. "23520" . "This habilitation thesis is devoted to selected rational techniques which are used in geometric modelling and also in other related CAx applications. Nowadays, this topic is very popular and one can find several journal papers, conference contributions and books devoted to this research area. Our study was motivated by the fact that most of geometrical operations used in Computer Aided Geometric Design do not preserve rationality of derived objects in general. A distinguished feature of our approach was an often usage of symbolic computations which has helped us to find several new results. Due to space limitations, we select only a few topics with particular emphasis on practical applications -- namely we present the geometric operation of convolution and its properties, offsetting and shapes with rational offsets, representation of geometric objects using MAT/MST and its application on trimming of offsets, and finally RCL parameterizations as a new class of rational curves and surfaces."@en . "228667" . . "L\u00E1vi\u010Dka, Miroslav" . . . . . . . "This habilitation thesis is devoted to selected rational techniques which are used in geometric modelling and also in other related CAx applications. Nowadays, this topic is very popular and one can find several journal papers, conference contributions and books devoted to this research area. Our study was motivated by the fact that most of geometrical operations used in Computer Aided Geometric Design do not preserve rationality of derived objects in general. A distinguished feature of our approach was an often usage of symbolic computations which has helped us to find several new results. Due to space limitations, we select only a few topics with particular emphasis on practical applications -- namely we present the geometric operation of convolution and its properties, offsetting and shapes with rational offsets, representation of geometric objects using MAT/MST and its application on trimming of offsets, and finally RCL parameterizations as a new class of rational curves and surfaces." . "Selected rational techniques for geometric modelling and related applications" . "Selected rational techniques for geometric modelling and related applications" . "Selected rational techniques for geometric modelling and related applications"@en . . "Selected rational techniques for geometric modelling and related applications"@en . . "Z(MSM4977751301)" . "1"^^ . . . . . "[E9F4A58F8E72]" . "1"^^ . . "RIV/49777513:23520/11:43899236!RIV12-MSM-23520___" . . . "RIV/49777513:23520/11:43899236" . . . . . "Rational convolutions, rational offsets, PH curves, PN surfaces, quadratic B\u00E9zier triangles, support function representation, medial axis/surface transform, trimmed offsets, RCL parameterizations"@en . .