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Fast method for raycasting a height-map?

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I am writing a simple raytracer, and I want to render terrain using a height map. I can already turn the heightmap into a series of triangles and raytrace it normally, but I feel like there should be a fast way to raytrace the raw height map and avoid having to use triangles at all. I am aware of the many different pixel shader effects that basically 'raytrace' to give more surface detail (aka parallax mapping, relief mapping, ect..) However, correct me if im wrong, but it seems like those methods only work when the camera is above the heighest point on the heightmap. Iv done a bit of googling but havent found any concrete papers or non triangle based methods for raycasting how I want. Does anyone know of any algorithms I can investigate for this? Thanks, Chris

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