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A GENETIC AND EQUILATERAL LATTICE ALGORITHMS FOR TRIANGULATION OF CLOSE POLYGONS

A GENETIC AND EQUILATERAL LATTICE ALGORITHMS FOR TRIANGULATION OF CLOSE POLYGONS. F. J. Lopez-Jaquez 1 , S.E. Ramirez-Jara 2 , N.G. Alba-Baena 1 1 Department of Industrial and Manufacturing Engineering, University of Juarez (UACJ) Ave. Del Charro 450 N Juarez , Chihuahua 32310, Mexico

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A GENETIC AND EQUILATERAL LATTICE ALGORITHMS FOR TRIANGULATION OF CLOSE POLYGONS

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  1. A GENETIC AND EQUILATERAL LATTICE ALGORITHMS FOR TRIANGULATION OF CLOSE POLYGONS F. J. Lopez-Jaquez1, S.E. Ramirez-Jara2, N.G. Alba-Baena1 1Department of Industrial and Manufacturing Engineering, University of Juarez (UACJ) Ave. Del Charro 450 N Juarez, Chihuahua 32310, Mexico Correspondingauthor’s e-mail: frlopezr@uacj.mx 2Department of Electric & Computer Engineering, University of Juarez Ave. Del Charro 450 N Juarez, Chihuahua 32310, Mexico

  2. outline INTRODUCTION POLYGON TRIANGULATION APPLYING A GENETIC ALGORITHM DNA CODE CROSSOVER AND MUTATION MECHANISMS FITNESS EVALUATION EVOLUTION EQUILATERAL LATTICE COMPUTER INTERFASE RESULTS CONSCLUTIONS AND FURTHER RESEARCH

  3. INTRODUCTION

  4. POLYGON TRIANGULATION APPLYING A GENETIC ALGORITHM DNA CODE

  5. POLYGON TRIANGULATION APPLYING A GENETIC ALGORITHMHULL SEGMENTATION AND TRIANGULATION

  6. CROSSOVER AND MUTATION MECHANISMS

  7. FITNESS EVALUATION AND EVOLUTION

  8. EQUILATERAL LATTICE

  9. EQUILATERAL LATTICE

  10. EQUILATERAL LATTICE

  11. Interface a) b) c) d)

  12. Fitness=10.057 Fitness=13.230 RESULTS n=114, TEA=352, TGA=190

  13. RESULTS n=44, TEA=352, TGA=190.

  14. RESULTADOS n=21, TEA=201, TGA=57

  15. RESULTADOS n=388, TEA=760, TGA=918

  16. Conclusions • The equilateral lattice algorithm introduces triangles while the genetic algorithm introduces lines, to compensate this, if the lattice used is 10 by 10 then the number of segmentation lines of the genetic algorithm will be 30. • Probably is not fare to compare directly the results of both algorithms but strictly use of the results obtained by equation 1 were used in this case. • The equilateral lattice algorithm can be seen as a special case of the genetic algorithm where all segmentation lines are arranged in a cross diagonal pattern producing an equilateral pattern but this individual is hard to obtain in a random procedure unless the objective function were modified to lead the algorithm to produce an equilateral pattern. • The genetic algorithm is a general solution and, probably with a few restrictions, it is possible to produces similar results than the equilateral pattern or better but for sure the time will still be longer due to the evolution process involved in the genetic algorithm. • If there is not concern on the processing time, that most of the time it is, the genetic algorithm is a powerful technique for searching of an optima individual and it could be adapted to support different objective functions. • In both algorithms the basic operation to find where segments cross each other, identify sub hulls and triangulation are similar but one benefit of the equilateral pattern is that the process is focused just in one possibility and the close polygon is triangulated, but there is not care on any quality measure, the end quality will be as good as the setting of the parameters of the algorithm. On the other hand, if there is care of a quality measure then the genetic algorithm has the ability to explore for a better solution but at expense of processing time. • Further research includes combination of both algorithms and triangulation of surfaces in XYZ space

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