Surface Construction Based on Quadrilateral Mesh

In this paper, a method of constructing smooth surface based on quadrilateral mesh by using C-curves is presented. Instead of using the conventional basis {t³, t², t, 1}, C-curves are developed by using the basis {sint, cost, t, 1}. Compared with the traditional cubic curves, C-curves can represent transcendental curves exactly such as the helix and the cycloid. Due to many other merits of C-curves, how to develop C-curves into surface becomes a very important problem. By extending the idea of side-vertex method proposed by Nielson, a method for constructing C¹ quadrilateral patches using C-curves is developed. The constructed patches interpolate the positions and the first derivatives of the boundary composite C-curves. Then a smooth surface is consequently derived by simply concatenating those patches.