아태비즈니스연구 (Asia-Pacific Journal of Business)

  • 제9권2호
  • /
  • Pages.1-13
  • /
  • 2018
  • /
  • 2233-5900(pISSN)
  • /
  • 2384-3934(eISSN)
강원대학교 경영경제연구소 (KNU The Institute of Management & Economy Research)
권호 표지

Using Piecewise Circular Curves as a 2D Collision Primitive

  • Ollington, Robert (Discipline of ICT, School of Technology, Environments and Design, College of Sciences and Engineering, University of Tasmania)
  • 투고 : 2018.06.01
  • 심사 : 2018.06.25
  • 발행 : 2018.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Physics simulation is an important part of many interactive 2D applications and collision detection and response is key component of this simulation. While methods for reducing the number of collision tests that need to be performed has been well researched, methods for performing the final checks with collision primitives have seen little recent development. This paper presents a new collision primitive, the n-arc, constructed from piecewise circular curves or biarcs. An algorithm for performing a collision check between these primitives is presented and compared to a convex polygon primitive. The n-arc is shown to exhibit similar, though slightly slower, performance to a polygon when no collision occurs, but is considerably faster when a collision does occur. The goodness of fit of the new primitive is also compared to a polygon. While the n-arc often gives a looser fit in terms of area, the continuous tangents of the n-arcs makes them a good choice for organic, soft or curved surfaces.

키워드

참고문헌

  1. Banchoff, T. and P. Giblin (1994), On the Geometlg of Piecewise Circular Curves, The American Mathematical Monthly 101, 5, 403-416. https://doi.org/10.1080/00029890.1994.11996965
  2. Bolton, K. (1975), Biarc Curves, Computer-Aided Design 7, 2 (Apr.), 89-92. https://doi.org/10.1016/0010-4485(75)90086-X
  3. Fu, P., O. R Walton and J. T. Harvey (2012), Polyarc Discrete Element for Efficiently Simulating Arbitrarily Shaped 2D Particles, International Journal for Numerical Methods in Engineering, 89(5), 599-617. https://doi.org/10.1002/nme.3254
  4. Jimene Z, P., F. Thomas and C. Torras (2001), 3D Collision Detection : A Survey, Computers & Graphics 25, 2, 269-285. https://doi.org/10.1016/S0097-8493(00)00130-8
  5. Krishnan, S., M. Gopi, M. Lin, D. Manocha and A. Pattekar (1998), Rapid and Accurate Contact Determination between Spline Models using ShellTrees, Computer Graphics Forum 17, 3 (Aug.), 315-326. https://doi.org/10.1111/1467-8659.00278
  6. Krishnan, S., A. Pattekar, M. C. Lin, and D. Manocha (1998), Spherical Shell : A Higher Order Bounding Volume for Fast Proximity Queries, In 3rd Workshop on the Algorithmic Foundations of Robotics, 177-190.
  7. Larsen, E., S. Gottschalk, M. Lin and D. Manocha (2000), Fast Distance Queries with Rectangular Swept Sphere Volumes, In IEEE International Conference on Robotics and Automation, Ieee, 3719-3726.
  8. Lin, M. C. and S. Gottschalk (1998), Collision Detection between Geometric Models : A Survey, In Proc. of IMA Conference on Mathematics of Surfaces, 602-608.
  9. Maier, G. and G. Pisinger (2013), Approximation of a Closed Polygon with a Minimum Number of Circular Arcs and Line Segments, Computational Geometry 46, 3 (Apr.), 263-275. https://doi.org/10.1016/j.comgeo.2012.09.003
  10. Maier, G., A. Schindler, F. Janda and S. Brummer (2013), Optimal Arc-spline Approximation with Detecting Straight Sections, In International Conference on Computational Science and Its Applications (June), Springer, Berlin, Heidelberg, 99-112.
  11. Riskus, A. (2006), Approximation of a Cubic Bezier Curve by Circular Arcs and Vice Versa, Information Technology and Control 35, 4, 371-378.
  12. Rosin, P. L. (1999), A Survey and Comparison of Traditional Piecewise Circular Approximations to the Ellipse, Computer Aided Geometric Design, 16(4), 269-286. https://doi.org/10.1016/S0167-8396(98)00049-1
  13. Rosin, P. L. and M. L. Pitteway (2001), The Ellipse and the Five-centred arch, The Mathematical Gazette, 85(502), 13-24. https://doi.org/10.2307/3620465
  14. Tong, Z., P. Fu, Y. F. Dafalias and Y. Yao (2014), Discrete Element Method Analysis of Non-Coaxial Flow under Rotational Shear, Inter- national Journal for Numerical and Analytical Methods in Geomechanics, 38(14), 1519-1540. https://doi.org/10.1002/nag.2290