arXiv subjects

Nengxiong Xu

Publications and source records attributed to Nengxiong Xu.

22 records · Page 2Linked to original sources

arXiv2012

An Algorithm for Finding Convex Hulls of Planar Point Sets

This paper presents an alternate choice of computing the convex hulls (CHs) for planar point sets. We firstly discard the interior points and then sort the remaining vertices by x- / y- coordinates separately, and later create a group ofquadrilaterals (e-Quads) recursively according to the sequences ofthe sorted lists of points. Finally, the desired CH is built based on a simple polygon derived from all e-Quads. Besides the preprocessing for original planar point sets, this algorithm has another mechanism of discarding interior point when form e-Quads and assemble the simple polygon. Compared with three popular CH algorithms, the proposed algorithm can generate CHs faster thanthe three but has a penalty in space cost.

cs.CG↗

arXiv2012

A Hybrid Approach for Optimizing Planar Triangular Meshes

Modified Direct Method (MDM) is an iterative scheme based on Jacobi iterations for smoothing planar meshes [4]. The basic idea behind MDM is to make any triangular element be as close to an equilateral triangle as possible. Basedon the MDM, a length-weighted MDM is proposed and then combined with edge swapping. In length-weighted MDM, weights of each neighboring node of a smoothed node are determined by the length of its opposite edge. Also, the MDM, Laplacian smoothing and length-weighted MDM are all combined with edge swapping, and then implemented and compared on both structured and unstructured triangular meshes. Examples show that length-weighted MDM is better than the MDM and Laplacian smoothing for structured mesh but worse for unstructured mesh. The hybrid approach of combining length-weighted MDM and edge swapping is much better and can obtain more even optimized meshes than other two hybrid approaches.

cs.CG↗

arXiv2012

Discrete Surface Modeling Based on Google Earth: A Case Study

Google Earth (GE) has become a powerful tool for geological, geophysical and geographical modeling; yet GE can be accepted to acquire elevation data of terrain. In this paper, we present a real study case of building the discrete surface model (DSM) at Haut-Barr Castle in France based on the elevation data of terrain points extracted from GE using the COM API. We first locate the position of Haut-Barr Castle and determine the region of the study area, then extract elevation data of terrain at Haut-Barr, and thirdly create a planar triangular mesh that covers the study area and finally generate the desired DSM by calculating the elevation of vertices in the planar mesh via interpolating with Universal Kriging (UK) and Inverse Distance Weighting (IDW). The generated DSM can reflect the features of the ground surface at Haut-Barr well, and can be used for constructingthe Sealed Engineering Geological Model (SEGM) in further step.

cs.GR↗

arXiv2012

The Modified Direct Method: an Approach for Smoothing Planar and Surface Meshes

The Modified Direct Method (MDM) is an iterative mesh smoothing method for smoothing planar and surface meshes, which is developed from the non-iterative smoothing method originated by Balendran [1]. When smooth planar meshes, the performance of the MDM is effectively identical to that of Laplacian smoothing, for triangular and quadrilateral meshes; however, the MDM outperforms Laplacian smoothing for tri-quad meshes. When smooth surface meshes, for trian-gular, quadrilateral and quad-dominant mixed meshes, the mean quality(MQ) of all mesh elements always increases and the mean square error (MSE) decreases during smoothing; For tri-dominant mixed mesh, the quality of triangles always descends while that of quads ascends. Test examples show that the MDM is convergent for both planar and surface triangular, quadrilateral and tri-quad meshes.

cs.CG↗