1. Modeling Complex Shapes in 3D Cindy Grimm cmg@cs.wustl.edu Zachary Byers Zcb1@cec.wustl.edu

2. Geometric Shapes are Easy • Defining the location of a regular geometric shape in 3D space is relatively trivial. There are known functions that define these shapes.

3. Non-Geometric Shapes are Hard • Imagine a function that describes this shape in 3D.

4. Complex Shapes are Currently Modeled Volumetrically • Modeling complex shapes, such as the heart in the previous slide, are often done using a volume of data, such as ultrasound, MRI, or CAT scan data. • The data makes a good picture, but has no embedded information about the actual shape it represents.

5. Another Approach: Manifolds • A mathematical technique for describing complicated surfaces by overlapping bits of simple surfaces. • Imagine an atlas. Each page of the atlas describes part of the surface of the earth, and each page overlaps other pages enough that you can easily traverse from one page to the next.

6. Examples • Get images from cindy.

7. Where this is going. • With volumetric rendering of complex shapes, there is no clean way to map a function to the shape. • When the shape you have is describe only by points in space, not in terms of surface, how do you apply a texture to the shape?

8. Everything is Easier in 2D. • Vectors representing flow of air applied to a 2D image.

9. What about 3D? • Suppose you have the model of an aorta and blood flow information. It would be nice to render the flow information on the surface of the aorta. • Manifolds make it as simple as 2D. The surface of the aorta is broken up into smaller pieces of overlapping surface, each smaller piece can have the vectors representing blood flow mapped onto it.