Study On The Representation And Shape Modification Of Curves And Surfaces In Geometric Design And Computation

Computer aided geometric design(CAGD)mainly researches curves and surfaces which vary in the free and complex forms, that is to say, curves and surfaces of freedom forms. Parametric curves and surfaces modeling and shape modification is one of the most important issue in CAGD.This thesis is devoted to construct Bezier curve with geometric constraints; to design piecewise cubic and quartic polynomial spline with adjusted interpolation points; to construct an extended quadratic B-spline curves; to design the general Bezier curves and surfaces based on a higher order approximation of function with local shape parameters; to study grid generation based on symmetric blend functions of boundary information. It is composed of seven chapters.In chapter 1, we briefly introduce the historical background and the present progress of problems that concern with curves and surfaces shape modification. The main works of this paper are concluded as well.In chapter 2, a new modeling method is used to construct Bezier curve with modified vectors based on constrained optimization. The control points are modified by using the optimization with signal and multiple constraints.In chapter 3, piecewise cubic and quartic polynomial curves with adjusted interpolation points are presented. The given representation is intergrated of cubic approximation and interpolating curve. By changing the values of local shape parameters, local approximating curves and local interpolating curves can be generated, respectively. Tension parameters are also considered to locally modify the shape of the curves.In chapter 4, presents a construction of an extened quadratic B-spline curves and its application. The properties of approximation conics are given based on the extended spline curves. The shape of the extended quadratic B-spline curves can be adjusted locally by changing the value of the shape parameters. Approximation for histograms also discussed by using the extended curves and the applications of the quadratic non-uniform B-spline curves can be extended as well.In chapter 5, generalized Bezier curves and surfaces with local shape parameters are presented. Based on a kind of higher approximate polynomials of a function, satisfying curves and surfaces can be generated by changing the given object derivative/partial derivatives vectors. Connecting of surface patches also considered.Chapter 6 presents a method to generate grid curves by defining and using a kind of symmetric blend functions. The expression of u-directional grid curves and v-directional grid curves with shape parameters are constructed.