(Created 2009-08-11.)
 GEOMETRY FMA135

Higher education credits: 6. Grading scale: TH. Level: G1 (First level). Language of instruction: The course might be given in English. Optional for: C4, D4, D4bg, E3, E3bg, F1, Pi1. Course coordinator: Director of Studies, Lars-Christer Böiers, Lars_Christer.Boiers@math.lth.se, Matematik. Recommended prerequisits: Linear algebra and derivatives from one variable calculus. Assessment: Written "take home" exam on each of the two parts of the course. Oral exam. Computer assignments. Further information: The course might be given in English. Home page: http://www.maths.lth.se/matematiklth/vitahyllan/vitahyllan.html.

Aim
The aim of the course is to introduce geometrical concepts of importance in modern engineering applications, e.g. computer aided design (CAD), computer aided manufacturing (CAM), computer graphics and computer vision, and to give examples of their use. A subgoal is to study how geometrical objects can be described numerically in a neat way.

Knowledge and understanding
For a passing grade the student must

be able to explain the basic parts of the theory in an oral examination.

exhibit understanding of different algorithms in computer geometry.

show knowledge of and understanding of the properties of different concepts in projective geometry, and be aware of how they appear in applications.

Skills and abilities
For a passing grade the student must

be able to integrate methods and views from different parts of the course to solve problems and answer questions within the framework of the course.

be able to write Matlab programs to solve mathematical problems within the course.

be able to explain the solution to a mathematical problem within the course, in writing and orally, with clear logic and using proper terminology.

Contents

• Curves and surfaces. Some fundamental differential geometry. Bezier curves. Interpolation.

• Projective geometry. Perspective.

Literature
Ufnarovski, V. Geometri. Mat.inst.
Holmstedt, T. Föreläsningar i projektiv geometri. Mat. inst.