Abstract:
Among the different bases which can be used in the representation of spline functions, the one consisting of the so-called B-spline functions is, due to its unique properties, of particular importance. In 1946, Schoenberg introduced the B-spline functions, but neither their computational power nor their geometric flexibility were fully appreciated at the time. They were only recognized later, with the emergence of stable algorithms for their calculation and with the systematic use of computers.
After intensive development and study, these functions became an indispensable tool in graphical computation, computer aided design, as well as in geometric modelling and in many other areas, and can presently be found in all recognized modelling software.
The main purpose of this dissertation is the study of the B-spline functions and their properties. Special emphasis will be given to those properties that are more relevant for their applications in computer aided design.
Another objective of this dissertation is to briefly describe the functional characteristics of the software program "DesignMentor". This freeware program was developed with the aim of helping the teaching and learning of concepts, properties and algorithms associated with the B-spline functions.