2,564 research outputs found
Algorithmic Perception of Vertices in Sketched Drawings of Polyhedral Shapes
In this article, visual perception principles were used to build an artificial perception model aimed at developing an algorithm for detecting junctions in line drawings of polyhedral objects that are vectorized from hand-drawn sketches. The detection is performed in two dimensions (2D), before any 3D model is available and minimal information about the shape depicted by the sketch is used. The goal of this approach is to not only detect junctions in careful sketches created by skilled engineers and designers but also detect junctions when skilled people draw casually to quickly convey rough ideas. Current approaches for extracting junctions from digital images are mostly incomplete, as they simply merge endpoints that are near each other, thus ignoring the fact that different vertices may be represented by different (but close) junctions and that the endpoints of lines that depict edges that share a common vertex may not necessarily be close to each other, particularly in quickly sketched drawings. We describe and validate a new algorithm that uses these perceptual findings to merge tips of line segments into 2D junctions that are assumed to depict 3D vertices
Searching edges in the overlap of two plane graphs
Consider a pair of plane straight-line graphs, whose edges are colored red
and blue, respectively, and let n be the total complexity of both graphs. We
present a O(n log n)-time O(n)-space technique to preprocess such pair of
graphs, that enables efficient searches among the red-blue intersections along
edges of one of the graphs. Our technique has a number of applications to
geometric problems. This includes: (1) a solution to the batched red-blue
search problem [Dehne et al. 2006] in O(n log n) queries to the oracle; (2) an
algorithm to compute the maximum vertical distance between a pair of 3D
polyhedral terrains one of which is convex in O(n log n) time, where n is the
total complexity of both terrains; (3) an algorithm to construct the Hausdorff
Voronoi diagram of a family of point clusters in the plane in O((n+m) log^3 n)
time and O(n+m) space, where n is the total number of points in all clusters
and m is the number of crossings between all clusters; (4) an algorithm to
construct the farthest-color Voronoi diagram of the corners of n axis-aligned
rectangles in O(n log^2 n) time; (5) an algorithm to solve the stabbing circle
problem for n parallel line segments in the plane in optimal O(n log n) time.
All these results are new or improve on the best known algorithms.Comment: 22 pages, 6 figure
Perimeter detection in sketched drawings of polyhedral shapes
Ponència presentada al STAG17: Smart tools and Applications in Graphics, celebrat a Catania (Ità lia) 11-12 setembre 2017This paper describes a new “envelope” approach for detecting object perimeters in line-drawings vectorised from
sketches of polyhedral objects.
Existing approaches for extracting contours from digital images are unsuitable for Sketch-Based Modelling, as they
calculate where the contour is, but not which elements of the line-drawing belong to it.
In our approach, the perimeter is described in terms of lines and junctions (including intersections and T-junctions)
of the original line drawing
Tropical cycles and Chow polytopes
The Chow polytope of an algebraic cycle in a torus depends only on its
tropicalisation. Generalising this, we associate a Chow polytope to any
abstract tropical variety in a tropicalised toric variety. Several significant
polyhedra associated to tropical varieties are special cases of our Chow
polytope. The Chow polytope of a tropical variety is given by a simple
combinatorial construction: its normal subdivision is the Minkowski sum of
and a reflected skeleton of the fan of the ambient toric variety.Comment: 22 pp, 3 figs. Added discussion of arbitrary ambient toric varieties;
several improvements suggested by Eric Katz; some rearrangemen
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