Abstract: A class of exponential uniform B-spline curves and surfaces with multiple shape
parameters is provided. They preserve the main properties of the exponential uniform B-spline
curves and surfaces, such as positive property, convexity-preserving property and so on. The
curves can be adjusted by changing the values of shape parameters without moving their control
points. So we can realize the entire or local adjustment of the curves. What’s more, the
exponential uniform B-spline curves can represent hyperbola, catenary and other transcendental
curves precisely. The corresponding surfaces can be constructed by using tensor product, so their
properties are similar to that of the curves. Plenty of numerical tests are given to show the
effectiveness of our method.

Key words: uniform B-spline, Blending function, exponential polynomial, shape parameters