Automatic graph drawers need to computer paths among vertices of a simple polygon which besides remainging in the interior need to exhibit crtain aesthetic properties. SOme of these require the incorporation of some information about the polygonal shape withour being too far from the actual shortest path. We present an algorithm to ocmpute a locally convex region that "contains" the shortest Euclidean path among two vertices of a simple polygon. The region has a boundary shape that "follows" the shortest path shape. A cubic Bezier spline in the region interior provides a "short and smooth" collision free curve between the two given vertices. THe obtained results appear ot be aesthetically pleasant and the methods used may be of independent interest. They are elelmentary and impelmentable. Figure 7 is a sample output produced by our current implementation.
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