Abstract:

A group of function containing three functions with parameter m is constructed. This group of function is linearly independent,which is named mB basis. The mB basis has nonnegativity, normalization, symmetry and special endpoint property. Based on the mB basis, a new kind of spline curve is defined, which is called mB curve. The mB curve segment can be converted into the form of Bézier curve. By virtue of the de Casteljau algorithm of Bézier curve, the recursive evaluation algorithm of the mB curve is given. The mB curve has the same endpoint behavior with the quadratic uniform B-spline curve, that is to say, the mB curve interpolates the midpoints of the first and the last sides of the control polygon, and tangent to the first and the last sides of the control polygon. Besides, the shape and continuity of the mB curve can be freely adjusted by the parameter m. And the adjustment can be either integral, or local. Using the tensor product method, the mB curve is extended to mB surface. The mB surface has similar properties with the mB curve.

Key words: B-spline curve;B-spline surface;shape parameter;continuity