In the course students will get introduced to the mathematical contents which are the basis for solving problems in the field of animation and computer graphics. The emphasis is on the connection of practical contents and concepts students are dealing with in other courses within this master programme with the mathematical formulation of those concepts.

Acquisition of complete knowledge about problems, tools and methods within engineering graphics and animation; understanding theoretical – mathematical basis in this field and the practical use.

Linear transformations of vector spaces. Change of base. Algebraic and geometric interpretation in the plane and the space. Affine and perspective geometry. Homogenous coordinates. Translation. Projection. Orthogonal matrices. Euler angles. Quaternions. Curves in the plane. Conic sections. Curves in the space. Displaying and generating surfaces. Rotational and other surfaces. Mapping of the surface. Main topological properties of 2D and 3D objects. Polynomial curve interpolation. Hermite curves, Bezier curves, Bernstein base. Splines. Surface interpolation.

Lectures and auditory practice. Parts of the practice can be organized in the computer laboratory. Consultations.