Aliasing & AntialiasingAssn 4 continuedAntialiasingSignal ProcessingSlide 5Slide 6Slide 7Slide 8Slide 9Slide 10The Sampling TheoremSlide 12Slide 13Slide 14Slide 15Fourier TheoryDavid Luebke 1 01/14/19Aliasing & AntialiasingDavid Luebke 2 01/14/19Assn 4 continued●Hopefully, assignment 4a was easy■Except for learning all the Cg infrastructure●Next up: Toon shading■Explain toon shading■Warm up: express your Phong shader as an NV30 fragment program■Then: write a toon shader as a NV30 fragment program■Extra credit: write a toon shader that runs on GF2X (GeForce 3/4)●Who wants a ray tracing assignment?David Luebke 3 01/14/19Antialiasing●Aliasing: signal processing term with very specific meaning●Aliasing: computer graphics term for any unwanted visual artifact●Antialiasing: computer graphics term for avoiding unwanted artifacts●We’ll tackle these in orderDavid Luebke 4 01/14/19Signal Processing●Raster display: regular sampling of a continuous function (Really?)●Think about sampling a 1-D function:David Luebke 5 01/14/19Signal Processing●Sampling a 1-D function:David Luebke 6 01/14/19Signal Processing●Sampling a 1-D function:David Luebke 7 01/14/19Signal Processing●Sampling a 1-D function:■What do you notice?David Luebke 8 01/14/19Signal Processing●Sampling a 1-D function: what do you notice?■Jagged, not smoothDavid Luebke 9 01/14/19Signal Processing●Sampling a 1-D function: what do you notice?■Jagged, not smooth■Loses information!David Luebke 10 01/14/19Signal Processing●Sampling a 1-D function: what do you notice?■Jagged, not smooth■Loses information!●What can we do about these?■Use higher-order reconstruction■Use more samples■How many more samples?David Luebke 11 01/14/19The Sampling Theorem●Obviously, the more samples we take the better those samples approximate the original function●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 functionDavid Luebke 12 01/14/19The Sampling Theorem●In other words, to adequately capture a function with maximum frequency F, we need to sample it at frequency N = 2F.●N is called the Nyquist limit.David Luebke 13 01/14/19The Sampling Theorem●An example: sinusoidsDavid Luebke 14 01/14/19The Sampling Theorem●An example: sinusoidsDavid Luebke 15 01/14/19The Sampling Theorem●Show Figure 4.2 in Watt & Watt (p. 113)David Luebke 16 01/14/19Fourier Theory●All our examples have been sinusoids●Does this help with real world signals? Why? ●Fourier theory lets us decompose any signal into the sum of (a possibly infinite number of) sine waves●Go to
View Full Document
Unlocking...