Final Project
Group Members
Nicolas Benitez
Michael Graeb
Goal
The goal of our project was to render a convincing image of the sky. More specifically, we were interested in modeling the sky such that the result:
1) Had convincing coloration
2) Provided appropriate lighting for the other elements in the scene
3) Contained realistic clouds
The image that we used as a reference to try to create these effects was the following image of the New York city skyline, taken from http://wwp.new-york-usa.com/:
Sky Simulation
Nico was responsible for simulating the color and exitant luminance of the sky. To do so, he implemented a new type of light source as a pbrt plugin. We made several attempts at modeling the sky before settling on the current system.
The first version of our sky model was based on A Practical Analytic Model for Daylight by Preetham et al. In the paper, Preetham describes a method for rendering skies based on Perez's phenomenological model for sky color. Perez defines a function based on five parameters that determine the shape and intensity of the sky gradient. Preetham used data from an intricate simulation of the sky and attempted to fit the five parameters to this data.
We implemented this model, but found the results to be insufficient for our purposes. The main problem that we encountered with this model was that it was very difficult to "tweak" the colorization of the sky, since it depended only on solar angle and a variable called "turbidity," which is similar to visibility. In order to better capture the color of the original image, we decided to attempt a more phisically-based model.
The model that we ended up using was mainly inspired by two papers: Modeling and Rendering of the Atmosphere Using Mie-Scattering by D. Jackel and B. Walter, and Display Method of the Sky Color Taking into Account Multiple Scattering, by T. Nishita.
According to both papers, the spectral properties of the atmosphere are well-described by Mie Theory, which uses Maxwell's equations to describe the interaction of light with spherical particles. Mie's general theory is very complicated and computationally intense. However, for small particles, Mie scattering reduces to an approximation called Rayleigh scattering, which explains phenomena such as the blue appearance of the daytime sky and red sunsets.
To try to make our system as flexible as possible, we modeled the sky as a set of an arbitrary number of different types of particles. This idea is similar to Walter's model, which used a set of concentric spheres to define areas of different optical properties. Each type of particle may define its own phase function, scattering coefficient, extinction coefficient (which is the same as the scattering coefficient for most atmospheric particles), and density distribution. Our final model used two types of particles: small particles, which we approximated using rayleigh scattering, and larger particles such as aerosols and soot, which we modeled with a highly forward-scattering phase function that was not very wavelength-dependant. Both types of particles fall off exponentially in density as a function of height.
To actually render the scene, we approximated the sun as a directional light with paralell rays. We computed the radiance coming from they sky along a ray in a way similar to the single-scattering volume integrator provided by pbrt (this method is described roughly the same in both papers as well). We took a fixed number of samples along the ray starting at the viewer and moving towards the outer edge of the atmosphere. At each step, we multiplied the radiance of the sun by the product of the phase function and scattering coefficient (together called the volume phase function). The result was then multiplied by the optical depth to the viewer and the optical depth to the sun from the current position along the ray. Because we did not implement multiple scattering, we had to multiply our optical depths by a correction factor so that the sky did not appear too dark.
References
Jörg Haber, Marcus Magnor, Hans-Peter Seidel. "Physically based Simulation of Twilight Phenomena". http://www.mpi-inf.mpg.de/departments/irg3/dtd/.