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GPU PRO 3 by Wolfgang Engel

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3
II
Volumetric Real-Time Water and
Foam Rendering
Daniel Scherzer, Florian Bagar, and
Oliver Mattausch
3.1 Introduction
Over the last decade, simulation and rendering of complex natural phenomena
such as fire, smoke, clouds, and fluids have been an active and most diverse
research area in computer graphics. Among these phenomena, water may be
the most fascinating and challenging problem, due to the familiarity that even a
Figure 3.1. The proposed algorithm allows water to be rendered in many ways.
119
120 II Rendering
casual observer has with the phenomenon. Although the visual quality of water
rendering is continually improving, we are still a long way from capturing all the
physical properties of real water, like the forming of foam and droplets and their
interaction with the environment.
In this chapter we present a method for creating a fully dynamic multilayered
real-time water rendering approach. This approach can represent the volumetric
properties of water and the physical formation of volumetric foam, thereby creat-
ing much higher visual fidelity than previous real-time approaches. It is based on
a very fast particle-based fluid simulation that is fully hardware-accelerated using
Nvidia PhysX and rendering in OpenGL, and therefore easily runs at real-time
frame rates. The algorithm has a small memory footprint and is simple to imple-
ment and integrate into existing rendering engines. Additionally, our method is
highly configurable from an artistic point of view, and thus can produce a multi-
plicity of visual appearances to help to create the desired atmosphere for a scene
(see Figure 3.1).
3.2 Simulation
In order to render believable water, we first have to simulate its behavior. The
dynamics of water as an incompressible fluid can be described by a version of
the Navier–Stokes equations, which apply Newton’s second law (conservation of
momentum) and conservation of mass to fluid motion. These equations relate the
body forces (gravity) and the contact forces (pressure and stress) that act on a
fluid. This results in nonlinear partial differential equations that are very hard to
solve (assuming that an exact solution for a given case even exists). As we do not
need an exact solution, but are mainly concerned with speed, we are fine with an
approximate numerical solution. Approximations in this problem domain mainly
use Euler integration. (There are more accurate methods, such as Runge-Kutta
or midpoint, but these take more time to evaluate.)
3.2.1 Smoothed-Particle Hydrodynamics
Smoothed-particle hydrodynamics (SPH) is a robust and fast way for simulat-
ing the behavior of water [Desbrun and Gascuel 96]. The main idea here is to
approximate a fluid by a particle system (a division of the fluid into discrete
elements) to calculate its dynamic behavior. Each particle has a mass and ad-
ditional properties, such as position, density, velocity, and lifetime. In classic
particle systems, each particle is updated based only on its properties, disregard-
ing particle-particle interaction for the sake of speed. For the simulation of fluids
this will not suffice because of the contact forces. Each particle can potentially
affect all other particles, which results in a computational complexity in the order
of O(n
2
)—too slow for practical purposes if we use tens of thousands of particles.

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