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Determining intersection curves between surfaces of two solids
Journal article   Peer reviewed

Determining intersection curves between surfaces of two solids

K ABDEL-MALEK and H. J YEH
Computer aided design, Vol.28(6-7), pp.539-549
1996
DOI: 10.1016/0010-4485(95)00068-2

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Abstract

Intersection curves between two parametric surfaces are numerically computed using continuation methods. A starting point to initiate the algorithm is determined using the Moore-Penrose pseudo-inverse. Singularities along the curve are detected using a row-rank deficiency of the Jacobian. At singular points where two or more curves intersect, bifurcation points are calculated. To numerically compute a multiple of curves at a bifurcation point, a 2nd-order expansion method is used to render the equation into a quadratic form, such that the tangents are computed. The solution is then switched to a bifurcation branch. The method is demonstrated for two intersecting surfaces having two intersecting curves. The method is also validated for special cases through a number of examples.
Applied Sciences Pattern recognition. Digital image processing. Computational geometry Artificial intelligence Exact sciences and technology Computer science; control theory; systems

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