The research team focuses on the development of new mathematical methods in geometric modelling, particulary in the description, data representation and modification of curves and surfaces with regard to their application in technical practice. The team is involved in the recognition of significant curves and surfaces given both exactly and approximately, and develops and implements algorithms based on a hybrid approach combining symbolic and numerical calculations, which are then used to solve current complex problems in geometric modelling.
As an innovative area of research and development with high application potential, the team addresses topics such as tool motion planning for CNC machining, shape optimization of hydraulic profiles in water turbines to enhance their performance, and symmetry recognition and reconstruction. Last but not least, the team is engaged in the modern field of approximate algebraic geometry, which involves the study of exact geometric operations on algebraic varieties with perturbed coefficients.