Work

Formula for Dupin cyclidic cube and Miquel point

Year: 2024

Type: article

Abstract: Dupin cyclides are surfaces conformally equivalent to a torus, a circular cone, or a cylinder. Their patches admit rational bilinear quaternionic Bézier (QB) parametrizations and are used in geometric design and architecture. Dupin cyclidic cubes are a natural trivariate generalization of Dupin cyclide patches. In this article, we derive explicit formulas for control points and weights of rational 3-linear QB parametrizations of Dupin cyclidic cubes and relate them with classical Miquel point construction.

Source: Lietuvos matematikos rinkinys

DOI: 10.15388/lmd.2024.37366

Authors: Jean Michel Menjanahary, Rimvydas Krasauskas

Institution: Vilnius University

Language: English

Topic: Advanced Numerical Analysis Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funder: European Commission

Awards: G434337789, learninG, pRocessing, And oPtimising shapES