Intersecting a freeform surface with a general swept surface

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Seong, Joon-Kyung ; Kim, Ku-Jin ; Kim, Myung-Soo ; Elber, Gershon ; Martin, Ralph Robert (2005)

We present efficient and robust algorithms for intersecting a rational parametric freeform surface with a general swept surface. A swept surface is given as a one-parameter family of cross-sectional curves. By computing the intersection between a freeform surface and each cross-sectional curve in the family, we can solve the intersection problem. We propose two approaches, which are closely related to each other. The first approach detects certain critical points on the intersection curve, and then connects them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of polynomial equations in the parameter space. We first present these algorithms for the special case of intersecting a freeform surface with a ruled surface or a ringed surface. We then consider the intersection with a general swept surface, where each cross-sectional curve may be defined as a rational parametric curve or as an implicit algebraic curve.
  • References (14)
    14 references, page 1 of 2

    [1] C. L. Bajaj, C. M. Hoffmann, R. E. Lynch, and J. E. H. Hopcroft. Tracing surface intersections. Computer Aided Geometric Design, Vol. 5, pp. 285-307, 1988.

    [2] C. L. Bajaj and G. Xu. NURBS approximation of surface-surface intersection curves. Advances in Computational Mathematics, Vol. 2, Num. 1, pp. 1-21, 1994.

    [3] J. de Pont, Essays on the Cyclide Patch, Ph.D. Thesis, Cambridge University Engineering Dept., Cambridge, 1984.

    [4] G. Elber. IRIT 9.0 User's Manual. The Technion-IIT, Haifa, Israel, 1997. Available at http://www.cs.technion.ac.il/ irit.

    [5] G. Elber, J.-J. Choi and M.-S. Kim, Ruled tracing. The Visual Computer, Vol. 13, No. 2, pp. 78-94, 1997.

    [6] G. Elber and M.-S. Kim, Geometric constraint solver using multivariate rational spline functions. Proc. of ACM Symposium on Solid Modeling and Applications, Ann Arbor, MI, June 4-8, 2001.

    [7] H.-S. Heo, S.J. Hong, J.-K. Seong, M.-S. Kim and G. Elber, The intersection of two ringed surfaces and some related problems. Graphical Models, Vol. 63, pp. 228-244, 2001.

    [8] H.-S. Heo, M.-S. Kim and G. Elber, Ruled/ruled surface intersection. Computer-Aided Design, Vol. 31, No. 1, pp. 33-50, 1999.

    [9] J. Hughes and T. Mo¨ller, Building an orthonormal basis from a unit vector. Journal of Graphics Tools, Vol. 4, No. 4, pp. 33-35, 1999.

    [10] D.-E. Hyun, B. Ju¨ttler and M.-S. Kim, Minimizing the distortion of affine spline motion. Graphical Models, Vol. 64, No. 2, pp. 128-144, 2002.

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