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Published in:
2019 | OriginalPaper | Chapter
ODF Using a 5-Point B-Spline
Published in: Fitting Splines to a Parametric Function
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A 5-point uniform B-spline is fit to a hypoTrochoid shape. The B-spline is initialized using a cubic Bézier. The B-spline basis functions are derived and re-expressed as Bernstein polynomials. It is shown how this relationship is analogous to the relationship between the B-spline control points and the set of cubic Bézier control points that we get when we use knot insertion to decompose the B-spline to a set of Béziers for purposes of rendering them. The ODF results are significantly simpler than the corresponding cubic Bézier ODF results, in that there is only one main solution branch. However, there is still a parameter discontinuity as the hypoTrochoid shape changes. The discontinuity is due to a simple merge of two solutions, which can be diagnosed using the eigenvalues of the second-order response matrix.