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Suppose I have a character and an array of 3D coordinates, separated at most a certain distance apart. I would like to have a character run across the points in the array, placing its feet exactly on those coordinates, while the animation still seems natural (given the path does not have many unnaturally sharp angles). How can I accomplish this?

I doubt it would work to just take a normal running animation based on Bézier curves, and then vary the points of the animation so that the foot bones will end up on the right place.

My next best guess would be to create a physical/mathematical model of a basic running animation. Then I would be deriving equations for the character position from projectile equations for mid flight and a simple model with two springs with variable spring coefficients for the legs during touchdown. I could then position the feet using an inverse kinematics setup for the legs and interpolate the IK anchor between the nodes in flight. This seems a bit overkill, however.

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