I present a data-driven model for isotropic bidirectional reflectance distribution functions (BRDFs) based on acquired reflectance data. Instead of using analytic reflectance models, each BRDF is represented as a dense set of measurements. This representation allows interpolation and extrapolation in the space of acquired BRDFs to create new BRDFs. Each acquired BRDF is treated as a single high-dimensional vector taken from the space of all possible BRDFs. Both linear (subspace) and non-linear (manifold) dimensionality reduction tools are applied in an effort to discover a lower-dimensional representation that characterizes the acquired BRDFs. To complete the model, users are provided with the means for defining perceptually meaningful parametrizations that allow them to navigate in the reduced-dimension BRDF space. On the low-dimensional manifold, movement along these directions produces novel, but valid, BRDFs.By analyzing a large collection of reflectance data, I also derive two novel reflectance sampling procedures that require fewer total measurements than standard uniform sampling approaches. Using densely sampled measurements the general surface reflectance function is analyzed to determine the local signal variation at each point in the function's domain. Wavelet analysis is used to derive a common basis for all of the acquired reflectance functions, as well as a non-uniform sampling pattern that corresponds to all non-zero wavelet coefficients. Second, I show that the reflectance of an arbitrary material can be represented as a linear combination of the surface reflectance functions. Furthermore, this analysis specifies a reduced set of sampling points that permits the robust estimation of the coefficients of this linear combination. These procedures dramatically shorten the acquisition time for isotropic reflectance measurements. I would like to thank Matt Brand for advising me on many parts of the project. Technical discussions with Matt, his algorithms, and his research code were essential in developing this data-driven reflectance model.

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In this article, we consider the design of a compact freeform optical surface that uniformly irradiates an arbitrary convex polygonal region from an extended light source, while controlling spill. This problem has attracted a large body of literature that has primarily covered highly symmetric special cases or cases where the solution is approximated by a zero-étendue design based on a point source. Practical versions of this illumination design problem will likely feature large asymmetric light-emitting diodes, compact lenses, and irregular targets on angled projection surfaces. For these settings, we develop a solution method based on an edge ray mapping that routes maximally off-axis rays from the edges of the source through the edge of the optic to the edges of the target polygon. This determines the sag and normals along the boundary of the freeform surface. A “spill-free” surface is then interpolated from the boundary information and optimized to uniformize the irradiance, while preserving the polygonal boundary. Highly uniform irradiances (relative standard deviation <2021