基于层次B样条的网格模型变形技术

针对常用的网格模型提出了一个基于层次B样条控制的三维网格空间变形框架．首先由用户交互地选取编辑区域，由程序完成编辑区域的参数化和均匀重采样；然后用层次B样条光顺拟合这些均匀采样点，所得的R样条曲面作为网格模型的基曲面，计算待编辑区域中网格顶点相对该B样条基曲面的局部坐标，该局部坐标平移、旋转不变，可视为模型的内蕴几何特征，并作为变形操作中的不变量．用户通过编辑层次B样条基曲面或者直接编辑三维网格模型，可实现多分辨率变形．实验结果表明：该方法操作直观方便，无论对整体还是局部变形，都能取得可控、可靠的变形效果，且采刚B样条曲面的控制手段易于与已有的造型系统合成．

Mesh Deformation with Hierarchical B-Splines

A novel mesh deformation framework controlled by hierarchical B-spline surfaces is proposed. First, region of interest (ROI) is selected interactively, then the ROI is automatically parameterized and re-sampled uniformly. The re-sampled points are fitted with hierarchical B-spline surfaces. The local coordinates of the vertices in the ROI corresponding to the hierarchical B-spline surfaces are computed. Being invariant in translation and rotation, these local coordinates could be regarded as intrinsic geometric variables for the mesh, remaining unchanged during deformation operation. Through editing the B-spline control points interactively or manipulating the mesh directly, the intended object deformation is achieved. Experimental results demonstrate that the proposed method provides a convenient and intuitive approach for both global and local deformation. Since the hierarchical B-splines are popular in current modeling systems, the proposed method can be easily integrated into them.