This special issue
includes a selection of papers from SCCG 2004 conference chaired by Prof.
Alexander Pasko (
There are two
competitions organized during the conference – SCCG Best Papers and SCCG Best
Presentations. They are based on evaluation by reviewers and public voting of
SCCG participants. Awarding of winners is a part of closing ceremony and the
diplomas with logos of sponsors are available at www.sccg.sk,
as well. As proposed
by Alexander Pasko and accepted by the editor-in-chief, Prof. Victor V. Pilyugin,
the winning papers are published in special issue of CGG, a prominent online
journal at http://elibrary.ru/cgg. The papers are
slightly extended and rewritten, based on SCCG discussions and inspirations.
After completing the selection, one can see that the unifying idea of all
five papers awarded can be formulated as discovering the tricky solutions
between speeding-up (modeling) and rendering quality criteria.
William Van Haevre et al. dealt with ray
density estimation for plant growth simulation. In particular, they evaluated
the varying indoor environment illumination while growing the plants using
intensity-modified rules for L-systems. The novel approach results in a
flexible and accurate algorithm to achieve more realistic vegetation. The
paper won the 3rd Best Presentation Award.
Mario Sormann et al. focused on a
solution of a complex task – creating models from image sequences as fast and
as good as possible. VR modeler is a novel interactive monocular 3D modeling
system with nicely separated intelligent 2D interaction and 3D
reconstruction. Besides that, the coarse and detailed precision of urban
models is supported for web presentation and other purposes. The results
already contributed to Virtual Heart of Central
Europe (www.vhce.info) which is a recent
European cultural heritage project.
The paper won the 3rd Best Paper Award.
Rui Rodrigues and Antonio Ramires Fernandes
report on prospective use of graphics cards. A significant part of 3D
reconstruction, especially epipolar
geometry computations, can be transferred into the GPU. This new idea offers
a remarkable gain up to two orders of magnitude in terms of computational
times. The paper won the 2nd Best Presentation Award.
Ivan Viola et al.
explored frequency domain volume rendering (FVR) because of computational
speed. Moving significant parts of computations to GPU, they report
acceleration by factor of 17. This allows for highly interactive framerates with varying
rendering quality. The quality depends on interpolation schemes. The authors
analyzed four of them to clarify the trade-off between performance and
quality. The paper won the 2nd Best Paper Award.
Last but not
least, Diego Gutierrez et al. contributed by a SIGGRAPH quality paper on
global illumination for inhomogeneous media. In total, there are 10 different
light-object interactions known and we simplify the model to achieve faster
solutions. The authors noticed that light rays travel a curved path while
going through inhomogeneous media where the index of
refraction is not constant. In addition, they took into account the way how
human perception deals with luminances.
In total, the phenomena like sunset, green flash, and bleaching are mastered to complete an
excellent research and a brilliant presentation. This is why only five papers
are here – Diego clearly won in both competitions.
For conclusion, I
have to recall the following. In 2003, one year ago, this message from
Alexander Pasko arrived
“Dear participants and
organizers of SCCG, your conference provides unique opportunity for young
researchers to make their efforts visible in the world, especially for those
who are not hypnotized by the visual quality of modern computer graphics
works in modeling, rendering, and animation. We all know that such a work
still requires tedious manual labor hampered by errorneous models and algorithms. Let us hope that
the next spiral of development will make our work in computer graphics more
close to a joyful mind game.”
I have to thank again to Alexander and to all people who contributed to SCCG 2004 in the spirit of these beautiful and clever words.
University of Zaragoza, Zaragoza, Spain
Francisco J. Seron,
University of Zaragoza, Zaragoza, Spain
University of Zaragoza, Zaragoza, Spain
University of Zaragoza, Zaragoza, Spain
Key words: Rendering, global illumination, photon mapping, natural phenomena, inhomogeneous media, realism
1. Light in the atmosphereSeveral of the atmospheric effects we see in nature, from mirages to the green flash, are owed to light traveling curved paths [Minnaert 1993], and therefore are impossible or exceedingly costly to simulate with synthetic imagery using standard Monte Carlo ray tracing techniques. Nevertheless, modeling of nature has been one of the most ambitious goals of the Computer Graphics community.
