Minimization, constraints and composite Bézier curves

Michel Bercovier; Arie Jacobi

doi:10.1016/0167-8396(94)90303-4

Minimization, constraints and composite Bézier curves

Michel Bercovier^*, Arie Jacobi

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

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

11 Scopus citations

Abstract

This paper presents a global method for approximation and/or construction of curves using constraints. The method is based on a min-max problem which describes approximation and differential geometric characteristics, constrained in order to achieve desired geometrical or physical effects. The numerical solution of the problem takes full advantage of the finite elements method and of constrained optimization algorithms.

Original language	English
Pages (from-to)	533-563
Number of pages	31
Journal	Computer Aided Geometric Design
Volume	11
Issue number	5
DOIs	https://doi.org/10.1016/0167-8396(94)90303-4
State	Published - Oct 1994

Keywords

Approximate conversion
Augmented Lagrangian formulation
Bézier curve
Finite element method (FEM)
Geometric continuity
Lagrange multipliers formulation
Offset curve
Penalty method
Uzawa method
Variational problem formulation

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10.1016/0167-8396(94)90303-4

Cite this

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abstract = "This paper presents a global method for approximation and/or construction of curves using constraints. The method is based on a min-max problem which describes approximation and differential geometric characteristics, constrained in order to achieve desired geometrical or physical effects. The numerical solution of the problem takes full advantage of the finite elements method and of constrained optimization algorithms.",

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AB - This paper presents a global method for approximation and/or construction of curves using constraints. The method is based on a min-max problem which describes approximation and differential geometric characteristics, constrained in order to achieve desired geometrical or physical effects. The numerical solution of the problem takes full advantage of the finite elements method and of constrained optimization algorithms.

KW - Approximate conversion

KW - Augmented Lagrangian formulation

KW - Bézier curve

KW - Finite element method (FEM)

KW - Geometric continuity

KW - Lagrange multipliers formulation

KW - Offset curve

KW - Penalty method

KW - Uzawa method

KW - Variational problem formulation

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JO - Computer Aided Geometric Design

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Minimization, constraints and composite Bézier curves

Abstract

Keywords

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