Cubic algebraic curves based on geometric constraints

Methods for curve modeling with cubic algebraic curves based on geometric constraints are introduced in this paper. A 1-parameter family of cubic curves with four given points as well as two tangent lines at the endpoints is constructed in the first part of the paper. A 1-parameter family and 2-para...

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Bibliographic Details
Published in:Computer aided geometric design 2001-05, Vol.18 (4), p.299-307
Main Authors: Sanyuan, Zhang, Hujun, Bao, Baogang, Wei
Format: Article
Language:English
Subjects:
Applied sciences
Computer aided design
Computer science
control theory
systems
Cubic algebraic curve
Cubic parametric curve
Curvature continuity
Exact sciences and technology
Geometric constraint
Interpolation
Software
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Summary:Methods for curve modeling with cubic algebraic curves based on geometric constraints are introduced in this paper. A 1-parameter family of cubic curves with four given points as well as two tangent lines at the endpoints is constructed in the first part of the paper. A 1-parameter family and 2-parameter family of cubic curve constructions are presented for interpolating two given endpoints and two given tangent lines as well as two given curvatures at the endpoints in the last part of the paper.
ISSN:0167-8396
1879-2332
DOI:10.1016/S0167-8396(01)00032-2