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 A rosette in a roman mosaic is an exponential transform of a periodic tiling
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Monthly Archives: January 2017
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
Accelerating functions with tables
To get fast function evaluations we use tables of function values f(x_i) at equidistant points x_i=i*Δ. Taking for any x the nearest point x_i with x_ix<Δ we can approximate f(x)≅f(x_i). This is the fastest and least accurate approximation. What is … Continue reading
Numerical performance
Curves do not need much calculations and are easy to generate. Rosettes, friezes and kaleidoscopes are different. They need many calculations for each pixel, often using several evaluations of trigonometric functions and exponential functions. Fortunately, our PCs are fast. A … Continue reading
Posted in programming
Tagged function evaluation, generative design, numerics, performance, programming, speed
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Curves
Frank Farris begins his book “Creating Symmetry” with symmetric curves of Nfold rotational symmetry. An example: He uses that we can interpret points (x,y) of the plane as complex numbers z=x+i*y. Thus a complex function f(t) of a real parameter t defines … Continue reading
Posted in Kaleidoscopes, programming
Tagged generative design, Geometry, ornament, Rotational symmetry
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