COMPUTER ANIMATION AND VIRTUAL WORLDS Comp. Anim. Virtual Worlds 2004; 15: 471–484 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/cav.10 ****************************************************************************************************** Rendering natural waters taking fluorescence into account By E. Cerezo* and F. J. Seron ************************************************************************************ The aim of the work presented here is to generalize a system, developed to treat general participating media, to make it capable of considering volumetric inelastic processes such as fluorescence. Our system, based on the discrete ordinates method, is adequate to treat a complex participating medium such as natural waters as it is prepared to deal with not only anisotropic but also highly peaked phase functions, as well as to consider the spectral behaviour of the medium’s characteristic parameters. It is also able to generate detailed quantitative illumination information, such as the amount of light that reaches the medium boundaries or the amount of light absorbed in each of the medium voxels. First, we present an extended form of the radiative transfer equation to incorporate inelastic volumetric phenomena. Then, we discuss the necessary changes in the general calculation scheme to include inelastic scattering. We have applied all this to consider the most common inelastic effect in natural waters: fluorescence in chlorophyll-a. Copyright # 2004 John Wiley & Sons, Ltd. Received: 1 January 2003; Accepted: 13 January 2004 KEY WORDS: fluorescence; inelastic phenomena; participating media; discrete ordinates; global illumination Introduction: Previous work The aim of the work presented here is to generalize a system developed to treat general participating media to make it capable of considering volumetric inelastic processes such as fluorescence. Our system is adequate to treat a complex participating medium such as natural waters. The interesting issue about natural waters and, in particular, about the oceanic medium, is that electromag- netic radiation interacts with the water and also with materials dissolved or suspended in it. This makes ocean phenomenologically rich. 1 Our system is able to deal with, and reproduce, the spectral behaviour of its char- acteristic parameters and to handle the highly anisotropic phase function that characterizes this kind of natural water. For the moment, fluorescence due to the most important pigment present in natural waters, chlorophyll- a, has been studied. Fluorescence in chlorophyll-a is characterized by an emission peak centred at 685 nm. Thus, part of the light of other wavelengths transfers to that wavelength value. Glassner 2 was the first, and until recently the only one, to consider fluorescence and phosphorescence when rendering scenes. His work focuses on the correct formulation of the rendering equation to include such effects. He also presents some results obtained with a public domain raytracer (Rayshade), adequately adapt- ed. When considering the more general case of scenes containing participating media, fluorescence is treated as a surface phenomenon; to deal with it, surfaces are characterized with a matrix that represents the transfer of energy from one wavelength to another one. As the transfer of energy, in most materials, is from large to small wavelengths the matrices are triangular. The visible spectrum is divided into intervals and a calculus is made for each of the wavelength values. In each of those calculations, energy is accumulated in the smaller wavelengths according to the surfaces’ characteristic matrices. Before beginning a new wavelength calculus, all objects of the scene are revised to select those with an appreciable emission to include them as sources in that ****************************************************************************************************** Copyright # 2004 John Wiley & Sons, Ltd. *Correspondence to: Eva Cerezo, Advanced Computer Graphics Group (GIGA), Departamento de Informa ´ticae Ingenieria de Sistemas, Universidad de Zaragoza, Campus Polite ´cnico del Actur, Edificio Ada Byron C/Marı ´a de Luna, 1, E-50018 Zaragoza, Spain. E-mail: ecerezo@unizar.es Contract/grant sponsor: Comisio ´n Interministerial de Ciencia y Tecnologı ´a; contract/grant numbers: TIC2000-0426-P4-02 and TIC2001-2392-C03-02.