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

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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

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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

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Fast approximations of the sine and cosine functions

I made up the web-page 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

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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_i-x|<Δ we can approximate f(x)≅f(x_i). This is the fastest and least accurate approximation. What is … Continue reading

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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

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Curves

Frank Farris begins his book “Creating Symmetry” with symmetric curves of N-fold 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

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