27306 lines
1.6 MiB
27306 lines
1.6 MiB
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(* Beginning of Notebook Content *)
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Notebook[{
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Cell[TextData[{
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StyleBox["Cloth DFG Approximation\n", "Title"],
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StyleBox["\nThis document explores an analytical approximation of the DFG \
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term in image-based lighting evaluation for a cloth BRDF.", "Text"]
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}], "Text",
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Cell[TextData[{
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StyleBox["Cloth BRDF", "Section"],
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StyleBox["\n", "Subtitle"],
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StyleBox["\nOur cloth BRDF uses an inverse Gaussian NDF based on the work of \
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Ashikhmin. We also use a different, simplified, visibility term \[Dash] as \
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suggested by Neubelt and Pettineo \[Dash]\[NonBreakingSpace]and a diffuse \
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component smoothed by the Fresnel. The full BRDF is as follows:", "Text"]
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Cell[TextData[StyleBox["The Ashikhmin distribution itself is defined by:", \
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Cell[TextData[StyleBox["Alternatively we can use the \
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\[OpenCurlyDoubleQuote]Charlie\[CloseCurlyDoubleQuote] distribution proposed \
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by Estevez and Kulla (Sony Imageworks):", "Text"]], "Text",
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Cell[TextData[{
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StyleBox["Analytical approximation", "Section"],
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StyleBox["\n", "Subtitle"],
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StyleBox["\nTo investigate possible approximations we use a reference \
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generated using our tool cmgen. The DFG reference is an RG16F OpenEXR image \
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computed by randomly sampling the hemisphere. Because it was not generated \
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using importance sampling, the reference uses ", "Text"],
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Cell[BoxData[
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FormBox[
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RowBox[{
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SuperscriptBox["2", "22"], " ", "samples"}], TraditionalForm]]],
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" per data point. The 3D plot of the reference shows that both data channels \
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can be approximated using a dual Gaussian. In practice we use a true Gaussian \
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multiplied by a simple inverse square."
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}], "Text",
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StyleBox["Analytical approximation of the \[OpenCurlyDoubleQuote]Charlie\
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\[CloseCurlyDoubleQuote] distribution", "Section"],
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StyleBox["\nWe follow a similar approach to approximate the \
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\[OpenCurlyDoubleQuote]Charlie\[CloseCurlyDoubleQuote] distribution. The \
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reference uses the same format and computation method as previously.\n\n",
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"\n\nThe approximation shown above is implemented in cmgen and used to \
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regenerated a reference image. The resulting image is compared below to the \
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analytical approximation to validate the implementation. "
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Annotation[#, "Charting`Private`Tag$29906#1"]& ]],
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