Improving Chen and Han's algorithm on the discrete geodesic problem

Xin, Shiqing; Wang, Guojin

doi:10.1145/1559755.1559761

Cited by 140 publications

(127 citation statements)

References 22 publications

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“…There are many existing methods for the calculation of a geodesic path. We use the method proposed by Xin et al [34], since it calculates the exact geodesic path that guarantees the non-intersection between each path. Although all these geodesic paths do not intersect with each other, they may have common points.…”

Section: Calculate Geodesic Paths Between the Bound Visual Verticesmentioning

confidence: 99%

Interactive Cutting of Thin Deformable Objects

Weng

Sourin

2018

Symmetry

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Simulation of cutting is essential for many applications such as virtual surgical training. Most existing methods use the same triangle mesh for both visualization and collision handling, although the requirements for them in the interactive simulation are different. We introduce visual-collision binding between high-resolution visual meshes and low-resolution collision meshes, and thus extend the spatially reduced framework to support cutting. There are two phases in our framework: pre-processing and simulation. In the pre-processing phase, the fvisual-collision binding is built based on the computation of geodesic paths. In the simulation phase, the cutting paths are detected on the collision triangles and then mapped to local 2D coordinates systems in which the intersections between visual mesh and the cutting paths are calculated. Both collision and visual meshes are then re-meshed locally. The visual-collision binding is updated after cutting, based on which the collision-simulation and visual-simulation embedding are updated locally. Experimental results show that our cutting method is an efficient and flexible tool for interactive cutting simulation.

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Section: Calculate Geodesic Paths Between the Bound Visual Verticesmentioning

confidence: 99%

Interactive Cutting of Thin Deformable Objects

Weng

Sourin

2018

Symmetry

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“…We compares the FWP method with other representative geodesic algorithms, including MMP [2], ICH [7], PCH [8], FMM [13], [14], [22], the heat method [16] and the label correcting (LC) method [23]. We classify these algorithms in two groups, i.e., macro and micro.…”

Section: Comparisonmentioning

confidence: 99%

“…Xin and Wang [7] observed that the slow performance of the CH algorithm is mainly due to the large amount of useless windows processed. They proposed a simple yet effective window filter to detect the useless windows, accompanied by a priority queue for window organization.…”

Section: Introductionmentioning

confidence: 99%

Fast Wavefront Propagation (FWP) for Computing Exact Geodesic Distances on Meshes

Wang

Liu

et al. 2015

IEEE Trans. Visual. Comput. Graphics

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Abstract-Computing geodesic distances on triangle meshes is a fundamental problem in computational geometry and computer graphics. To date, two notable classes of algorithms, the Mitchell-Mount-Papadimitriou (MMP) algorithm and the Chen-Han (CH) algorithm, have been proposed. Although these algorithms can compute exact geodesic distances if numerical computation is exact, they are computationally expensive, which diminishes their usefulness for large-scale models and/or timecritical applications. In this paper, we propose the fast wavefront propagation (FWP) framework for improving the performance of both the MMP and CH algorithms. Unlike the original algorithms that propagate only a single window (a data structure locally encodes geodesic information) at each iteration, our method organizes windows with a bucket data structure so that it can process a large number of windows simultaneously without compromising wavefront quality. Thanks to its macro nature, the FWP method is less sensitive to mesh triangulation than the MMP and CH algorithms. We evaluate our FWP-based MMP and CH algorithms on a wide range of large-scale real-world models. Computational results show that our method can improve the speed by a factor of 3-10.

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“…Therefore, Dijkstra's algorithm has been successfully applied in such fields [16] as operational research, computer science, geographic information science and transportation, etc.…”

Section: Dijkstra's Algorithmmentioning

confidence: 99%

“…Based on this insight, this essay makes an attempt to apply Dijkstra's algorithm [14][15][16][17] which settles the shortest path problem of the graph theory to the energy conservation optimization of the main cutting edge curve of the twist drill. A specific method used in determining the main cutting edge curve in the helicoid rake face of the twist drill that minimizes the drilling power is introduced.…”

Section: Introductionmentioning

confidence: 99%

The energy conservation optimization design of the cutting edges of the twist drill based on Dijkstra’s algorithm

Xiong

2015

Int J Adv Manuf Technol

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The energy conservation optimization design about geometrical shape and dimensions of the cutting edges (lips) of the twist drill is meant to determine the main cutting edge curve in the rake face that minimizes the drilling power. Dijkstra's algorithm is introduced and applied to serve the above purpose. The rake surface of the twist drill is discretized into a set of nodes and arcs between the adjacent nodes, which together compose a digraph. Cutting angles of elementary cutting tools on the lips of a twist drill are determined by the method of displaying planar image; those angles, together with undeformed chip thickness and width, are substituted into the empirical model of cutting force for elementary cutting tool to obtain the weights of arcs in the digraph, that is, the drilling power. Then, a main cutting edge curve in the rake face that minimizes the drilling power is generated using Dijkstra's algorithm. Meanwhile, an improvement in Dijkstra's algorithm procedures is put forward to reduce time and space complexities of the process and improve smoothness and machinability of the cutting edge curve. A computer program is developed with Matlab 2011b to determine the main cutting edge curve. The calculation results with 0.50 % carbon steel show that the new curved cutting edge reduces the drilling power by 7~8 %, compared to a conventional straight cutting edge.

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Improving Chen and Han's algorithm on the discrete geodesic problem

Cited by 140 publications

References 22 publications

Interactive Cutting of Thin Deformable Objects

Interactive Cutting of Thin Deformable Objects

Fast Wavefront Propagation (FWP) for Computing Exact Geodesic Distances on Meshes

The energy conservation optimization design of the cutting edges of the twist drill based on Dijkstra’s algorithm

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