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CS 445 / CS 645

CS 445 / CS 645. Antialiasing. Today. Final Exam Thursday, December 13 th at 7:00 Project 4-1 Out Movies. Samples. Sampling Errors. Some objects missed entirely, others poorly sampled. Supersampling. Take more than one sample for each pixel and combine them

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CS 445 / CS 645

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  1. CS 445 / CS 645 Antialiasing

  2. Today • Final Exam • Thursday, December 13th at 7:00 • Project 4-1 Out • Movies

  3. Samples

  4. Sampling Errors • Some objects missed entirely, others poorly sampled

  5. Supersampling • Take more than one sample for each pixel and combine them • Do you actually render more pixels? • Can you combine the few pixels you have? • How many samples is enough? • How do we know no features are lost?

  6. Unweighted Area Sampling • Average supersampled points • All points are weighted equally

  7. Weighted Area Sampling • Points in pixel are weighted differently • Flickering occurs as object movesacross display • Overlapping regions eliminates flicker

  8. How is this done today?Full Screen Antialiasing • Nvidia GeForce2 • OpenGL: scale image 400% and supersample • Direct3D: scale image 400% - 1600% • 3Dfx Multisampling • 2- or 4-frame shift and average • Nvidia GeForce3 • Multisampling but with fancy overlaps • ATI SmoothVision • Programmer selects samping pattern

  9. GeForce3 • Multisampling • After each pixel is rendered, write pixel value to two different places in frame buffer

  10. GeForce3 - Multisampling • After rendering two copies of entire frame • Shift pixels of Sample #2 left and up by ½ pixel • Imagine laying Sample #2 (red) over Sample #1 (black)

  11. GeForce3 - Multisampling • Resolve the two samples into one image by computing average between each pixel from Sample 1 (black) and the four pixels from Sample 2 (red) that are 1/ sqrt(2) pixels away

  12. GeForce3 - Multisampling • No AA Multisampling

  13. GeForce3 - Multisampling • 4x Supersample Multisampling

  14. Signal Theory • Convert spatial signal to frequency domain

  15. Signal Theory • Represent spatial signal as sum of sine waves (varying amplitude and phase shift)

  16. Fourier Analysis • Convert spatial domain to frequency domain • U is a complex number representing amplitude and phase shift • i = sqrt (-1)

  17. Fourier Transform • Examples of spatial and frequency domains

  18. Nyquist Rate • The lower bound on the sampling rate equals twice the highest frequency component in the image’s spectrum • This lower bound is the Nyquist Rate

  19. Flaws with Nyquist Rate • Samples may not align with peaks

  20. Flaws with Nyquist Rate • When sampling below Nyquist Rate, resulting signal looks like a lower-frequency one

  21. Sampling in the Frequency Domain • Remember, sampling was defined as multiplying a grid of delta functions by the continuous image • This is called a convolution in frequency domain The sampling grid The function beingsampled

  22. Convolution • This amounts to accumulating copies of the function’s spectrum sampled at the delta functions of the sampling grid

  23. Filtering • To lower Nyquist rate, remove high frequencies from image: low-pass filter • Only low frequencies remain • Sinc function is common filter: • sinc(x) = sin (px)/px Frequency Domain Spatial Domain

  24. Sinc Filter • Slide filter along spatial domain and compute new pixel value that results from convolution

  25. Bilinear Filter • Sometimes called a tent filter • Easy to compute • just linearly interpolate between samples • Finite extent and no negative values • Still has artifacts

  26. Sampling Pipeline

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