Hermite subdivision schemes for manifold-valued Hermite data

Hofit Ben-Zion Vardi, Nira Dyn, Nir Sharon

Research output: Contribution to journalArticlepeer-review

Abstract

This paper introduces a family of subdivision schemes that generate curves over manifolds from manifold-Hermite data. This data consists of points and tangent directions sampled from a curve over a manifold. Using a manifold-Hermite average based on the De Casteljau algorithm as our main building block, we show how to adapt a geometric approach for curve approximation over manifold-Hermite data. The paper presents the various definitions and provides several analysis methods for characterizing properties of both the average and the resulting subdivision schemes based on it. Demonstrative figures accompany the paper's presentation and analysis.

Original languageEnglish
Article number102342
JournalComputer Aided Geometric Design
Volume111
DOIs
StatePublished - Jun 2024

Keywords

  • De Casteljau algorithm
  • Manifold-Hermite approximation
  • Manifold-Hermite data,
  • Manifold-Hermite Lane-Riesenfeld subdivision schemes

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design

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