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with Polynomial Filters Josiah Manson and Scott Schaefer Texas - PowerPoint PPT Presentation

Jan 22, 2024 •268 likes •976 views

Analytic Rasterization of Curves with Polynomial Filters Josiah Manson and Scott Schaefer Texas A&M University Motivation Motivation Motivation Motivation Motivation Motivation Motivation Constant colors Color gradients Motivation

  1. Analytic Rasterization of Curves with Polynomial Filters Josiah Manson and Scott Schaefer Texas A&M University

  2. Motivation

  3. Motivation

  4. Motivation

  5. Motivation

  6. Motivation

  7. Motivation

  8. Motivation Constant colors Color gradients

  9. Motivation

  10. Input Curve Boundary Piecewise Filter

  11. Input [Duff, 1989] [Manson and Schaefer, 2011] “Polygon scan conversion by “Wavelet Rasterization ” exact convolution” Curve Boundary Piecewise Filter

  12. Signal Sampling

  13. Signal Sampling

  14. Signal Sampling

  15. Signal Sampling

  16. Signal Sampling

  17. Signal Sampling

  18. Image Sampling Image

  19. Image Sampling Pixel positions

  20. Image Sampling Evaluate at point

  21. Image Sampling Center filter at point

  22. Image Sampling Center filter at point

  23. Image Sampling Center filter at point

  24. Image Sampling Multiply

  25. Image Sampling Integrate

  26. Image Sampling Repeat for all pixels

  27. Derivation

  28. Derivation

  29. Derivation

  30. Derivation

  31. Derivation

  32. Derivation

  33. Derivation

  34. Derivation

  35. Filter Integrals

  36. Filter Integrals C C h h a a Zero Zero Zero Constant n n g g e e s s

  37. Filter Pieces

  38. Scanline Rasterization

  39. Scanline Rasterization

  40. Scanline Rasterization

  41. Scanline Rasterization Changing

  42. Scanline Rasterization Changing Constant

  43. Scanline Rasterization

  44. Scanline Rasterization

  45. Scanline Rasterization

  46. Scanline Rasterization

  47. Scanline Rasterization +

  48. Scanline Rasterization

  49. Scanline Rasterization

  50. Scanline Rasterization +

  51. Scanline Rasterization

  52. Scanline Rasterization

  53. Scanline Rasterization +

  54. Scanline Rasterization

  55. Scanline Rasterization

  56. Scanline Rasterization +

  57. Scanline Rasterization

  58. Scanline Rasterization

  59. Filter Pieces = +

  60. Filter Pieces = +

  61. Rational Curves

  62. Cubic Curves Input image Mitchell-Netravali

  63. Anti-aliasing Point sampling 16x MSAA tent Analytic tent ATI Radeon HD 5700

  64. Anti-aliasing Box

  65. Anti-aliasing Tent

  66. Anti-aliasing Lanczos 3

  67. Anti-aliasing Radial 3

  68. Timings (ms)

  69. Parallelism

  70. Conclusions • Analytic prefiltering • Fast algorithm – Smooth curves – Independent curves and filter pieces – High-quality filters – High parallelism – Color gradients

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