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.

References

Jörg Haber, Marcus Magnor, Hans-Peter Seidel. "Physically based Simulation of Twilight Phenomena". http://www.mpi-inf.mpg.de/departments/irg3/dtd/.