SIGGRAPH 2005 신 승 호 신 승 호

Water Drops on Surfaces Huamin Wang Peter J. Mucha Greg Turk Georgia Institute of Technology

Introduction  Small-scale liquid motions such as water drops, Surface tension effect become too strong.  The core algorithm is a virtual surface method.  Fluid solver represents and updates the liquid surface using the particle level set method.

Algorithm Overview  Euler method to solve for viscous momentum diffusion.  External forces such as gravity update the velocity field.  Semi-Lagrangian method to calculate the velocity advection.  Projection step solves a Poisson equation to make the velocity field divergent free.  We complete the signed distance function by the fast marching algorithm.

Physical Background  Pressure difference across the surface.  Surface tension dependent with mean curvature k.  Three different interface Liquid-air, Liquid-solid, solid-air.  : Stable contact angle.  : Interfacial tension coefficients. (1) (2)

Virtual Surface : curved contact line between solid surface and liquid surface : solid surface normal : liquid surface normal

Dynamic Contact Angle Model  Using two stable contact angles : receding (minimum) stable contact angle : advancing (maximum) stable contact angle  Wettable solid surfaces : wetted advancing contact angle

Applications and Results Shape of Drops with different stable contact angles

Shell Maps Serban D. Porumbescu Brian Budge Louis Feng Kenneth I. Joy Institute for Data Analysis and Visualization Computer Science Department University of California, Davis

Introduction  Shell map is a bijective(one-to-one) mapping between shell space and texture space.  Shell maps allow considerable flexibility object.  Texture space can contain geometric objects, procedural volume textures, scalar fields, or others.

Offset Surface Generation  Shell space is the region between a base surface and an offset surface to the base.  S and So must have the same number of triangles and the same mesh connectivity.  So should have no self intersections and should not intersect S.

Prisms and Tetrahedra Construction  Prisms in shell space correspond to prisms in texture space.  Prisms are split into three tetrahedra.

Modeling and Rendering with Shell Maps  Geometry textures can be rendered using ray-tracing.  Rays intersect tetrahedra in shell space (a).  Points marched in shell space are transformed to texture space for density calculations. This method effectively traces curved rays through texture space (b).

Results  Increase in geometric distortion as the offset height.  Green base surface pinches back on itself and the resulting blue offset surface is restricted in height.

Results  weave texture  Star pattern