Cool post. The Lipschitz trick here relies on the assumption that the gradient has magnitude 1 everywhere. Evaluating the SDF in a box and using the Lipschitz

Cool post. The Lipschitz trick here relies on the assumption that the gradient has magnitude 1 everywhere. Evaluating the SDF in a box and using the Lipschitz property lets you get some quick estimates on the range of the SDF over the box. This is a close cousin of the monotonicity interval inclusion: e.g., if f'([a, b]) > 0, then f([a, b]) is a subset of [f(a), f(b)]. Rounded interval arithmetic makes this rigorous on a computer; you can also do it in multiple dimensions, with higher derivatives, successively tightening inclusions for lower derivatives, etc.