An Algorithm to Find the Shortest Path through Obstacles of Arbitrary Shapes and Positions in 2D
Bibliographic record
Abstract
An algorithm is described to find the shortest route through a field of obstacles of arbitrary shapes and positions. It has the appreciable advantage of not having to find mathematical formulas to represent the obstacles: it works directly with a digital image of the terrain and is implemented solely with standard graphical functions. Key to this algorithm is the definition of digraphs, the edges of which are built with obstacle bitangents and border enveloping convex arcs that incorporate the fundamental features of shortest paths. These graphs have a remarkably lower cardinality than those that have been proposed before to solve this problem; their edges are a concatenation of sequences of what individual edges and nodes are in formerly defined graphs. Furthermore, a thorough analysis of the topology of the terrain yields a procedure to eliminate the edges that have no possibility of being part of the shortest path. The A* graph optimization algorithm is adapted to deal with this type of graph. A new quite general theorem is proved, which applies to all graphs in which the triangle inequality holds, which allows the discarding of one of the normal steps of the A* algorithm. The effectiveness of the algorithm is demonstrated by calculating the shortest path for real complex terrains of areas between 25 km2 and 900 km2. In all cases, the required calculation time is less than 0.6 s on a Core i7-10750H CPU @ 2.60 GHz laptop computer.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".