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1. Introduction
   1. organization
   2. preliminaries and definitions
      1. The straight skeleton of a simple polygon
      2. The straight skeleton of a planar straight-line graph
      3. Roof and terrain model
      4. The motorcycle graph
   3. applications
      1. Mitered offset curves and NC- machining
      2. Building roofs and generating terrains
      3. Mathematical origami and the fold-and-cut problem
      4. Shape reconstruction and contour interpolation
      5. Polygon decomposition
      6. Area collapsing in geographic maps and centerlines of roads
   4. prior work
      1. Runtime bounds for the straight skeleton
      2. Algorithms for computing straight skeletons and motorcycle graphs
      3. Aichholzer et al., 1995
      4. Aichholzer and Aurenhammer, 1996
      5. Eppstein and Erickson, 1999
      6. Cheng and Vigneron, 2002
      7. Felkel and Obdrzalek, 1999
      8. Implementations
      9. Summary
   5. generalizations and related problems
      1. Linear axis
      2. Weighted straight skeleton
      3. Straight skeleton of polyhedra in R³
      4. City Voronoi diagrams
2. computing the straight skeleton
   1. geometric properties of the straight skeleton
   2. the triangulation-based approach
      1. The number of reappearances of diagonals
      2. Good triangulations and bad polygons
      3. Steiner triangulations without flip events
   3. a novel wavefront-type approach
      1. Motivation
      2. The extended wavefront and a novel straight-skeleton algorithm
      3. Runtime analysis and conclusion

1. a generalized motorcycle graph
   1. motivation and definition
   2. geometric properties of the generalized motorcycle graph
   3. the lower envelope based on the generalized motorcycle graph
2. The general wavefront-type algorithm
   1. Details of the general algorithm
   2. Runtime analysis
   3. Details of the implementation Bone
   4. Experimental results and runtime statistics
3. Summary
4. Motorcycle graphs
5. Prior and related work
   1. Applications of motorcycle graphs and related problems
   2. Prior work
   3. Geometric properties of the motorcycle graph
6. Stochastic considerations of the motorcycle graph
   1. Number of intersections of bounded rays
   2. Implications to the motorcycle graph
7. A simple and practice-minded implementation
   1. Details of the algorithm
   2. Runtime analysis
   3. Experimental results and runtime statistics
   4. Extending the computation beyond the unit square

1. Extracting the motorcycle graph from the straight skeleton