doc. Mgr. Jaroslav Hrdina, Ph.D.
E-mail:   hrdina@fme.vutbr.cz  WWW:   http://www.zam.fme.vutbr.cz/~hrdina/ Dept.:   Institute of Mathematics Dept. of Algebra and Discrete Mathematics Position:   Head of Department Room:   A1/1822 Dept.:   Institute of Mathematics Dept. of Algebra and Discrete Mathematics Position:   Associate Professor Room:   A1/1822

Supervised courses:

• Algebraic Theory of Control (VTR)
• Algebraic Theory of Control (VTR-A)
• Algebraic Theory of Control (VTR-K)
• Fundamentals of Linear Algebra (TLA)
• Geometric Control Theory (9GTR)
• Introduction to Game Theory (0TH)
• Introduction to Game Theory (0TH-A)
• Linear Algebra II (SLB)
• Mathematics for Applications (9MPA)

Publications:

• HRDINA, J.; VAŠÍK, P.; NÁVRAT, A.; HILDENBRAND, D.:
  Local Controllability of Snake Robots Based on CRA, Theory and Practice, SPRINGER BASEL AG
  journal article in Web of Science
• HRDINA, J.; NÁVRAT, A.; VAŠÍK, P.:
  Conic Fitting in Geometric Algebra Setting, Birkhauser Verlag AG
  journal article in Web of Science
• HRDINA, J.; VAŠÍK, P.; NÁVRAT, A.:
  GAC Application to Corner Detection Based on Eccentricity,
  Advances in Computer Graphics, pp.564-570, ISBN 978-3-030-22513-1, (2019), Springer Nature Switzerland AG 2019
  conference paper
  akce: Computer Graphics International, Calgary, 17.06.2019-20.06.2019
• HRDINA, J.; NÁVRAT, A.; VAŠÍK, P.:
  CRA-based robotic snake control,
  Introduction to Geometric Algebra Computing, pp.141-154, ISBN 9781498748384, (2018), Chapman and Hall/CRC
  book chapter
• HRDINA, J.; NÁVRAT, A.:
  Binocular Computer Vision Based on Conformal Geometric Algebra, Springer Basel AG
  journal article in Web of Science
• HRDINA, J.; VAŠÍK, P.; NÁVRAT, A.:
  Control of 3-Link Robotic Snake Based on Conformal Geometric Algebra, Springer Basel AG
  journal article in Web of Science
• HOLUB, M.; HRDINA, J.; VAŠÍK, P.; VETIŠKA, J.:
  Three-axes error modeling based on second order dual numbers, Springer-Verlag
  journal article in Web of Science

List of publications at Portal BUT

Abstracts of most important papers:

• HRDINA, J.; VAŠÍK, P.; MATOUŠEK, R.; NÁVRAT, A.:
  Geometric algebras for uniform colour spaces, John Wiley & Sons, Ltd
  journal article in Web of Science
  We show the advantages and disadvantages of specific geometric algebras and propose practical implementations in colorimetry. The colour space CIEL∗a∗b∗ is endowed by an Euclidean metric; the neighbourhood of a point is therefore a sphere, and the choice of a conformal geometric algebra is thus obvious. For the colour space CMC(l:c), the neighbourhood is an ellipsoid and thus we choose the quadric geometric algebra to linearize the metric by means of the scalar product. We discuss the distance problems in colour spaces with these particular geometric algebras applied.
• HRDINA, J.; NÁVRAT, A.:
  Binocular Computer Vision Based on Conformal Geometric Algebra, Springer Basel AG
  journal article in Web of Science
  We apply the conformal geometric algebra (CGA) to the generalized binocular vision problem. More precisely, we reconstruct a 3D line from its images on the image planes of two cameras whose mutual position is specified by a given Euclidean transformation which depends on an arbitrary number of parameters. We represent all transformations by CGA elements which allows us to derive the general equations of 3D line reconstruction by formal CGA elements manipulation. The transformation equations can be solved w.r.t. either motor or projection unknown parameters. We present two specific examples, show the explicit form of two particular motors and solve the appropriate equations completely.
• HOLUB, M.; HRDINA, J.; VAŠÍK, P.; VETIŠKA, J.:
  Three-axes error modeling based on second order dual numbers, Springer-Verlag
  journal article in Web of Science
  The aim of the paper is to employ the dual numbers in the multi axes machine error modelling in order to apply the algebraic methods in computations. The calculus of higher order dual numbers allows us to calculate with the appropriate geometric parametrization effectively. We test the model on the phantom data based on the real machine tool. The results of our analysis are used for the geometric manufacturing accuracy description of the work space, together with the reduction of the measuring time.
• HRDINA, J.; VAŠÍK, P.:
  Dual Numbers Approach in Multiaxis Machines Error Modeling, Hindawi
  journal article in Web of Science
  Multiaxis machines error modeling is set in the context of modern differential geometry and linear algebra. We apply special classes of matrices over dual numbers and propose a generalization of such concept by means of general Weil algebras. We show that the classification of the geometric errors follows directly from the algebraic properties of the matrices over dual numbers and thus the calculus over the dual numbers is the proper tool for the methodology of multiaxis machines error modeling.