Several reduced deformation models in computer animation, such as linear blend skinning, point-based animation, embedding in finite element meshes, cage-based deformation, or subdivision surfaces, define surface vertex positions through convex combination of a rather small set of linear transformations. In this paper, we present an algorithm for computing tight normal bounds for a surface patch with an arbitrary number of triangles, with a cost linear in the number of governor linear transformations. This algorithm for normal bound computation constitutes the key element of the Bounded Normal Tree (BN-Tree), a novel culling data structure for hierarchical self-collision detection. In situations with sparse self-contact, normal-based culling can be performed with a small output-sensitive cost, regardless of the number of triangles in the surface.

@InProceedings\{SGO09,
  author       = "Schvartzman, Sara C. and Gascón, Jorge and Otaduy, Miguel A.",
  title        = "Bounded Normal Trees for Reduced Deformations of Triangulated Surfaces",
  booktitle    = "Proc. of the ACM SIGGRAPH / Eurographics Symposium on Computer Animation",
  year         = "2009",
  url          = "http://gmrv.es/Publications/2009/SGO09"
}