## Optimized Antialiasing Patterns

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This page contains the best antialiasing patterns found using the method in our paper A Weighted Error Metric and Optimization Method for Antialiasing Patterns. Note that these patterns are not necessarily optimal with respect to the quality metric introduced in the paper, but they should be quite close.

The text files associated with each pattern contain the positions and weights of the sampling points. Each line in a file defines one sampling point using three floating-point values: x and y coordinates and weight. The x and y coordinates range from zero to the width of the reconstruction kernel, and the weights are scaled so that they sum to one. For patterns with multiple reconstruction kernels, a separate file is given for each kernel.

Update Sept. 2010: There was an error in the exporting code of the original optimizer which caused negative sample weights to be mistakenly clamped to zero. I have recalculated the weights with a new Monte Carlo optimizer and updated the pattern files. E2 values of the patterns have also been computed more accurately.

### Pattern Families P(1, 1, n)

 SPP Family E2 Sample positions and weights 2 P(1, 1, 2) 0.696 pattern-P11-2.txt 3 P(1, 1, 3) 0.480 pattern-P11-3.txt 4 P(1, 1, 4) 0.359 pattern-P11-4.txt 5 P(1, 1, 5) 0.301 pattern-P11-5.txt 6 P(1, 1, 6) 0.274 pattern-P11-6.txt

### Pattern Families P(4, 1+, n)

 SPP Family E2 Sample positions and weights 2 P(4, 1+, 2) 0.359 pattern-P41P-2.txt 3 P(4, 1+, 3) 0.301 pattern-P41P-3.txt 4 P(4, 1+, 4) 0.274 pattern-P41P-4.txt 5 P(4, 1+, 5) 0.259 pattern-P41P-5.txt 6 P(4, 1+, 6) 0.249 pattern-P41P-6.txt

### Pattern Families P(1, 4, n)

 SPP Family E2 Sample positions and weights 2 P(1, 4, 2) 0.465 pattern-P14-2.txt 3 P(1, 4, 3) 0.335 pattern-P14-3.txt 4 P(1, 4, 4) 0.241 pattern-P14-4.txt 5 P(1, 4, 5) 0.197 pattern-P14-5.txt 6 P(1, 4, 6) 0.168 pattern-P14-6.txt

### Pattern Families P(4, 4, n)

 SPP Family E2 Sample positions and weights 2 P(4, 4, 2) 0.328 pattern-P44-2-a.txt pattern-P44-2-b.txt pattern-P44-2-c.txt pattern-P44-2-d.txt 3 P(4, 4, 3) 0.228 pattern-P44-3-a.txt pattern-P44-3-b.txt pattern-P44-3-c.txt pattern-P44-3-d.txt 4 P(4, 4, 4) 0.177 pattern-P44-4-a.txt pattern-P44-4-b.txt pattern-P44-4-c.txt pattern-P44-4-d.txt 5 P(4, 4, 5) 0.150 pattern-P44-5-a.txt pattern-P44-5-b.txt pattern-P44-5-c.txt pattern-P44-5-d.txt 6 P(4, 4, 6) 0.129 pattern-P44-6-a.txt pattern-P44-6-b.txt pattern-P44-6-c.txt pattern-P44-6-d.txt