Water

Water, as stated above, is the most difficult natural object to handle. Not only does it move in extremely complex ways but it also refracts and reflects light both internally and externally.

Early Methods

The earliest attempts at rendering water all used bump mapping (Blinn^[6]), height maps created by the perturbation of flat surfaces (Schachter^[7]) and ray tracing (Newell^[8]). These early techniques all lacked two important abilities of water and more specifically, waves. They could not interact or cast shadows. Later, these techniques were enhanced by the introduction of particle systems (Reeves^[9]) and the development of algorithms to simulate the interaction between liquids and solids.

Recent Methods

The introduction of reflection, refraction and caustics algorithms in the early nineties finally completed the basis for rendering water. Recent works implement combinations of particles and textures in combination with fast solvers for the differential equations concerned with fluid motion. Also, Premoze et al.^[10] includes whitecaps that form on water where waves break.

Rain

The two main subsets of rain rendering methods are: Particle-based and Physically-based. The first lends higher frame rates whereas the second aims at the physical correctness thereof. Rousseau et al.^[11] introduces a method to realistically render rain in real-time. The shape of a raindrop (in polar coordinates) is given by:

r(θ) = a(1 + C₀cos(0θ) + … + C₁₀cos(10θ)X),

where Cx is the shape coefficient (which depends on the radius) for cosine distortion as obtained from Chaung et al.^[12] and θ is the polar elevation from the center of the drop. The speed of rain (which we have calculated by interpolating data from ^[12]) may be estimated rather accurately by:

s(r) = 0.35r³ - 3.2r² + 9.5r - 0.1,

where r is the radius of the drop and s is given in m/s. Rousseau also calculates the Fresnel factor to prove that only the outer-most 10% of a raindrop will show any reflections and their method therefore neglects the computation thereof except when near light sources. The drop is mapped with a texture that has been captured from the screen, flipped and distorted.

Clouds