By D. Forsyth, J. Ponce

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In particular, from the perspective of our patch, every other patch in the world that it can see is an area source, with exitance B(v). 6. 16. Terminology for expression derived in the text for the interreflection kernel. 16 and visible(u, v) = 1 if u can see v, 0 if u can’t see v visible(u, v)K(u, v) is usually referred to as the interreflection kernel. This means that our model is: B(u) = E(u) + ρd (u) visible(u, v)K(u, v)B(v)dAv world In particular, the solution appears inside the integral. Equations of this form are known as Fredholm integral equations of the second kind.

7. An infinitesimal patch views a circular area source of constant exitance frontally along the axis of symmetry of the source. Compute the radiosity of the patch, due to the source exitance E(u) as a function of the area of the source and the distance between the center of the source and the patch. You may have to look the integral up in tables — if you don’t, you’re entitled to feel pleased with yourself — but this is one of few cases that can be done in closed form. It will be easier to look up if you transform it to get rid of the cosine terms.

5. A small sphere casts a shadow on a larger sphere. Describe the possible shadow boundaries that occur. 6. Explain why it is difficult to use shadow boundaries to infer shape, particularly if the shadow is cast onto a curved surface. 7. An infinitesimal patch views a circular area source of constant exitance frontally along the axis of symmetry of the source. Compute the radiosity of the patch, due to the source exitance E(u) as a function of the area of the source and the distance between the center of the source and the patch.

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