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Antialiased_lanczos.png (128 × 128 pixels, file size: 9 KB, MIME type: image/png)

Summary

Description
English: Antialiased chessboard using the Lanczos algorithm, made by myself based on the source in File:Antialiased.png's description. This one should be relatively close to an ideal filter, primarily because I used a lot of taps (several million) for the more problematic pixels.
Date 23 December 2008 (original upload date)
Source Transferred from en.wikipedia to Commons.
Author Sesse at English Wikipedia

Licensing

Public domain This work has been released into the public domain by its author, Sesse at English Wikipedia. This applies worldwide.
In some countries this may not be legally possible; if so:
Sesse grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Source

Here's the source I used, written by myself. The choice of 16384x16384 might have been overkill; I cannot spot any significant differences between this and using 1024x1024 taps all over the image. The generation took about an hour on one core of an Intel Q9450.

Compile and link with

gcc -O3 -o antialias antialias.c -lm -std=gnu99
 #include <stdio.h>
 #include <stdlib.h>
 #include <math.h>

 /*
  * Do a finer sampling the higher up we get in the picture,
  * since there's much more detail there.
  */
 #define SAMPLES_FROM_Y(y) ((16384 * 512) / (y*y + 512))
 #define MAX_SAMPLES SAMPLES_FROM_Y(0)

 float weights[MAX_SAMPLES][MAX_SAMPLES];

 static inline int color(double x, double y)
 {
         double t, z;
         int i, j, k;

         x = x * (1.0 / 128.0) - 0.5;
         y = y * (1.0 / 2048.0);

         t = 1.0 / (y + 0.001);
         z = t * x;
         i = floor(t);
         j = floor(z);
         k = i + j;
         return ((k % 2) != 0);
 }

 static double sinc(double x)
 {
         static const double cutoff = 1.220703668e-4;  /* sqrt(sqrt(eps)) */

         if (abs(x) < cutoff) {
                 /* For small |x|, use Taylor series instead */
                 const double x2 = x * x;
                 const double x4 = x2 * x2;

                 return 1.0 - x2 / 6.0 + x4 / 120.0;
         } else {
                 return sin(x) / x;
         }
 }

 static double lanczos_tap(double x)
 {
         if (x < -3.0 || x > 3.0)
                 return 0.0;
         if (x < 0.0)
                 return sinc(-x*M_PI) * sinc(-x*M_PI / 3.0);
         else
                 return sinc(x*M_PI) * sinc(x*M_PI / 3.0);
 }

 static void precalculate_weights(unsigned num_samples)
 {
         double total = 0.0;
         for (int yi = 0; yi < num_samples; ++yi) {
                 double sy = 6.0 * ((double)yi / num_samples - 0.5);
                 double wy = lanczos_tap(sy);
                 for (int xi = 0; xi < num_samples; ++xi) {
                         double sx = 6.0 * ((double)xi / num_samples - 0.5);
                         weights[yi][xi] = wy * lanczos_tap(sx);
                         total += weights[yi][xi];
                 }
         }

         double inv_total = 1.0 / total;
         for (int yi = 0; yi < num_samples; ++yi) {
                 for (int xi = 0; xi < num_samples; ++xi) {
                         weights[yi][xi] *= inv_total;
                 }
         }
 }

 static double antialiased_color(double x, double y, unsigned num_samples)
 {
         double acc = 0.0;
         double delta = 6.0 / num_samples;
         int xi, yi;
         double sx, sy;

         for (yi = 0, sy = y - 3.0; yi < num_samples; ++yi, sy += delta) {
                 for (xi = 0, sx = x - 3.0; xi < num_samples; ++xi, sx += delta) {
                         if (color(sx, sy)) {
                                 acc += weights[yi][xi];
                         }
                 }
         }
         return acc;
 }

Original upload log

The original description page was here. All following user names refer to en.wikipedia.
Date/Time Dimensions User Comment
2011-03-19 16:41 128×128× (11220 bytes) Dicklyon compromise, since for many displays it goes too far to do full sRGB gamma hack
2010-09-23 03:06 128×128× (14944 bytes) Ancient Anomaly Aactually it was still too dark. This one should be correct.
2010-09-23 03:03 128×128× (11220 bytes) Ancient Anomaly Reverted to version as of 09:07, 23 December 2009 #808080 is NOT halfway between black and white, sRGB is not linear
2010-07-20 12:48 128×128× (10284 bytes) Technion Reverted to version as of 14:27, 23 December 2008: Revert to original image by Sesse. In original image, gray at top of image is #808080, halfway between black and white as would be expected; in Dicklyon’s modified version, gray at top is much lighter t
2009-12-23 09:07 128×128× (11220 bytes) Dicklyon Adjust tone scale, since no gamma correction was applied when the image was created.\
2008-12-23 14:27 128×128× (10284 bytes) Sesse Antialiased chessboard using the Lanczos algorithm, made by myself based on the source in [[File:Antialiased.png]]'s description. This one should be relatively close to an ideal filter, primarily because I used a lot of taps (several million) for the more

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Date/TimeThumbnailDimensionsUserComment
current09:51, 17 May 2023Thumbnail for version as of 09:51, 17 May 2023128 × 128 (9 KB)PhreneticcReduced file weight with FileOptimizer in lossless compression mode.
10:23, 19 March 2011Thumbnail for version as of 10:23, 19 March 2011128 × 128 (15 KB)File Upload Bot (Magnus Manske) {{BotMoveToCommons|en.wikipedia|year={{subst:CURRENTYEAR}}|month={{subst:CURRENTMONTHNAME}}|day={{subst:CURRENTDAY}}}} {{Information |Description={{en|Antialiased chessboard using the Lanczos algorithm, made by myself based on the source in File:Antialia

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