RBD | Shortest Path Between two points is a straight line?

An interesting post on linkedin appeared the other day and I felt compelled to try it in Houdini. The fastest way to get from a to b is a straight line ... unless gravity is involved.

If I were to show you the following picture, would the ball following the straight line or the curved line reach the end point sooner? The curved line (green) will be longer in distance, the straight line is indicated in red.


In answer to this question, collision objects were created from the curves. The red line is an add node with two points - start and end, and the green line is also an add node, however with two points to manipulate the curve and run through a polyspline node. These were then extruded to create collision objects and two separate sims were run with equivalent spheres each colored to match the path. The answer is the curved line will beat the straight every time. Thanks to gravity, the acceleration makes up for the distance.



This can be seen better when we shrink the spheres and stretch out the line, but just as the real life experiment shows, the simulation has the curved ball winning.