Research On A Number Of Triangular Bézier Curves And Surfaces With Parameters

This 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 deals with a class of 3-degree continuous trigonometric curves with the shape parameter,the curve that interpolates start point and end point is analogous to Bézier curve,the larger isλ,the curve comes more near the control polygon,the elliptic and parabolic arcs can be represented exactly by the curve.Based on the blending functions,a method of generating C~2 3-degree continuous trigonometric curves with the shape parameter is obtained,the segmented curves are all shape-preserving to the given polygon,the results have definite geometric meanings,but when each curve have same parameter,the curve are C~2continuous.The third chapter proposes an explicit formula that a rational triangular Bézier patch of degree n converts to a degenerate rational rectangular Bézier patch of degree n×n by homogeneous coordinates,which is an extension of a triangular Bézier patch of degree n converts to a degenerate rectangular Bézier patch of degree n×n.Comparing with the traditional triangular Bézier patch of degree n converts to degenerate rectangular Bézier patch of degree n×n,by changing the value of power factor,the approaching degree of control nets can be adjusted.,thus increased the surface degree of freedom.It enable to have a better flexibility to its surface shape control.The fourth chapter by introducing a number of shape parameters constructed on the domain of the triangular surface,It has similar nature of triangular Bézier surface:the angle of interpolation points,symmetry,convex hull,and affine invariant geometric invariance,Changes in the value of the parameter that can do the overall control and can do partial control,has better flexibility to the triangular rational Bézier surface.The fifth chapter sums up the full text and propose the next assumption.