Surface polygonization is the process by which a representative polygonal mesh of a surface is constructed for rendering or analysis purposes. This work presents a new surface polygonization algorithm specifically tailored to be applied to a large class of models which are created with parametric surfaces. This method has particular application in the area of building virtual environments from computer-aided-design (CAD) models. The algorithm is based on an edge reduction scheme that collapses two vertices of a given polygon edge onto one new vertex. A two step approach is implemented consisting of boundary edge reduction followed by interior edge reduction. A maximin optimization is used to determine the location of the new vertex. The concept of a visible region as the location space of the new vertex is introduced. The method presented here differs from existing methods in that it takes advantage of the fact that for many models, the exact surface representation of the model is known before the polygonization is attempted. Because the precise surface definition is known, a maximin optimization procedure, that uses the surface information, can be used to locate the new vertex. The algorithm attempts to overcome the deficiencies in existing techniques while minimizing the number of polygons required to represent a surface and still maintaining surface integrity in the rendered model. This paper presents the algorithm and testing results.