Problem
Given two polygons in 3D space (one containing a starting point, the other a goal point), what is the most optimal path between them where:
- We can only travel along the surface of the polygons or "jump"
- The "jump" operation is defined at the regular 4.9t^2 + vt + h where the starting velocity can be 0 (falling) or 9.8 units/second. (This is in the y direction)
- We travel at a constant speed of 10 units/second in the x/z direction
- The optimal path is defined as the shortest time spent traveling on the polygons' surface or jumping
- We know a jump is possible between the polygons
- The polygons are not overlapping when projected onto the x/z plane, but may touch (lets not worry about this case right now, one problem at a time)
Situation
This is for a pathfinder running in 3D space using a navigation mesh (a bunch of polygons) in a hierarchical structure. This problem is a simplified version of the original in which polygons can be overlapping, height can restrict movements and jumps, or you don't always have a start and goal point on your two polygons (this jump may be in the middle of a set of undetermined jumps).