Class Polyhedron
Summary
Represents a three-dimensional closed geometric solid defined by flat polygonal faces.
Represents a three-dimensional closed geometric solid defined by flat polygonal faces.
 Polyhedron | Represents a three-dimensional closed geometric solid defined by flat polygonal faces. |
 v | Specifies the vertices of this polyhedron. |
| f | Specifies the individual faces of this polyhedron. |
 ctor | The default constructor creates a null polyhedron. |
| NumVertices()[const] | Returns the number of vertices in this polyhedron. |
| NumFaces()[const] | Returns the number of faces in this polyhedron. |
| NumEdges()[const] | Returns the number of (unique) edges in this polyhedron. |
| VertexArrayPtr() (+1 overload) | Returns a pointer to an array of vertices of this polyhedron. |
| Vertex(vertexIndex)[const] | Returns the |
| Edge(edgeIndex)[const] | Returns the |
| Edges()[const] | Returns all the (unique) edges of this polyhedron. |
| Faces()[const] | |
| EdgeIndices()[const] | Returns all the (unique) edges of this polyhedron, as indices to the polyhedron vertex array. |
| FacePolygon(faceIndex)[const] | Returns a polygon representing the given face. |
| FacePlane(faceIndex)[const] | Returns the plane of the given polyhedron face. |
| FaceNormal(faceIndex)[const] | Returns the normalized normal vector of the given face. |
| ExtremeVertex(direction)[const] | Returns the index of the vertex of this polyhedron that reaches farthest in the given direction. |
| ExtremePoint(direction)[const] | Computes an extreme point of this Polyhedron in the given direction. |
| ProjectToAxis(...)[const] | Projects this Polyhedron onto the given 1D axis direction vector. |
| ConvexCentroid()[const] | Returns the exact center of mass of the convex hull of this polyhedron. |
| ApproximateConvexCentroid()[const] | If this Polyhedron is a tetrahedron, this is the center of mass for the Polyhedron. |
| SurfaceArea()[const] | Computes the total surface area of the faces of this polyhedron. |
| Volume()[const] | Computes the internal volume of this polyhedron. |
| MinimalEnclosingAABB()[const] | Returns the smallest AABB that encloses this polyhedron. |
| MergeAdjacentPlanarFaces() | |
| FaceIndicesValid()[const] | Tests if the faces in this polyhedron refer to valid existing vertices. |
| FlipWindingOrder() | Flips the winding order of all faces in this polyhedron. |
| OrientNormalsOutsideConvex() | Assuming that this polyhedron is convex, reorients all faces of this polyhedron so that each face plane has its normal pointing outwards. |
| RemoveRedundantVertices() | Removes from the vertex array all vertices that are not referred to by any of the faces of this polyhedron. |
| IsNull()[const] | Returns true if this polyhedron has 0 vertices and 0 faces. |
| IsClosed()[const] | Returns true if this polyhedron is closed and does not have any gaps. |
| IsConvex()[const] | Returns true if this polyhedron is convex. |
| EulerFormulaHolds()[const] | Returns true if the Euler formula (V + F - E == 2) holds for this Polyhedron. |
| FacesAreNondegeneratePlanar(epsilon)[const] | Tests whether all the faces of this polyhedron are non-degenerate (have at least 3 vertices) and in case they have more than 3 vertices, tests that the faces are planar. |
| ClipLineSegmentToConvexPolyhedron(...)[const] | Clips the line/ray/line segment specified by L(t) = ptA + t * dir, tFirst <= t <= tLast, inside this |
| NearestVertex(point)[const] | Returns the index of the nearest vertex to the given point. |
| Contains(point)[const] (+7 overloads) | Tests if the given object is fully contained inside this closed polyhedron. |
| FaceContains(...)[const] | Tests if the given face of this Polyhedron contains the given point. |
| FaceContainmentDistance2D(...)[const] | A helper for Contains() and FaceContains() tests: Returns a positive value if the given point is contained in the given face, and a negative value if the given point is outside the face. |
| ContainsConvex(point,epsilon)[const] (+2 overloads) | Tests if the given object is fully contained inside this |
| ClosestPoint(...)[const] (+2 overloads) | Computes the closest point on this polyhedron to the given object. |
| ClosestPointConvex(point)[const] | Returns the closest point on this |
| Distance(point)[const] | Returns the distance between this polyhedron and the given object. |
| Intersects(lineSegment)[const] (+11 overloads) | Tests whether this polyhedron and the given object intersect. |
| IntersectsConvex(line)[const] (+2 overloads) | Tests whether this |
| MergeConvex(point) | |
| Translate(offset) | Translates this Polyhedron in world space. |
| Transform(transform) (+3 overloads) | Applies a transformation to this Polyhedron. |
| SetEquals(p2) | Tests if these two polyhedrons represent the same set of points. |
| SwapVertices(i,j) | Swaps two vertices in the vertex array and updates all faces of this polyhedron so that the volume represented by this polyhedron stays the same. |
| CanonicalizeFaceArray() | Converts the list of faces into a canonical order for easier comparison. |
| ContainsFace(face)[const] | Returns true if one of the faces of this Polyhedron has the same ordered of indices as the given Face. |
| FindClosestVertex(pt,outDistanceSq)[const] | Searches each vertex of this polyhedron to find the closest vertex to the given target point. |
| Triangulate()[const] | |
| ToString()[const] | |
| ConvexHull(...)[static] | Creates a Polyhedron object that represents the convex hull of the given point array. |
| Tetrahedron(...)[static] | See http://paulbourke.net/geometry/platonic/. |
| Octahedron(...)[static] | See http://paulbourke.net/geometry/platonic/. |
| Hexahedron(...)[static] | See http://paulbourke.net/geometry/platonic/. |
| Icosahedron(...)[static] | See http://paulbourke.net/geometry/platonic/. |
| Dodecahedron(...)[static] | See http://paulbourke.net/geometry/platonic/. |