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Category Archives: programming
Color transformation
I am now discussing color transformations for creating kaleidoscopic images with twocolor symmetry. Each pixel has three color components: red, green and blue. Their values are between 0 and 255. Thus we can think that a pixel color is a point with … Continue reading
Posted in Kaleidoscopes, programming
Tagged Colors, false colors, negative image, transformation, twocolor symmetry
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Kaleidoscopes with twofold color symmetry.
A checkerboard is a square lattice with twofold color symmetry. The alternating black and white squares make it more interesting than a simple square lattice. Thus I want to have too some twofold color symmetry for our kaleidoscopes. Farris has done this … Continue reading
Posted in Kaleidoscopes, programming
Tagged color symmetry, kaleidoscope, programming, twocolor symmetry
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How to generate rosettes
A rosette is an image with rotational symmetry. For pfold symmetry we can use the methods of the last post “Anamorphosis and symmetries” with a simple power as a mapping function between output and input images: Here z=x+iy relates to … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming
Tagged anamorphosis, image processing, programming, Rotational symmetry
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Anamorphosis and symmetries
As proposed by Farris in “Creating Symmetry” we can use anamorphosis to make images of any symmetry from some other input image. Here I briefly discuss how I am doing it and what you will find in my next program. Each … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming
Tagged kaleidoscope, programming, symmetry
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Approximating the logarithm function
I still want fast approximations of the logarithm and the inverse tangent function for my work. I don’t know if they are really needed, but they are nice pillow problems to keep you from ruminating those stupid things happening now. If x is … Continue reading
Approximating the exponential function
The garden has frozen over and I have caught a cold. It is hard to do difficult work. Thus I continue to find fast approximations of transcendental functions. This is more fun than solving crossword puzzles. The exponential function is not … Continue reading
Posted in programming
Tagged exponential function, numerics, performance, programming, speed
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Fast approximations of the sine and cosine functions
I made up the webpage http://bookofgames.ch/fastSin.html to check out the different approximations for sine and cosine functions. Load it and make your own tests. You can use the “save”function of your browser to download the code, change and use it for … Continue reading