh
//
//Version 1. Check that each vertex exists only once in the final mesh
//Make sure the triangles have the correct orientation
public static Mesh Triangle3ToCompressedMesh(HashSet <Triangle3> triangles)
{
if (triangles == null)
{
return(null);
}
//Step 2. Create the list with unique vertices
//A hashset will make it fast to check if a vertex already exists in the collection
HashSet <MyVector3> uniqueVertices = new HashSet <MyVector3>();
foreach (Triangle3 t in triangles)
{
MyVector3 v1 = t.p1;
MyVector3 v2 = t.p2;
MyVector3 v3 = t.p3;
if (!uniqueVertices.Contains(v1))
{
uniqueVertices.Add(v1);
}
if (!uniqueVertices.Contains(v2))
{
uniqueVertices.Add(v2);
}
if (!uniqueVertices.Contains(v3))
{
uniqueVertices.Add(v3);
}
}
//Create the list with all vertices
List <MyVector3> meshVertices = new List <MyVector3>(uniqueVertices);
//Step3. Create the list with all triangles by using the unique vertices
List <int> meshTriangles = new List <int>();
//Use a dictionay to quickly find which positon in the list a Vector3 has
Dictionary <MyVector3, int> vector2Positons = new Dictionary <MyVector3, int>();
for (int i = 0; i < meshVertices.Count; i++)
{
vector2Positons.Add(meshVertices[i], i);
}
foreach (Triangle3 t in triangles)
{
MyVector3 v1 = t.p1;
MyVector3 v2 = t.p2;
MyVector3 v3 = t.p3;
meshTriangles.Add(vector2Positons[v1]);
meshTriangles.Add(vector2Positons[v2]);
meshTriangles.Add(vector2Positons[v3]);
}
//Step4. Create the final mesh
Mesh mesh = new Mesh();
//From MyVector3 to Vector3
Vector3[] meshVerticesArray = new Vector3[meshVertices.Count];
for (int i = 0; i < meshVerticesArray.Length; i++)
{
MyVector3 v = meshVertices[i];
meshVerticesArray[i] = new Vector3(v.x, v.y, v.z);
}
mesh.vertices = meshVerticesArray;
mesh.triangles = meshTriangles.ToArray();
//Should maybe recalculate bounds and normals, maybe better to do that outside this method???
//mesh.RecalculateBounds();
//mesh.RecalculateNormals();
return(mesh);
}
//Transform a direction from local to world
public MyVector3 LocalToWorld_Dir(MyVector3 localDir)
{
MyVector3 worldDir = MyQuaternion.RotateVector(orientation, localDir);
return(worldDir);
}
//
// Vector operations
//
public static float Dot(MyVector3 a, MyVector3 b)
{
float dotProduct = (a.x * b.x) + (a.y * b.y) + (a.z * b.z);
return(dotProduct);
}
public static List <InterpolationTransform> GetTransforms_UpRef(_Curve curve, List <float> tValues, MyVector3 upRef)
{
List <InterpolationTransform> orientations = new List <InterpolationTransform>();
foreach (float t in tValues)
{
InterpolationTransform transform = InterpolationTransform.GetTransform_UpRef(curve, t, upRef);
orientations.Add(transform);
}
return(orientations);
}
public Triangle3(MyVector3 p1, MyVector3 p2, MyVector3 p3)
{
this.p1 = p1;
this.p2 = p2;
this.p3 = p3;
}