The Design and Implementation of Planar Maps in CGAL

Flato, Eyal; Halperin, Dan; Hanniel, Iddo; Nechushtan, Oren

doi:10.1007/3-540-48318-7_14

Cited by 28 publications

(24 citation statements)

References 6 publications

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“…We use the visible contour segments as a boundary to define regions of homogeneous shading. These regions are organized by a wingededge structure called a planar map, constructed in our prototype by the CGAL Arrangement Package [FHHN99]. The specific kind/combination of shading represented by each region must next be established by a classification step.…”

Section: Contour Visibility Via Occlusion Querymentioning

confidence: 99%

Stylized Vector Art from 3D Models with Region Support

Eisemann

Winnemöller

Hart

et al. 2008

Computer Graphics Forum

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We describe a rendering system that converts a 3D meshed model into the stylized 2D filled-region vector-art commonly found in clip-art libraries. To properly define filled regions, we analyze and combine accurate but jagged face-normal contours with smooth but inaccurate interpolated vertex normal contours, and construct a new smooth shadow contour that properly surrounds the actual jagged shadow contour. We decompose region definition into geometric and topological components, using machine precision for geometry processing and raster-precision to accelerate topological queries. We extend programmable stylization to simplify, smooth and stylize filled regions. The result renders 10K-face meshes into custom clip-art in seconds.

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Section: Contour Visibility Via Occlusion Querymentioning

confidence: 99%

Stylized Vector Art from 3D Models with Region Support

Eisemann

Winnemöller

Hart

et al. 2008

Computer Graphics Forum

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“…Devillers et al [7] compared the run-time of common walking techniques for random point-location queries in general triangulations in R 2 , R 3 and R d . Flato et al [12] described the Arrangement package 1 of Cgal (Computational Geometry Algorithms Library), with several point-location strategies that it implements. Our paper was motivated by the experimental results in that work.…”

Section: Related Workmentioning

confidence: 99%

The complexity of the outer face in arrangements of random segments

Alon

Halperin

Nechushtan

et al. 2008

Proceedings of the Twenty-Fourth Annual Symposium on Computational Geometry

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We investigate the complexity of the outer face in arrangements of line segments of a fixed length in the plane, drawn uniformly at random within a square. We derive upper bounds on the expected complexity of the outer face, and establish a certain phase transition phenomenon during which the expected complexity of the outer face drops sharply as a function of the total number of segments. In particular we show that up till the phase transition the complexity of the outer face is almost linear in n, and that after the phase transition, the complexity of the outer face is roughly proportional to √ n. Our study is motivated by the analysis of a practical point-location algorithm (so-called walk-alonga-line point-location algorithm) and indeed, it explains experimental observations of the behavior of the algorithm on arrangements of random segments.

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“…Within Cgal there are means to construct and manipulate arrangements of curves in the plane [15], namely the subdivision of the plane into vertices, edges, and twodimensional faces induced by a collection of curves. Arrangements can serve as a key ingredient in complete solutions to motion-planning problems with two dofs (this connection as well as the underlying software support for it are described in [18]).…”

Section: Complete Solutions: Theory and Practicementioning

confidence: 99%

Hybrid Motion Planning: Coordinating Two Discs Moving among Polygonal Obstacles in the Plane

Hirsch

Halperin

2004

Springer Tracts in Advanced Robotics

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The basic motion-planning problem is to plan a collision-free motion for objects moving among obstacles between free initial and goal positions, or to determine that no such motion exists. The basic problem as well as numerous variants of it have been intensively studied over the past two decades yielding a wealth of results and techniques, both theoretical and practical. In this paper, we propose a novel approach to motion planning, hybrid motion planning, in which we integrate complete solutions along with Probabilistic Roadmap (PRM) techniques in order to combine their strengths and offset their weaknesses. We incorporate robust tools, that have not been available before, in order to implement the complete solutions. We exemplify our approach in the case of two discs moving among polygonal obstacles in the plane. The planner we present easily solves problems where a narrow passage in the workspace can be arbitrarily small. Our planner is also capable of providing correct nontrivial "no" answers, namely it can, for some queries, detect the situation where no solution exists. We envision our planner not as a total solution but rather as a new tool that cooperates with existing planners. We demonstrate the advantages and shortcomings of our planner with experimental results.

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The Design and Implementation of Planar Maps in CGAL

Cited by 28 publications

References 6 publications

Stylized Vector Art from 3D Models with Region Support

Stylized Vector Art from 3D Models with Region Support

The complexity of the outer face in arrangements of random segments

Hybrid Motion Planning: Coordinating Two Discs Moving among Polygonal Obstacles in the Plane

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