Multithreaded Paraboloid Mapping - Practical Rendering and Computation with Direct3D 11 - page 576

and then divide all three components by the z-component to produce the form shown in
Equation (13.5). This equality is shown in Equation (13.7):
(13.7)
With this equation, we have the desired x and y coordinates that will define where
in the paraboloid map the object will appear. We will use this equality to perform our pa-
raboloid projection while generating the paraboloid maps later in this chapter. By placing
each vertex of an object into the appropriate location in the paraboloid map, we can use the
rasterizer stage to fill in its contents. Since each paraboloid can represent one half-space
around itself, we will use two paraboloid maps to represent the entire area around the point
that we are interested in.
13.1.2 Paraboloid Map Sampling
With the ability to generate a pair of paraboloid maps around a desired point in our scene,
we also need to be able to know where to sample our paraboloid maps to find the appropri-
ate reflection contents. Typically, when rendering the reflective object that the paraboloid
maps have been generated for, we will have that object's surface normal vector, as well
as the viewing vector from the camera to that point in space. In this situation, the viewing
vector and surface normal can be used to calculate the direction that the view vector is
reflected into. It is this vector that we want to find in our paraboloid maps. The relationship
between these vectors is depicted in Figure 13.7.
Fortunately, the lookup process is quite similar to what we did when we generated the
paraboloid map. We will know what viewing direction was used to generate the paraboloid
Figure 13.7. The vectors associated with sampling a paraboloid map.