# Level Set Graphics

**Interactive modeling based on level set representations**

PhD student, Michael Bang Nielsen.

Level sets are dynamic implicit surfaces and were originally developed within the context of computational physics. However, in recent years, level sets have found great application in the area of computer graphics and related areas such as computer vision. This is mainly due to their ability to easily represent complex deforming surfaces and account for changes in topological properties. Typically level sets are sampled on a uniform grid and the propagation of the surface is described by a partial differential equation. Since the 2D dynamic implicit surface is represented on a 3D grid, strict limitations are imposed on the size of the 3D grid feasible in terms of memory requirements and computational resources. Existing narrow band methods account for the computational resource aspect by only solving for the level set propagation near the implicit surface as opposed to the entire 3D grid. However, the entire 3D grid is still represented in memory.

This project focuses on enhancing the practical feasibility of level sets with special attention to their application in geometrical modeling and rendering. Our work concentrates on developing sparse, adaptive representations and building novel geometrical modeling methodologies and tools.

**Texturing dynamic implicit models**

PhD student, Anders Brodersen

When working with polygon based models, a standard tool for adding extra details without increasing the number of polygons is texture mapping, where an image is *painted* on top of the polygons. One of the drawbacks of implicit models is that texturing an implicit model is not as straight forward as with polygons.

One advantage of implicit models on the other hand is that it is easy to alter the shape of the model. Because of this it is interesting to investigate the possibilities for using a texture to change the shape of the model in ways similar to bump/displacement mapping only taking advantage of the extra flexibility of the implicit model.

In this project we focus on developing novel algorithms for texturing dynamic implicit models and how this can be extended to enable arbitrary model deformations using *geometric textures*. Furthermore we will be looking for answers to the question of how the texture should be affected when the shape of the model changes, as is by no means obvious.