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One of the perennial problems that we have come across in a variety of contexts, including [http://www.evilmadscientist.com/2012/cnc-halftones-with-ascii-art/ CNC artwork] and producing artwork for the [http://shop.evilmadscientist.com/productsmenu/tinykitlist/171-egg-bot Egg-Bot], is the difficulty of creating good-quality toolpaths– i.e., vector artwork representing halftones –when starting from image files.  One of the finest solutions that we’ve ever come across is [http://mrl.nyu.edu/~ajsecord/stipples.html Adrian Secord's algorithm], which uses an iterative relaxation process to optimize a weighted  [http://en.wikipedia.org/wiki/Voronoi_diagram Voronoi diagram], mathematically producing a set of points (stipples) that can closely approach the appearance of a traditional stipple drawing.   
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One of the perennial problems that we have come across in a variety of contexts, including [http://www.evilmadscientist.com/2012/cnc-halftones-with-ascii-art/ CNC artwork] and producing artwork for the [http://evilmadscience.com/productsmenu/tinykitlist/171-egg-bot Egg-Bot], is the difficulty of creating good-quality toolpaths– i.e., vector artwork representing halftones –when starting from image files.  One of the finest solutions that we’ve ever come across is [http://mrl.nyu.edu/~ajsecord/stipples.html Adrian Secord's algorithm], which uses an iterative relaxation process to optimize a weighted  [http://en.wikipedia.org/wiki/Voronoi_diagram Voronoi diagram], mathematically producing a set of points (stipples) that can closely approach the appearance of a traditional stipple drawing.   
  
 
Another important technique is [[TSP art]], where the image is represented by a single continuous path.  You can generate a path like this by connecting all of the dots in a stipple diagram.  Designing a route that visits each dot exactly once (and minimizing the distance travelled) is an example of the famous [http://en.wikipedia.org/wiki/Travelling_salesman_problem Travelling Salesman Problem] (or just “TSP”), and an optimal TSP path can give a surprisingly good grayscale representation of an image.    From the standpoint of toolpaths (for the Egg-bot and most other CNC machines), a TSP path is even nicer than stipples, because little or no time is spent raising and lowering the tool.
 
Another important technique is [[TSP art]], where the image is represented by a single continuous path.  You can generate a path like this by connecting all of the dots in a stipple diagram.  Designing a route that visits each dot exactly once (and minimizing the distance travelled) is an example of the famous [http://en.wikipedia.org/wiki/Travelling_salesman_problem Travelling Salesman Problem] (or just “TSP”), and an optimal TSP path can give a surprisingly good grayscale representation of an image.    From the standpoint of toolpaths (for the Egg-bot and most other CNC machines), a TSP path is even nicer than stipples, because little or no time is spent raising and lowering the tool.

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