 Polyhedron[Class Summary] |
 v |
| f |
 ctor |
| NumVertices()[const] |
| NumFaces()[const] |
| NumEdges()[const] |
| VertexArrayPtr() (+1 overload) |
| Vertex(vertexIndex)[const] |
| Edge(edgeIndex)[const] |
| Edges()[const] |
| Faces()[const] |
| EdgeIndices()[const] |
| FacePolygon(faceIndex)[const] |
| FacePlane(faceIndex)[const] |
| FaceNormal(faceIndex)[const] |
| ExtremeVertex(direction)[const] |
| ExtremePoint(direction)[const] |
| ProjectToAxis(...)[const] |
| ConvexCentroid()[const] |
| ApproximateConvexCentroid()[const] |
| SurfaceArea()[const] |
| Volume()[const] |
| MinimalEnclosingAABB()[const] |
| MergeAdjacentPlanarFaces() |
| FaceIndicesValid()[const] |
| FlipWindingOrder() |
| OrientNormalsOutsideConvex() |
| RemoveRedundantVertices() |
| IsNull()[const] |
| IsClosed()[const] |
| IsConvex()[const] |
| EulerFormulaHolds()[const] |
| FacesAreNondegeneratePlanar(epsilon)[const] |
| ClipLineSegmentToConvexPolyhedron(...)[const] |
| NearestVertex(point)[const] |
| Contains(point)[const] (+7 overloads) |
| FaceContains(...)[const] |
| FaceContainmentDistance2D(...)[const] |
| ContainsConvex(point,epsilon)[const] (+2 overloads) |
| ClosestPoint(...)[const] (+2 overloads) |
| ClosestPointConvex(point)[const] |
| Distance(point)[const] |
| Intersects(lineSegment)[const] (+11 overloads) |
| IntersectsConvex(line)[const] (+2 overloads) |
| MergeConvex(point) |
| Translate(offset) |
| Transform(transform) (+3 overloads) |
| SetEquals(p2) |
| SwapVertices(i,j) |
| CanonicalizeFaceArray() |
| ContainsFace(face)[const] |
| FindClosestVertex(pt,outDistanceSq)[const] |
| Triangulate()[const] |
| ToString()[const] |
| ConvexHull(...)[static] |
| Tetrahedron(...)[static] |
| Octahedron(...)[static] |
| Hexahedron(...)[static] |
| Icosahedron(...)[static] |
| Dodecahedron(...)[static] |
Polyhedron::IsConvex
Syntax
bool Polyhedron::IsConvex() const; [26 lines of code]Returns true if this polyhedron is convex.
The running time is O(F*V) ~ O(V^2).
See Also
Work in progress:
Todo: in bool Polyhedron::IsConvex() const:
Real-Time Collision Detection, p. 64: A faster O(n) approach is to compute for each face F of P the centroid C of F, and for all neighboring faces G of F test if C lies behind the supporting plane of G. If some C fails to lie behind the supporting plane of one or more neighboring faces, P is concave, and is otherwise assumed convex. However, note that just as the corresponding polygonal convexity test may fail for a pentagram this test may fail for, for example, a pentagram extruded out of its plane and capped at the ends.