The Generalized B-Spline Surface Subdivision And Applying To Surface Blending And Volume Rendering

In the field of 3D computer graphics,subdivision surface is the most import method of representing a smooth surface.The study of quadratic and cubic B-spline surfaces lead respectively to the two well known subdivision methods,the Doo-Sabin and Catmull-Clark methods.Fang et at 2014 proposed a generalized surface subdivision scheme.Several well-known subdivision schemes,are special cases of the generalized subdivision method.One can use the tension parameter to change the shape of subdivision surfaces.This article by applying the generalized B-spline subdivision scheme to the blending of surfaces,further propose a scheme of surface blending.The blending scheme can be used to blend surfaces of general mesh and any order B-spline mesh.It is very easy to adjust the shape of the blend surface because this scheme allows to set the order and tensor parameter of the surface.Since the generalized B-spline surface subdivision scheme can accurately generate bi-degree surface,the blend scheme can also be used to the blending of bi-degree surfaces.This article also provide the instances of the blending of bi-degree surfaces.This article also apply the generalized B-spline surface subdivision method in Volume Rendering.By extending the subdivision scheme from surface subdivision to solid subdivision,I further propose a generalized B-spline solid subdivision scheme which can set the tension parameter and order.Then applying the solid subdivision to the tetrahedral volume datasets,which increases the cell number of the datasets to improve the approximation accuracy.Furthermore,in this article,I try to use WebGL to render the volume datasets.Because WebGL currently does not support storing or sampling 3D textures,I have to store it in a way that can be used by 2D textures.For this reason we can store a png image file with all the Z slices one next to the other making a mosaic of 2D slices.Once the png file is loaded into memory as a 2D texture,we can later sample it as it if was a 3D texture using our own custom function.