Interpolatory convexity-preserving subdivision schemes for curves and surfaces

N. Dyn; D. Levin; D. Liu

doi:10.1016/0010-4485(92)90057-H

Interpolatory convexity-preserving subdivision schemes for curves and surfaces

N. Dyn^*, D. Levin, D. Liu

^*Corresponding author for this work

School of Mathematical Sciences

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

Abstract

Interpolatory convexity-preserving subdivision shcemes for curves and surfaces are introduced, and a convergence analysis is presented. The schemes are defined by geometric constructions, and they are nonlinear in the control points. It is shown, by geometry-based proofs, that the limit curves and surfaces are C¹.

Original language	English
Pages (from-to)	211-216
Number of pages	6
Journal	CAD Computer Aided Design
Volume	24
Issue number	4
DOIs	https://doi.org/10.1016/0010-4485(92)90057-H
State	Published - Apr 1992

Keywords

convexity
curves
interpolation
subdivision
surfaces

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10.1016/0010-4485(92)90057-H

Cite this

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title = "Interpolatory convexity-preserving subdivision schemes for curves and surfaces",

abstract = "Interpolatory convexity-preserving subdivision shcemes for curves and surfaces are introduced, and a convergence analysis is presented. The schemes are defined by geometric constructions, and they are nonlinear in the control points. It is shown, by geometry-based proofs, that the limit curves and surfaces are C1.",

keywords = "convexity, curves, interpolation, subdivision, surfaces",

author = "N. Dyn and D. Levin and D. Liu",

note = "Funding Information: This work was supported by USA-Israel Binational Science Foundation Grant 86-00243. The authors are",

year = "1992",

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AU - Levin, D.

AU - Liu, D.

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N2 - Interpolatory convexity-preserving subdivision shcemes for curves and surfaces are introduced, and a convergence analysis is presented. The schemes are defined by geometric constructions, and they are nonlinear in the control points. It is shown, by geometry-based proofs, that the limit curves and surfaces are C1.

AB - Interpolatory convexity-preserving subdivision shcemes for curves and surfaces are introduced, and a convergence analysis is presented. The schemes are defined by geometric constructions, and they are nonlinear in the control points. It is shown, by geometry-based proofs, that the limit curves and surfaces are C1.

KW - convexity

KW - curves

KW - interpolation

KW - subdivision

KW - surfaces

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Interpolatory convexity-preserving subdivision schemes for curves and surfaces

Abstract

Keywords

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