In this case, if you can imagine a bivariate function whose distance you want between two points to be minimized(Say, some general “Cost” function with independent variables of time and money), then solving for the geodesic is absolutely essential. Plus, also… energy minimization, distance minimization around an obstacle/hill, whatever-minimization! It’s such a fantastic concept! This concept will possibly be absolutely crucial to computer vision systems that work solely on mathematical algorithms(Although “visual” computer vision systems will probably operate more on “approximates” so that it “Looks the best” like how people operate.).