2. Previous worksThere are several examples that simulate the behavior of light in the atmosphere, such as the works of Musgrave  or Nishita . There is also some previous work on curved ray tracing in inhomogeneous media. Berger and Trout  recreate mirages by subdividing the medium into various homogeneous layers, with a different index of refraction for each one. Musgrave  proposes a purely reflective model as the means of forming mirages, while Groeller  uses sources of nonlinearity such as gravity centers, gravity lines, chaotic systems and parametric curved rays. Stam and Languenou  propose a solution by obtaining the differential equation that describes the trajectory of the ray from the equation of the light wave. Finally, Serón et al.  describe a more general method, free of the restrictions that appear in the above papers regarding the dependences of the index of refraction, and propose a partial solution to the problem using the general equation, based on Fermat’s principle, that describes the phenomenon. None of these works, though, can successfully follow the complete light paths: from the lights through inhomogeneous media to interaction with geometry, through inhomogeneous media again before finally reaching the eye. The basic problem of following all these paths is explained in the next section.
3. Curved photon mappingTraditionally, light travelling trough inhomogeneous media has been simulated by using ray tracing techniques [Glassner 1989]. Basically, in backward ray tracing, a ray is shot from the eye into the scene until it reaches an object, and from that intersection point more rays are shot towards the lights to find the color of the corresponding pixel.
3.1. Trajectory of the photonsThe main forte of Lucifer is its capability of providing a full global illumination solution in inhomogeneous media, by accurately curving both photons and eye rays as they travel through the medium. As a starting point to obtain this curved trajectory of the photons, we take Fermat’s principle [Glassner 1995], which can be formulated as “light, in going between two points, traverses the route l having the smallest optical path length L”. The optical path L is defined as the index of refraction times the traveled path. In its differential form, it can be written as dL=ndl. According to Fermat’s principle, the optical path along a light ray trajectory must be a minimum, therefore =0, where is given by:
where xi are the components of l. Given that , considering dxi as variables and taking increments we get so that equation 3.1 results:
Since the different considered trajectories start in the fixed points A and B, and , so equation 3.2 results as follows:
This equation must be true for any value of ,
which lets us come up with the equation to obtain the trajectory of a
light ray in an inhomogeneous medium with a known index of refraction,
where l is the length of the arc, n is the index of refraction of the medium and
with (j=1,2,3) are the coordinates of the point. If the index of
refraction is known for every point of the medium, we first calculate
that index and the slope of the curve at step i, advance
along the direction of the tangent to reach step i+1, and calculate the
new index of refraction and tangent again. To calculate the direction
of the tangent we first obtain a numerical approximation by
discretizing the equation, effectively replacing differentials by
increments. We then apply the Richardson’s extrapolation algorithm to
select an optimal integration step for each instant, given an estimate
of the tolerable error. The process ends when we get to the
intersection point of the photon with an object, and gets started again
if the Russian Roulette algorithm does not absorb the photon at the
Figure 3.1: Test scene for the curved photon mapping algorithm. Left: resulting illumination. Right: the curved photon map used
4. Atmosphere profile managerAs we have said, the atmosphere is an inhomogeneous medium with changing parameters, like temperature or pressure. This is what causes some of its optical effects, such as mirages or the green flash, and it is also the reason why they can be seen only under certain, very specific conditions. In order to simulate some of these phenomena, we then need to have a model of the atmosphere that is versatile enough to be adapted specifically for a desired effect.
is the density we want to obtain, T is the temperature, P is the
pressure, M is the mean mass of the molecules of a mixed atmosphere (
28.96e-3 kg/mol typically) and R is the gas constant, 8.314510 J/mol·K.
a and b are constants which depend on the medium. In case of air a =
28.79e-5 and b = 5.67e-5. The Sellmeier’s approximation could also be
used instead [Born and Wolf 2002].
