Abstract
We consider geometric Hermite subdivision for planar curves, i.e., iteratively refining an input polygon with additional tangent or normal vector information sitting in the vertices. The building block for the (nonlinear) subdivision schemes we propose is based on clothoidal averaging, i.e., averaging w.r.t. locally interpolating clothoids, which are curves of linear curvature. To this end, we derive a new strategy to approximate Hermite interpolating clothoids. We employ the proposed approach to define the geometric Hermite analogues of the well-known Lane-Riesenfeld and four-point schemes. We present numerical results produced by the proposed schemes and discuss their features.
Highlights
Linear subdivision schemes are widely used in various areas such as geometric modeling, multiscale analysis, and for solving PDEs, and are rather well studied; references are for instance [11, 18, 23, 37]
We present a family of geometric Hermite subdivision schemes for the generation of planar curves where the data to be refined are point-vector pairs, the latter serving as information on tangents or normals
If j ( ) is a sequence of integers such that t = lim →∞ 2− j ( ), lim arg p (t ). This is analogous to standard Hermite subdivision, where the slope of the limit must coincide with the limit of slopes, and that is why we suggest to call the procedures introduced here Geometric Hermite subdivision
Summary
Linear subdivision schemes are widely used in various areas such as geometric modeling, multiscale analysis, and for solving PDEs, and are rather well studied; references are for instance [11, 18, 23, 37]
Sign-in/Register to view highlights & summary 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.
