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Moving the mouse quickly results in a low number of input points. This in turn reduces the number of output points and since it seems the output values are interpolated with a straight line, bad looking mappings are easily produced. Better mappings would be produced if the line in the input plane is interpolated with multiple points and all those points are then mapped to the output plane.
The attached image shows what I'm talking about. The red line is produced by quickly dragging the mouse, and the green line is when moving slowly. I'm saying the mapper should automatically work in such a way so that the output of both of these is of the same "quality".
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