the steps which have lead to equation 4.3 have been based so far on the
USA Standard Atmosphere, which does not provide the special atmospheric
conditions under which some phenomena can be seen. Any desired
condition, though, can be reproduced if instead of taking the initial
pressure and temperature values from the USA Standard Atmosphere we use
the specific pressure and temperature conditions that lead to the
phenomenon we want to reproduce, which can usually be found in the
where x is the distance in the direction parallel to the Earth’s surface, is the height of the inversion layer about which the added temperature profile is centered, is the temperature jump across the inversion and the diffuseness parameter a(x) determines the width of the jump.
5. Validation of the methodTo validate our approach this far we have designed several scenes, aimed at mimicking some well-known or spectacular atmospheric effects, the green flash amongst them. Photons were not used in these images to light the scene. They were designed mainly to test both our method of resolution of the curved trajectories and our atmosphere profile manager. We used simple geometry combined with textures taken from real pictures, but the sizes of the objects (sun, Earth…) and the atmosphere data are taken from the real world, in order not to fake the effect. We consider the properties of the atmosphere to be independent of x, since the changes in that coordinate are usually small and can be neglected. Considering a gradient also in that direction would enable us to simulate some other phenomena, like the Novaya Zemlya effect [van der Werf et al. 2003].
5.1. MiragesThere are two types of mirages: inferior and superior. The inferior mirage occurs when there is a decrease of temperature with increasing height. As a consequence, the rays approaching the ground are curved upwards, generating an inverted image of the object in the ground. Since the mirage image appears under the location of the real object, the effect is known as inferior mirage. This can typically happen when an asphalt road has been overheated by the sun rays. The ground heated by an intense solar radiation causes a pronounced heating of the air layers near the ground. As a consequence of that temperature gradient, the index of refraction increases with height and the rays become curved towards the region in which the index of refraction is greater. Figure 5.1 shows an inferior mirage on the road near the horizon. This has been obtained by making the index of refraction in a particular portion of the road lower than the rest, an effect caused by a local heating of the air above the road.
Figure 5.1: Inferior mirage on the road.Superior mirages occur when the temperature increases as the height increases, which causes the light rays to be bent downwards. The image appears above the position of the real object, therefore the effect is known as superior mirage. These type of mirages happen usually at sea, when the water is colder than the air above it.
5.2. Sunset effectsOther interesting refraction phenomena occur during sunsets. The flattened sun is probably the most common one, and happens when the atmosphere has an index of refraction that decreases with height. It is so common because usually the density of the air decreases as one moves away from the Earth, and so the index of refraction decreases as well. As a result of this, the sun is not seen as a perfect circle, but appears rather flattened along the vertical axis. The rays become curved downwards, towards the areas with a greater index of refraction, causing the distortion of the sun. Moreover, the sun appears to be higher than it really is.
Figure 5.2: Simulated sunset effects and their real counterparts (flattened sun, split sun and double sun).
6. The green flashSo far, dispersion has not been taken into account for the mirages and sunsets simulations, since its effect in the phenomena is negligible. However, every refraction phenomenon includes a certain degree of dispersion, and some atmospheric refraction phenomena provoke a greater dispersion of light, and the green flash is arguably the most spectacular of them all. As our first step towards a complete simulation of the effect, we are going to reproduce the so-called standard green flash, an effect that occurs even in a Standard Atmosphere, taking refraction as a function of wavelength.
6.1. The human visual system: S·E·K·E·RTo correctly display the images calculated in Lucifer, we then feed them into S·E·K·E·R. This standalone application runs a tone reproduction algorithm that maps images from real, calculated luminances to final display luminances, while simulating several mechanisms of the human visual system.
6.2. BleachingWhat makes the green flash specially interesting, from a Computer Graphics point of view, is the fact that not only is the effect caused by the wavelength dependency of the index of refraction (as opposed to the mirages and sunsets presented before), but it is magnified by the human visual system as well, through a process known as bleaching. This means that, in order to simulate it properly, we need both a correct global illumination algorithm for inhomogeneous media (validated in Section 4), and a model of the human observer that takes bleaching into account.
