analytic rasterization of curves with polynomial filters
DESCRIPTION
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. Input. Curve Boundary. Piecewise Filter. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/1.jpg)
Analytic Rasterization of Curves with Polynomial Filters
Josiah Manson and Scott SchaeferTexas A&M University
![Page 2: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/2.jpg)
Motivation
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Motivation
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Motivation
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Motivation
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Motivation
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Motivation
![Page 8: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/8.jpg)
Motivation
Constant colors Color gradients
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Motivation
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Input
Curve Boundary Piecewise Filter
![Page 11: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/11.jpg)
Input
Curve Boundary Piecewise Filter
[Manson and Schaefer, 2011]“Wavelet Rasterization”
[Duff, 1989]“Polygon scan conversion by
exact convolution”
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Signal Sampling
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Signal Sampling
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Signal Sampling
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Signal Sampling
![Page 16: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/16.jpg)
Signal Sampling
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Signal Sampling
![Page 18: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/18.jpg)
Image Sampling
Image
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Image Sampling
Pixel positions
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Image Sampling
Evaluate at point
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Image Sampling
Center filter at point
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Image Sampling
Center filter at point
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Image Sampling
Center filter at point
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Image Sampling
Multiply
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Image Sampling
Integrate
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Image Sampling
Repeat for all pixels
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Derivation
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Derivation
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Derivation
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Derivation
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Derivation
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Derivation
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Derivation
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Derivation
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Filter Integrals
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ConstantZeroZero
Filter Integrals
Zero
Changes
Changes
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Filter Pieces
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Scanline Rasterization
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Scanline Rasterization
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Scanline Rasterization
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Scanline Rasterization
Changing
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Scanline Rasterization
ConstantChanging
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Scanline Rasterization
![Page 44: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/44.jpg)
Scanline Rasterization
![Page 45: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/45.jpg)
Scanline Rasterization
![Page 46: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/46.jpg)
Scanline Rasterization
![Page 47: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/47.jpg)
Scanline Rasterization
+
![Page 48: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/48.jpg)
Scanline Rasterization
![Page 49: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/49.jpg)
Scanline Rasterization
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Scanline Rasterization
+
![Page 51: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/51.jpg)
Scanline Rasterization
![Page 52: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/52.jpg)
Scanline Rasterization
![Page 53: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/53.jpg)
Scanline Rasterization
+
![Page 54: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/54.jpg)
Scanline Rasterization
![Page 55: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/55.jpg)
Scanline Rasterization
![Page 56: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/56.jpg)
Scanline Rasterization
+
![Page 57: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/57.jpg)
Scanline Rasterization
![Page 58: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/58.jpg)
Scanline Rasterization
![Page 59: Analytic Rasterization of Curves with Polynomial Filters](https://reader035.vdocuments.us/reader035/viewer/2022062309/5681375f550346895d9eee4a/html5/thumbnails/59.jpg)
Filter Pieces
= +
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Filter Pieces
+=
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Rational Curves
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Cubic Curves
Input image Mitchell-Netravali
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Anti-aliasing
Point sampling 16x MSAA tent Analytic tent
ATI Radeon HD 5700
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Anti-aliasing
Box
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Anti-aliasing
Tent
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Anti-aliasing
Lanczos 3
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Anti-aliasing
Radial 3
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Timings (ms)
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Parallelism
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Conclusions• Analytic prefiltering– Smooth curves– High-quality filters– Color gradients
• Fast algorithm– Independent curves
and filter pieces– High parallelism