A technical exploration of how bounding boxes can be automatically tracked when shapes undergo arbitrary transforms in the Ao geometry kernel. Shapes are represented as distance functions, and bounding boxes must update correctly when transforms like rotation or scaling are applied. The key insight is that transformed bounds require applying the inverse transform using interval arithmetic to ensure the result fully encloses the new shape. Since most practical transforms are affine, the solution involves detecting whether a transform is affine, extracting its matrix representation, inverting it, and applying it to the original bounding box intervals. This approach handles all but two operations (tapering) in Ao's transform library.
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