Polygon Offsetting by Computing Winding Numbers

Chen, Hong; McMains, Sara

doi:10.1115/detc2005-85513

Cited by 31 publications

(11 citation statements)

References 20 publications

(21 reference statements)

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“…Without knowing details of the offsetting algorithm employed by these codes, it is impossible to pin down the exact reason why the two excess areas in Figure 8a are not removed. Both libraries seem to compute winding numbers [8] in order to weed out incorrect regions within the union of elementary offset areas that form the raw offset polygons.…”

Section: Comparison With Other Approachesmentioning

confidence: 99%

Computing Mitered Offset Curves Based on Straight Skeletons

Palfrader¹,

Held²

2015

Computer-Aided Design and Applications

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We study the practical computation of mitered and beveled offset curves of planar straight-line graphs (PSLGs), i.e., of arbitrary collections of straight-line segments in the plane that do not intersect except possibly at common end points. The line segments can, but need not, form polygons. Similar to Voronoi-based offsetting, we propose to compute a straight skeleton of the input PSLG as a preprocessing step for mitered offsetting. For this purpose, we extend and adapt Aichholzer and Aurenhammer's triangulation-based straight-skeleton algorithm to make it process real-world data on a conventional finite-precision arithmetic.We implemented this extended algorithm in C and use our implementation for extensive experiments. All tests demonstrate the practical suitability of using straight skeletons for the offsetting of complex PSLGs. Our main practical contribution is strong experimental evidence that mitered offsets of PSLGs with 100 000 segments can be computed in about ten milliseconds on a standard PC once the straight skeleton is available and that our implementation clearly is the fastest code for mitered offsetting even if the computational costs of the straight-skeleton computation are included in the timings.

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Section: Comparison With Other Approachesmentioning

confidence: 99%

Computing Mitered Offset Curves Based on Straight Skeletons

Palfrader¹,

Held²

2015

Computer-Aided Design and Applications

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“…This feature of topological inconsistency makes the polygon offsetting problem difficult to tackle. Tremendous efforts have been made to maintain the robustness of offsetting operation [11][12][13], however, often times, such efforts increase the algorithm complexity dramatically.…”

Section: Data Flow For Hybrid Stereolithography Systemmentioning

confidence: 99%

Image-Based Slicing and Tool Path Planning for Hybrid Stereolithography Additive Manufacturing

Zhou

2017

Journal of Manufacturing Science and Engineering

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The hybrid stereolithography (SLA) process integrates a laser scanning-based system and a mask projection-based system. Multiple laser paths are used to scan the border of a 2D pattern, whereas a mask image is adopted to solidify the interior area. By integrating merits of two subsystems, the hybrid SLA process can achieve high surface quality without sacrificing productivity. For the hybrid system, closed polygonal contours are required to direct the laser scanning, and a binary image is also needed for the mask projection. We proposed a novel image-based slicing method. This approach can convert a 3D model into a series of binary images directly, and each image is corresponding to the cross section of the model at a specific height. Based on the resultant binary image, we use an image processing method to gradually shrink the pattern in the image. Boundaries of the shrunk image are traced and then restored as polygons to direct the laser spot movement. The final shrunk image serves as the input for the mask projection. Experimental results of test cases demonstrate that the proposed method is substantially more efficient than the traditional approaches. Its accuracy is also studied and discussed.

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“…To ensure that the Carre mesh resides entirely within the vacuum vessel boundary used elsewhere within XGC0 (e.g., to identify lost particles), the boundary input to Carre is shifted inward by 5 mm. This shift is implemented as a "polygon offset" using the Clipper library [20,21].…”

Section: Vacuum Vessel Filling Meshmentioning

confidence: 99%

Energy Conservation Tests of a Coupled Kinetic-kinetic Plasma-neutral Transport Code

Stotler¹,

Chang²,

Ku³

et al. 2012

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Abstract. An approach to coupling two kinetic particle codes for the simulation of neutral-plasma interactions in magnetic fusion devices is described. The behavior of the neutral atoms and molecules is modeled with a Monte Carlo code. The plasma species are simulated with a particle-in-cell code that integrates the guiding center equations of motion and computes a self-consistent electric field. The coupling algorithm is designed to conserve mass in the neutral-plasma exchanges to statistical accuracy. Although energy is not fully conserved due to the velocity dependence of the charge exchange cross section and the kinetic character of both species, the impact of this non-conservation on the overall simulation is negligible.

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Polygon Offsetting by Computing Winding Numbers

Cited by 31 publications

References 20 publications

Computing Mitered Offset Curves Based on Straight Skeletons

Computing Mitered Offset Curves Based on Straight Skeletons

Image-Based Slicing and Tool Path Planning for Hybrid Stereolithography Additive Manufacturing

Energy Conservation Tests of a Coupled Kinetic-kinetic Plasma-neutral Transport Code

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