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This PDF discusses bump mapping, a special case of displacement mapping. A surface is represented as a function \$\overrightarrow{O}\left(u,\,v\right):\:\Bbb R^2\mapsto\Bbb R^3\$. In bump mapping, we shift this surface by \$\delta\overrightarrow{O}=B(u,\,v)\overrightarrow{N}\$, with \$\overrightarrow{N}=\overrightarrow{O}_u\times\overrightarrow{O}_v\$ the surface normal. What happens in more general displacement mapping? Do we, for example, replace \$B\$ with a matrix, or include multiples of \$\overrightarrow{O}_u,\,\overrightarrow{O}_v\$ in \$\delta\overrightarrow{O}\$? If there's too broad a variety of displacement maps to describe in one answer, I'll settle for one or more mathematically detailed references.

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  • \$\begingroup\$ I can't give you a mathematical reference. But displacement mapping uses 3 channels of a texture to displace the vertices of a mesh by using 1 channel for each x y z axis. I think there are no other forms of displacement mapping. \$\endgroup\$ – Bartimaeus Sep 24 '19 at 17:16
  • \$\begingroup\$ @Bartimaeus That would be something like \$\delta O_i=\sum_j B_{ij}(u,\,v)N_j\$, i.e. \$B\$ is replaced with a matrix, which was one of my guesses. Thanks! \$\endgroup\$ – J.G. Sep 24 '19 at 17:28

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