Abstract
Given a segment of a conic section in the form of a rational quadratic Bézier curve and any positive odd integer n, a geometric Hermite interpolant, with 2 n contacts, counting multiplicity, is presented. This leads to a G n−1 spline approximation having an approximation order of O( h 2 n ). A bound on the Hausdorff error of the Hermite interpolant is provided. Both the interpolation and error bound are extended to an important subclass of rational biquadratic Bézier surfaces. For low n, the approximation provides a method for converting the so-called analytic curves and surfaces used in CAGD to polynomial spline form with very small error.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
