Course detail

Geometrical Algorithms

FSI-0AVAcad. year: 2023/2024

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

Guarantor

doc. Mgr. Petr Vašík, Ph.D.

Department

Institute of Mathematics (ÚM)

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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

DORST, Leendert, D.H.F FONTIJNE a Stephen MANN. Geometric algebra for computer science: an object-oriented approach to geometry. Rev. ed. Burlington, Mass.: Morgan Kaufmann Publishers, c2007. Morgan Kaufmann series in computer graphics. ISBN 978-0-12-374942-0. (EN)
HILDENBRAND, Dietmar. Foundations of geometric algebra computing. Geometry and computing, 8. ISBN 3642317936. (EN)
HILDENBRAND, Dietmar. Introduction to geometric algebra computing. Boca Raton, 2018. ISBN 978-149-8748-384. (EN)
PERWASS, Christian. Geometric algebra with applications in engineering. Berlin: Springer, c2009. ISBN 354089067X. (EN)
MOTL, Luboš a Miloš ZAHRADNÍK. Pěstujeme lineární algebru. 3. vyd. Praha: Karolinum, 2002. ISBN 80-246-0421-3. (CS)
GONZÁLEZ CALVET, Ramon. Treatise of plane geometry through geometric algebra. 1. Cerdanyola del Vallés: [nakladatel není známý], 2007. TIMSAC. ISBN 978-84-611-9149-9. (EN)

Recommended reading

HILDENBRAND, Dietmar. Introduction to geometric algebra computing. Boca Raton, 2018. ISBN 978-149-8748-384. (EN)
MOTL, Luboš a Miloš ZAHRADNÍK. Pěstujeme lineární algebru. 3. vyd. Praha: Karolinum, 2002. ISBN 80-246-0421-3. (CS)

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. Mgr. Petr Vašík, Ph.D.

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.