Cubic Trigonometric Polynomial Curves And Surfaces With Multi-shape Parameters

In Computer Aided Geometry Design, most of the curves are generated by the polynomials, but they have some defects, such as they can't express the circle and ellipse accurately. Trigonometric functions have many advantages in expressing quadratic curves, for instance, conic curves. Many scholars begin to construct basic functions by trigonometric polynomials functions. On this basis, this thesis focuses on the construction of cubic trigonometric polynomial curves and surfaces with shape parameter.In this thesis, the first chapter introduces the development of curve and surface modeling and present researching situation of trigonometric polynomial splines.In chapter 2, for one thing, a class of trigonometric spline curves on four-point piecewise scheme presented by Han xuli are recommended; for another thing, the author presents a similar class of trigonometric curves with a shape parameter. In chapter 3, we introduce cubic trigonometric polynomial curves with a shape parameter presented by Han xuli. In addition, trigonometric polynomial uniform B-splines with a shape parameter are described. Finally, the author presents an extension of trigonometric polynomial curves by using the concept of weights. In chapter 4, the author presents cubic trigonometric polynomial spline curves with multi-shape parameters. In chapter 5, firstly, we introduce bicubic trigonometric polynomial Coons pacth with shape parameters; secondly, we construct bicubic trigonometric polynomial surfaces with multi-shape parameters; finally, the author fits some space surfaces by using bicubic trigonometric polynomial spline surfaces.