## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2013, Special Issue (2013), Article ID 237984, 9 pages.

### Firefly Algorithm for Polynomial Bézier Surface Parameterization

Akemi Gálvez and Andrés Iglesias

**Full-text: Open access**

#### Abstract

A classical issue in many applied fields is to obtain an approximating surface to a given set of data points. This problem arises in Computer-Aided Design and Manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. Very often, the preferred approximating surface is polynomial, usually described in parametric form. This leads to the problem of determining suitable parametric values for the data points, the so-called surface parameterization. In real-world settings, data points are generally irregularly sampled and subjected to measurement noise, leading to a very difficult nonlinear continuous optimization problem, unsolvable with standard optimization techniques. This paper solves the parameterization problem for polynomial Bézier surfaces by applying the firefly algorithm, a powerful nature-inspired metaheuristic algorithm introduced recently to address difficult optimization problems. The method has been successfully applied to some illustrative examples of open and closed surfaces, including shapes with singularities. Our results show that the method performs very well, being able to yield the best approximating surface with a high degree of accuracy.

#### Article information

**Source**

J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 237984, 9 pages.

**Dates**

First available in Project Euclid: 14 March 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1394807368

**Digital Object Identifier**

doi:10.1155/2013/237984

**Zentralblatt MATH identifier**

06950572

#### Citation

Gálvez, Akemi; Iglesias, Andrés. Firefly Algorithm for Polynomial Bézier Surface Parameterization. J. Appl. Math. 2013, Special Issue (2013), Article ID 237984, 9 pages. doi:10.1155/2013/237984. https://projecteuclid.org/euclid.jam/1394807368

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