%T Planar Graphs and Sparse Graphs from Efficient Motion Planning in the Plane %A L. Paul Chew %R Technical Report PCS-TR90-146 %I Dartmouth College, Computer Science %C Hanover, NH %D 1990 %U http://www.cs.dartmouth.edu/reports/TR90-146.pdf %X Given a source, a destination, and a number of obstacles in the plane, the Motion Planning Program is to determine the best path to move an object (a robot) from the source to the destination without colliding with any of the obstacles. For us, motion is restricted to the plane, the robot is represented by a point, and the obstacles are represented by a set of polygons with a total of n vertices among all the polygonal obstacles.