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Um pouco mais sobre modelos de objetos

Um pouco mais sobre modelos de objetos. Ray Path Categorization. Ray Path Categorization . Nehab, D.; Gattass, M. Proceedings of SIBGRAPI 2000, Brazil, 2000, pp. 227-234. Ray Path Categorization.   -. Curvas e Superfícies. modelagem paramétrica. y. y'. x'. x.

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Um pouco mais sobre modelos de objetos

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  1. Um pouco mais sobre modelos de objetos

  2. Ray Path Categorization Ray Path Categorization.Nehab, D.; Gattass, M.Proceedings of SIBGRAPI 2000, Brazil, 2000, pp. 227-234.

  3. Ray Path Categorization   -

  4. Curvas e Superfícies modelagem paramétrica

  5. y y' x' x Requisitos: Independência de eixos

  6. y x Requisitos: Valores Múltiplos

  7. Requisitos: Controle Local y x

  8. Requisitos: Redução da Variação polinômio de grau elevado

  9. Requisitos: Continuidade Variável

  10. Requisitos: Versatilidade

  11. Finalizando: Formulação matemática tratável Requisitos: Amostragem Uniforme Dsn Ds3 Ds2 Ds4 Ds1 DsiDsj

  12. t=1 t=0 t=0 t=0 t=1 t=1 u1 u0 u2 un Solução Curva representada por partes através de polinômios de grau baixo (geralmente 3) t=1 t=0 Parametrização

  13. z V2 Vn-1 t=1 V1 Vn t=0 V3 P(t) V0 y x Curvas de Bézier P. de Casteljau, 1959 (Citroën) P. de Bézier, 1962 (Renault) - UNISURF Forest 1970: Polinômios de Bernstein onde: pol. Bernstein coef. binomial

  14. Bézier Cúbicas z V1 V3 P(t) V0 V2 y x

  15. B0,3 B1,3 1 (1-t)3 3(1-t)2t 3 0 0 1 1 t t B3,3 B2,3 1 3(1-t)t2 t3 -3 0 1 t B0,3 +B1,3 +B2,3 +B3,3 0 1 t 1 0 1 t Polinômios Cúbicos de Bernstein

  16. R(0) z V1 V3 P(t) V0 V2 y x R(1) Propriedades da Bézier Cúbica

  17. Controle da Bézier Cúbica

  18. Redução de n=3 para n=2 Bezier n=2

  19. Redução de n=2 para n=1 Bezier n=1

  20. (1-t) t Cálculo de um Ponto Mostre que:

  21. Subdivisão de Bézier Cúbicas . . .

  22. Construção de uma Bezier u=1/2 P(1/2)

  23. Introduction toSubdivision Surfaces Adi Levin

  24. Subdivision Curves and Surfaces • Subdivision curves • The basic concepts of subdivision. • Subdivision surfaces • Important known methods. • Discussion: subdivision vs. parametric surfaces.

  25. Corner Cutting

  26. Corner Cutting 3 : 1 1 : 3

  27. Corner Cutting

  28. Corner Cutting

  29. Corner Cutting

  30. Corner Cutting

  31. Corner Cutting

  32. Corner Cutting

  33. A control point The limit curve The control polygon Corner Cutting

  34. The 4-point scheme

  35. The 4-point scheme

  36. The 4-point scheme 1 : 1 1 : 1

  37. The 4-point scheme 1 : 8

  38. The 4-point scheme

  39. The 4-point scheme

  40. The 4-point scheme

  41. The 4-point scheme

  42. The 4-point scheme

  43. The 4-point scheme

  44. The 4-point scheme

  45. The 4-point scheme

  46. The 4-point scheme

  47. The 4-point scheme

  48. The 4-point scheme

  49. The 4-point scheme A control point The limit curve The control polygon

  50. Subdivision curves • Non interpolatory subdivision schemes • Corner Cutting • Interpolatory subdivision schemes • The 4-point scheme

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