这是本文档旧的修订版！

1. ABSTRACT
2. 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
3. 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
   4. 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
   5. 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
   6. Summary
4. Motorcycle graphs
   1. Prior and related work
      1. Applications of motorcycle graphs and related problems
      2. Prior work
      3. Geometric properties of the motorcycle graph
   2. Stochastic considerations of the motorcycle graph
      1. Number of intersections of bounded rays
      2. Implications to the motorcycle graph
   3. 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
   4. Extracting the motorcycle graph from the straight skeleton
      1. Approximating the motorcycle graph by the straight skeleton
      2. Computing the motorcycle graph
      3. Constructing the straight skeleton is P-complete
   5. Concluding remarks
   6. Notation
   7. Examples
   8. Bibliography
   9. Index

Run completed on your latest polygon log and diagnostics saved. Here’s the short summary and what I recommend next.

What I ran • Executed the harness with your latest available log (selected: C:\Users\11402\Desktop\SkeletonLogs\skeleton_debug_20250925_211825.log). • Generated full diagnostics (boundary/skeleton CSVs, wavefront times, meta).

Key results • Completed: True • Boundary vertices parsed: 18 (note: it’s 9 unique points repeated twice) • Skeleton segments: 12 • Triangles: 48 • Wavefront samples: 7 • Time: 0.343s • ValleySummary: initReflex=8, written=8, missing=2 ◦ Warnings: ValleyMissing for reflex at (319,171) with two different IDs (duplicate entries)

Why the two “missing” valleys appear • Your boundary in the log contains two identical loops (the same 9 vertices repeated). That creates duplicate reflex vertices at the same location with different IDs. The algorithm writes one valley for the “real” instance and then reports the duplicate as “missing.” This is a parsing artifact, not an algorithmic failure.

Diagnostics location (most relevant files) • D:\在家加班\骨架库(最新20250923)\骨架库(最新20250917)(1)\HDSkeleton\Harness\bin\Debug\diag_runs_harness\FROM_LOG\ ◦ from_log_boundary.csv (parsed boundary that was fed into the run) ◦ from_log_skeleton.csv (aggregated skeleton segments) ◦ run_20250925_212154_592\ ▪ boundary.csv, skeleton.csv, wavefront_times.txt, meta.txt

Recommendations • Let me add a normalization pass to the log loader so it: ◦ Removes consecutive duplicate points ◦ If the list is two identical halves, keeps only the first half ◦ Drops a final vertex if it equals the first (implicit closure) • Then rerun. Expected effect: the duplicate (319,171) entries collapse to one, clearing the two ValleyMissing warnings. • Optional follow-ups: ◦ Add a –csv <file> mode to feed raw x,y coordinates directly (bypasses log parsing). ◦ If you want to investigate the “calcMovingSteinerSpeed: mv or pv is null” warnings, I can add targeted debug guards/logs, but they didn’t affect completion here.

How to rerun locally • Latest log: D:\在家加班\骨架库(最新20250923)\骨架库(最新20250917)(1)\HDSkeleton\Harness\bin\Debug\HDSkeletonHarness.exe –log latest • Specific log file: HDSkeletonHarness.exe –log “C:\path\to\your\skeleton_debug_YYYYMMDD_HHMMSS.log”

Would you like me to implement the de-duplication in the log loader now and rerun to verify the ValleyMissing warnings disappear?