基于弹性模型的三角网格曲面优化展开

根据材料力学中杆件的变形及弹性变形能分析,提出了曲面展开的弹性变形模型。根据边的变形情况,将曲面展开分为约束展开和无约束展开,并对每种展开方法进行分析。特别是约束展开时产生的变形能,根据曲面展开时的判断准则,对弹性变形能进行释放,得到优化的曲面展开。最后给出了曲面展开的算法步骤及实例。该方法中曲面展开的局部精度较易控制,因此较之以前的方法,更能有效地解决CAD/CAGD中曲面展开问题。

Optimal flattening of triangulated surfaces based on elastic model

According to elastic mechanics,a new based on elastic model optimal development of doubly curved surfaces is put forward in this paper.According to the change of the edges,there have two kinds of developments:unconstrained flattening and constrained flattening,which are analyzed respectively.When deciding whether one particular pattern is better than another,the distributed energy required to flatten the 3D surface should be considered.The relaxing procedure of the strain energy required to force 3D shape to the plane pattern is discussed in detail.As optimal criterion,the distortions of the area and the length must be considered.At last the flattening algorithm is presented.Compared with the others,this method can easily control the local precision.it is an effective method for developing doubly curved surfaces in CAD/CAGD.