By D. Forsyth, J. Ponce
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5; usually, we assume that E is constant over the source. Area sources do not produce dark shadows with crisp boundaries. This is because, from the perspective of a viewing patch, the source appears slowly from behind the occluding object (think of an eclipse of the moon — it is an exact analogy). It is common to distinguish between points in the umbra (a Latin word, meaning “shadow”) — which cannot see the source at all — and points in the penumbra (a compound of Latin words, meaning “almost shadow”) — which see part of the source.
6. Interreﬂections: Global Shading Models 45 where Ai is the area of the i’th patch. If we insist that the exitance on each patch is constant, too, we obtain the model: Bi = Ei + Baverage incoming at i from j all j = Ei + Kij Bj , all j where Kij = 1 ρd (x) visible(x, v)K(x, v)dAv dAx Ai patch i patch j This is a system of linear equations in Bi (although an awfully big one — Kij could be a million by a million matrix), and as such can in principle be solved. ]. 3 The qualitative eﬀects of interreﬂections We should like to be able to extract shape information from radiosity.
8 Assignments Exercises 1. How many steradians in a hemisphere? 2. We have proven that radiance does not go down along a straight line in a non-absorbing medium, which makes it a useful unit. Show that if we were to 20 Radiometry — Measuring Light Chapter 1 use power per square meter of foreshortened area (which is irradiance), the unit must change with distance along a straight line. How signiﬁcant is this diﬀerence? 3. An absorbing medium: assume that the world is ﬁlled with an isotropic absorbing medium.