Bump map depth scale?

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Pfhorrest
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How do lightness differences in bump map translate to apparent depth in terms of world units?

For example, say I want to create a cone-shaped bump on a texture, and I want the cone to have an apparent 45 degree slope from base perimeter to point. If the point at the center of the cone is 100% (white) and the base perimeter of the cone is 0% (black), what radius (in WU) would the cone need to be for that black-to-white gradient to render as an apparent 45% slope?

Alternately but equivalently, say I want a box-shaped bump on a texture, and I want that box bump to look cubic, not tall or flat. If the bump is rendered as a white square on a black background in the bump map, how big would that square need to be to appear just as wide as it is tall when rendered?

A related question: what lightness in the bump map corresponds to the apparent depth of flat, non-bumpy textures? Are all bumps raised from the flat plane (so black is flat), recessed into the flat plane (so white is flat), or both ways (so 50% grey is flat)? Or something else?
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treellama
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Hmm, maybe an answer to your last question will shed some light on the first two:

As it happens, solid black, solid white, and solid gray *all* correspond to the "apparent depth" of a flat, non-bumpy texture! Try it out.
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Hopper
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Bump mapping is not equivalent to extruding a texture. For starters, read up on the differences between "height map" and "normal map". Standard bump mapping uses only the normal map, which changes the lighting based on slopes, but doesn't raise or lower anything from the flat plane.

Aleph One's default bump shader also does iterative parallax mapping, which does use the height map, but I barely understand that myself. Fortunately, there are guides on the internet that do a much better job of explaining it than I could.
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Pfhorrest
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Is there documentation somewhere about how to create bump maps for Aleph One? I had assumed that it would be an MML attribute on a replacement texture tag akin to glow maps, but looking at the MML documentation I don't see anything about bump anything anywhere.
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treellama
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The normal/height (I forgot about parallax mapping!) maps for Aleph One textures are combined into one texture, which is specified using the "offset_image" attribute. Aorta can create normal maps from a height map you give it, and outputs a file suitable for use in the offset_image attribute.
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goran
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From experience the depth (or height) is not that great. Black to white ~0,050 WU . No data or anything to back it up, just my own observation.
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CryoS
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completely unrelated question, does aleph one support normal maps?
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