Systems and methods are provided herein for an AV to more efficiently, quickly, and accurately determine a likelihood of collision with another object, for example, by recursive triangulation. A candidate trajectory of the AV is then selected for controlling the AV based on the determined likelihood(s) of collision. According to one example, the likelihood of collision is determined by: 1) recursively triangulating a convex hull that defines all of the locations in which a collision would occur between the object and the AV (e.g., in a manner similar to the Sierpiński method), and 2) multiplying the area of each resulting triangular region by the value of a probability density that defines all of the locations in which a collision would occur between the object and the AV function in that region.