G1 continuous bifurcating and multi-bifurcating surface generation with B-splines

Abstract

ABSTRACTAs an extension to the work done by various authors, this paper proposes a new methodology to construct bifurcating surface by using only a single open B-spline surface equation, which is contrary to conventional approach of stitching surface patches. The paper emphasizes on G1 continuity at the junction of two branches as well as on overall G1 continuity of the generated surface, by exploiting the concept of disjoint surface through knot value repetition. The proposed method allows the flexibility to have irregular non-uniform cross-sections in the generated surface. The ends of the dichotomous surface generated can also be so structured that when the algorithm if used in iteration, will produce multi-level of bifurcation with the overall surface to be G1 continuous, at the sub-division(s) of a branch into further branches.