LS(2)-Equivalence conditions of control points and application to planar Bezier curves

Abstract

Having an important role in CAD and CAM systems the Bezier and B- spline curves and surfaces and NURBS modelling are based on control points belongs to these curves and surfaces. So the invariants of these curves and surfaces are the invariants of the control points of these curves and surfaces. In this study we studied the equivalence conditions of compared two different control point systems under the linear similarity transformations LS(2) in R2 according to the invariant system of these control points. Finally the equivalence conditions of two planar Bezier curves is examined.