In the above video, Aravind Baskar uses a saddle graph to design a four-bar function generator. A saddle graph is essentially a road map of a higher dimensional design space. Once a cost function is defined across a design space, all local minima (and saddles) can be found using polynomial homotopy continuation. Saddles exist in between minima. Any path between two minima which itself minimizes the maximum objective along the way, must pass through a saddle. A saddle graph organizes these connections between minima. Dragging your mouse across the edges of a saddle graph, the designer travels along these 1D roads from minima to minima in a higher dimensional design space. Performance metric data is displayed along the way.

Why not just pick the best minima and move on? Because cost functions rarely represent what designers are actually looking for, shifting the notion of “best” off the minima.