Geometric algebra

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course will explain 3D graphics and 3D kinematics using the modern formalism of geometric algebra.

Requirements:

Syllabus of lectures:

1. Linear spaces and bilinear forms.

2. Orthogonality w.r.t. a bilinear form. Symplectic and quadratic geometry. Orthogonal group.

3. Classical vector model of geometric algebra.

4. Clifford algebra, inner and outer products.

5. Generalised inner and outer products; their geometric meaning.

6. Transformations as elements of geometric algebra, outermorphisms.

7. Versors, rotors and spinors.

8. Basic linear transformatins in 3D.

9. Projective model of geometric algebra.

10. Computations in projective model.

11. Geometry of Minkowski's spacetime, conformal and affine splits.

12. Conformal model of geometric algebra.

13. Computations in conformal model.

Syllabus of tutorials:

Study Objective:

Study materials:

[1] Leo Dorst, Daniel Fontijne, Stephen Mann, Geometric algebra for Computer science, Elsevier, 2007.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: