A Method for Local Interpolation with Tension Trigonometric Spline Curves and Surfaces

In this work a family of tension trigonometric curves analogous to those of cubic Bézier curves is presented. Some properties of the proposed curves are discussed. We propose an efficient interpolating method based on the tension trigonometric splines with various properties, such as partition of unity, geometric invariance and convex hull property, etc. This new interpolating method is applied to construct curves and surfaces. Moreover, one can adjust the shape of the constructed curves and surfaces locally by changing the tension parameter, the latter is included mainly because of its importance for object visualization. To illustrate the performance and the practical value of this model as well as its accuracy and efficiency, we present some modeling examples. Mathematics Subject Classification: 65T40, 65D05, 65D17, 76B45.