Abstract: The approximate multi-degree reduction problem of triangular Bézier surface of degree n is researched by minimizing the defined distance function.A detailed process of the degree reduction for triangular Bézier surfaces is presented based on unconstraint，then the problem of multi-degree reduction is transformed into computational methods for nonlinear optimization.Through combining multi-degree reduction with geometric continuity of surfaces，a realized process of the degree reduction is presented based on GC¹ constraint.Experimental results show that this algorithm is very efficient.

Key words: triangular Bézier surfaces, multi-degree reduction, GC¹ joining, geometric continuity

摘要： 研究给定的n次三角Bézier曲面在L2范数下的一次降多阶的逼近问题，给出了在无约束条件下的三角Bézier曲面降阶求解的详细过程，将降阶问题转化为非线性最优化问题求解，并将降阶过程与曲面的几何连续拼接结合在一起，给出了降阶同时满足GC¹拼接的实现过程。实验结果表明，该方法简单实用，降阶逼近效果好。

关键词: 三角Bézier曲面, 降阶, GC¹拼接, 几何连续