A Subdivision Method Reproducing Conics With Non-uniform Data

In the recent twenty years, with the prevalence and progressively broad applicationof computer technology, subdivision method has become a focus of study in computeraided geometric design and computer graphics in the world.After reviewing the general situation and history of subdivision, we appraise thecharacter and the classification of subdivision. Then the author introduces the importantoutlines of existent schemes of curve and surface and the theory involved in the study ofsubdivision. At the same time, the author introduces Doo-Sabin scheme, Catmull-Clarkskill, Loop method etc. as examples of subdivision templets.As to curve subdivision, given the initial control points in a class of curves, it's ameaningful work to construct a subdivision scheme to reproduce this category of curves,The scheme given in [21] can reproduce conics from the uniform initial control pointson the conics, however, it doesn't work for the non-uniform case. For the thought of"piecewise" theorem, we present a three-point interpolatory subdivision scheme whichcan be used to reproduce the conics at the vicinity of the initial control points for the non-uniform case. And we can reproduce the conics from the non-uniform data combiningthese two schemes.In this thesis the author not only presents the proof of the convergence of the pre-sented scheme, but also the nature of reproducing conics at the vicinity of the initialcontrol points. And the numerical experiment also give us the feasibility of our method.Besides, using the theorems about the convergency of various parameter four-pointinterpolatory subdivision scheme, we give a proof of the conjecture of the C~1 continuityof the local control subdivision scheme presented in the paper [23].