Research On Weighted Algebraic Hyperbolic B-Spline Curves

The thesis is composed of five chapters.In the first chapter, the author briefly introduces the background and the main content of this thesis. The second chapter focuses on the B-spline curve’s definition and properties. The third chapter introduces a class of Algebra Hyperbolic Spline Curve. At first, the author introduces the definition and properties of Algebra Hyperbolic basis function with multiple shape parameters. And then, Algebra Hyperbolic Spline Curve’definition and properties are introduced, the shape of such curves can be adjusted totally or locally by changing the values of the shape parameters.In the fourth chapter, a class of blending spline curves unified by algebraic and hyperbolic polynomial using weight method is presented in this paper, named weighted algebraic hyperbolic B-spline curves. The blending spline curve can include cubic B-spline curve as special case and reach the both sides of cubic B-spline curve. Not only can the shape of the curve be adjusted totally or locally, but also the type of some segments of a blending curve can be switched by taking different values of the weight parameters. Without solving system of equations and etting weight parameters be-(e-1)2-4+4e-2e2, the curve can interpolate certain control points directly. With the weight parameter and the positions of the control points chosen properly, the defined curves can be used to precisely represent some conies and transcendental curves.In the end, the author summarizes full text, innovations and theories, actual meaning, and prospects the research work of aftertime.