How to find where to cast a ray to avoid collision in Bullet?

Question

Say we have an object at point A. It wants to find out if it can move to point B. It has limited velocity so it can only move step by step. It casts a ray at direction it is

Answer 1

One way to look at this is as a shadow casting problem. Make A the "light source" and then decide whether each point in the scene is in or out of shadow. Those not in shadow are accessible by rays from A. The other areas are not. If you find B is in shadow, then you need only locate the nearest point in the scene that is in light.

If you discretize this problem into "pixels," then the above approach has very well-known solutions in the huge computer graphics literature on shadow rendering. For example, you can use a Shadow Map to paint each pixel with a boolean flag that indicates whether it's in shadow or not. Finding the nearest lit pixel is just a simple search of growing concentric circles around B. Both of these operations can be made extremely fast by exploiting GPU hardware.

One other note: You can treat a general object path finding problem as a point path problem. The secret is to "grow" the obstacles by an appropriate amount using Minkowski Differences. See for example this work on robot path planning.