Savant & StandAlone
Savant Savant
I’ve been wondering how to calculate the most efficient route across a rugged terrain—like the quickest path a lone traveler could take. What’s your take on that kind of problem?
StandAlone StandAlone
StandAlone thinks the simplest way is to treat the terrain as a weighted graph, where each move has a cost equal to the effort needed to cross that section. Use Dijkstra if you want a guaranteed shortest path, or A* if you can estimate the distance to the goal. Just plug the terrain data into a grid, assign higher costs to rougher spots, and let the algorithm find the route that minimizes total effort. It’s all about letting the math do the work while you stay ready to adjust if the path isn’t what the numbers say.
Savant Savant
That’s a solid baseline, but if the terrain changes as you walk you’ll need a dynamic version—maybe a continuous‑time model or a time‑dependent graph. Also, the cost function matters: if the effort grows non‑linearly with slope, a simple linear weight won’t capture fatigue. If you can approximate that, you’ll get a more realistic route.
StandAlone StandAlone
StandAlone says: if the ground shifts while you’re moving, you need a time‑dependent graph or a continuous‑time model. Then tweak the cost function so steep grades cost more than linearly—maybe an exponential or quadratic factor. Run an A* that re‑evaluates the costs on the fly, or use a dynamic programming approach that updates the best path as you go. That gives you a route that really reflects the fatigue you’ll actually feel.
Savant Savant
Sounds clever—just be careful that the cost function stays convex; otherwise the A* heuristic might become unreliable. Also, if the terrain shifts too quickly you might need a receding horizon approach, recomputing only the next few steps to keep the computation tractable.
StandAlone StandAlone
You’re right, keeping the cost convex keeps the heuristic sane. A receding horizon works best when the terrain changes fast—plan a few steps ahead, execute, then re‑plan. Just make sure each update runs fast enough to keep you moving, not thinking.
Savant Savant
Nice, that’s basically the model I was thinking of—keep it lean, keep it convex, and you’ll be moving before the path even feels like a path.