Representation of Curves and Surfaces

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This intensive course is an introduction to the mathematics of geometric modelling. The aim is to provide students with an understanding of and ability to use computer-aided techniques for the representation of geometric objects.

These geometric objects are defined in terms of basic graphical primitives, including points, lines, curves and surfaces. A mathematical representation is needed of each primitive for us to be able to store and manipulate them by computer.

The course is intended for students of technology, design or natural sciences who will encounter design and modelling tasks in association with curves and surfaces. If you’re interested in computer graphics applications, such as computer-aided design (CAD) and computer-aided manufacturing (CAM), and have a basic knowledge of differential calculus of several variables and of linear algebra, this course will help you further.

Representation of Curves and Surfaces is mainly targeted at students in Master's programmes, but BSc and PhD students can also be considered. Industry professionals who want to revisit the theory of curves and surfaces and wish to learn of the latest academic insights may also find the course particularly useful.

The course starts from the most fundamental geometric objects of points and lines, proceeding to more flexible Bézier curves and non-uniform rational B-splines (NURBS). Their basic properties as well as the related numerical algorithms will be examined with modern computer software. The course will also address the use of splines in numerical analysis of partial differential equations.

The course consists of preparatory self-study material, two weeks of lectures and hands-on exercises in computer class. A company visit and/or an industry visitor demonstration will be arranged. All materials will be delivered free of charge.

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(at)helsinki.fi.