https://github.com/danmadeira/bezier-curve

Cálculo da curva de Bézier em PHP
https://github.com/danmadeira/bezier-curve

b-spline b-splines bezier bezier-curve bezier-curves cubic-bezier curve function php quadratic-bezier

Last synced: about 2 months ago
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Cálculo da curva de Bézier em PHP

• Host: GitHub
• URL: https://github.com/danmadeira/bezier-curve
• Owner: danmadeira
• License: gpl-3.0
• Created: 2021-03-21T16:20:49.000Z (almost 4 years ago)
• Default Branch: main
• Last Pushed: 2021-03-21T16:22:03.000Z (almost 4 years ago)
• Last Synced: 2023-10-20T07:51:34.788Z (about 1 year ago)
• Topics: b-spline, b-splines, bezier, bezier-curve, bezier-curves, cubic-bezier, curve, function, php, quadratic-bezier
• Language: PHP
• Homepage:
• Size: 28.3 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

Awesome Lists containing this project

README

        
## Cálculo da curva de Bézier em PHP

Este é um código em PHP que contém funções que implementam o cálculo da curva de Bézier (quadrática e cúbica). Os algoritmos estão escritos em uma estrutura simples e semelhante a aplicação pura das respectivas equações, para deixar o código o mais limpo possível, e assim, didático.

As curvas de Bézier, cúbica e quadrática:

![Bezier Curves](img/bezier.png?raw=true)

### Referências

- AHLBERG, J. H.; NILSON, E. N.; WALSH, J. L. *The Theory of Splines and Their Applications*. Academic Press, 1967.

- BARNHILL, R. E.; RIESENFELD, R. F. *Computer Aided Geometric Design*. Academic Press, 1974.

- BAYDAS, S.; KARAKAS, B. *Defining a curve as a Bezier curve*. Journal of Taibah University for Science, Vol. 13, No. 1, pp. 522-528, 2019.

- BERTKA, B. T. *An Introduction to Bezier Curves, B-Splines, and Tensor Product Surfaces with History and Applications*. University of California Santa Cruz. May 30th, 2008.

- BISWAS, S.; LOVELL, B. C. *Bézier and Splines in Image Processing and Machine Vision*. Springer-Verlag London Limited, 2008.

- BOOR, C. *A Practical Guide to Splines, Revised Edition*. Applied Mathematical Sciences, Volume 27. Springer-Verlag New York, 2001.

- CASSELMAN, B. *From Bézier to Bernstein*. Feature Column, Monthly essays on mathematical topics. American Mathematical Society, November 2008. Disponível em: 

- FARIN, G. *Curves and Surfaces for CAGD: A Practical Guide, 5th Edition*. The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling. Morgan Kaufmann Publishers, 2002.

- FARIN, G.; HANSFORD, D. *Mathematical Principles for Scientific Computing and Visualization*. A K Peters, 2008.

- FARIN, G.; HANSFORD, D. *Practical Linear Algebra: A Geometry Toolbox, Third Edition*. CRC Press, 2014.

- FARIN, G.; HOSCHEK, J.; KIM, M.-S. *Handbook of Computer Aided Geometric Design*. Elsevier Science B.V., 2002.

- FAROUKI, R. T. *The Bernstein polynomial basis: a centennial retrospective*. Department of Mechanical and Aerospace Engineering, University of California. March 3, 2012.

- FAROUKI, R. T.; NEFF, C. A. *Analytic properties of plane offset curves*. Computer Aided Geometric Design, Vol. 7, pp. 83-99, 1990.

- GALLIER, J. *Curves and Surfaces in Geometric Modeling: Theory and Algorithms*. Department of Computer and Information Science, University of Pennsylvania, November 21, 2018. Disponível em: 

- HUGHES, J. F.; VAN DAM, A.; MCGUIRE, M.; SKLAR, D. F.; FOLEY, J. D.; FEINER, S. K.; AKELEY, K. *Computer Graphics: Principles and Practice, Third Edition*. Pearson Education, 2014.

- KAMERMANS, M. *A Primer on Bézier Curves*. Pomax, 2020. Disponível em: 

- PRAUTZSCH, H.; BOEHM, W.; PALUSZNY, M. *Bezier and B-Spline Techniques*. Mathematics and Visualization Series. Springer-Verlag Berlin Heidelberg, 2002.

- SIMONI, R. *Teoria Local das Curvas*. Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Curso de Licenciatura em Matemática. Florianópolis, 2005.

- WEISSTEIN, E. W. *Bézier Curve*. MathWorld: A Wolfram Web Resource. Disponível em: