Need of NURBS:

Some cause for the widespread acceptance and popularity of NURBS in the CAD/CAM and graphics community are as:

• They offer a common mathematical for designing and representing both standard analytic shapes (conics, quadrics surfaces of revolution etc.) and free-form curves and surfaces. Thus, both analytic and free-form shapes are represented precisely and a unified database may store both.
• Manipulating the control points as well as the weights, NURBS provide the flexibility to design a large variety of shapes.
• Evaluation is reasonably fast & computationally stable.
• NURBS have apparent geometric interpretations, making them specifically useful for designers, who contain a very good knowledge of geometry -especially descriptive geometry.
• NURBS have a powerful geometric tool kit (knot insertion/refinement/ removal, splitting, degree elevation, etc.), which may be utilized throughout to design, analyze, process, and interrogate objects.
• NURBS are invariant under scaling, rotation, translation, and shear as well as parallel and perspective projection.
• NURBS are genuine generalizations of non-rational B-spline forms as well as rational and non-rational Bezier curves and surfaces.