Rational Ruled surfaces construction by interpolating dual unit vectors representing lines

Abstract

In this paper, a new representational model is introduced for the rational family of ruled surfaces in Computer Graphics. The surface parameterization is constructed using the NURBS basis functions and line geometry. The ruled surface is defined by interpolating directly dual unit vectors representing lines, which is a single parametric surface and its shape depends on the control lines. All the advantages of the NURBS basis such as shape control and the local modification property are also applicable and bequeathed to the dual NURBS ruled surface. The problem of drawing the lines defined by dual unit vectors is also resolved. Towards this direction, we propose a simple technique to calculate the surface’s striction curve in order to draw the rulings of the surface within the striction curve neighborhood. The on-screen 3D plot of the surface is realized in a pre-defined specific region close to the striction curve. With the proposed technique a natural representation of the ruled surface is derived. The shape of the surface can be intrinsically manipulated via the control lines that possess one more degree of freedom than the control points. Our method can find application not only in CAD but in the areas of NC milling and EDM.