/// <summary>
/// Takes two points, one of which is in the volume and one of which isn't.
///
/// Finds the distance along the segment a...b that intersects the boundary of the volume.
///
/// Note: this assumes that there is only one such intersection! If this is not the case, use a finer mesh.
/// </summary>
public static Vector3 FindBoundary(Vector3 a, Vector3 b, IVolume volume)
{
Debug.Assert(volume.Contains(a) != volume.Contains(b));
bool contains = volume.Contains(a);
Vector3 v1 = a, v2 = b;
for (int i = 0; i < 10; i++) {
Vector3 mid = (v1+v2)/2;
if (contains == volume.Contains(mid)) {
v1 = mid;
} else {
v2 = mid;
}
}
return (v1 + v2) / 2;
}
public IVolume AddPlan(IntPoint[] points, IVolume abovePlan = null, float scale = 100)
{
IVolume output = AddPlan(NewPlan(), abovePlan);
int pointCount = points.Length;
Vector3 goPos = transformposition;
Quaternion goInvRot = Quaternion.Inverse(transformrotation);
for (int p = 0; p < pointCount; p++)
{
Vector3 v3 = goInvRot * (new Vector3(points[p].X / scale, 0, points[p].Y / scale) - goPos);
Vector2Int v2Int = new Vector2Int(v3.x, v3.z);
if (output.Contains(v2Int))
{
continue;
}
output.AddPoint(v2Int);
}
return(output);
}
public static void Split(Mesh input, IVolume volume,
out Mesh output, out bool[] trisInside)
{
/**
*
* for triangle in input
* if triangle is entirely inside or outside
* add to corresponding mesh
* else split triangle into 4 pieces.
* three go in one mesh, one goes into the other
*
* Splitting a triangle, Before:
*
* * vA
* / \
* boundary --- /---\ ---
* / \
* vB1 *-------* vB2
*
*
* After:
*
* * vA
* vMid1 / \ vMid2
* boundary --- *---* ---
* / \ / \
* vB1 *---*---* vB2
* vMidB
*
**/
int np = input.points.Length, nt = input.triangles.Length;
List<Vector3> points = input.points.ToList();
List<Vector3> norms = input.normals.ToList();
List<Mesh.Triangle> tris = new List<Mesh.Triangle>();
List<bool> trisIn = new List<bool>();
for(int i = 0; i < nt; i++){
var tri = input.triangles[i];
Vector3 vA = input.points[tri.vertexA];
Vector3 vB = input.points[tri.vertexB];
Vector3 vC = input.points[tri.vertexC];
int ncontains =
(volume.Contains(vA) ? 1 : 0) +
(volume.Contains(vB) ? 1 : 0) +
(volume.Contains(vC) ? 1 : 0);
if (ncontains==3) {
tris.Add(tri);
trisIn.Add(true);
} else if (ncontains==0){
tris.Add(tri);
trisIn.Add(false);
} else {
// see comment above for explanation
Debug.Assert(ncontains == 1 || ncontains == 2);
bool containsA = (ncontains==1);
int ixA, ixB1, ixB2;
if (volume.Contains(vA) == containsA) {
ixA = tri.vertexA;
ixB1 = tri.vertexB;
ixB2 = tri.vertexC;
} else if (volume.Contains(vB) == containsA) {
ixA = tri.vertexB;
ixB1 = tri.vertexA;
ixB2 = tri.vertexC;
} else {
Debug.Assert(volume.Contains(vC) == containsA);
ixA = tri.vertexC;
ixB1 = tri.vertexA;
ixB2 = tri.vertexB;
}
Vector3 vAO = input.points[ixA];
Vector3 vB1 = input.points[ixB1];
Vector3 vB2 = input.points[ixB2];
Vector3 vMid1 = FindBoundary(vAO, vB1, volume);
Vector3 vMid2 = FindBoundary(vAO, vB2, volume);
Vector3 vMidB = input.points[ixB1]*0.5f + input.points[ixB2]*0.5f;
points.Add(vMid1); points.Add(vMid2); points.Add(vMidB);
float b1 = (vMid1 - vAO).Length / ((vB1 - vAO).Length + float.Epsilon);
float b2 = (vMid2 - vAO).Length / ((vB2 - vAO).Length + float.Epsilon);
Debug.Assert(0 <= b1 && b1 <= 1 && 0 <= b2 && b2 <= 1);
Vector3 nMid1 = input.normals[ixA] * (1 - b1) + input.normals[ixB1] * b1;
Vector3 nMid2 = input.normals[ixA] * (1 - b2) + input.normals[ixB2] * b2;
Vector3 nMidB = input.normals[ixB1] * 0.5f + input.normals[ixB2] * 0.5f;
nMid1.Normalize(); nMid2.Normalize(); nMidB.Normalize();
norms.Add(nMid1); norms.Add(nMid2); norms.Add(nMidB);
//norms.Add(input.normals[ixA]); norms.Add(input.normals[ixA]); norms.Add(input.normals[ixA]);
var tri1 = new Mesh.Triangle(ixA, points.Count - 3, points.Count - 2);
var tri2 = new Mesh.Triangle(ixB1, points.Count - 3, points.Count - 1);
var tri3 = new Mesh.Triangle(points.Count - 3, points.Count - 2, points.Count - 1);
var tri4 = new Mesh.Triangle(ixB2, points.Count - 2, points.Count - 1);
tri1.normal = tri2.normal = tri3.normal = tri4.normal = tri.normal;
tris.Add(tri1); tris.Add(tri2); tris.Add(tri3); tris.Add(tri4);
trisIn.Add(containsA);
trisIn.Add(!containsA);
trisIn.Add(!containsA);
trisIn.Add(!containsA);
}
}
// done
Logger.info("split mesh, started with " + nt + " tris, added " + (tris.Count-nt));
Debug.Assert(points.Count==norms.Count);
output = new Mesh(points.ToArray(), norms.ToArray(), tris.ToArray());
trisInside = trisIn.ToArray();
}