Investigation of approximate multi-degree reduction of triangular Bézier surfaces based on GC~1 constraint

The approximate multi-degree reduction problem of triangular Bezier surface of degree n is researched by minimizing the defined distance function.A detailed process of the degree reduction for triangular Bezier surfaces is presented based on un-constraint,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 pre-sented based on GC1 constraint.Experimental results show that this algorithm is very efficient.