The effective pupil area for estimating retinal luminance is less than
the actual pupil area because the relative contribution of light to the
sensation of brightness decreases as the light enters the pupil at
increasing distance from the center of the pupil. This is called the
Stiles-Crawford effect [Smith 1988]. It is a phenomenon of cone (or
photopic) vision and does not occur for rod (or scotopic) vision. It is
thought to be due to cone geometry. The ratio between effective and
actual pupil area is called the effectivity ratio, a quantity that
varies with pupil diameter and takes into account the Stiles-Crawford
effect. The effective pupil area is thus the actual pupil area times
this ratio R, expressed in the eq. 6.2.
d is pupil diameter in mm. Estimated retinal luminance I (eq. 6.1,
expressed in trolands), taking R, the pupil area and the scene
luminance L into account, is:
obtained I plus the half bleaching constant, the following equation may
be used to approximate the effect of bleaching in the stationary state
p is the percentage of unbleached pigment; I is the intensity of
bleaching light, in trolands; I0 is the half bleaching constant , also
Figure 6.2: relation between perception threshold and bleached pigment (after [webvision.med.utah.edu])
Figure 6.3: Left: Close up of the green flash with the bleaching algorithm applied. Right: Green pixels enhanced by bleaching
7. ResultsOur approach to obtain a full global illumination solution in inhomogeneous media is based on exploiting the independency in the photon map algorithm between light propagation (photon casting and tracing, first pass) and visibility determination (ray tracing, second pass). This idea is implemented by the curved photon-mapping algorithm. It works the same way than the standard photon-mapping algorithm, but it can handle inhomogeneous media as well by using Fermat’s principle and solving equation 3.4 to obtain curved paths.
8. Future workThe results obtained so far show the viability of the approach. As the system gets refined over time, we nevertheless plan to generate better images that mimic some more complex natural phenomena, such as ducting or the Novaya Zemlya effect [van der Werf et al. 2003].
Figure 8.1: A picture of the green flash
AcknowledgementsThis research was partly done under the sponsorship of the Spanish Ministry of Education and Research through the projects TIC-2000-0426-P4-02 and TIC-2001-2392-C03-02.
ARVO , J.. 1986. Backward ray tracing, in Developments in ray tracing, ACM SIGGRAPH ’86 Seminar Notes, volume 12.
BERGER, M. and TROUT , T. 1990. Ray tracing mirages, IEEE Computer Graphics and Applications, 11(5), may 1990, 36-41.
BORN, M. and WOLF, E. Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Cambridge University Press, ISBN 0-521-642221, 2002.
BRUTON, D. 1996 Optical determination of atmospheric temperature profiles, submitted to the Office of Graduate Studies of Texas A&M University, 1996.
BURDEN, R. L. and DOUGLAS FAIRES J. 1995. Numerical Analysis PWS, Boston, USA.
CORNSWEET, T.N. 1970. Visual Perception. New York. Academic Press.
HARWERT, R.S. and SPERLING, H.B. 1971. Prolonged color blindness induced by intense spectral light in reshus monkeys. Science, 174, 520-523.
HARWERT, R.S. and SPERLING, H.B. 1975. Effects of intense visible radiation on the increment threshold spectral sensitivity of the rhesus monkey eye. Vision Research, 15, 1193-1204.HUNT, R.W.G. 1995 The reproduction of colour, Chapter 31. Fountain Press, England.
JENSEN, H. W. 2001. Realistic image synthesis using photon mapping, AK Peters, ISBN 1-56881-147-0.
LAFORTUNE , E. P. and WILLEMS, Y. D. 1993. Bidirectional path tracing. In Compugraphics ’93, 95-104.
GEISLER, W.S. 1978. The effects of photopigment depletion on brightness and threshold. Vision Res., 18, 269-278.
