Professor Colm Mulcahy

Department of  Mathematics - Spelman College

Wavelets - a new tool for imaging, graphics and Hollywood
Friday, March 19, 1999, 7:00 - 8:00, Room E104 of Moench Hall.

Abstract: Wavelets are a relatively recent arrival on the scene, and have already found numerous applications both within mathematics and in digital imaging, computer graphics, animation, video and audio.  The new generation of digital feature films emerging from Hollywood are also poised to use these techniques.

Wavelets provide an alternative to classical Fourier methods for one- and multi-dimensional data analysis and synthesis, and are better suited to data which lack periodicity or contain sudden changes.

This talk will introduce the basics of wavelets via a popular application to compression of images, data and audio.  Prerequisites will be kept to a minimum: anybody who can add, subtract and divide by two should feel quite at home.

The curves and surfaces of the digital age
Saturday, March 20, 1999,  9:30-10:30 Room E104 of Moench Hall.

Abstract: Curves and surfaces are all around us in this digital age.  Computer graphics, video and film (both animated and traditional), computer-aided geometric design, signal and image processing, font design, cartography, meteorology, and data visualization are some of the areas which rely heavily on these geometric objects.

      We'll show how to combine simple ideas from linear algebra and multivariable calculus to explore a wide class of interesting curves and surfaces, using basic polynomial and piecewise-polynomial methods.  A frequent goal is data fitting, whether exact (interpolation) or approximate (Bezier or least squares methods), and a popular approach is to use splines.  Computer algebra systems such as Maple can be used to take the drudgery out of the algebraic manipulations and provide immediate visual access to the shapes which result.