Refine Search. Content Type. Release Date. Book VDM ' Ed No description available. Ed The generic term "graph-grammars" refers to a variety of methods for specifying possibly infinite sets of graphs or sets of maps. The area of graph-grammars originated in the ….

## نتیجه جستجو - robotics

The theory features a simple, natural notion of control structure which is much broader than …. Ed The papers collected in this volume are most of the material presented at the Advanced School on Mathematical Models for the Semantics of Parallelism, held in Rome, September …. The manner of its inception and support by the US Department of Defense ….

Book Systems of Reductions Benninghofen, B. Ed The collection of papers published in this book was initially presented at the Workshop on Software Factories and Ada, held on Capri, May , The subject of the book is …. Ed This book is focused on the performance evaluation of database machines, i. Book Advances in Petri Nets Proceedings of an Advanced Course, Bad Honnef, 8. September Brauer, W. Ed The present volume is the second of two parts which constitute the proceedings of the Advanced Course on Petri Nets in Bad Honnef.

It discusses tools supporting the design of …. Book Graph Reduction Fasel, J.

### About this book

Ed This volume describes recent research in graph reduction and related areas of functional and logic programming, as reported at a workshop in The papers are based on the …. Please enter a number between and. Web of Science You must be logged in with an active subscription to view this. Keywords shortest path , shortest path map , Euclidean distance , obstacle avoidance , quad-tree , planar subdivision , weighted distance.

Publication Data. ISSN print : Publisher: Society for Industrial and Applied Mathematics. John Hershberger and Subhash Suri. Algorithmica 81 :6, Computational Geometry 77 , Information Sciences , Journal of Manufacturing Science and Engineering Approaches for Clustering Polygonal Obstacles. Information Technology - New Generations, Combinatorial Optimization and Applications, European Journal of Operational Research :1, Robotics and Autonomous Systems 93 , Simulating Heterogeneous Crowd with Interactive Behaviors, Geographical Analysis 48 :2, The International Journal of Robotics Research 35 :5, Automatica 65 , Geometric Shortest Paths in the Plane.

Encyclopedia of Algorithms, Computational Geometry 48 :9, GeoInformatica 19 :3, ACM Transactions on Algorithms 11 :4, Algorithmic Foundations of Robotics XI, Algorithms and Computation, Theoretical Computer Science , ACM Transactions on Graphics 33 :5, Discrete Applied Mathematics , Journal of Computing and Information Science in Engineering 14 Computational Geometry.

Computing Handbook, Third Edition, Algorithmica 69 :1, Computer-Aided Design 48 , Siu-Wing Cheng and Jiongxin Jin. International Journal of Geographical Information Science 27 , A triangle mesh is a type of polygon mesh in computer graphics. It comprises a set of triangles typically in three dimensions that are connected by their common edges or corners [ 18 ]. With individual triangles, the system has to operate on three vertices for every triangle.

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In mathematics and computational geometry, the triangle mesh can be expressed in a Delaunay triangulation for a set V of vertices in the plane is a triangulation DT V such that no vertex in V is inside the circle of any triangle in DT V [ 19 ]. A ridge is a curve consisting of ridge point: A point lies on a ridge if its neighbourhood can be subdivided by a line passing through it, and such that the surface in each half-neighbourhood is monotonically decreasing when moving away from the line [ 21 ].

In this section, a Delaunay triangulation-based method will combine the concepts of Ahuja-Dijkstra algorithm and ridge points to construct a directed graph and to obtain the shortest possible path length on the quadratic surfaces. Compared to another Delaunay triangulation method [ 4 ], Fermat points are replaced by the ridge points; this is mainly due to the fact that Fermat points cannot connect the shortest line between two neighbour triangles on the quadratic surface.

Next, a source point and a destination point are spotted, then three ridge points in the same triangle will be connected together to generate an extra small triangle and three extra path segments between the vertices and neighbour triangles diagonal vertices. These extra connections as shown in Figure 1 b will be used to search for the near-shortest path by using the Ahuja-Dijkstras algorithm expressed by E f.

Illustration of the ridge points. Step 1. Create a ridge point between two neighbouring triangles as shown in Figure 1 a. Step 2. Obtain the shortest path by connecting these two vertices E, F with the ridge point.

Generate the shortcuts of any two consecutive segments by performing the Function 1. Sort the shortcuts by their corresponding length improvements in a descending order. Algorithm : The triangle mesh-based shortest path on the quadric surfaces. Construct a triangle mesh G by the Delaunay triangulation on the data, locate a source point and a destination point. Compute the shortest path between the neighbouring vertices based on the ridge points on the quadric surface by performing Function 1.

Step 3. Step 4. Figure 2 illustrates the detailed process. Figure 2 a shows the initiation of a triangle mesh G , then a source point S and a destination point D are depicted in Figure 2 b. Next, ridge points will be inserted into the triangle mesh in order to generate extra path connections as shown in Figure 2 c. Figure 2 d shows that each ridge point will connect with the others in the same triangle and three extra path segments between the vertices and neighbour triangles diagonal vertices.

Finally, Figure 2 f shows the final result after the PathShortening. Illustration of the Delaunay triangulation algorithm. A near-shortest path algorithm on the Quadratic surface is the fastest in the literature. Theorem 1. The time complexity of the algorithm in the triangle mesh G is O n log n , where n denotes the number of triangles.

Proof: We can generate Delaunay triangulation as a triangle mesh with time of O n log n [ 22 ], as a result, time complexity in Step 1 is O n log n [ 23 ]. We therefore know that all the time complexity for Steps 2 and 3 are O n. Therefore, the overall time complexity for PathShortening is O n log n. Theorem 2.

## Unobstructed Shortest Paths in Polyhedral Environments

The space complexity of constructing the triangle mesh in the quadratic surface is O n , where n is the number of triangles. Therefore, the space complexity is bounded by O n. Hence, the space complexity is O n. The performance of Delaunay triangulation-based path algorithm has been analysed for evaluating the near-shortest path with several real GIS maps in the Matlab Language.

Figure 3 shows one of the experimental results with a GIS map, where the solid line is the near-shortest path and dashed lines are the shortcuts.