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A fast triangle to triangle intersection test for collision detection

COMPUTER ANIMATION AND VIRTUAL WORLDS 2006年第5期17卷 527-535页

作者： Tropp, Oren Tal, Ayellet Shimshoni, Ilan Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel

The triangle-to-triangle intersection test is a basic component of all collision detection data structures and algorithms. This paper presents a fast method for testing whether two triangles embedded in three dimensions intersect. Our technique solves the basic sets of linear equations associated with the problem and exploits the strong relations between these sets to speed up their solution. Moreover, unlike previous techniques, with very little additional cost, the exact intersection coordinates can be determined. Finally, our technique uses general principles that can be applied to similar problems such as rectangle-to-rectangle intersection tests, and generally to problems where several equation sets are strongly related. We show that our algorithm saves about 20% of the mathematical operations used by the best previous triangle-to-triangle intersection algorithm. Our experiments also show that it runs 18.9% faster than the fastest previous algorithm on average for typical scenarios of collision detection (on Pentium 4). Copyright (c) 2006 John Wiley & Sons, Ltd.

关键词： triangle to triangle intersection collision detection

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An Improved Algorithm for triangle to triangle intersection Test

An Improved Algorithm for Triangle to Triangle Intersection ...

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IEEE International Conference on Information and Automation 2015

作者： Ye, Xiufen Huang, Le Wang, Lin Xing, Huiming Harbin Engn Univ Coll Automat Harbin Heilongjiang Peoples R China

ISBN: (纸本)9781467391047

The triangle-to-triangle intersection test is a basic component of all collision detection data structures and algorithms. There are many algorithms that have been put forward in this area until now. Among these algorithms, there is one proposed by YU Hai-yan based on projection theory which can simplify the three-dimensional test into the two-dimensional test and certificate its robustness theoretically. However, the long calculation time can not satisfy the real-time performance. In this paper, an improved algorithm is proposed firstly. Then, the GPU parallel computing is adopted to accelerate our algorithm. Finally, some experiments were carried to validate the improved algorithm. Through the experiments, it shows that the improved algorithm is up to 13 times faster than the original algorithm on average when the triangles' number increases to 2 million and the acceleration times will also increase when much more triangles are detected at the same time and however the algorithm is also stable.

关键词： triangle to triangle intersection collision detection GPU parallel computing projection theory

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A Cartesian cut cell free surface capturing method for 3D water impact problems

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS 2013年第10期71卷 1238-1259页

作者： Hu, Z. Z. Causon, D. M. Mingham, C. G. Qian, L. Manchester Metropolitan Univ Sch Comp Math & Digital Technol Ctr Math Modelling & Flow Anal Manchester M1 5GD Lancs England

A Cartesian cut cell mesh generation procedure is developed together with a finite volume Euler solver for a two-fluid system with a free surface. A fast and robust triangle to triangle overlap scheme is used to determine the intersection of a body-surface with the background Cartesian mesh. Improvements to the cut cell routines include a new treatment for multiple cuts within a single cell and a surface trimming procedure to ensure a good quality mesh around solid boundaries. The formulae for calculating all necessary information about a cut cell are also presented. These are generic and can be used for arbitrarily irregular boundary elements. A collocated finite volume method with a high resolution Godunov-type scheme in space is used for discretization of the governing flow equations. By computing in both the air and water regions simultaneously in a consistent manner, the free surface is automatically captured as a contact discontinuity in the density field without the need for any special free surface tracking method. The algorithm incorporates the artificial compressibility method with a dual time stepping strategy to maintain a divergence free velocity field. The mathematical formulation including its numerical implementation of the method is reviewed and results for a number of test cases are also presented. Copyright (c) 2012 John Wiley & Sons, Ltd.

关键词： triangle to triangle intersection Cartesian cut cell free surface capturing 3D Euler equations artificial compressibility method

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