1. Animation and Rendering of Complex Water Surfaces Douglas Enright Stephen Marschner Ronald Fedkiw

2. Challenges of modeling water Water is common; we expect water to move in certain ways Water is common; we expect water to move in certain ways Water’s motion is complex and varies at different points on and under the surface Water’s motion is complex and varies at different points on and under the surface

3. Previous works [Foster and Fedkiw 2001] used a volumetric model of water [Foster and Fedkiw 2001] used a volumetric model of water Declared that particles couldn’t make a desirable enough surface for liquids Declared that particles couldn’t make a desirable enough surface for liquids Derived an implicit surface from the velocity of the particles Derived an implicit surface from the velocity of the particles

4. Theory A) Shape to be modeled A) Shape to be modeled B) Implicit Surface model B) Implicit Surface model C) [Foster and Fedkiw 2001] model (particles inside only) C) [Foster and Fedkiw 2001] model (particles inside only) D) New method D) New method

5. Theory Two sets of particles (“water” and “air”) placed in the surface region Two sets of particles (“water” and “air”) placed in the surface region No need to have particles far from the surface No need to have particles far from the surface Particles have different radius, between.1min and.5min Particles have different radius, between.1min and.5min

6. Execution Two surfaces derived, an implicit function and a particle-based system Two surfaces derived, an implicit function and a particle-based system An error check is made to look for disagreements An error check is made to look for disagreements Implicit function repaired using the system of particles Implicit function repaired using the system of particles Every few frames, more particles should be added to assure the system has enough to handle an increase in surface area Every few frames, more particles should be added to assure the system has enough to handle an increase in surface area

7. Extrapolation Method Take the equation on the right, Take the equation on the right, t is fictitious time t is fictitious time N is the normal to the implicit surface N is the normal to the implicit surface V is the velocity of the particle V is the velocity of the particle u is the velocity of the surface u is the velocity of the surface

8. The ugly part This equation is used to handle momentum This equation is used to handle momentum v represents the viscosity v represents the viscosity p is the density p is the density p is the pressure p is the pressure g is gravity g is gravity