A constructive approach to implicitizing rational surfaces with LCI base points by moving planes and moving quadrics

Yisheng Lai; Falai Chen; Xiaoran Shi; Yu Gao

doi:10.1016/j.cagd.2021.102051

A constructive approach to implicitizing rational surfaces with LCI base points by moving planes and moving quadrics

Yisheng Lai
, Falai Chen^*
, Xiaoran Shi
, Yu Gao

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

This paper provides an elementary and constructive treatment to implicitizing tensor product rational surfaces whose base point locus is a local complete intersection (lci) by the method of moving planes and moving quadrics. The approach is much more elementary than that by Busé and Chen (2021) which relies on very advanced algebraic tools such as Rees algebras and symmetric algebras, etc. An effective algorithm is also presented to compute moving planes and moving quadrics that comprise a compact determinantal representation of the implicit equation of a rational surface.

Original language	English
Article number	102051
Journal	Computer Aided Geometric Design
Volume	92
DOIs	https://doi.org/10.1016/j.cagd.2021.102051
State	Published - Jan 2022

Keywords

Implicitization
Moving plane
Moving quadric
Rational surface
Syzygy module
μ-Basis

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10.1016/j.cagd.2021.102051

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title = "A constructive approach to implicitizing rational surfaces with LCI base points by moving planes and moving quadrics",

abstract = "This paper provides an elementary and constructive treatment to implicitizing tensor product rational surfaces whose base point locus is a local complete intersection (lci) by the method of moving planes and moving quadrics. The approach is much more elementary than that by Bus{\'e} and Chen (2021) which relies on very advanced algebraic tools such as Rees algebras and symmetric algebras, etc. An effective algorithm is also presented to compute moving planes and moving quadrics that comprise a compact determinantal representation of the implicit equation of a rational surface.",

keywords = "Implicitization, Moving plane, Moving quadric, Rational surface, Syzygy module, μ-Basis",

author = "Yisheng Lai and Falai Chen and Xiaoran Shi and Yu Gao",

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year = "2022",

month = jan,

doi = "10.1016/j.cagd.2021.102051",

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T1 - A constructive approach to implicitizing rational surfaces with LCI base points by moving planes and moving quadrics

AU - Lai, Yisheng

AU - Chen, Falai

AU - Shi, Xiaoran

AU - Gao, Yu

PY - 2022/1

Y1 - 2022/1

N2 - This paper provides an elementary and constructive treatment to implicitizing tensor product rational surfaces whose base point locus is a local complete intersection (lci) by the method of moving planes and moving quadrics. The approach is much more elementary than that by Busé and Chen (2021) which relies on very advanced algebraic tools such as Rees algebras and symmetric algebras, etc. An effective algorithm is also presented to compute moving planes and moving quadrics that comprise a compact determinantal representation of the implicit equation of a rational surface.

AB - This paper provides an elementary and constructive treatment to implicitizing tensor product rational surfaces whose base point locus is a local complete intersection (lci) by the method of moving planes and moving quadrics. The approach is much more elementary than that by Busé and Chen (2021) which relies on very advanced algebraic tools such as Rees algebras and symmetric algebras, etc. An effective algorithm is also presented to compute moving planes and moving quadrics that comprise a compact determinantal representation of the implicit equation of a rational surface.

KW - Implicitization

KW - Moving plane

KW - Moving quadric

KW - Rational surface

KW - Syzygy module

KW - μ-Basis

UR - https://www.scopus.com/pages/publications/85119915965

U2 - 10.1016/j.cagd.2021.102051

DO - 10.1016/j.cagd.2021.102051

M3 - 文章

AN - SCOPUS:85119915965

SN - 0167-8396

VL - 92

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

M1 - 102051

ER -

A constructive approach to implicitizing rational surfaces with LCI base points by moving planes and moving quadrics

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Keywords

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