Faster ASV decomposition for orthogonal polyhedra using the Extreme Vertices Model (EVM)

The alternating sum of volumes (ASV) decomposition is a widely used technique for converting a B-Rep into a CSG model. The obtained CSG tree has convex primitives at its leaf nodes, while the contents of its internal nodes alternate between the set union and difference operators. This work first shows that the obtained CSG tree T can also be expressed as the regularized Exclusive-OR operation among all the convex primitives at the leaf nodes of T, regardless the structure and internal nodes of T. This is an important result in the case in which EVM represented orthogonal polyhedra are used because in this model the Exclusive-OR operation runs much faster than set union and difference operations. Therefore this work applies this result to EVM represented orthogonal polyhedra. It also presents experimental results that corroborate the theoretical results and includes some practical uses for the ASV decomposition of orthogonal polyhedra.Postprint (published version

Spatiotemporal Characteristics of the Largest HIV-1 CRF02_AG Outbreak in Spain: Evidence for Onward Transmissions

Background and Aim: The circulating recombinant form 02_AG (CRF02_AG) is the predominant clade among the human immunodeficiency virus type-1 (HIV-1) non-Bs with a prevalence of 5.97% (95% Confidence Interval-CI: 5.41–6.57%) across Spain. Our aim was to estimate the levels of regional clustering for CRF02_AG and the spatiotemporal characteristics of the largest CRF02_AG subepidemic in Spain.Methods: We studied 396 CRF02_AG sequences obtained from HIV-1 diagnosed patients during 2000–2014 from 10 autonomous communities of Spain. Phylogenetic analysis was performed on the 391 CRF02_AG sequences along with all globally sampled CRF02_AG sequences (N = 3,302) as references. Phylodynamic and phylogeographic analysis was performed to the largest CRF02_AG monophyletic cluster by a Bayesian method in BEAST v1.8.0 and by reconstructing ancestral states using the criterion of parsimony in Mesquite v3.4, respectively.Results: The HIV-1 CRF02_AG prevalence differed across Spanish autonomous communities we sampled from (p < 0.001). Phylogenetic analysis revealed that 52.7% of the CRF02_AG sequences formed 56 monophyletic clusters, with a range of 2–79 sequences. The CRF02_AG regional dispersal differed across Spain (p = 0.003), as suggested by monophyletic clustering. For the largest monophyletic cluster (subepidemic) (N = 79), 49.4% of the clustered sequences originated from Madrid, while most sequences (51.9%) had been obtained from men having sex with men (MSM). Molecular clock analysis suggested that the origin (tMRCA) of the CRF02_AG subepidemic was in 2002 (median estimate; 95% Highest Posterior Density-HPD interval: 1999–2004). Additionally, we found significant clustering within the CRF02_AG subepidemic according to the ethnic origin.Conclusion: CRF02_AG has been introduced as a result of multiple introductions in Spain, following regional dispersal in several cases. We showed that CRF02_AG transmissions were mostly due to regional dispersal in Spain. The hot-spot for the largest CRF02_AG regional subepidemic in Spain was in Madrid associated with MSM transmission risk group. The existence of subepidemics suggest that several spillovers occurred from Madrid to other areas. CRF02_AG sequences from Hispanics were clustered in a separate subclade suggesting no linkage between the local and Hispanic subepidemics

Conversión de un árbol CSG a su forma normal disyuntiva. Implementación de una versión gráfica interactiva

This work presents a graphical and interactive implementation of an algorithm that transforms CSG trees into its Disjunctive Normal Form.Postprint (published version

Implementación del algoritmo de subdivisión recursiva de poliedros

Recursive Subdivision is a scheme for modeling solids limited by complex surfaces. In this case, an initial polyhedron acts as a sketch of the final surface, which is automatically generated by the subdivision algorithm. This work presents an implementation for this algorithm in a way that is compatible with an existing local scene format definition and provides some clues for determining the polyhedron's size at each step of the process

Implementación del algoritmo de subdivisión recursiva de poliedros

Recursive Subdivision is a scheme for modeling solids limited by complex surfaces. In this case, an initial polyhedron acts as a sketch of the final surface, which is automatically generated by the subdivision algorithm. This work presents an implementation for this algorithm in a way that is compatible with an existing local scene format definition and provides some clues for determining the polyhedron's size at each step of the process

Conversión de un árbol CSG a su forma normal disyuntiva. Implementación de una versión gráfica interactiva

This work presents a graphical and interactive implementation of an algorithm that transforms CSG trees into its Disjunctive Normal Form

Faster ASV decomposition for orthogonal polyhedra using the Extreme Vertices Model (EVM)

The alternating sum of volumes (ASV) decomposition is a widely used technique for converting a B-Rep into a CSG model. The obtained CSG tree has convex primitives at its leaf nodes, while the contents of its internal nodes alternate between the set union and difference operators. This work first shows that the obtained CSG tree T can also be expressed as the regularized Exclusive-OR operation among all the convex primitives at the leaf nodes of T, regardless the structure and internal nodes of T. This is an important result in the case in which EVM represented orthogonal polyhedra are used because in this model the Exclusive-OR operation runs much faster than set union and difference operations. Therefore this work applies this result to EVM represented orthogonal polyhedra. It also presents experimental results that corroborate the theoretical results and includes some practical uses for the ASV decomposition of orthogonal polyhedra

Faster ASV decomposition for orthogonal polyhedra using the Extreme Vertices Model (EVM)

The alternating sum of volumes (ASV) decomposition is a widely used technique for converting a B-Rep into a CSG model. The obtained CSG tree has convex primitives at its leaf nodes, while the contents of its internal nodes alternate between the set union and difference operators. This work first shows that the obtained CSG tree T can also be expressed as the regularized Exclusive-OR operation among all the convex primitives at the leaf nodes of T, regardless the structure and internal nodes of T. This is an important result in the case in which EVM represented orthogonal polyhedra are used because in this model the Exclusive-OR operation runs much faster than set union and difference operations. Therefore this work applies this result to EVM represented orthogonal polyhedra. It also presents experimental results that corroborate the theoretical results and includes some practical uses for the ASV decomposition of orthogonal polyhedra

Representation and boundary extraction of a 3D digital image using the EVM model

In recent published papers we have presented the Extreme Vertices Model (EVM), a concise and complete model for representing orthogonal polyhedra. This model exploits the simplicity of its domain by allowing robust and simple algorithms for set-membership classification and Boolean operations that do not need to perform floating-point operations. A digital image is geometrically analogue to an orthogonal polyhedron and can therefore be represented with the EVM. In this paper we discuss the performance in terms of space occupancy and algorithm complexity of representing digital binary images by this model. We also present a boundary extraction algorithm of a 3D digital image using the EVM and discuss its performance.Postprint (published version

Representation and boundary extraction of a 3D digital image using the EVM model

In recent published papers we have presented the Extreme Vertices Model (EVM), a concise and complete model for representing orthogonal polyhedra. This model exploits the simplicity of its domain by allowing robust and simple algorithms for set-membership classification and Boolean operations that do not need to perform floating-point operations. A digital image is geometrically analogue to an orthogonal polyhedron and can therefore be represented with the EVM. In this paper we discuss the performance in terms of space occupancy and algorithm complexity of representing digital binary images by this model. We also present a boundary extraction algorithm of a 3D digital image using the EVM and discuss its performance