lecture06

lecture06 - CS 551/651 Advanced Computer Graphics...

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David Luebke 1 CS 551/651: Advanced Computer Graphics Antialiasing Continued: Prefiltering and Supersampling

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David Luebke 2 Recap: The Sampling Theorem The sampling theorem: A continuous bandlimited function can be completely represented by a set of equally spaced samples, if the samples occur at more than twice the frequency of the highest frequency component of the function To capture a function with maximum frequency F , sample it at frequency N = 2 F . N is called the Nyquist limit .
David Luebke 3 Recap: Fourier Theory Can decompose any signal I(x) into a spectrum of sine waves F(u) F(u) is complex; we represent it with: |F(u)| = [Real(u) 2 + Imag(u) 2 ] 1/2 Ø(u) = tan -1 [Real(u)/Imag(u)] These are called the amplitude and phase spectra Back to transparencies…

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David Luebke 4 Recap: Aliasing Sampling a function = multiplying I(x) by sampling fn S x = convolving F(u) by sampling fn S 1/x = copying F(u) at regular intervals If the copies of F(u) overlap, high frequencies “fold over”, appearing as lower frequencies This is known as aliasing
David Luebke 5 Prefiltering Eliminate high frequencies before sampling Convert I(x) to F(u) Apply a low-pass filter (e.g., multiply F(u) by a box function) Then sample. Result: no aliasing! So what’s the problem?

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David Luebke 6 Prefiltering Eliminate high frequencies before sampling Convert I(x) to F(u) Apply a low-pass filter (e.g., multiply F(u) by a box function) Then sample. Result: no aliasing! Problem: most rendering algorithms generate sampled function directly e.g., Z-buffer, ray tracing
David Luebke 7 Supersampling The simplest way to reduce aliasing artifacts is supersampling Increase the resolution of the samples Average the results down Sometimes called postfiltering Create virtual image at higher resolution than the final image Apply a low-pass filter Resample filtered image

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David Luebke 8 Supersampling: Limitations Q: What practical consideration hampers supersampling? A:
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lecture06 - CS 551/651 Advanced Computer Graphics...

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