Abstract: This paper provides a different solution to represent basic smooth elements like
triangular and quadrilateral surface patches from mesh using C-B spline curves. C-B spline curves
are developed by the basis {sin t, cos t, t, 1}, and it overcomes some shortcomings of the B-spline
and non-uniform rational B-splines (NURBS) model, for example, they have to increase
unnecessary control point in order to satisfy the data grid topology, their derivative and integral
are complex and tedious, their degrees are too high, and it is difficult to discuss their continuous
conditions. How to develop C-B spline curves into surface becomes an important problem. In this
paper, the interpolation operators are constructed by using side-vertex method and a convex
combination of these operators is achieved. The C-B spline curves are developed into triangular
and quadrilateral surface patches which can be used in reverse engineering of CAD.

Key words: triangular surface, quadrilateral surface, C-B spline, side-vertex method