Efficient algorithms for boundary extraction of 2D and 3D orthogonal pseudomanifolds

Abstract

In this paper we present algorithms to extract the boundary representation of orthogonal polygons and polyhedra, either manifold or pseudomanifold. The algorithms we develop reconstruct not only the polygons of the boundaries but also the hole-face inclusion relationship. Our algorithms have a simple input so they can be used to convert many different kinds of models to B-Rep. In the 2D case, the input is the set of vertices, and in the 3D case, some small additional information must be supplied for every vertex. All proposed algorithms run in O(n log n) time and use O(n) space, where n is the number of vertices of the input. Moreover, we explain how to use our proposal to extract the boundary from the well-known voxel and octree models as well as from three vertex-based models found in the related literature: the neighbourhood, the EVM, and the weighted vertex list models.

Compact Union of Disjoint Boxes: An Efficient Decomposition Model for Binary Volumes

“…EVM is actually a complete solid model with very fast Boolean operations, it is an implicit B-Rep model, i.e., all the geometry and topological relations concerning faces, edges and vertices of the represented OPP can be obtained from the EVM [43] and therefore represents OPP unambiguously [55].…”

A Practical and Robust Method to Compute the Boundary of Three-dimensional Axis-aligned Boxes

“…This information encodes the local topology of the vertex (see Figure 1) and it is required to prevent ambiguity in the reconstruction. It is the input needed, in addition to the vertex coordinates, for the B-rep extraction by Vigo et al (Vigo et al, 2012). There are ten basic local configurations for a vertex.…”

“…Furthermore, the union of axis-aligned boxes is an orthogonal polyhedron. Their constrained structure has enabled advances on complex or unsolved problems for arbitrary shapes (Bournez et al, 1999;Vigo et al, 2012).…”

“…The output of the presented method is a B-rep of the union of the boxes. For this purpose, we apply the results presented by Vigo et al (Vigo et al, 2012). Their algorithm obtains the B-rep from the list of vertices in an orthogonal polyhedron's boundary and additional information concerning the local topology of each vertex.…”

Skeletal representations of orthogonal shapes

“…Orthogonal shapes are a subset of polytopes, where the facets hyperplanes are restricted to be axis aligned. The constrained structure of orthogonal shapes has enabled advances on complex or unsolved problems for arbitrary shapes [44]. In the main, computation of orthogonal shape properties is robust and is less complex compared with more general shape representations.…”