Monotonic curvature plays an important role in industrial design and styling of curves with aesthetic shapes, e.g., in automobile and aircraft design [1].Used in conventional parametric CAD/CAM systems, general B-splines are not adequate for aesthetic requirements.Except for the straight line and circle, monotonic curvature distribution, associated with pleasing shape, is very difficult to achieve.So Farin suggested that a fair curve has a curvature plot with relatively few regions of monotonically varying curvature.Starting from this basis, work on B-spline fairing was developed mainly in three direction: knot-removal-reinsertion methods, optimization methods based on minimizing an energy function, and filtering approaches based on B-spline wavelets.Visual curve completion (interpolating a curve segment, with continuity, to fill a gap) is a fundamental problem for human visual understanding [2].Aesthetically pleasingly shaped curves usually have monotonically varying curvature [3].While the shape of a curve is primarily defined by its curvature distribution, monotonicity of curvature is not easily achieved and controlled.To overcome this problem,