Representation of Curves and Surfaces

This is a course about convenient ways to mathematically define curves and surfaces in practical design, imaging, and fitting tasks. Starting from the classical interpolation of points we proceed to more flexible Bézier splines, non-uniform rational B-splines (NURBS) together with some generalizations of them. Approximation properties of these will be shown and their numerical algorithms will be studied together with modern computer software. Also the use of splines in finite element analysis of partial differential equations will be touched.

The course will consist of preparatory self-study material, two weeks of lectures and hands-on type exercises in computer class, visit to a company and visitor demonstrations from industry. All material will be delivered free of charge. Social activities will also be organized.

Basic knowledge of differential calculus of several variables is a prerequisite for the course. The course is suitable for students of technology, design, and natural sciences who will encounter tasks of fitting and drawing of curves and surfaces and modeling phenomena on them. The target audience is mainly students in master's programs, but in many areas also BSc and PhD students could be considered.

The course is organized by:
Department of Mathematics and Systems Analysis, Aalto University and Finnish Society for Computational Sciences

Please direct any questions concerning the content of this course to the coordinator, Antti Niemi, antti.h.niemi(at)aalto.fi. Any questions on the general arrangements (accommodation, scholarship, etc.) should be addressed to the Summer School's office at summer-school@helsinki.fi.