/// <summary>
/// Build open influence region with 3 faces for a given edge.
/// </summary>
/// <param name="edge">The given edge.</param>
/// <param name="edges">All existing edges.</param>
/// <param name="ap1">Allowed point 1</param>
/// <param name="ap2">Allowed point 2</param>s
/// <param name="innerPoints">Points that approximately lie inside the influence region (polyhedron).</param>
/// <returns>The polyhedron.</returns>
private ConvexPolyhedron BuildPolyhedron2(Edge edge, Dictionary <Edge, Edge> edges, out int ap1, out int ap2, out List <int> innerPoints)
{
buildPCounter++;
ap1 = -1;
ap2 = -1;
int i = edge.vertex1;
int j = edge.vertex2;
int k = edge.vertex3;
// check if the i and j vertices are chosen correctly
if (Vector3.Dot(Vector3.Cross(PointCloud[k].Position - PointCloud[i].Position, PointCloud[k].Position - PointCloud[j].Position), edge.normal) < 0)
{
i = edge.vertex2;
j = edge.vertex1;
}
// positions of i, j and k
Vector3 ip = PointCloud[i].Position;
Vector3 jp = PointCloud[j].Position;
Vector3 kp = PointCloud[k].Position;
Vector3 n1 = Vector3.Cross(edge.normal, jp - ip).normalized;
Vector3 n3 = (Vector3.Cross(n1 + Mathf.Tan(Mathf.Deg2Rad * regionAngle) * (ip - jp).normalized, edge.normal)).normalized;
Vector3 n2 = Vector3.Cross(edge.normal, n1 + Mathf.Tan(Mathf.Deg2Rad * regionAngle) * (jp - ip).normalized).normalized;
float s = sMult * (float)Math.Max(PointCloud[i].UniformityDegree, PointCloud[j].UniformityDegree) * (PointCloud[i].MinEdge + PointCloud[j].MinEdge) / 2;
ConvexPolyhedron polyhedron = new ConvexPolyhedron();
polyhedron.AddFace(n1, ip);
polyhedron.AddFace(n2, ip);
polyhedron.AddFace(n3, jp);
polyhedron.AddFace(-n1, s * -n1 + (ip + jp) / 2);
polyhedron.AddFace(edge.normal, ip + s * edge.normal); // top face
polyhedron.AddFace(-edge.normal, ip - s * edge.normal); // bottom face -
innerPoints = VoxelSet.GetInnerPoints(polyhedron, false, influenceRegion2, (ip + jp) / 2);
Vector3?pLeft = null, pRight = null;
float minAngleLeft = 181f, minAngleRight = 181f;
foreach (var point in innerPoints)
{
if (point == i || point == j)
{
continue;
}
Edge left = new Edge(point, i, Vector3.back);
Edge right = new Edge(point, j, Vector3.back);
if (edges.ContainsKey(left))
{
float angleLeft = Vector3.Angle(ip - jp, PointCloud[point].Position - ip);
if (angleLeft < minAngleLeft)
{
minAngleLeft = angleLeft;
pLeft = PointCloud[point].Position;
ap1 = point;
}
}
if (edges.ContainsKey(right))
{
float angleRight = Vector3.Angle(jp - ip, PointCloud[point].Position - jp);
if (angleRight < minAngleRight)
{
minAngleRight = angleRight;
pRight = PointCloud[point].Position;
ap2 = point;
}
}
}
ConvexPolyhedron p = new ConvexPolyhedron();
p.AddFace(n1, ip);
if (pLeft == null)
{
p.AddFace(n2, ip);
}
else
{
p.AddFace(Vector3.Cross((Vector3)pLeft - ip, edge.normal).normalized, ip);
}
if (pRight == null)
{
p.AddFace(n3, jp);
}
else
{
p.AddFace(-Vector3.Cross((Vector3)pRight - jp, edge.normal).normalized, jp);
}
polyhedron.AddFace(-n1, s * -n1 + (ip + jp) / 2);
return(p);
}
/// <summary>
/// Build an influence region of the given edge.
/// </summary>
/// <param name="edge">The edge, which influence region to be foind.</param>
/// <param name="edges">The set of existing edges.</param>
/// <returns>Polyhedron object that is the influence region.</returns>
private ConvexPolyhedron BuildPolyhedron(Edge edge, Dictionary <Edge, Edge> edges, out int ap1, out int ap2, out List <int> innerPoints)
{
if (influenceRegion2)
{
return(BuildPolyhedron2(edge, edges, out ap1, out ap2, out innerPoints));
}
buildPCounter++;
ap1 = -1;
ap2 = -1;
int i = edge.vertex1;
int j = edge.vertex2;
int k = edge.vertex3;
// check if the i and j vertices are chosen correctly
if (Vector3.Dot(Vector3.Cross(PointCloud[k].Position - PointCloud[i].Position, PointCloud[k].Position - PointCloud[j].Position), edge.normal) < 0)
{
i = edge.vertex2;
j = edge.vertex1;
}
// positions of i, j and k
Vector3 ip = PointCloud[i].Position;
Vector3 jp = PointCloud[j].Position;
Vector3 kp = PointCloud[k].Position;
// the size of the polyhedron
float s = (float)Math.Max(PointCloud[i].UniformityDegree, PointCloud[j].UniformityDegree) * (PointCloud[i].MinEdge + PointCloud[j].MinEdge) / 2;
// bary center of the triangle ijk
Vector3 p = (ip + jp + kp) / 3;
// center of the edge ij
Vector3 p_m = (ip + jp) / 2;
// normal of the triangle (polygon) ijk
Vector3 N = edge.normal;
ConvexPolyhedron polyhedron = new ConvexPolyhedron();
Vector3 n1 = Vector3.Cross(edge.normal, jp - ip).normalized;
polyhedron.AddFace(n1, ip); // test
polyhedron.AddFace(N, p_m + 2 * s * N); // top face
polyhedron.AddFace(-N, p_m - 2 * s * N); // bottom face -
polyhedron.AddFace(-Vector3.Cross(N, ip - p).normalized, ip); // face containing pi -
polyhedron.AddFace(Vector3.Cross(N, jp - p).normalized, jp); // face containing pj
Vector3 N5 = Vector3.Cross(jp - ip, N).normalized;
polyhedron.AddFace(N5, p_m + s * N5);
// here it checks whether there are some edges inside the influnce region
// that are connected to i or j
var points = VoxelSet.GetInnerPoints(polyhedron, smartUpdate, influenceRegion2, p_m);
Vector3?pLeft = null, pRight = null;
//float minAngleLeft = 181f, minAngleRight = 181f;
float minAngleLeft = 90 + regionAngle, minAngleRight = 90 + regionAngle;
foreach (var point in points)
{
if (point == i || point == j)
{
continue;
}
Edge left = new Edge(point, i, Vector3.back);
Edge right = new Edge(point, j, Vector3.back);
if (edges.ContainsKey(left))
{
float angleLeft = Vector3.Angle(jp - ip, PointCloud[point].Position - ip);
if (angleLeft < minAngleLeft)
{
minAngleLeft = angleLeft;
pLeft = PointCloud[point].Position;
ap1 = point;
}
}
if (edges.ContainsKey(right))
{
float angleRight = Vector3.Angle(ip - jp, PointCloud[point].Position - jp);
if (angleRight < minAngleRight)
{
minAngleRight = angleRight;
pRight = PointCloud[point].Position;
ap2 = point;
}
}
}
// additional faces that we need to hold geometry integrity
if (pLeft != null)
{
polyhedron.AddFace(-Vector3.Cross(N, (Vector3)pLeft - ip).normalized, ip);
}
if (pRight != null)
{
polyhedron.AddFace(Vector3.Cross(N, (Vector3)pRight - jp).normalized, jp);
}
innerPoints = points;
return(polyhedron);
}
