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\newlabel{fig:overview}{{1.1}{5}{Overview of contribution photon mapping workflow. Green paths denote inputs (parameters and sensor positions), while red paths denote output. Light source contributions for modifier mod are binned using an $\left \lfloor \sqrt {nbins}\right \rfloor ^2$ Shirley-Chiu disk-to-square mapping, and wavelet compressed for a fraction \var {precomp} of photons by \mkpmap . These contributions are saved along with the corresponding photons in separate files for each modifier, grouped in a subdirectory under the parent photon map \var {pmapfile}. The photons and their precomputed contributions are subsequently paged on demand, uncompressed, and cached by \rcontrib , which passes the contributions to the standard contribution calculation used by \rcClassic . \relax }{figure.caption.2}{}}
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\newlabel{fig:coeffRange}{{2.2}{10}{Logarthmic plot of absolute wavelet coefficient magnitudes after normalisation. The coefficients (magenta crosses) are clustered in bands of increasing frequency from left to right, with the number of coefficients doubling in consecutive bands due to the wavelet transform's multiresolution analysis. In this example, the dynamic range of the coefficients is limited to ca. 10 orders of magnitude. It is also evident that the coefficients at the bottom between $10^{-19}$ and $10^{-20}$ are negligible and can be omitted. It follows therefore that it suffices to encode coefficients up to the green line at ca. $4.6^{-10}$; this corresponds to an effective range of $[2^{-31}, 1]$, which can be encoded using a 5-bit binary mantissa. In practice, thresholding the coefficients will further reduce this dynamic range. \relax }{figure.caption.4}{}}
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\newlabel{fig:waveletCoeffsFull}{{3.4}{19}{Sample output of wavelet unit test for 16$\times $16 bins, showing the wavelet coefficient matrix after a full transform. The coloured fields identify the coefficient type ( red = approximation $s$, green = detail $d$) and the successive transform steps, from right to left. Each iteration generates coefficients from those of prior iterations at higher resolutions: approximations of prior details $sd$ (lower left), details of prior approximations $ds$ (upper right), details of prior details $dd$ (lower right), approximations of prior approximation $ss$ (upper left). Each subsequent iteration then recurses into the upper left submatrix, using the approximations $ss$ as increasingly coarse representations of the original contributions as input. After the final iteration, the red submatrix in the upper left corner contains the 3$\times $3 coarsest approximations. \relax }{figure.caption.9}{}}
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