RENDERING THE PHENOMENA OF VOLUME ABSORPTION IN HOMOGENEOUS TRANSPARENT MATERIALS

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1 RENDERING THE PHENOMENA OF VOLUME ABSORPTION IN HOMOGENEOUS TRANSPARENT MATERIALS YINLONG SUN, F. DAVID FRACCHIA, AND MARK S. DREW School of Computing Science, Simon Fraser University, Burnaby, BC, Canada V5A 1S6 {sun, fracchia, ABSTRACT Volume absorption is a crucial factor to the appearance of transparent objects such as colored glass and liquids. Due to the involvement of the spectral absorptivities of materials and path lengths of lights, volume absorption can generate interesting color variations. In this paper, we model volume absorption for homogeneous transparent materials using Bouguer-Lambertian law, and render its phenomena using a spectrum-based ray tracer. Our rendered images successfully display the subtle variations of colors due to volume absorption. We also compare our approach to an RGB-based one which assigns color tristimulus values for three monochromatic wavelengths, and show that the latter approach has significant errors and is thus inadequate for rendering volume absorption. This work expands the capability of rendering natural phenomena and can be used to improve the realism of computer generated imagery. Keywords: Volume absorption, natural phenomena, transparent materials, colors, ray tracing. 1 INTRODUCTION In realistic image synthesis we deal with two essential categories of objects: opaque and transparent (including translucent). Generally speaking, rendering transparent objects is much more complicated than opaque ones, as it involves not only all the factors for opaque objects such as illumination and surface properties, but also those specific to transparent objects such as particle scattering and volume absorption. Particle scattering (e.g., Rayleigh scattering) attenuates lights by redistributing them into all possible spatial directions related optical phenomena have been modeled and rendered [1,7,9,11]. Volume absorption also attenuates lights, but the attenuation does not modify the direction of light propagation within transparent materials. Although volume absorption is crucial to the appearance of transparent objects, to our knowledge no research has considered it to date. An important property of volume absorption is its dual characteristic: absorption depends not only on spectral absorptivities of materials, but also on the path lengths over which lights travel inside transparent objects. Due to this property, volume absorption can cause continuously varying but closely related colors across transparent objects. Because of the involvement of light paths, which depend on object boundaries as well as illumination directions, we cannot associate or describe transparent objects with fixed colors as we do for opaque ones. This implies that the common RGB-based approach does not suffice to render volume absorption and therefore we need to adopt an approach based on full spectral information [5,6,10,12,13]. In this paper, we apply a spectrum-based approach to modeling and rendering volume absorption in homogeneous transparent objects. Here homogeneous has two implications. First, transparent objects are clear and specular so that particle scattering is negligible. Second, refractive indices are uniform within transparent objects this ensures that lights still travel in straight lines inside the objects. Colored glass, gemstones, and liquid solutions (dye or chemical) are all examples of homogeneous transparent objects. The principle that governs volume absorption in homogeneous transparent materials is well known, viz., Bouguer-Lambertian law. Based on this law, the rendering of volume absorption can be easily carried out using ray tracing, as lengths of light paths inside transparent objects can be computed from the intersections between light rays and object boundaries, and these are readily available in any ray tracer. The resulting images successfully demonstrate the characteristics of volume absorption, including subtle variation of colors over transparent objects. We have also explored the possibility of rendering volume absorption with an RGB-based ray tracer by approximately associating color tristimulus values to three monochromatic wavelengths. However, the results have significant errors and prove inadequate in comparison to our spectrum-based approach. 2 PRINCIPLES OF VOLUME ABSORPTION Bouguer-Lambertian law [2,8,14] rigorously states that the internal transmittance for light traveling from one point to another inside a homogeneous transparent material is given by T internal a( λ) l ( λ) = 10, (1) where a(λ) is the spectral absorptivity of the material and l is the length of the light path. Note that internal transmittance applies only to one material and is therefore

