Caustics and Water Simulation
Donna Calhoun and Lillie Kittredge
CSE 557, Winter 2004
Intro
We simulated the movement of water and used photon mapping to simulate caustics as would be seen in such a simulation. Both of these goals are for the purpose of creating more realistic animation.Process
Our project had two parts:- simulating movement of water
- rendering caustics via photon mapping
Water simulation
![[animated gif of raytraced water simulation]](shortmovie.gif)
Above is an animated gif of the water simulation in action. The charming fellow floating on the pond is our character from the animation project, Mr. Duck. The pond surface is floating in space so that the caustics in the photon-mapped images wouldn't be blocked by tank walls. The unfortunate coloring of the surface is explained below.
The water simulation implements the algorithm from O'Brien and
Hodgins, 1995. The main element of the water simulation is a
collection of virtual vertical columns of water (see diagram), each of
which keeps track of its current volume. There are virtual pipes
between neighboring columns which allow water to flow from one to the
other, dependant on the flow in that pipe at the last time step, and
the difference between the pressures of the two columns. Pressure on
a column is a function of its height, the density of the fluid, the
force of gravity, and also of the force being exerted on the surface
of the water by external objects and forces. In order to keep track
of these forces, the surface of the water is kept as an array of
control points, which are implemented as particles from our animator project's
particle system. These control points are then interpreted as the
vertices of a triangle mesh. Unfortunately, the mesh lacks information
about normals at the vertices, and so the surface has not been
rendered using the phong interpolation that would have made it appear
smoother.
Making the simulation work required adding a damping factor to the flow integration. We also diverged from O'Brien & Hodgins' algorithm in a few places for the sake of speed. We kept only one copy of each virtual pipe, rather than a copy for each volume to which that pipe is incident. A quirk of the simulation algorithm is that the volumes of the columns run the risk of going negative. In order to correct this problem, O'Brien & Hodgins scaled back the size of all the pipes taking volume away from the unfortunate column and reran the flow integration step. We simplified this process by just stealing the missing volume equally from the surrounding columns.
Caustics
The process of rendering the caustics is described here.Results
Though we had hoped to create an animation which demonstrated the water flowing and the caustics produced by the water changing along with it, time constraints unfortunately prevented us from doing so. In leiu of the whole animation, the following should give you an idea of what the animation would have looked like:
![[image of the duck rendered with photons]](photonduck.jpg)
![[image of the duck's photon map] align=center>
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<h4>References</h4>
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<li><a href=](photonduck_ph.jpg)
O'Brien, J. F., Hodgins, J. K., 1995. Dynamic Simulation of Splashing
Fluids. Proceedings of Computer Animation `95, Geneva Switzerland, April
19-21, pp 198-205.