多分辨率B-样条代数曲面研究及其可视化应用

The design and edit of the complex topological geometric shape are difficulty and hot in the geometric modeling. In this project, we investigate some fundamental theories, surface design, multiresolution edit and rendering algorithms in the B-spline algebraic surface. The research contents and results mainly include: The tensor-product de Casteljau algorithm is investigated which is basic algorithm in the B-spline algebraic surface. The related fast algorithm is given. A new approach of Bernstein polynomial composition algorithm is proposed, which is based on polynomial interpolation and symbolic computation. It is faster one order than previous one. For surface deign method, a new fast distance surface computation approach is proposed based on optimized arc spline approximation for 2D NURBS curve skeletons. A convolution surface modeling based on line segment primitive with polynomial density distribution is also given such that modeling a surface of varying radius is possible. In general the B-spline algebraic surface is polygonized during shape modification. Some accurate free-form deformation algorithms are proposed for polygonal object modification. Based on automatically generated arbitrary lattice and Catmull-Clark subdivision volume, multiresolution geometric shape edit is achieved. A prototype system is also accomplished for shape edit. An accelerated ray-tracing B-spline algebraic surface is proposed to generate realistic image. In addition to above contents, a new isosurface extraction is deigned which can extract multi-isosurface in one pass. To sum up, the above fundamental theories and algorithms enrich the research of B-spline algebraic surface and also provide the basis for the applications of computer animation and scientific visualization

在代数曲面造型的研究中，设计方法、交互的形状操作及绘制技术是其中的难点。本项目着重研究基于双正交B- 样条小波基的代数曲面的基本性质、多分辨率B-样条代数曲面的设计托巫葱薷姆椒ā⑶娴氖凳被嬷萍际醯戎匾侍猓⒔芯砍晒τ糜诩负卧煨汀⒓扑慊⑻迨菰煨鸵约疤迨莸慕馕龌嬷频攘煊蛑小