24 lines
1.7 KiB
TeX
24 lines
1.7 KiB
TeX
\newpage
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\subsection{Sample generators}
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\label{sec:samplers}
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When rendering an image, Mitsuba has to solve a high-dimensional integration problem that involves the
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geometry, materials, lights, and sensors that make up the scene. Because of the mathematical complexity
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of these integrals, it is generally impossible to solve them analytically --- instead, they
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are solved \emph{numerically} by evaluating the function to be integrated at a large number of
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different positions referred to as \emph{samples}. Sample generators are an essential ingredient to this
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process: they produce points in a (hypothetical) infinite dimensional hypercube $[0,1]^{\infty}$ that
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constitute the canonical representation of these samples.
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To do its work, a rendering algorithm, or \emph{integrator}, will send many queries to the sample generator.
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Generally, it will request subsequent 1D or 2D components of this infinite-dimensional ``point'' and map
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them into a more convenient space (for instance, positions on surfaces). This allows it to construct
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light paths to eventually evaluate the flow of light through the scene.
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Since the whole process starts with a large number of points in the abstract space $[0,1]^{\infty}$,
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it is natural to consider different ways of positioning them. Desirable properties of a sampler are
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that it ``randomly'' covers the whole space evenly with samples, but without placing samples too close
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to each other. This leads to such notions as \emph{stratified sampling} and \emph{low-discrepancy}
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number sequences. The samplers in this section make different guarantees on the quality of generated
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samples based on these criteria. To obtain intuition about their behavior, the provided point plots
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illustrate the resulting sample placement.
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