Curves And Surfaces Modeling Based On Wavelets

This dissertation summaries the researches on the curves and surfaces based on wavelets, which includes the smoothing of Quasi-uniform B-spline curves based on wavelets and the application of wavelets on curves and surfaces modeling.Generally, the resolution levels are limited to discrete integer level. But integer resolution levels sometimes can't meet our needs in smoothing curves, such as one level curve have too many details, but the other one don't have enough. Due to above problems, this dissertation introduce continuous-resolution levels, and describe how to obtain shapes that have continuous partial derivative and second order partial derivative with respect to the resolution level by interpolating the shapes at integer resolution levels.Based on the most widely used approaches of variational modeling of quasi-uniform B-spline curves and surfaces, this dissertation provide a new method of constructing curves and surfaces. For example, one curve has good details; the other one has good profile. Using wavelets, one curve which possesses both good details and good profile can be obtained. And the speed is not bad.