Methods for optimization of scene graphs must balance many competing demands. They must simultaneously optimize the attribute hierarchy, transformation hierarchy, and bounding volume hierarchy, all while maintaining enough functional structure to support animations (e.g., articulated figures). They may even consider a hierarchy of normals. The problem is that many logically independent hierarchies are folded into one.

Please address one or both of the following questions:

1. Describe a new representation in which many attributes (e.g., transformations, normals, bounding volumes, material properties) are hierarchical, but not folded all into one tree. How does a rendering engine traverse your new representation, evaluating the attributes at each node efficiently during traversal?
   
2. Describe a method to balance the competing demands of scene graph optimization. Can you think of an algorithm that simultaneously optimizes all attributes of a single scene graph all at once?

Please email me your one/two paragraph answer before class on Tuesday, February 17.