Representation a single vector is not enough how do we represent multiple surface normals?
Previous Work Gaussian Distributions –(Olano and North 97) –(Schilling 97) –(Toksvig 05) Mixture Models –(Fournier 92) –(Tan, et.al. 05) 3D Gaussian 2D covariance matrix 1D Gaussian mixture of Phong lobes mixture of 2D Gaussians no general solution
Our Contributions Theoretical Framework –Normal Distribution Function (NDF) –Linear averaging for filtering –Convolution for rendering –Unifies previous works New normal map representations –Spherical harmonics –von Mises-Fisher Distribution Simple, efficient rendering algorithms
Normal Distribution Function (NDF) Describes normals within region Defined on the unit sphere Integrates to one Extended Gaussian Image (Horn 84)