Elliptical Arcs In Quartic Rational Bezier Form And An Approximation By Quartic Bezier Curves

The elliptical curves play a very important role in Computer Aided Geometric Design and Computer Graphics. This paper discusses elliptical arcs in quartic rational Bezier form and an approximation of elliptical arcs by quartic Bezier curves.In the first chapter, we introduce the research background and content about the Computer Aided Geometric Design, the research current situation of the elliptical arcs and each chapter arrangements.In the second chapter, we give the definition and properties of the Bezier curve and Non-uniform rational Bezier curve, especially the four Bezier curve and quartic rational Bezier curve.In the third chapter, we are given on the x and y axis of symmetry of ellipse arc in quartic rational Bezier form, and give specific expression of the control points and weights, which have a good geometrical meaning.In the fourth chapter, using transform in the three-dimensional space about circular arc in quartic rational Bezier form we get general elliptical arcs in quartic rational Bezier form.In the fifth chapter, according to the methods which we have introduced in the third and fourth chapter, we carry on the MATLAB experiment.In the sixth chapter, we use an approximation method for elliptic arcs by quartic Bezier curves. Firstly, based on the symmetry of elliptic arcs and Bezier curves, the control points with unknown parameters are determined. Then according to the distribution of the error function’s roots, the parameters of control point are further determined. Finally our method has better approximation accuracy.