2 Spectral absorptivity (1/m) Fig. 1: Examples of spectral absorptivities. Internal transmittance red glass light blue glass Wavelength (nm) Wavelegnth (nm) Fig. 2: Curves of internal transmittances for light path lengths of 1, 2, 4, 6, 8, 10 and 12 mm from top to bottom (cf. [8]). conceptually different from transmittance which applies to an interface of two materials or an entire transparent object [14]. Spectral absorptivity can be interpreted as the ratio between the absorbed and incident spectral power distributions (SPDs) of light over a unit propagation length, thus its dimension is inverse meters. Like spectral reflectance for opaque materials, spectral absorptivity is a characteristic of transparent materials; that is, it is independent of illumination and can be determined by experimental measurement. Fig. 1 shows two typical spectral absorptivity curves: the curve for light blue glass is fairly smooth, while the one for red glass has an abrupt change. This can cause significant difference in the appearance of objects made of light blue glass and red glass, as will be shown below. According to Bouguer-Lambertian law, internal transmittance, and thus the corresponding color, is very sensitive to the light path length l. In fact, increasing l not only decreases color intensity and deepens color saturation, but can also change the hue (the trace in color space as a function of l is not linear, as shown on pages in [2]). Qualitatively, these relationships can be seen from the curves in Fig. 2, which are the internal transmittances of light blue glass with l equal to 1, 2, 4, 6, 8, 10 and 12 mm from top to bottom (cf. [8]). For liquid solutions, it is important to also consider the dependence of the internal transmittance on liquid concentration. From Beer s law [2,8,14] we have T interal a ( λ) cl ( λ) = 10, (2) where c is concentration and a (λ) is the absorption per unit concentration per unit light path length. Note, however, that Beer s law is an approximation, especially at high concentrations. 3 ALGORITHMS It is straightforward to render light absorption phenomena with ray tracing, which requires only adding two new features to a regular ray tracer (cf. p. 780 in [3]). First, we should provide spectral absorptivities for all transparent objects so that the data can be conveniently retrieved when needed. (A simple implementation is to let every transparent object have a pointer pointing to the data of its spectral absorptivities.) Second, at the end of the computation for light shading (i.e., before returning the shade value), we should apply the attenuation according to Bouguer-Lambertian law. Fig. 3 displays pseudocode for a ray tracing function which is extended to handle volume absorption. This pseudocode is the same as a regular ray tracer except that a new code block has been added at the end of the function to handle the attenuation due to volume absorption. Note that the computation for attenuation (the last line of the new code block) should be applied to all components of SPDs. If we represent spectral functions by sampling, the computation becomes T a( λ ) l internal i = for all sampled wavelengths λ i. i ( λ ) = 10, i 1,..., N (3) As mentioned above, a color-based approach is not appropriate for rendering volume absorption because spectral absorptivities cannot be effectively described in terms of colors. If we do use an RGB-based ray tracer to render volume absorption, then the question is how to compute absorption attenuation for RGB triplets. A possible approach is that, for the red, green and blue components, we use the values of spectral absorptivity at the wavelengths corresponding to red, green and blue, respectively. For instance, we could use wavelengths nm, nm and nm, which are the values used in measuring the CIE color matching functions [14]. However, this approach will introduce significant errors because the three sampled values are strongly affected by the local peaks or valleys of spectral curves. Finally, we emphasize that the extension for volume absorption can be applied to any ray tracers. In other words, an extended ray tracer provides the new capability for volume absorption while retaining all the capabilities of the original one. For instance, if the original ray tracer handles Fresnel reflectance, the extended one does as well.

3 // Ray tracing shading function extended to include volume absorption attenuation SPD getshade( const Ray& incidray, // incident ray, input int depth // recursive trace depth, input ) { depth++; SPD lightshade = 0; // empty SPD bool hasintersection = getclosestintersection ( // function call incidray, // incident tracing ray, input interspoint, // the closest intersection point, to return surfnormal // surface normal direction, to return ); if (! hasintersection) { return lightshade; } compute contributions of reflection, refraction, light sources as in a regular ray tracer // detailed steps are ignored, refer to page 780 of Ref. [3] add the contributions to lightshade } // code block for absorption attenuation if (incidray is inside a transparent object) { // incidray has a pointer to the transparent object in which it propagates get spectralabsorptivity from the transparent object get raystartpoint from incidray; // raystartpoint is attribute of incidray double lightpathlength = distance between interspoint and raystartpoint lightshade *= exp(-spectralabsorptivity*lightpathlength); // attenuation } return lightshade; Fig. 3: Pseudocode for the ray tracing function extended with light absorption attenuation. 4 RESULTS AND DISCUSSION We present and discuss the full spectral results generated using an extended ray tracer as described in Fig. 3 (with consideration of Fresnel reflectance). The images in Fig. 4 demonstrate the typical phenomena associated with volume absorption. The objects in the two images are the same geometrically: each is a hexagonal pyramid (the bottom face is a regular hexagon), but the materials are red glass and light blue glass. The camera is directed toward the object from above and a white light source is located below the pyramid. Thus white lights from the light source transmit through the object and become colored due to selective volume absorption. For both objects in Fig. 4, the colors near the hexagonal edges appear less saturated (whiter) because the corresponding light paths within the glass are short and thus little light is absorbed. Considering the extreme case of zero path length, no light is absorbed and therefore the colors should be the same as those radiated from the light source. On the other hand, when approaching the axial center the colors appear more saturated and also lose intensity. This is because the All the images in this paper can be viewed at URL: corresponding light paths within the material are lengthened. Interestingly, the colors on the red object vary abruptly while on the blue one they vary smoothly. This is a consequence of the different shapes of the corresponding spectral absorptivities (see Fig. 1). Due to multiple internal reflections, transparent polygonal objects typically demonstrate colors with piecewise variations in intensity and saturation. This phenomenon is clearly seen in both the truncated cube of red glass and the brilliant cut diamond of light blue glass in Fig. 5. The images in Fig. 6 are used to compare the results generated using the full spectral approach (left column) and the RGB-triplets approach (right column). The images in the top row are bottles of red wine and the bottom row is white wine. The spectral absorptivities for the red and white wines are given in Fig. 7. We can see that the results from the RGB-based approach significantly differ from those of the spectrum-based approach, especially for the white wine case. The unreliable three-point sampling of spectral absorptivities is the source of error in the RGB approach. For the white wine, the values of the spectral absorptivity at the red and blue sampling wavelengths (700.0 nm and nm) are much larger than the average in their corresponding color regions, resulting in over-absorption of the red and blue

