Structured Penumbral Irradiance Computation

A definitive understanding of irradiance behavior in penumbral regions has been hard to come by, mainly due to the computational expense of determining the visible parts of an area light source. Consequently, sampling strategies have been mostly ad hoc, and evaluation of the resulting approximations has been difficult. In this paper, the structure of penumbral irradiance is investigated empirically and numerically. This study has been made feasible by the use of the discontinuity mesh and the backprojection, an efficient data structure representing visibility in regions of partial occlusion. Regions of penumbrae in which irradiance varies nonmonotonically are characterized empirically, and numerical tests are performed to determine the frequency of their occurrence. This study inspired the development of two algorithms for the construction of interpolating approximations to irradiance: one algorithm reduces the number of edges in the mesh defining the interpolant domain; and the other algorithm chooses among linear, quadratic, and mixed interpolants based on irradiance monotonicity. Results from numerical tests and images are presented that demonstrate good performance of the new algorithms for various realistic test configurations.

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