Abstract
This paper introduces a new method for generating the helical tool-paths for both implicit and parametric surfaces. The basic idea is to describe the helical curves as the solutions of an initial-value problem of ordinary differential equations. This system can be obtained from the fact that the helical curve exhibits a constant angle φ with an arbitrary given vector D, which is assumed to be the axis of the helical curve. The resulting system of differential equations is then integrated by applying standard numerical techniques. The performance of the proposed method is discussed by means of some illustrative examples of helical curves on parametric and implicit surfaces.
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Puig-Pey, J., Gálvez, A., Iglesias, A. (2004). Helical Curves on Surfaces for Computer-Aided Geometric Design and Manufacturing. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3044. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24709-8_81
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DOI: https://doi.org/10.1007/978-3-540-24709-8_81
Publisher Name: Springer, Berlin, Heidelberg
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