Category Archives: programming

Anti-aliasing for improving image quality

About a year ago I have briefly shown in my post “smoothing images” that averaging can be important to get good images without pixel noise. For my kaleidoscope app, see http://geometricolor.ch/sphericalKaleidoscopeApp.html, I have improved on these ideas and that’s what … Continue reading

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Straight lines in elliptic and hyperbolic space

A straight line is the shortest path between two points. Discussing curved space we would better call them geodesic lines to avoid confusion. I want to discuss these geodesic lines for surfaces of a sphere, elliptic space and hyperbolic space. … Continue reading

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How to program fast kaleidoscopes

This post repeats parts of earlier posts but I am trying to expand the ideas and explain them better. First, I am showing you how to make rosettes with rotational symmetry and mirror symmetry. This is easier than making kaleidoscopic images, … Continue reading

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Five fold rotational symmetry: Tuning the harmonics

In “better images from higher harmonics ?” I have replaced the basic sine and cosine functions by Fourier series approaching a symmetric triangular wave. This gave images with more details and somewhat smaller bulls-eyes. Here I want to show similar results … Continue reading

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Smoothing images

The image quality suffers if the mapping functions X(x,y) and Y(x,y) of the position (x,y) of a pixel of the output image to the position (X,Y) of the sampled input image pixel are strongly contracting or expanding. For contracting mappings … Continue reading

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Better images from higher harmonics ?

Maybe you have noticed that a lot of round shapes without details in the recent images of this blog. They resemble bulls-eyes. Here is an example: It’s a periodic image with square symmetry and no mirror symmetry. Its big grey … Continue reading

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Color symmetry upon rotation

Now I want to present color symmetry upon rotation for periodic and quasi-periodic kaleidoscopes. We have n different versions how to show the pixel colors of the input image in the new output image. For a color symmetry we have … Continue reading

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