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Intersection of a ruled surface with a free-form surface

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An Erratum to this article was published on 01 September 2007

Abstract

This paper presents a simple method for computing the intersection curve of a ruled surface and a free-form surface. The basic idea is to reduce the problem of surface intersection to the one of projecting an appropriate curve such as a directrix of the ruled surface, along its indicatrix curve (direction vector field of its generating lines), onto the free-form surface; the projection curve is just the intersection curve. With techniques in classical differential geometry, we derive the differential equations of the intersection curve in the cases of parametrically and implicitly defined free-form surfaces. The intersection curve naturally inherits the parameter of the chosen directrix. Moreover, it is independent of the base surface geometry and its parameterization, and is obtained by numerically solving the initial-value problem for a system of first-order ordinary differential equations in the parametric domain associated to the surface representation for parametric case or in 3D space for implicit case. Some experimental examples are also given to demonstrate that the presented method is effective and potentially useful in computer aided design and computer graphics.

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Authors and Affiliations

  1. Research Center of CAD/CAM Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, People’s Republic of China

    Xiaoping Wang & Liyan Zhang

  2. College of Information Engineering, Qingdao University, Qingdao, 266071, People’s Republic of China

    Weizhong Zhang

Authors
  1. Xiaoping Wang
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  2. Weizhong Zhang
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  3. Liyan Zhang
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Correspondence to Xiaoping Wang.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s11075-007-9128-9

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Wang, X., Zhang, W. & Zhang, L. Intersection of a ruled surface with a free-form surface. Numer Algor 46, 85–100 (2007). https://doi.org/10.1007/s11075-007-9118-y

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  • DOI: https://doi.org/10.1007/s11075-007-9118-y

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