Ear-clipping Based Algorithms of Generating High-quality Polygon Triangulation

A basic and an improved ear clipping based algorithm for triangulating simple polygons and polygons with holes are presented. In the basic version, the ear with smallest interior angle is always selected to be cut in order to create fewer sliver triangles. To reduce sliver triangles in further, a bound of angle is set to determine whether a newly formed triangle has sharp angles, and edge swapping is accepted when the triangle is sharp. To apply the two algorithms on polygons with holes, "Bridge" edges are created to transform a polygon with holes to a degenerate polygon which can be triangulated by the two algorithms. Applications show that the basic algorithm can avoid creating sliver triangles and obtain better triangulations than the traditional ear clipping algorithm, and the improved algorithm can in further reduce sliver triangles effectively. Both of the algorithms run in O(n2) time and O(n) space.Comment: Proceedings of the 2012 International Conference on Information Technology and Software Engineering Lecture Notes in Electrical Engineering Volume 212, 2013, pp 979-98

Improved algorithms for ear-clipping triangulation

We consider the problem of improving ear-slicing algorithm for triangulating a simple polygon. We propose two variations of ear-slicing technique for generating “good-quality” triangulation. The first approach is based on searching for the best triangle along the boundary. The second approach considers polygon partitioning on a pre-process before applying the ear-slicing. Experimental investigation reveals that both approaches yield better quality triangulation than the standard ear-slicing method

Simple yet robust triangulation for polygons containing multiple holes for real-time 3D industrial applications

In industrial applications such as CAD modeling, manufacture or automated systems, it is common to work with data models that are represented by polygonal shapes, or models that produce polygonal shapes out of complex geometry defined by lines and curves. However, this data has to be converted to a triangular mesh before it can be processed and/or rendered by the GPU. Existing solutions that generate triangular mesh out of polygonal shapes either do not support holes or have limitations on how many holes can be present at the same time. Most modern advanced solutions need considerable effort to implement, debug and maintain, which involves significant development costs. In this work, an alternative solution is proposed, which is relatively simple to implement yet is sufficiently robust to handle all possible input scenarios handling any number of holes, or inner polygons in an outer polygon, assuming that polygons do not intersect each other or themselves, and makes no assumptions about the winding order of polygon vertices. The proposed solution involves initial pre-processing work, merging inner polygons into an outer polygon, and then performing polygon triangulation using one of the two proposed variations of an Ear Clipping algorithm. The proposed solution is shown to handle practically an unlimited number of holes in polygon independently of its shape. Quality and performance comparison between two techniques is also provided and discussed, along with the images of a real life CAD application, which implements the proposed solution

Degree Constrained Triangulation

Triangulation of simple polygons or sets of points in two dimensions is a widely investigated problem in computational geometry. Some researchers have considered variations of triangulation problems that include minimum weight triangulation, de-launay triangulation and triangulation refinement. In this thesis we consider a constrained version of the triangulation problem that asks for triangulating a given domain (polygon or point sites) so that the resulting triangulation has an increased number of even degree vertices. This problem is called Degree Constrained Triangulation (DCT). We propose four algorithms to solve DCT problems. We also present experimental results based on the implementation of the proposed algorithms. The implementation is done in Java programming language with user friendly graphical interface

Isotropic Surface Remeshing

International audienceThis paper proposes a new method for isotropic remeshing of tri- angulated surface meshes. Given a triangulated surface mesh to be resampled and a user-specified density function defined over it, we first distribute the desired number of samples by generalizing error diffusion, commonly used in image halftoning, to work directly on mesh triangles and feature edges. We then use the resulting sam- pling as an initial configuration for building a weighted centroidal Voronoi tessellation in a conformal parameter space, where the specified density function is used for weighting. We finally create the mesh by lifting the corresponding constrained Delaunay trian- gulation from parameter space. A precise control over the sampling is obtained through a flexible design of the density function, the latter being possibly low-pass filtered to obtain a smoother grada- tion. We demonstrate the versatility of our approach through vari- ous remeshing examples

