A simple technique for surface modeling

Abstract

Traditionally, a single unique curve or surface is generated by an algorithm for each set of control points, with Bezier and B-spline being two of the famous techniques used. -- Recently, there has been increasing interest in the generation of many different curves or surfaces by a single technique for a set of control points. The Beta2-spline technique is a recent example of this idea. It uses a parameter called β₂ to act as a pulling agent, or tension, on the B-spline curve or surface. However, the curves or surfaces lose their smooth appearance as they are pulled closer to the set of control points. This could be an undesirable feature when smooth interpolation of the control points is desired. -- The Bezier technique has been one of the most famous techniques in the computer aided design industry. It is capable of representing most of the geometric entities of practical interest. However, it has a shortcoming: the Bezier curve or surface bears little resemblance to the shape of the control polygon or the net respectively. -- This paper proposes a simple technique which serves to overcome the two disadvantages mentioned above. The proposed technique employs a parameter called ℸ, to act as a pulling agent on the Bezier curve or surface. The pulled curves or surfaces have better mimicking properties than that of the Bezier. They always have a smooth appearance, even when interpolating the set of control points.