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Efficient Curves Rasterization Using Polynomial Filters

This study explores analytic rasterization of curves with polynomial filters for enhanced image sampling and pixel evaluation. The methodology involves filter integrals, piecewise boundaries, and scanline rasterization techniques. Researchers Josiah Manson and Scott Schaefer from Texas A&M University present a detailed derivation and implementation of this novel approach. The innovation offers constant color gradients and seamless image rendering.

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Efficient Curves Rasterization Using Polynomial Filters

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  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] “Polygon scan conversion by exact convolution” [Manson and Schaefer, 2011] “Wavelet Rasterization” 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 Zero C h a n g e s Zero Zero C h a n g e s Constant

  37. Filter Pieces

  38. ScanlineRasterization

  39. ScanlineRasterization

  40. ScanlineRasterization

  41. ScanlineRasterization Changing

  42. ScanlineRasterization Changing Constant

  43. ScanlineRasterization

  44. ScanlineRasterization

  45. ScanlineRasterization

  46. ScanlineRasterization

  47. ScanlineRasterization +

  48. ScanlineRasterization

  49. ScanlineRasterization

  50. ScanlineRasterization +

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