Let's say I have a matrix of values that represent heights with function $f(x,y)$ and I am trying to find the "lowest value path" beween two points. So this would be the reverse of hill climbing, as in optimization, taking gradient and following that etc, but in a way, I guess I need the anti-gradient - not the direction of steepest climb but the non-steepest walk.
I need this for a mapping application, I have elevation values on a grid and I am trying to find a path between those points that require minimum amt of climbing.
I guess I could create a cost function that gives highest values for high elevation + furthest points to destination + non-smoothness of paths, and do optimization on that. I was just wondering if anyone worked with such cost functions before, or there is another calculus trick I have to utilize.
Keywords: flattest route