Optimal lofted B-spline surface interpolation based on serial closed contours
Shutao Tang
TL;DR
This paper introduces a novel method for lofted B-spline surface interpolation of serial closed contours, addressing control point complexity and providing new theoretical conditions for guaranteed interpolation.
Contribution
It presents two new conjectures for closed B-spline curve interpolation and derives conditions ensuring invertibility, extending existing open-curve interpolation theories to closed contours.
Findings
Validated conjectures through numerical experiments
Derived conditions for full-rank interpolation matrices
Enhanced control over B-spline surface complexity
Abstract
Modern shape design and capture techniques often lead to the geometric data presented in the form of serial rows of data points. In general, the number of data points varies from row to row. Lofted or skinned B-spline surface interpolation is a technique that generates a B-spline surface that passes through these data points precisely. The traditional process often causes a large increase in the number of control points of the resulting B-spline surface. Much of the work to date in mitigating the effects of this increase has been restricted to open section-curves. The lofting of sequential closed contours using the interpolation technique has not been addressed in the existing literature. In this paper, we present two novel conjectures relating to closed B-spline curve interpolation. We derive the equivalent closed B-spline interpolation condition of the well-established…
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Advanced Vision and Imaging