Abstract
This paper addresses two interesting problems in geometric processing of surfaces: (1) the determination of the curves on a surface having a constant angle with a prescribed constant direction (helical curves) and (2) the construction of the curve of contact between the surface and the cone circumscribing the surface, with its vertex at the observation point (silhouette curves). Both problems are formulated by using geometric and differential arguments leading to initial value problems of systems of explicit first-order ordinary differential equations that can be efficiently solved through standard step-by-step numerical integration methods. For each problem, the interesting cases of surfaces given in implicit and parametric form are discussed. Some illustrative examples show the good performance of the proposed methods.
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Puig-Pey, J., Gálvez, A., Iglesias, A., Corcuera, P., Rodríguez, J. (2008). Some Problems in Geometric Processing of Surfaces. In: Advances in Mathematical and Statistical Modeling. Statistics for Industry and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4626-4_22
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DOI: https://doi.org/10.1007/978-0-8176-4626-4_22
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