
Quadrilateral meshes for PSLGs
We prove that every planar straight line graph with n vertices has a con...
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Nonobtuse triangulations of PSLGs
We show that any planar straight line graph (PSLG) with n vertices has a...
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Drawing Graphs with Circular Arcs and RightAngle Crossings
In a RAC drawing of a graph, vertices are represented by points in the p...
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Angles of ArcPolygons and Lombardi Drawings of Cacti
We characterize the triples of interior angles that are possible in non...
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Efficient constructions of the Prefersame and Preferopposite de Bruijn sequences
The greedy Prefersame de Bruijn sequence construction was first present...
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Neural Network Based Reconstruction of a 3D Object from a 2D Wireframe
We propose a new approach for constructing a 3D representation from a 2D...
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Table Based Detection of Degenerate Predicates in Free Space Construction
The key to a robust and efficient implementation of a computational geom...
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Polygons with Prescribed Angles in 2D and 3D
We consider the construction of a polygon P with n vertices whose turning angles at the vertices are given by a sequence A=(α_0,…, α_n1), α_i∈ (π,π), for i∈{0,…, n1}. The problem of realizing A by a polygon can be seen as that of constructing a straightline drawing of a graph with prescribed angles at vertices, and hence, it is a special case of the well studied problem of constructing an angle graph. In 2D, we characterize sequences A for which every generic polygon P⊂ℝ^2 realizing A has at least c crossings, for every c∈ℕ, and describe an efficient algorithm that constructs, for a given sequence A, a generic polygon P⊂ℝ^2 that realizes A with the minimum number of crossings. In 3D, we describe an efficient algorithm that tests whether a given sequence A can be realized by a (not necessarily generic) polygon P⊂ℝ^3, and for every realizable sequence the algorithm finds a realization.
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