Interval analysis, computer graphics algorithms and social networks

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Interval analysis uses real compact intervals for algorithm development as opposed to real numbers. This enables the inclusion of both computational and experimental error in the computations and to develop algorithms that deliver guaranteed result within intervals. In this area it is proposed to continue the work on devising efficient methods for the range of functions using interval analysis techniques. The result of this investigation will be applied to the interval Newton method, the interval generalization of Newton's method in numerical analysis for the solution of non-linear equations. It is also proposed to investigate the degree elevation and reduction of interval Bezier curves and surfaces. These curves and surfaces are interval generalizations of the commonly used Bezier curves and surfaces in computer graphics. They based on the interval Bernstein polynomials first investigated by the PI. When Bernstein polynomials are degree elevated and reduced the error committed in the computations means that the polynomial degree is no longer correct. In computer graphics, it is proposed to continue the work on rendering efficiency in particular on GPU's. A sophisticated indexing scheme will be considered that avoid superfluous computations. In computational geometry, the work on efficient intersections for 3D solids will be continued. This work is of importance for several areas which involve geometric computations such as for example computer graphics, GIS and solid modeling, This work used techniques from interval analysis combined with exact computation tools. Applied problems in social networks will be considered as they pertain to local industry needs. In particular the work with a local company on a scheme for charitable donations has been successful. Support for this project was provided by MITACS and will be applied for from MITACS for the next phase. A local company that is a world class leader in crowdsourcing is developing an expanded system for which they need expert advise and implementation assistance. An application by the PI and a colleague for MITACS support is currently being considered.