Wednesday, February 24, 2010

Lossy Vector Compression

An evenly sampled vector outline is essentially a 2D signal. This isn't the 2D of a raster image, where you have a 2D space with a 3D (RGB) value at each point. It's a 1D space with a 2D (XY) value at each point. You can do a frequency domain decomposition on this signal, which is the foundation for most image compression algorithms. What would it look like to do the usual compression tricks? Quantization of the amplitudes, high frequency removal, etc.?

The interesting thing about this transformation is that line drawings as frequency-decomposable entities already have a tradition established in Harmonographs. To recreate any drawing with a harmonograph would simply require N pendulums on each axis, each with a length proportional to the square of the frequency represented (given the mathematical definition of a pendulum). You would give all the pendulums equal mass, place them at an angle corresponding to the amplitude, and then release them at the right time. This could recreate any line drawing.

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