Curve Subdivision Scheme And Its Application

Nowadays,subdivision techniques are widely used to create smooth curves and surfaces in many fields such as computer-aided geometric design,computer graphics,computer animation.Subdivision method is a way of refining grids repeatedly based on certain rules in order to achieve a sequence of grids are claimed to converge to a limit,which is the smooth curve or surface.This thesis designs several effective curve subdivision schemes.Firstly,we proposed a family of 6-point binary approximation subdivision scheme,and the crucial issue in subdivision,that is,the smoothness of the scheme,has been discussed by using the Laurent polynomial method for a certain range of parameter.The limit curves produced by our subdivision scheme could attain high order continuity.The H?lder exponent of the limit curves is also calculated.Furthermore,the properties of monotonicity preservation and convexity preservation of the subdivision scheme are discussed.The subdivision scheme generates a family of1 9CC limiting curves for certain range of parameter t.Especially,when t takes some specific values,the limiting curves will turn out to be fractals.Secondly,we present two parameters binary 5-point subdivision scheme with support [-4,4].The convergence and smoothness of the scheme are discussed by using Laurent polynomial method.H?lder regularity of the subdivision scheme is analyzed.Moreover,we also discuss the monotonicity preservation and convexity preservation of the scheme for certain ranges of parameter.Lastly,a class of new interpolation and approximation blending 6-point binary subdivision scheme with two parameters is presented.The smoothness of the scheme is analyzed by the Laurent polynomial method,and the limit curve is at least 4C continuous.The scheme achieves higher continuity and approximating results compared with the existing combined 6-point binary subdivision schemes.Furthermore,the uniform subdivision scheme is extended to non-uniform subdivision scheme.