Two-dimensional fire growth models such as FARSITE and Prometheus, the Canadian wildland fire growth model designed to work in Canadian fuel complexes, have been developed that apply such semi-empirical relationships and others regarding ground-to-crown transitions to calculate fire spread and other parameters along the surface. Certain assumptions must be made in models such as FARSITE and Prometheus to shape the fire growth. For example, Prometheus and FARSITE use the Huygens principle of wave propagation. A set of equations that can be used to propagate (shape and direction) a fire front using an elliptical shape was developed by Richards in 1990. Although more sophisticated applications use a three-dimensional numerical weather prediction system to provide inputs such as wind velocity to one of the fire growth models listed above, the input was passive and the feedback of the fire upon the atmospheric wind and humidity are not accounted for.