Graphics Reference
In-Depth Information
facet hits yet another microfacet, etc. Because we're assuming that the surfaces
on which these microfacets reside are globally flat (at least relative to the scale of
individual microfacets), we can assume that each microfacet interacts with only
a few neighbors, thus reducing the complexity of the rendering problem. When
we get to limiting cases like light arriving at a glancing angle, when many facets
might shadow a single one, this simplifying assumption can break down.
Exercise 27.1:
In Gouraud shading, we have color values at the three vertices of a
triangle, and we interpolate those values across the interior of the triangle. Since
this is typically done on a raster screen, one approach is to work from top to bot-
tom, linearly interpolating values along each edge, and then within a single row
of pixels linearly interpolating between the two ends. In a typical triangle, there
will be a top vertex, a bottom vertex, and a middle vertex. As we pass the middle
vertex, we'll need to start traversing a different edge. Alternatively, we could do
interpolation from the top to the middle row, and from the bottom to the middle
row.
(a) Show that if we compute the intersection of an edge with a row center exactly
(rather than rounding to the nearest pixel center), the result is exactly the barycen-
tric interpolation of the vertex values.
(b) Show that as we move from one row to the next, working down from the top
vertex to the middle vertex, the starting value for each pixel row differs from the
starting value for the previous row by the same amount.
(c) Use the idea of part (b) to develop a low-operation-count implementation of
Gouraud shading in the 2D tested, using “pixels” that are each small, colored rect-
angles to visualize your results.
(d) Suppose we were to apply the same idea to shade a convex quadrilateral: We
work from top to bottom, computing interpolated values along the two edge points
in each row, and then linearly interpolate along the row. If we rotate the quadri-
lateral (keeping the assigned color values at each vertex), does the interpolated
shading appear to rotate as well?
Exercise 27.2:
It's very common to photograph either the moon or a light-
house being reflected in fairly calm (but not completely flat) water. The usual
depiction shows the bright reflection appearing as a wedge that grows wider as it
approaches the viewer, with the wedge point either near the lighthouse or (in the
case of the moon) near the horizon. Find such a photograph, describe the notable
features of the reflection (such as the shape of the wedge), and explain them in
terms of the physical models you've seen in this chapter.
Exercise 27.3:
A bookshelf holds three topics, one with a white binding and
two with black bindings. The shelf itself is made of polished wood. Looking down
at the shelf, you can see the reflection of the spines of the topics. Near the bottom
of the spines, the division between the white and black reflections appears quite
sharp. But if you look at the reflections of a region near the top of the spines,
the division is quite blurry. Explain why. Is it a Fresnel effect, because of the
difference in viewing angle? Why or why not? How could you test this idea?
Hint: Actually set up the experiment!
Exercise 27.4:
In the Phong model, as typically expressed, there's a diffuse
color, expressed as an RGB triple, and a diffuse reflectance.
