Abstract: NURBS curves are widely used in complex curves and curved surfaces of industrial product design, but geometry processing problems of curve discrete are found in practical applications. According to the NURBS curve discrete problems, a method of curve discrete based on equal arc-length principle is put forward. Step function is introduced to control the length of the discrete curve, and the precision of curve discrete can be controlled by adjusting step function through integration and iterative methods. The approximation accuracy of curve division is checked by error checking algorithm. The rationality and validity of the NURBS curve discrete based on equal arc-length principle are verified by practical calculation example.

Key words: Non-Uniform Rational B-Spline（NURBS） curves, curve discrete, equal arc-length, curve approximation

摘要： NURBS曲线广泛应用于工业产品复杂曲线曲面设计中，但在实际应用中常遇到曲线离散的几何处理问题。针对NURBS曲线离散问题，提出了一种按等弧长原则对NURBS曲线进行离散的方法。该方法引入步长函数控制离散曲线段的弧长，采用积分法和迭代法调整步长函数以控制曲线的离散精度，通过误差检验方法校验曲线离散的逼近精度。通过实际算例，验证了NURBS曲线等弧长离散算法的合理性和有效性。

关键词: 非均匀有理B样条曲线（NURBS）, 曲线离散, 等弧长, 曲线逼近