Abstract:

Based on the space {1,t,sint,cost,sin2t}, we propose a class of quasi-algebraic trigonometric Hermite parametric spline curves. The curves  have the properties of the standard cubic parametric Hermite curves, and with proper conditions they can be used to represent some engineering curves exactly, such as circle, ellipse and parabola etc. What's more, the shape of the curves can be modified by changing the value of shape parameters while the interpolation condition remains  unchanged. In order to obtain optimal parameters, a mathematical model based on the fairing criterion is established, and the shape parameters solved by this model can make the curves satisfy C1 or C2 continuous as required. Examples show that the shape parameters solved by the model can guarantee good smoothness of the curves.