Autonomous Navigation with Obstacle Avoidance for Unmanned Aircraft Systems using MILP

Autonomous coordination among multiple aerial vehicles to ensure a collision free airspace is a critical aspect of today’s airspace. With the rise of Unmanned Aerial Vehicles (UAVs) in the military and commercial sectors, obstacle avoidance in a densely populated airspace is necessary. This thesis investigates finding optimal or near-optimal trajectories in real-time for aircraft in complex airspaces containing a large number of obstacles. The solution for the trajectories is described as a linear program subject to mixed integer constraints, known as a Mixed Integer Linear Program (MILP). The resulting MILP problem is solved in real time using a well-known, public domain MILP solver. In addition, an Exhaustive, Breadth-First Search algorithm was implemented and is used for comparison in terms of execution time and flight path optimality. The Exhaustive Search algorithm is comprised of a multi-branch tree structure that iterates through all possible flight paths from source to target. The MILP solution was implemented in both PC based and embedded system environments. The embedded system environment was implemented on an onboard processor to develop trajectories for each individual aircraft in real time

Hyper-real-time ice simulation and modeling using GPGPU

Simulation of the behaviour of a ship operating in pack ice is a computationally intensive process to which General Purpose Computing on Graphical Processing Units (GPGPU) can be applied. GPGPU is the use of a GPU (graphics processing unit) to do general purpose scientific and engineering computing. The model for GPU computing is to use a CPU and GPU together in a heterogeneous co-processing computing platform. The sequential part of the application runs on the CPU and the computationally-intensive part is accelerated by the GPU. From the users perspective, the application just runs faster because it is using the high-performance of the GPU to boost performance. This thesis presents an efficient parallel implementation of such a simulator developed using the NVIDIA Compute Unified Device Architecture (CUDA). This simulator can be used to give users the ability to analyze ice-interactions for design, assessment and training purposes. This thesis also describes the execution of experiments to evaluate the performance of the simulator and to validate the numerical modeling of ship operations in pack ice. It also describes the useful applications that have been done using this simulator in planning ice management activities

An investigation into automated processes for generating focus maps

The use of geographic information for mobile applications such as wayfinding has increased rapidly, enabling users to view information on their current position in relation to the neighbouring environment. This is due to the ubiquity of small devices like mobile phones, coupled with location finding devices utilising global positioning system. However, such applications are still not attractive to users because of the difficulties in viewing and identifying the details of the immediate surroundings that help users to follow directions along a route. This results from a lack of presentation techniques to highlight the salient features (such as landmarks) among other unique features. Another problem is that since such applications do not provide any eye-catching distinction between information about the region of interest along the route and the background information, users are not tempted to focus and engage with wayfinding applications. Although several approaches have previously been attempted to solve these deficiencies by developing focus maps, such applications still need to be improved in order to provide users with a visually appealing presentation of information to assist them in wayfinding. The primary goal of this research is to investigate the processes involved in generating a visual representation that allows key features in an area of interest to stand out from the background in focus maps for wayfinding users. In order to achieve this, the automated processes in four key areas - spatial data structuring, spatial data enrichment, automatic map generalization and spatial data mining - have been thoroughly investigated by testing existing algorithms and tools. Having identified the gaps that need to be filled in these processes, the research has developed new algorithms and tools in each area through thorough testing and validation. Thus, a new triangulation data structure is developed to retrieve the adjacency relationship between polygon features required for data enrichment and automatic map generalization. Further, a new hierarchical clustering algorithm is developed to group polygon features under data enrichment required in the automatic generalization process. In addition, two generalization algorithms for polygon merging are developed for generating a generalized background for focus maps, and finally a decision tree algorithm - C4.5 - is customised for deriving salient features, including the development of a new framework to validate derived landmark saliency in order to improve the representation of focus maps