Geometric models based on trajectories of Bézier rational curves

The result is a product - geometric models and their graphic primitives based on Bézier's rational curves trajectories. The models include the analytical representation of the curves through their parametric equations. After algorithmization, a prototype of a geometric modeling graphic system will be developed, allowing for demonstrations applicable in different industrial areas. Plug-ins will also be developed, applicable in computer design systems and module which allow the new models to be used in 3D printer management. The need for an infinite variety of smooth curves and surfaces will be satisfied, and the result is not visually but analytically controlled. Target areas are robotics, computer graphics, automotive, ship and aircraft engineering, design and construction, bioinformatics, medicine, etc. Direct users are designers, as well as autonomously operating automated systems in the industry. The aim is to develop geometric models that are novel and which as Béziers' standard curves are a basic tool in design. Two fixed points and a number of control points are used in the standard Bézier curves. By manipulating the control points, a smooth enough curve is produced for a particular application. The models proposed in the project cover mainly practical situations in which the peaks of the base figure remain fixed. In this case, we get a family of smooth curves or surfaces, which we call Beziers trajectories that fill the inside of this figure. The project includes the realization of an entrepreneurial idea on the market, which includes the employment of professional researchers and researchers in geometry and topology and experienced professionals in the field of process automation. Minimum technical equipment will be purchased for the team work as well as external services authorized for this program will be used for a better startup

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