Advanced Modeling

Nowadays (triangle) meshes are by far the most commonly used representation for modeling geometric objects in computer graphics. However, in many situations meshes are not well suited. For instance the creation of convincing models for fluids, smoke, fire, organic structures, repetitive structures, etc., is very tedious and sometimes impossible using meshes. There are several reasons why meshes are not well suited for these tasks: Fuzzy object boundaries: Many real world phenomena do not have clearly defined object boundaries. Therefore it is impossible to model them with a surface representation approach (like meshes). The modeling of these phenomena requires volumetric representation approaches. Large deformations of the surface: Modeling of objects that deform over time (such as wave fronts in a wave propagation simulation) are very hard to model using meshes. These objects are often modeled and rendered more conveniently using particle or grid based methods. Changing topology: Meshes have only limited use for models that change their topology over time (i.e., holes are introduced or removed, they split and merge, etc.). Meshes are mainly not very well suited for this situations because they are tedious to model and many algorithms on meshes were developed assuming that the topology is constant. In some situations (often in combination with physical simulations) topology changes are better handled with alternative modeling techniques. High geometric complexity: Certain phenomena exhibit huge geometric complexity. Although it is possible to model them with meshes, it is often more convenient to model them with an alternative method. In many