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Dynamic tools in mathematical education

Theory of free-form curves constitutes an important theoretical part of the geometric core of computer graphics and computer aided geometric modeling and design. Engineering students often deal with these structures and their practical applications in different fields of technical sciences without full and proper understanding of all basic concepts. Several examples of demonstration applets are presented for illustration of basic properties of three types of free-form curves and their rational equivalents, which are most frequently appearing in menus of commonly available CAGD systems used in mechanical engineering practice, as Ferguson-Overhauser curve, Bézier cubic and Coons B-spline cubic. These instructional materials were produced in the dynamic mathematical software GeoGebra, and they are available as self-standing web-based dynamic applications for free usage in several on-line databases of e-learning materials.