Some remarks on geometric continuity of rational surface patches. (English) Zbl 0817.65013

Jüttler, Bert; Wassum, Peter

Comput. Aided Geom. Des. 9, No. 2, 143-157 (1992).

Summary: The geometric continuous joint between two rational surface patches is considered as a special case of the geometric continuous joint between two hypermanifolds in \(\mathbb{R}^ 4\). Furthermore, a criterion concerning the independence of the equations resulting from the necessary and sufficient conditions for geometric continuity is developed. By solving the continuity conditions for one of the patches, explicit conditions for geometric continuity are determined. These conditions generally provide five free form-parameters such yielding one parameter more than the conditions known up to now.

MSC:

65D17

Computer-aided design (modeling of curves and surfaces)

Keywords:

hypercones; rational Bézier surface patches; explicit continuity conditions; explicit representation of Bézier control points; computer aided geometric design; geometric continuity

References:

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