
Recent Posts
Recent Comments
Archives
 September 2019
 August 2019
 July 2019
 April 2019
 March 2019
 November 2018
 October 2018
 September 2018
 August 2018
 March 2018
 February 2018
 January 2018
 December 2017
 November 2017
 September 2017
 August 2017
 July 2017
 June 2017
 May 2017
 February 2017
 January 2017
 November 2016
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 June 2012
 May 2012
 April 2012
Categories
Meta
Category Archives: programming
Inversion in a single circle
You might think that discussing the inversion in a circle is somewhat underwhelming. But, as I am using multiple inversion in many circles to create fractal images, I found that there are some important ideas you will not find so … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming, Tilings
Tagged inversion, inversion in a circle, mirror symmetry
Leave a comment
Antialiasing 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
Posted in Kaleidoscopes, programming
Tagged antialiasing, image processing, smoothing images
Leave a comment
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
Posted in Kaleidoscopes, programming
Tagged elliptic geometry, geodesic line, hyperbolic geometry, Poincaré disc, straight line
1 Comment
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
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 bullseyes. Here I want to show similar results … Continue reading
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
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 bullseyes. Here is an example: It’s a periodic image with square symmetry and no mirror symmetry. Its big grey … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming
Tagged anamorphosis, kaleidoscope, programming
Leave a comment
Color symmetry upon rotation
Now I want to present color symmetry upon rotation for periodic and quasiperiodic 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
Rotational symmetry from space with an odd number of dimensions
We now look at the easier case for the post “Quasiperiodic and periodic kaleidoscope from higher dimensional space“, where the embedding space has an odd number of dimensions, p=2q+1. The unit vectors lie at equal angles and form a star … Continue reading
Rotations, mirrorsymmetry and the scalar product
In the last post we have seen that scalar products between a pixel’s position in the output image and certain vectors e define periodic and quasiperiodic designs. We want symmetric images and thus we have to see how the scalar product changes … Continue reading
Posted in Anamorphosis, Kaleidoscopes, programming, Tilings
Tagged Math, mirror symmetry, Rotational symmetry
Leave a comment