Bivariate transfer functions on unstructured grids

Yuyan Song, Wei Chen, Ross MacIejewski, Kelly P. Gaither, David S. Ebertt

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Multi-dimensional transfer functions are commonly used in rectilinear volume renderings to effectively portray materials, material boundaries and even subtle variations along boundaries. However, most unstructured grid rendering algorithms only employ one-dimensional transfer functions. This paper proposes a novel pre-integrated Projected Tetrahedra (PT) rendering technique that applies bivariate transfer functions on unstructured grids. For each type of bivariate transfer function, an analytical form that pre-integrates the contribution of a ray segment in one tetrahedron is derived, and can be precomputed as a lookup table to compute the color and opacity in a projected tetrahedron on-the-fly. Further, we show how to approximate the integral using the pre-integration method for faster unstructured grid rendering. We demonstrate the advantages of our approach with a variety of examples and comparisons with one-dimensional transfer functions.

Original languageEnglish (US)
Pages (from-to)783-790
Number of pages8
JournalComputer Graphics Forum
Issue number3
StatePublished - Jun 2009
Externally publishedYes

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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