一种基于NURBS曲面控制的多分辨率自由变形算法

摘要

提出一种针对非均匀有理B样条(NURBS)曲面的自由变形算法,将Loop细分技术引入到NURBS曲面的自由变形中,并提出了通过细分层次控制进行精确多分辨率变形的方法.算法首先根据模型的结构特征确定初始控制顶点,然后对逐步细分的控制曲面片建立局部坐标系,计算每层细分生成的曲面控制点局部坐标,最后根据变形偏移量重新计算各细分层次下网格点新做标,进而实现多分辨率变形.通过虚拟环境中小麦叶折断变形实验,验证了所提算法可以应用于由NURBS曲面表示的作物模型的变形操作,在到达某一细分层次时,若控制点数小于某一阚值且自由变形时间增加较小,可以使该例中自由变形具有良好的精确性和实时性.%A free-form deformation (FFD) algorithm for NURBS surfaces is proposed. The Loop subdivision technique is introduced into multi-resolution FFD to achieve precise multi-resolution FFD by controlling the subdivision levels. The initial control vertex is confirmed by the algorithm according to the structural characteristics of the model. The local coordinate system of the gradually-subdivided control earner region is established, and then the camber control point local coordinate generated in the subdivision process of each level is calculated. Finally, the new coordinate of the grid points beneath each subdivision level is recomputed according to the deformation offset amount to achieve the multi-resolution FFD. The broken deformation experiment of a wheat leaf in the virtual environment verifies that this algorithm can be used for the deformation of the object model defined by NURBS surfaces. It can make the algorithm to has high accuracy and real-time performance.