• Journal of the Society of Naval Architects of Korea
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• v.34 no.4
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• pp.127-138
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• 1997

In this study, a new technique is presented, by which one can define ship hull form with full fairness from the input data of lines. For curve modeling, the de Casteljau Algorithm and Bezier control points are used to express free curves and to establish the unified curve modeling technique which enables one to convert non-uniform B-spline (NUB) curve or cubic spline curve into composite Bezier curves. For surface modeling, the mesh curve net which is required to define surface of ship hull form is interpolated by the method of the unified curve modeling, and the boundary curve segments of Gregory surface patches are generated by remeshing(rearranging) the given mesh curve net. From these boundary information, composite Gregory surfaces of good quality in fairness can be formulated.

• International Journal of CAD/CAM
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• v.9 no.1
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• pp.25-29
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• 2010

Let $S_n^r(\Omega)$ be the spline space of degree n and smoothness r with respect to $\Omega$ where $\Omega$ is a triangulation of a planner polygonal domain. Dimensions of $S_n^r(\Omega)$ over the so-called unconstricted triangulation were given by Farin in [J. Comput. Appl. Math. 192(2006), 320-327]. In this paper, a counter example is given to show that the condition used in the main result in Farins paper is not correct, and then an improved necessary and sufficient condition is presented.