Bounding volumes for linearly interpolated shapes

Bounding volumes are crucial for culling in interactive graphics applications. For dynamic shapes, computing a bounding volume for each frame could be very expensive. We analyze the situation for a particular class of dynamic geometry, namely, shapes resulting from the linear interpolation of several base shapes. The space of weights for the linear combination can be decomposed into cells so that in each cell a particular vertex is maximal (resp. minimal) in a given direction. This cell decomposition of the weight space allows deriving bounding volumes from the weight vectors rather than the generated geometry. We present algorithms to generate the cell decomposition, to map from weights to cells, and to efficiently compute the necessary data structures. This approach to computing bounding volumes for dynamic shapes proves to be beneficial if the geometry representation is large compared to the number of base shapes.