On the Stretch Factor of the Constrained Delaunay Triangulation

2006 ◽  
Author(s):  
Prosenjit Bose
Keyword(s):  
Delaunay Triangulation ◽  
Constrained Delaunay Triangulation ◽  
Stretch Factor

A Constrained Delaunay Triangulation Algorithm Based on Incremental Points

2011 ◽  
Vol 90-93 ◽  
pp. 3277-3282 ◽  
Author(s):  
Bai Chao Wu ◽  
Ai Ping Tang ◽  
Lian Fa Wang
Keyword(s):  
Information System ◽  
Data Structures ◽  
Delaunay Triangulation ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Three Dimensional ◽  
Geographical Information ◽  
Two Dimensional ◽  
Data Set ◽  
Constrained Delaunay Triangulation

The foundation ofdelaunay triangulationandconstrained delaunay triangulationis the basis of three dimensional geographical information system which is one of hot issues of the contemporary era; moreover it is widely applied in finite element methods, terrain modeling and object reconstruction, euclidean minimum spanning tree and other applications. An algorithm for generatingconstrained delaunay triangulationin two dimensional planes is presented. The algorithm permits constrained edges and polygons (possibly with holes) to be specified in the triangulations, and describes some data structures related to constrained edges and polygons. In order to maintain the delaunay criterion largely，some new incremental points are added onto the constrained ones. After the data set is preprocessed, the foundation ofconstrained delaunay triangulationis showed as follows: firstly, the constrained edges and polygons generate initial triangulations，then the remained points completes the triangulation . Some pseudo-codes involved in the algorithm are provided. Finally, some conclusions and further studies are given.

Simplex Methods for Optimal Control of Unmanned Aircraft Flight Trajectories

2017 ◽  
Author(s):  
Michael D. Zollars ◽  
Richard G. Cobb
Keyword(s):  
Delaunay Triangulation ◽  
Unmanned Aircraft ◽  
Collocation Methods ◽  
Barycentric Coordinates ◽  
Flight Trajectory ◽  
Orthogonal Collocation ◽  
Aircraft Flight ◽  
Constrained Delaunay Triangulation ◽  
Flight Trajectories ◽  
Aircraft System

The feasibility of using a constrained Delaunay triangulation method for determining optimal flight trajectories of unmanned air vehicles in a constrained environment is explored. Current methods for developing optimal flight trajectories have yet to achieve computational times that allow for real-time implementation. The proposed method alleviates the dependency of problem specific parameters while eliminating constraints on the Non-Linear Program. Given an input of obstacles with n vertices, a constrained Delaunay triangulation is performed on the space. Converting the vertices of the triangulation to barycentric coordinates on a phased approach defines the state bounds and max time for each phase. With two-dimensional aircraft dynamics, direct orthogonal collocation methods are performed to compute the optimal flight trajectory. Results illustrate computational times and feasibility of Small Unmanned Aircraft System flight trajectories through polygon constraints.

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