A kind of example problem class is Qs about collisions/intersections at some point in time. In addition to the types of variations above, the Qs might be qualified by geometric approximation or probability or intervals in space or time. What are the languages for theorems – Complexity Theory from Comp Sci? Decidability Theory? It hasn’t been sorted.

Example of advanced future application: simulating what a particular clothing purchase would look like & feel like on your actual body. This is a mixture of data gathering, VR, & mapping of tactile & proprioception to neural signal/stimulation. It’s not science fiction – just not the engineering reality of today.

Same story for furniture you sit on.

Structure From Motion involves both geometric & statistical reasoning, usually with an assumption of rigidity. Sets of theory & assumptions & generalizations are open lanes for work here that could shed light on where useful inference is a tractable problem. For computer vision, range finding LIDAR may be more beneficial in many circumstances but is less directly related to inferences about similarity & identity of objects “in view” across related & unrelated scenes.
Ex applicatin: a set of cameras to automatically obtain good shots of a sports event in progress – their activity may be informed by predictions of what is more likely to occur next in dynamic sequence.

Can you construct a model-based argument for an optimized lawn sprinkler?

Can you tell if a given sprinkler is good variety from a distance? Or if the one you are looking at is probably broken/damaged/blocked?

Consider optimizing a robot that paints houses with a brush. There’s a lot of bits with details & where humans use visual & tactile feedback to make judgments about efficacy.

We like the idea of visual/PR & physical models being highly correlated & making mutual supportive predictions. That principle is like Structure From Motion – an inference to matches that would be tricky to explain in a different way.