GEISLER, W.S. 1979. Evidence for the equivalent background hypothesis in cones. Vision Res., 19, 799-805.
GLASSNER, A. S. 1989. An introduction to ray tracing, Academic Press Inc.
GLASSNER, S. A. 1995. Principles of digital image synthesis. Morgan Kauffman Publishers, Inc. ISBN 1-55860-276-3.
GROELLER, E. 1995. Nonlinear ray tracing: visualizing strange worlds, Visual Computer 11(5), Springer Verlag, 1995, 263-274
MINNAERT, M.G.J. 1993. Light and color in the outdoors, Springer-Verlag 1993.
MUSGRAVE, F. K. 1990. A note on ray tracing mirages, IEEE Computer Graphics and Applications, 10(6), 1990, 10-12.
MUSGRAVE , F. K. 1993. Methods for realistic landscape rendering, PhD. Thesis, Yale University.
NISHITA ,T. 1998. Light scattering models for the realistic rendering of natural scenes, Proceedings of rendering Techniques ’98, 1-10.
PATTANAIK, S.N., TUMBLIN, J., YEE, H. and GREENBERG, D.P. 2000. Time-dependent visual adaptation for fast realistic image display. In ACM Proceedings 2000. ACM Press, 2000.
PREETHAM, A.J. 2003 Modeling Skylight and Aerial Perspective. ATI Research, ACM SIGGRAPH 2003
RUSHTON, W.A.H. 1963. The density of chlorolabale in the foveal cones of a protanope. Journal of Physiology’63, 168, 360-373.
RUSHTON, W.A.H. 1965. Cone pigment kinetics in the deuteranope. Journal of Physiology’65, London, 176, 38-45.
RUSHTON, W.A.H. 1972. Pigments and signals in colour vision. In Journal of Physiology‘72, London, 220, 1-21P.
RUSHTON , W.A.H. and HENRY, G.H.. 1968. Bleaching and regeneration of cone pigments in man. Vision Research 8, 617-631.
SERÓN, F.J., GUTIÉRREZ, D., GUTIÉRREZ, G. and CEREZO, E. 2002. An implementation of a curved ray tracer for inhomogeneous atmospheres. In ACM Transactions on Graphics, 2002.
SMITH,V.C., POKORNY, J. and DIDDIE, K.R. 1988. Color matching and the Stiles-Crawford effect in observers with early age-related macular changes. Journal of the Optical Society of America A, Volume 5, Issue 12, 2113-December 1988.
SPERLING, H.G. 1986. Intense spectral light induced cone specific lesions of the retina and the effects of anesthesia. In Hazards of Light eds. Cronly-Dillon, J.R. et al., pp. 153-167. Oxford: Pergamon.
STAM , J. and LANGUENOU, E. 1996. Ray tracing in non-constant media. In Proceedings of Rendering Techniques ’96, 225-234
VAN DER WERF, S. Y., GÜNTHER, G. P. and LEHN, W. H. 2003. Novaya Zemlya effects and sunsets. Applied Optics, Vol. 42, No. 3, 20-1-2003
VEACH , E. and GUIBAS, L. 1994. Bidirectional estimators for light transport. In Fifth Eurographics Workshop on Rendering, 1994, 147-162.
WALRAVEN, J. 1981. Perceived colour under conditions of chromatic adaptation: evidence for gain control by mechanisms. Vision Res., 21, 611-630.
WARD, G., RUSHMEIER, H. and PIATKO, C. 1997. A visibility matching tone reproduction operator for high dynamic range scenes. IEEE Transactions on Visualization and Computer Graphics, 3(4), pp. 291-306. October-November 1997
WYSZECKI, G. and STILES, W.S. 1982. Color Science: Concepts and Methods, Quantitative Data and Formulae. John Wiley and Sons, 2 edition.
YOUNG, A.T. 2000. Visualizing sunsets III. Visual adaptation and green flashes, Journal of the Optical Society of America A, vol. 17, pp. 2129-2139. December