2010-08-21

A personal annotations of Veach's thesis (16) p.168

p.116 4.6 Adjoint operator


I look back to the chapter 4.6 since adjoint operator is important topic now. This operator is written as Hermitian. This is a conjugate transpose, I just imagine what could be imaginary energy. There was a story about Hilbert space, so, maybe this is related with that. But until chapter 7, this operator indicates only real symmetry.

In the light transport equation, the light emitted to a surface and reflected, then reaches to the camera. If the camera and the light exchanged, the equation should be the same. I think that is this adjoint operator about.

Acknowledgements
Carsten W. gives me a comment my understanding sounds OK. Thanks.

p.122 particle tracing Equation 4.32's comment's comment

My blog explain why the weight is there. But if you see p.226 Equation (8.9) explains brief and precise. Also it is general, since I only handled two cases, instead, Veach's form is an integral form and everything is there. How simple he explained this.

p.226 vertex

Whenever I heard 'vertex' I imagine a point of a triangle/polygon. In this paper, a vertex is a sampling point. Sampling points are connected by edges. Some say 'the distance' as the number of vertices, but in this paper, the distance is number of edges. These have one number difference.

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