Optimized Antialiasing Patterns

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

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