Course detail
Geometrical Algorithms
FSI-0AV Acad. year: 2023/2024 Summer semester
A survey on advanced structures om multi-linear algebra and, consequently, their application in Euclidean space transformation. Introduction to the theory of geometric algebras and algorithms for elementary tasks of analytic geometry. Simple geometric algorithms for the rigid body motion using Euclidean transformations.
Language of instruction
Czech
Number of ECTS credits
3
Supervisor
Department
Entry knowledge
Elementary notions of algebra and linear algebra.
Rules for evaluation and completion of the course
Graded assessment: semester project, oral exm.
Lectures, non-compulsory attendance.
Aims
Introduction of advanced mathematical structures and their applications in engineering.
Enhancement of skills that are necessary for applying advanced mathematical structures.
Type of course unit
Lecture
26 hours, optionally
Syllabus
1. Review: vector space, basis, dimension, scalar product, bilinear and quadratic forms.
2. Euclidean transformations of two and three dimensional space.
3. Inner and outer product, exterior algebra.
4. Clifford algebra.
5.-6. Introduction to geometric algebras, special cases of CRA (G3,1) and CGA (G4,1).
7.-8. Computation in geometric algebras.
9. Fundamental tasks of analytic geometry in geometric algebras.
10. Software for symbolic calculations and visualisation in geometric algebras (Python, CLUCalc).
11.-12. Euclidean transformations in geometric algebra, rigid body motion.
13. Consultations to semester project.