//Each point defines a plane,
//we get polyhedra enclosed by all such planes
public List <List <Vector3> > GetPlaneCutPolygons(Vector3[] points)
{
List <List <Vector3> > polys = new List <List <Vector3> >();
for (int i = 0; i < points.Length; i++)
{
Vector3 p = points[i];
Plane plane = new Plane(p.normalized, p);
//Project everything on a point-based plane
//and find 2d rays of intersection with other planes
Vector3 planeBasisX = p.GetSomeOrthogonal().normalized;
Vector3 planeBasisY = Vector3.Cross(p, p.GetSomeOrthogonal()).normalized;
List <Ray2D> intersWithOther = new List <Ray2D>();
for (int j = 0; j < points.Length; j++)
{
if (i == j)
{
continue;
}
Plane other = new Plane(points[j].normalized, points[j]);
Ray? possibleInter = plane.GetIntersection(other);
if (possibleInter == null)
{
continue;
}
Ray inter = possibleInter.Value;
Ray2D interInPlane = new Ray2D(
Extensions.ProjectOnPlanarBasis(planeBasisX, planeBasisY, inter.origin - p),
Extensions.ProjectOnPlanarBasis(planeBasisX, planeBasisY, inter.direction)
);
//Set winding dir
if (Extensions.PerpDot(interInPlane.direction, interInPlane.origin) > 0)
{
interInPlane.direction = -interInPlane.direction;
}
intersWithOther.Add(interInPlane);
}
//Find nearest ray
float smallestSqrDist = float.MaxValue;
Vector2 nearestPoint = Vector2.zero;
int nearestRayIndex = -1;
for (int j = 0; j < intersWithOther.Count; j++)
{
Ray2D r = intersWithOther[j];
Vector2 candidateNearestPoint = r.GetNearestPointOnRay(Vector2.zero);
if (candidateNearestPoint.sqrMagnitude < smallestSqrDist)
{
smallestSqrDist = candidateNearestPoint.sqrMagnitude;
nearestPoint = candidateNearestPoint;
nearestRayIndex = j;
}
}
List <Vector2> polyVertices = new List <Vector2>();
//Go clockwise searching nearest intersections between current ray and others
int startRayIndex = nearestRayIndex;
int rayIndex = startRayIndex;
int prevRayIndex = rayIndex;
Vector2 position = nearestPoint;
do
{
Ray2D ray = intersWithOther[rayIndex];
smallestSqrDist = float.MaxValue;
Vector2 nearestNextPosition = Vector2.zero;
for (int j = 0; j < intersWithOther.Count; j++)
{
Ray2D otherRay = intersWithOther[j];
if (j == rayIndex || j == prevRayIndex)
{
continue;
}
Vector2 inters = ray.GetIntersection(otherRay);
if ((inters - position).sqrMagnitude < smallestSqrDist && Vector2.Dot(ray.direction, inters - position) > 0)
{
smallestSqrDist = (inters - position).sqrMagnitude;
nearestNextPosition = inters;
nearestRayIndex = j;
}
}
position = nearestNextPosition;
polyVertices.Add(position);
prevRayIndex = rayIndex;
rayIndex = nearestRayIndex;
} while (rayIndex != startRayIndex);
List <Vector3> polyVertices3D = new List <Vector3>();
foreach (Vector2 v in polyVertices)
{
polyVertices3D.Add(p + v.x * planeBasisX + v.y * planeBasisY);
}
polys.Add(polyVertices3D);
}
return(polys);
}