The invention relates to visualizing freeform surfaces, like NURBS surfaces, from three-dimensional construction data via Virtual beams from a virtual camera are sent out of a virtual image plane in a scene having at least one object and at least one freeform surface. Lighting values are calculated for each point where a beam intersects the freeform surface. The lighting values are then attributed to the pixels associated with the different points of intersection. The freeform surface is defined by two parameters (u, v), and related equations define all points of the surface of the freeform surface The subdivision of the freeform surface for determining the intersections with the beams based on the two parameters (u, v) is regular, so that the surface fragments form meshes of a two-dimensional grid of the freeform surface in the parameter space.