Polynomial 2D Biharmonic Coordinates for High-order Cages

Fuente: arXiv
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Hauptverfasser: Liu, Shibo, Liu, Ligang, Fu, Xiao-Ming
Format: Preprint
Veröffentlicht: 2025
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author Liu, Shibo
Liu, Ligang
Fu, Xiao-Ming
author_facet Liu, Shibo
Liu, Ligang
Fu, Xiao-Ming
contents We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of any order. Central to our derivation is the use of the high-order boundary element method. We demonstrate the practicality and effectiveness of our method on various 2D deformations. In practice, users can easily manipulate the Bezier control points to perform the desired intuitive deformation, as the biharmonic coordinates provide an enriched deformation space and encourage the alignment between the boundary cage and its interior geometry.
format Preprint
id arxiv_https___arxiv_org_abs_2501_15279
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Polynomial 2D Biharmonic Coordinates for High-order Cages
Liu, Shibo
Liu, Ligang
Fu, Xiao-Ming
Graphics
We derive closed-form expressions of biharmonic coordinates for 2D high-order cages, enabling the transformation of the input polynomial curves into polynomial curves of any order. Central to our derivation is the use of the high-order boundary element method. We demonstrate the practicality and effectiveness of our method on various 2D deformations. In practice, users can easily manipulate the Bezier control points to perform the desired intuitive deformation, as the biharmonic coordinates provide an enriched deformation space and encourage the alignment between the boundary cage and its interior geometry.
title Polynomial 2D Biharmonic Coordinates for High-order Cages
topic Graphics
url https://arxiv.org/abs/2501.15279