Issue No. 03 - May/June (2003 vol. 23)
Ron Goldman , Rice University
<p>Elementary problems in 3D geometry can often be reduced to solving two simple simultaneous vector equations-one involving only the dot product and the other only the cross product-in one vector unknown. This article presents a general technique for solving such equations and then applies this method to derive explicit formulas for many of the linear transformations used in the standard 3D graphics pipeline.</p>
rendering, illumination effects, radiosity, texture mapping, illumination model, lightmaps, ambient light, form factor, obscurance, production rendering
R. Goldman, "Deriving Linear Transformations in Three Dimensions," in IEEE Computer Graphics and Applications, vol. 23, no. , pp. 66-71, 2003.