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

2. Motivation

8. Constant colorsColor gradients

9. Motivation

10. Input Curve BoundaryPiecewise Filter

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

12. 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

35. Filter Integrals

36. ConstantZero Filter Integrals Zero ChangesChanges ChangesChanges

37. Filter Pieces

38. Scanline Rasterization

41. Changing

42. Scanline Rasterization Constant Changing

43. Scanline Rasterization

47. +

50. +

53. +

56. +

59. Filter Pieces =+

60. +=

61. Rational Curves

62. Cubic Curves Input imageMitchell-Netravali

63. Anti-aliasing Point sampling16x MSAA tentAnalytic 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 – Smooth curves – High-quality filters – Color gradients Fast algorithm – Independent curves and filter pieces – High parallelism