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Real-time polygonal-light shading with linearly transformed cosines

Published:11 July 2016Publication History
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In this paper, we show that applying a linear transformation---represented by a 3 x 3 matrix---to the direction vectors of a spherical distribution yields another spherical distribution, for which we derive a closed-form expression. With this idea, we can use any spherical distribution as a base shape to create a new family of spherical distributions with parametric roughness, elliptic anisotropy and skewness. If the original distribution has an analytic expression, normalization, integration over spherical polygons, and importance sampling, then these properties are inherited by the linearly transformed distributions.

By choosing a clamped cosine for the original distribution we obtain a family of distributions, which we call Linearly Transformed Cosines (LTCs), that provide a good approximation to physically based BRDFs and that can be analytically integrated over arbitrary spherical polygons. We show how to use these properties in a realtime polygonal-light shading application. Our technique is robust, fast, accurate and simple to implement.

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      cover image ACM Transactions on Graphics
      ACM Transactions on Graphics  Volume 35, Issue 4
      July 2016
      1396 pages
      ISSN:0730-0301
      EISSN:1557-7368
      DOI:10.1145/2897824
      Issue’s Table of Contents

      Copyright © 2016 ACM

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      Publication History

      • Published: 11 July 2016
      Published in tog Volume 35, Issue 4

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