Abstract
In this paper, geometric modelling is discussed to represent free-form curves and surfaces for computer-aided design systems using the B-spline. The B-spline is convenient to use for interactive design, and has no specific geometric restrictions to represent complicated curves and surfaces with a small number of points. The number of knots is reduced by the condition that the distance between a given curve and an approximate representation exists within a prescribed tolerance. The placement of knots is found interactively using an approach that concentrates the knots in the region of the large curvature. The smoothing of surfaces is performed by the identity condition of curvature derivatives on both sides of the knot point vector. The proposed methods are applied to the geometric modelling of a turbine blade, and the numerical results illustrate the superiority of the proposed methods.
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