Steep parallax mapping is one name for the class of algorithms that trace rays against heightfields. The idea is to walk along a ray that has entered the heightfield's volume, finding the intersection point of the ray with the heightfield. This closest intersection is what part of the heightfield is truly visible. Relief mapping and parallax occlusion mapping are other common names for these techniques.
Interval mapping improves on the usual binary search done in relief mapping by creating a line between known inside and outside points and choosing the next sample point by intersecting this line with a ray, rather than using the midpoint as in a traditional binary search.
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“Switzerland is a small, steep country, much more up and down than sideways, and is all stuck over with large brown hotels built on the cuckoo clock style of architecture.”
—Ernest Hemingway (1899–1961)