1. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Capacity-Constrained Point Distributions ..Complementary Material.. Michel Alves dos Santos Ps-Graduao em Engenharia de Sistemas e Computao Universidade Federal do Rio de Janeiro - UFRJ - COPPE Cidade Universitria - Rio de Janeiro - CEP: 21941-972 Docentes Responsveis: Prof. Dsc. Ricardo Marroquim & Prof. PhD. Cludio Esperana {michel.mas, michel.santos.al}@gmail.com January, 2014January, 2014January, 2014January, 2014January, 2014January, 2014January, 2014January, 2014January, 2014January, 2014January, 2014January, 2014January, 2014January, 2014January, 2014January, 2014January, 2014 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC

2. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Some More Results... Using: Regular Density Functions Custom Density Functions Images as Boundary Functions Images as Density Functions Now we will see other results obtained with the technique... Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 3. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Regular Density Functions :: Circular f (x, y) = c; (x, y) x2 + y2 radius Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC Optimized Points Voronoi Tessellation 4. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Regular Density Functions :: Circular Figure: The gure above shows the number of points and samples for each set. In the table below we can view times of generation, times of optimization and steps until convergence. The results are an average of 15 executions. #Points #Samples Generation Time Optimization Time Optimization Steps* 1024 524288 00.06 seconds 03.54 seconds 160 2048 1048576 00.12 seconds 08.69 seconds 199 4096 2097152 00.24 seconds 20.78 seconds 167 Optimization Steps*: number of iterations until convergence. Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 1024 Points 524288 Samples 2048 Points 1048576 Samples 4096 Points 2097152 Samples 5. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions All tabled numerical results shown in this presentation are an average of 15 executions for each set of points. Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 6. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Fences f (x, y) = 0.75e(625x2 y2 ) Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC Optimized Points Voronoi Tessellation 7. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Fences Figure: The gure above shows the density function, optimized points and your voronoi diagram. In the table below we can view times of generation, times of optimization and steps until convergence for each set of points. #Points #Samples Generation Time Optimization Time Optimization Steps* 1024 32768 11.73 seconds 00.18 seconds 16 2048 65536 54.62 seconds 00.44 seconds 15 4096 131072 267.43 seconds 01.33 seconds 18 Optimization Steps*: number of iterations until convergence. Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 8. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Natural Log f (x, y) = log (x2 + y2 + 0.1) Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC Optimized Points Voronoi Tessellation 9. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Natural Log Figure: The gure above shows the density function, optimized points and your voronoi diagram. In the table below we can view times of generation, times of optimization and steps until convergence for each set of points. #Points #Samples Generation Time Optimization Time Optimization Steps* 1024 32768 19.28 seconds 00.24 seconds 16 2048 65536 85.40 seconds 00.76 seconds 20 4096 131072 429.79 seconds 02.34 seconds 22 Optimization Steps*: number of iterations until convergence. Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 10. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Half Valley f (x, y) = x2 + 3 sin (y) Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC Optimized Points Voronoi Tessellation 11. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Half Valley Figure: The gure above shows the density function, optimized points and your voronoi diagram. In the table below we can view times of generation, times of optimization and steps until convergence for each set of points. #Points #Samples Generation Time Optimization Time Optimization Steps* 1024 32768 02.89 seconds 00.19 seconds 14 2048 65536 12.24 seconds 00.55 seconds 23 4096 131072 62.42 seconds 01.63 seconds 21 Optimization Steps*: number of iterations until convergence. Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 12. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Hilly f (x, y) = cos (2x2 + 2y) sin (3x + 3y2 ) Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC Optimized Points Voronoi Tessellation 13. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Hilly Figure: The gure above shows the density function, optimized points and your voronoi diagram. In the table below we can view times of generation, times of optimization and steps until convergence for each set of points. #Points #Samples Generation Time Optimization Time Optimization Steps* 1024 32768 06.13 seconds 00.29 seconds 37 2048 65536 27.58 seconds 00.71 seconds 32 4096 131072 133.47 seconds 02.46 seconds 50 Optimization Steps*: number of iterations until convergence. Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 14. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Two Valleys f (x, y) = ((x2 1)(y2 4)+x2 +y2 5)/((x2 +y2 +1)2 )+1 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC Optimized Points Voronoi Tessellation 15. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Two Valleys Figure: The gure above shows the density function, optimized points and your voronoi diagram. In the table below we can view times of generation, times of optimization and steps until convergence for each set of points. #Points #Samples Generation Time Optimization Time Optimization Steps* 1024 32768 04.52 seconds 00.24 seconds 21 2048 65536 19.91 seconds 00.61 seconds 19 4096 131072 97.40 seconds 01.99 seconds 26 Optimization Steps*: number of iterations until convergence. Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 16. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Water Fall f (x, y) = (4x2 1)e(x2 y2 ) + 0.5 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC Optimized Points Voronoi Tessellation 17. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Water Fall Figure: The gure above shows the density function, optimized points and your voronoi diagram. In the table below we can view times of generation, times of optimization and steps until convergence for each set of points. #Points #Samples Generation Time Optimization Time Optimization Steps* 1024 32768 02.71 seconds 00.24 seconds 24 2048 65536 12.57 seconds 00.58 seconds 21 4096 131072 69.70 seconds 02.02 seconds 17 Optimization Steps*: number of iterations until convergence. Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 18. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: The Ramp f (x, y) = sin (x cos (y)) + 0.5 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC Optimized Points Voronoi Tessellation 19. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: The Ramp Figure: The gure above shows the density function, optimized points and your voronoi diagram. In the table below we can view times of generation, times of optimization and steps until convergence for each set of points. #Points #Samples Generation Time Optimization Time Optimization Steps* 1024 32768 12.80 seconds 00.24 seconds 15 2048 65536 64.60 seconds 00.70 seconds 18 4096 131072 298.21 seconds 01.87 seconds 17 Optimization Steps*: number of iterations until convergence. Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 20. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Half Moon f (x, y) = x3 3x 2y2 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC Optimized Points Voronoi Tessellation 21. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Half Moon Figure: The gure above shows the density function, optimized points and your voronoi diagram. In the table below we can view times of generation, times of optimization and steps until convergence for each set of points. #Points #Samples Generation Time Optimization Time Optimization Steps* 1024 32768 05.29 seconds 00.22 seconds 15 2048 65536 23.08 seconds 00.54 seconds 16 4096 131072 121.19 seconds 01.74 seconds 20 Optimization Steps*: number of iterations until convergence. Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 22. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Funnel f (x, y) = (sin ( x2 + y2))/( x2 + y2 + 1) Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC Optimized Points Voronoi Tessellation 23. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: Funnel Figure: The gure above shows the density function, optimized points and your voronoi diagram. In the table below we can view times of generation, times of optimization and steps until convergence for each set of points. #Points #Samples Generation Time Optimization Time Optimization Steps* 1024 32768 03.71 seconds 00.16 seconds 13 2048 65536 17.84 seconds 00.53 seconds 22 4096 131072 89.28 seconds 01.69 seconds 20 Optimization Steps*: number of iterations until convergence. Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 24. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: The Cake f (x, y) = sin ( x2 + y2) Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC Optimized Points Voronoi Tessellation 25. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Custom Density Functions :: The Cake Figure: The gure above shows the density function, optimized points and your voronoi diagram. In the table below we can view times of generation, times of optimization and steps until convergence for each set of points. #Points #Samples Generation Time Optimization Time Optimization Steps* 1024 32768 02.76 seconds 00.18 seconds 16 2048 65536 12.91 seconds 00.49 seconds 18 4096 131072 70.28 seconds 01.72 seconds 17 Optimization Steps*: number of iterations until convergence. Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 26. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Image as Boundary and Density Functions All tabled numerical results shown in this presentation are an average of 15 executions for each set of points. Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC VisualizationofBoundaryRegions 27. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Image as Boundary :: Torus Figure: Image as Boundary. Input image with 735x735, points and regions. #Points #Samples Generation Time Optimization Time Optimization Steps 32 212992 18.3042 minutes 7.37 seconds 968 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 28. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Image as Boundary :: Pear Figure: Image as Boundary. Input image with 656x656, points and regions. #Points #Samples Generation Time Optimization Time Optimization Steps 32 196608 14.477 minutes 5.41 seconds 613 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 29. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Image as Boundary :: Horse Figure: Image as Boundary. Input image with 705x705, points and regions. #Points #Samples Generation Time Optimization Time Optimization Steps 32 212992 26.7697 minutes 4.15 seconds 337 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 30. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Image as Boundary :: Bunny Figure: Image as Boundary. Input image with 645x645, points and regions. #Points #Samples Generation Time Optimization Time Optimization Steps 32 229376 17.1552 minutes 12.77 seconds 1142 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 31. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Image as Boundary :: Planck Figure: Image as Boundary. Input image with 645x645, points and regions. #Points #Samples Generation Time Optimization Time Optimization Steps 32 196608 15.1542 minutes 5.92 seconds 548 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 32. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Stippling :: Image as Density Function Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC SomeMoreStipplingResults 33. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Stippling - Famous Face Figure: Famous Faces. Input image with 1000x1000 pixels and stippling result. #Points #Samples Generation Time Optimization Time Optimization Steps 8192 524288 19.5017 minutes 6.93 seconds 26 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 34. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Stippling - Famous Face Figure: Famous Faces. Input image with 1000x1000 pixels and stippling result. #Points #Samples Generation Time Optimization Time Optimization Steps 8192 524288 33.8668 minutes 6.75 seconds 29 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 35. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Stippling - Famous Face Figure: Famous Faces. Input image with 1000x1000 pixels and stippling result. #Points #Samples Generation Time Optimization Time Optimization Steps 8192 524288 28.1835 minutes 7.04 seconds 24 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 36. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Stippling - Famous Face Figure: Famous Faces. Input image with 1000x1000 pixels and stippling result. #Points #Samples Generation Time Optimization Time Optimization Steps 8192 524288 38.3498 minutes 11.88 seconds 31 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 37. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Stippling - Famous Face Figure: Famous Faces. Input image with 1000x1000 pixels and stippling result. #Points #Samples Generation Time Optimization Time Optimization Steps 8192 524288 28.1648 minutes 9.26 seconds 31 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 38. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Stippling - Secords Shoes Figure: Secords Shoes. Samples and stippling result. Input image with 1000x1000. #Points #Samples Generation Time Optimization Time Optimization Steps 5120 163840 7.73667 minutes 1.87 seconds 20 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 163840 Samples 5120 Points Input 39. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Results :: Stippling - Stanford Bunny Figure: Stanford Bunny. Input image with 475x475 pixels and stippling result. #Points #Samples Generation Time Optimization Time Optimization Steps 8192 393216 162.041 minutes 6.33 seconds 30 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC 8192 Points 393216 Samples Input Stippling 40. Universidade Federal do Rio de Janeiro - UFRJ - Campus Cidade Universitria - Rio de Janeiro - Ilha do Fundo, CEP: 21941-972 - COPPE/PESC/LCG Capacity-Constrained Point Distributions :: A Variant of Lloyds Method :: Computational Geometry Discipline :: Laboratory Seminar :: January, 2013 Thanks Thanks for your attention! Michel Alves dos Santos - michel.mas@gmail.com Michel Alves dos Santos - (Alves, M.) MSc Candidate at Federal University of Rio de Janeiro. E-mail: michel.mas@gmail.com, malves@cos.ufrj.br Lattes: http://lattes.cnpq.br/7295977425362370 Home: http://www.michelalves.com Phone: +55 21 2562 8572 (Institutional Phone Number) http://www.facebook.com/michel.alves.santos http://www.linkedin.com/prole/view?id=26542507 Michel Alves dos Santos: Laboratrio de Computao Grca - LCG Ps-Graduao em Engenharia de Sistemas e Computao - PESC