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Representing Conics using NURBS of Degree Two *
Author(s) -
Qin Kaihuai,
Sun Jiaguang,
Wang Xuefu
Publication year - 1992
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/1467-8659.1150285
Subject(s) - conic section , vertex (graph theory) , mathematics , knot (papermaking) , degree (music) , representation (politics) , square (algebra) , arc length , computer science , geometry , arc (geometry) , discrete mathematics , graph , physics , chemical engineering , politics , political science , acoustics , law , engineering
In this paper, a new method is presented for representing conics precisely using NURBS of degree two. The method requires only four control vertices to represent a full circle using the full circumscribing square‐based representation, which is less than the number required with the other methods using the square control vertex configuration.9, 10, 13 The paper also derives a new condition for NURBS to represent conics precisely and shows the sufficient and necessary conditions for representation of a circular arc, and gives the definition and the knot vector formulae of a periodic NURBS curve.