Geometry and Topology of the Minkowski Product

The Minkowski product can be viewed as a higher dimensional version of interval arithmetic. We discuss a collection of geometric constructions based on the Minkowski product and on one of its natural generalizations, the quaternion action. We also will present some topological facts about these products, and discuss the applications of these constructions to computer aided geometric design

Comments on event driven animation

Event driven animation provides a general method of describing controlling values for various computer animation techniques. A definition and comments are provided on genralizing motion description with events. Additional comments are also provided about the implementation of twixt

A Control Cluster Approach to Non-linear Deformation

Modeling plausible deformation of the objects has been an important task in computer animation and game design industry. The approach proposed in the paper deals with a polygonal mesh deformation splitting the vertices of the mesh into two types: cluster vertices and free vertices. With the user defining the shape of the mesh key areas with the help of cluster vertices, the algorithm takes advantage of non-linear geometric deformation for calculating free vertices position. The approach could be used both for creating a sequence of altered model shapes to produce a character animation (with the help of user-created control cluster data) and for visualizing some ecological processes

System Identification for Nonlinear Control Using Neural Networks

An approach to incorporating artificial neural networks in nonlinear, adaptive control systems is described. The controller contains three principal elements: a nonlinear inverse dynamic control law whose coefficients depend on a comprehensive model of the plant, a neural network that models system dynamics, and a state estimator whose outputs drive the control law and train the neural network. Attention is focused on the system identification task, which combines an extended Kalman filter with generalized spline function approximation. Continual learning is possible during normal operation, without taking the system off line for specialized training. Nonlinear inverse dynamic control requires smooth derivatives as well as function estimates, imposing stringent goals on the approximating technique

Protein Nano-Object Integrator: Generating Atomic-Style Objects for Use in Molecular Biophysics

As researchers obtain access to greater and greater amounts of computational power, focus has shifted towards modeling macroscopic objects while still maintaining atomic-level details. The Protein Nano-Object Integrator (ProNOI) presented here has been designed to provide a streamlined solution for creating and designing macro-scale objects with atomic-level details to be used in molecular simulations and tools. To accomplish this, two different interfaces were developed: a Protein Data Bank (PDB), PDB-focused interface for generating regularly-shaped three-dimensional atomic objects and a 2D image-based interface for tracing images with irregularly shaped objects and then extracting three-dimensional models from these images. Each interface is dependent upon the C++ backend utility for generating the objects and ensures that the output is consistent across each program. The objects are exported in a standard PDB format which allows for the visualization and manipulation of the objects via standard tools available in Molecular Computational Biophysics

Designing Smooth Motions of Rigid Objects: Computing Curves in Lie Groups

Consider the problem of designing the path of a camera in 3D. As we may identify each camera position with a member of the Euclidean motions, SE(3), the problem may be recast mathematically as constructing interpolating curves on the (non-Euclidean) space SE(3). There exist many ways to formulate this problem, and indeed many solutions. In this thesis we shall examine solutions based on simple geometric constructions, with the goal of discovering well behaved and computable solutions. In affine spaces there exist elegant solutions to the problem of curve design, which are collectively known as the techniques of Computer Aided Geometric Design (CAGD). The approach of this thesis will be the generalization of these methods and an examination of computation on matrix Lie groups. In particular, the Lie groups SO(3) and SE(3) will be examined in some detail