Robustness of subdivision-surface methods

北美的航空航天和汽车工业严重依赖实体造型系统，即计算机辅助设计(CAD)系统。这些系统中用来表示对象的数学模型很容易出错。这至少有三个原因：1.因为表示两个对象的交点(连接)的曲线必须是近似的，因为它们的程度(复杂性)非常高；2.因为计算机只能近似地进行算术运算；以及3.因为不同的系统使用不同的和稍微不兼容的方法来表示建模的对象。当一个模型从一个计算机系统转移到另一个计算机系统时，经常会出现错误。当错误出现时，人类必须干预以纠正它们，这会导致成本非常迅速地上升。据美国政府机构的研究估计，实体建模系统中的错误，包括系统之间的模型转移，仅在汽车行业每年的经济成本就超过1亿美元。

The aerospace and automotive industries in North America rely heavily on solid modelling systems, i.e., computer-aided design (CAD) systems. The mathematical models used in these systems, to represent objects, are prone to error. This is true for at least three reasons: 1. because the curves representing the intersections (joining) of two objects must be approximate, due to their very high degree (complexity) 2. because computers can only do arithmetic approximately, and 3. because different systems use different and slightly incompatible methods to represent the modelled objects. The errors often appear when a model is transferred from one computer system to another. When errors appear, a human must intervene to correct them, and this causes costs to rise very rapidly. The economic costs of errors in solid-modelling systems, including the transfer of models between systems, has been estimated by US government agency studies to be over one hundred million dollars per year in the automotive industry alone.