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There might be a Monte Carlo solver based on this.


If a splitting plane passes through a convex leaf object, do we consider all of its surface area or just the part on one side of the splitting plane (for kd-tree)? If we consider entire area, then it seems like this probability could end up > 1.


With acceleration structures the convex shapes we're considering are generally axis aligned bounding boxes, so whether the shapes in the scene are convex doesn't matter. For a kd-tree if the plane passes through an object then that increases the cost for visiting both child nodes, but it doesn't affect the intersection probabilities.