AbstractDuring the design of an object using a CAD (computer aided design) platform, the user can visualize the ongoing model at every moment. Visualization is based on a discrete representation of the model that coexists with the exact analytical representation of the object. Most CAD systems have this discrete representation available, and each of them applies its own construction methodology. This paper presents a new method to build a discrete (“triangulated” with quadrilaterals and triangles) model for CAD surfaces. It presents two major particularities: most elements are aligned with iso-parametric curves and the accuracy of the surface approximation is controlled. In addition, we present a new technique of surface mesh generation that is based on this discrete model. Several examples are presented to confirm the efficacy of this approach.