Abstract
Extending a Ball B-spline Curve (BBSC) is a useful function in the shape modelling of freeform tubular objects. In this paper, we aim to obtain a cubic BBSC B‾(t‾) that can smoothly and fairly extend a given cubic BBSC B(t) to a target ball R. BBSCs with one endpoint satisfying G2 continuity with B(t) and the other endpoint passing through R are optional extending results. We choose the fairest of these BBSCs as the extension result. Our contributions are threefold. First, using one polynomial segment such as Bézier to represent extending parts is often inadequate due to its limited representation ability. We use piecewise polynomials, namely, B-spline, to expand the solution space of this problem. Second, we define a strain energy function for BBSCs to describe their fairness. Third, we exploit the matrix representation of B-splines to obtain an explicit solution of the functional optimization problem in the BBSC extension algorithm. Experimental results are provided to prove the effectiveness of our method.
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