Analytic Rasterization of Curves with Polynomial Filters Josiah

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

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

Motivation

Motivation

Motivation

Motivation

Motivation

Motivation

Motivation

Motivation

Motivation

Motivation

Motivation

Motivation

Motivation Constant colors Color gradients

Motivation Constant colors Color gradients

Motivation

Motivation

Input Curve Boundary Piecewise Filter

Input Curve Boundary Piecewise Filter

Input [Manson and Schaefer, 2011] “Wavelet Rasterization” Curve Boundary [Duff, 1989] “Polygon scan conversion

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

Signal Sampling

Signal Sampling

Signal Sampling

Signal Sampling

Signal Sampling

Signal Sampling

Signal Sampling

Signal Sampling

Signal Sampling

Signal Sampling

Signal Sampling

Signal Sampling

Image Sampling Image

Image Sampling Image

Image Sampling Pixel positions

Image Sampling Pixel positions

Image Sampling Evaluate at point

Image Sampling Evaluate at point

Image Sampling Center filter at point

Image Sampling Center filter at point

Image Sampling Center filter at point

Image Sampling Center filter at point

Image Sampling Center filter at point

Image Sampling Center filter at point

Image Sampling Multiply

Image Sampling Multiply

Image Sampling Integrate

Image Sampling Integrate

Image Sampling Repeat for all pixels

Image Sampling Repeat for all pixels

Derivation

Derivation

Derivation

Derivation

Derivation

Derivation

Derivation

Derivation

Derivation

Derivation

Derivation

Derivation

Derivation

Derivation

Derivation

Derivation

Filter Integrals

Filter Integrals

Filter Integrals Zero C h a n g e s Zero C h a

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

Filter Pieces

Filter Pieces

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization Changing

Scanline Rasterization Changing

Scanline Rasterization Changing Constant

Scanline Rasterization Changing Constant

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization +

Scanline Rasterization +

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization +

Scanline Rasterization +

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization +

Scanline Rasterization +

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization +

Scanline Rasterization +

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Scanline Rasterization

Filter Pieces = +

Filter Pieces = +

Filter Pieces = +

Filter Pieces = +

Rational Curves

Rational Curves

Cubic Curves Input image Mitchell-Netravali

Cubic Curves Input image Mitchell-Netravali

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

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

Anti-aliasing Box

Anti-aliasing Box

Anti-aliasing Tent

Anti-aliasing Tent

Anti-aliasing Lanczos 3

Anti-aliasing Lanczos 3

Anti-aliasing Radial 3

Anti-aliasing Radial 3

Timings (ms)

Timings (ms)

Parallelism

Parallelism

Conclusions • Analytic prefiltering – Smooth curves – High-quality filters – Color gradients •

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

Analytic Rasterization of Curves with Polynomial Filters JosiahAnalytic Rasterization of Curves with Polynomial Filters Josiah
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