Mathematical Methods   Chair: Michael Gleischer , University of Wisconsin   Decremental Delaunay Triangulation   New results on removing points from a Delaunay triangulation and computing decremental Delaunay triangulation.   Richard Hammersley Schlumberger 8311 North RR 620 Austin, Texas 78726 USA hammersley@austin.apc.slb.com   Enhancing the Efficiency and Versatility of Directly Manipulated Free-Form Deformation   Exploitation of matrix sparsity and intuitive manipulation of first- derivative properties to enhance speed and versatility in directly manipulated FFD.   James Gain University of Cambridge Computer Laboratory New Museums Site Pembroke Street Cambridge CB2 3QG UNITED KINGDOM jeg24@cl.cam.ac.uk   Multi-Dimensional Quaternion Interpolation   In this search for a multi-variate version of Shoemake's famous "slerp" function, two methods (using RBFs) have been implemented to continuously interpolate between several kinematic animation examples that differ along emotional input axes, such as happiness and fatigue. The extrinsic version was incorporated in the Swamped! interactive exhibit at SIGGRAPH 98, and the intrinsic version is used in the Millennium Motel (SIGGRAPH 99).   Michael Patrick Johnson Massachusetts Institute of Technology 20 Ames Street, E15-320G Cambridge, Massachusetts 02139 USA aries@media.mit.edu   Fast Polygon Mesh Querying by Example   An efficient method for comparing a low-resolution polygon mesh query model to a database of complex models using voxelisation and wavelet decomposition.   James Gain University of Cambridge Computer Laboratory New Museums Site Pembroke Street Cambridge CB2 3QG UNITED KINGDOM jeg24@cl.cam.ac.uk