4 components and thus making the wine appear green. This example demonstrates the inadequacy of an RGB-based approach for rendering volume absorption. Spectral absorptivity (1/m) red wine Fig. 7: Spectral absorptivities of red and white wines. 5 FUTURE DIRECTIONS AND CONCLUSIONS In realistic image synthesis there has been increasing interest in full spectrum rendering, driven by the goals of achieving better accuracy [6,12,13], handling fluorescent illumination [10,12,13], and rendering spectrum-sensitive phenomena such as light interference [5] and fluorescence and phosphorescence [4]. This paper shows that volume absorption is another important reason for adopting a spectrum-based approach. As future research, our work can be extended to render liquid solutions with varying concentrations according to Beer s law. This is especially interesting in situations where the solution concentration changes with height (due to gravity), resulting in gradually varying colors. Furthermore, we can combine volume absorption with particle scattering or light dispersion to generate comprehensive phenomena associated with transparent objects. In conclusion, we have modeled volume absorption for homogeneous transparent materials based on Bouguer- Lambertian law and rendered the associated phenomena using a spectrum-based ray tracer. The rendered images successfully demonstrate the interesting and detailed characteristics of the phenomena. This work can be used to enhance rendering of natural phenomena and thus improve the realism of computer generated imagery. ACKNOWLEDGEMENTS white wine Wavelength (nm) We would like to thank Thomas Calvert, Alain Fournier, and John Dill for useful discussions. This research was supported by research and equipment grants from Natural Sciences and Engineering Research Council (NSERC), Canada. Thanks also to the Graphics and Multimedia Research Lab and the School of Computing Science at Simon Fraser University. REFERENCE [1] J. F. Blinn, Light Reflection Functions for Simulation of Clouds and Dusty Surfaces, Computer Graphics, Proc. of ACM SIGGRAPH 82, 1982, [2] R. M. Evans, An Introduction to Color (New York: John Wiley & Sons, 1961). [3] J. D. Foley et al., Computer Graphics Principles and Practice (Reading MA: Assison-Wesley, 1996). [4] A. S. Glassner, A Model of Fluorescence and Phosphorescence, Proc. of the Fifth Eurographics Workshop on Rendering, 1994, [5] J. S. Gondek et al., Wavelength Dependent Reflection Functions, Computer Graphics, Proc. of ACM SIGGRAPH 94, 1994, [6] R. A. Hall and D. P. Greenberg, A Testbed for Realistic Image Synthesis, IEEE Computer Graphics & Appl., 3(6), 1983, [7] P. Hanrahan and W. Krueger, Reflection from Layered Surfaces due to Subsurface Scattering, Computer Graphics, Proc. of SIGGRAPH 93, 1993, [8] D. L. MacAdam, Color Measurement Theme and Variations (Berlin: Springer-Verlag, 1985), [9] T. Nishita et al., Display of Clouds Taking into Account Multiple Anisotropic Scattering and Sky Light, Computer Graphics, Proc. of ACM SIGGRAPH 96, 1996, [10] M. S. Peercy, Linear Color Representations in Full Spectral Rendering, Computer Graphics, Proc. of SIGGRAPH 93, 1993, [11] H. Rushmeier and K. Torrance, The Zonal Method for Calculating Light Intensities in the Presence of a Participating Medium, Computer Graphics, Proc. of ACM SIGGRAPH 87, 1987, [12] Y. Sun, M. S. Drew, and F. D. Fracchia, Representing spectral functions by a composite model of smooth and spiky components for efficient full-spectrum photorealism, IEEE Workshop on Photometric Modeling for Computer Vision and Graphics, 1999, [13] Y. Sun, F. D. Fracchia, and M. S. Drew, A Composite Model for Representing Spectral Functions, Simon Fraser University, Technical Report SFU CMPT TR , This report can be found at ftp://fas.sfu.ca/pub/cs/tr/1998/ CMPT ps.gz. [14] G. Wyszecki and W. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas (New York: Wiley, 1982).

5 Fig. 4: Continuous color variations generated by volume absorption. The objects in the two images are identical hexagonal pyramids, but the materials are red glass and light blue glass (see Fig. 1). The camera is directed toward the object from above and a white light source is located below the pyramid. White lights from the light source transmit through the object and become colored due to volume absorption. Fig. 5: A truncated cube of red glass (left) and a brilliant cut diamond of light blue glass (right) demonstrate colors with piecewise variations in both intensity and saturation due to the effect of volume absorption.

6 Fig. 6: Bottles of red (top row) and white (bottom row) wine rendered with the spectrum-based approach (left column) and the RGB-based approach (right column). The significant color differences demonstrate the inadequacy of the RGB-based approach for rendering volume absorption.

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