Reconstructing orthogonal polyhedra from putative vertex sets

Biedl, Thérèse; Genç, Burkay

doi:10.1016/j.comgeo.2011.04.002

Cited by 19 publications

(16 citation statements)

References 4 publications

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“…One particular problem is reconstructing a 2D orthogonal shape from point data [4,5,6,7]. In existing works, points are either assumed to be anywhere within the polygon boundary or exactly required to be the vertices of the polygon.…”

Section: Introductionmentioning

confidence: 99%

Covering oriented points in the plane with orthogonal polygons is NP-complete

Evrendilek

Genç

Hnich

2010

Electronic Notes in Discrete Mathematics

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Section: Introductionmentioning

confidence: 99%

Covering oriented points in the plane with orthogonal polygons is NP-complete

Evrendilek

Genç

Hnich

2010

Electronic Notes in Discrete Mathematics

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“…There is another model that uses a vertex list [23], but it is restricted to orthogonally convex polyhedra which are the subset of orthogonal polyhedra, which satisfy the following condition: any axis-parallel line intersects the polyhedron in at most one line segment. This restricted class of polyhedra can be represented with all its vertices and without any associated information.…”

Section: Previous Workmentioning

confidence: 99%

“…An edge ab is called vertical if it is parallel to the y axis, and horizontal if parallel to the x axis. A polygon, see [23], is a set P in a plane whose boundary is composed by an external closed curve and a set, possibly empty, of internal closed curves, defining the holes of the polygon. Each curve is the union of a finite number of line segments.…”

Section: Notations and Overview Of The Algorithmsmentioning

confidence: 99%

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

et al. 2012

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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.

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“…The following is the steps for grouping vertices, and implement them in PROCEDURE GroupingVertices( (4,1,3) v12 (7,1,5) v7 (4,4,5) v (7,4,5) p2 activities:…”

Section: Grouping Verticesmentioning

confidence: 99%

“…Generally, there are two type of data structures in polyhedra representation: edge-based data structure and vertex based data structure [7]. Aquilera and Ayala represented an orthogonal polyhedra by using extreme vertices only [2].…”

Section: A Data Structure For Orthogonal Polyhedronmentioning

confidence: 99%

An algorithm for splitting an orthogonal polyhedron with an orthogonal polyplane

Marzal

Xie

Fung

2011

2011 International Conference on Uncertainty Reasoning and Knowledge Engineering

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Marzal, J., Xie, H. and Fung, C.C. (2011)AnAbstract -Splitting of an orthogonal polyhedron is an essential operation in many orthogonal polyhedron related problems. This paper proposes an algorithm for splitting an orthogonal polyhedron with an orthogonal polyplane. There are four major steps of this algorithm: 1) sort the vertices of the orthogonal polyhedron in ABC-sorted order; 2) calculate the vertices at the intersection between the orthogonal polyhedron and the polyplane; 3) find the polyplane vertices, and 4) group the updated vertices into two groups of orthogonal polyhedra. Overall, the algorithm performs with O(n log n) time where n is the number of vertices of a given orthogonal polyhedron.

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Reconstructing orthogonal polyhedra from putative vertex sets

Cited by 19 publications

References 4 publications

Covering oriented points in the plane with orthogonal polygons is NP-complete

Covering oriented points in the plane with orthogonal polygons is NP-complete

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

An algorithm for splitting an orthogonal polyhedron with an orthogonal polyplane

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