Viewing parameter dependent approximation of NURBS-models for fast visualization and animation using a discrete multiresolution representation

To represent the surfaces of objects using trimmed NURBS is the most common way in current available CAD-systems. Examples of such surfaces are ship hulls, the outer surfaces of aeroplanes or the interior of cars. For visualization purposes such surfaces are approximated by triangles. Even for small parts, like the door of a car thousands of triangles are needed for such an approximation. The IRIS Inventor built in approximation tool e.g. uses 498613 triangles to visualize such a car door. This approximation is independent of the viewing parameters and, therefore, independent from the door size in pixel space. The real-time visualization of a whole car in such a way is impossible even on high-performance graphics workstations. We present a new and simple approach for managing viewing parameter dependent approximations of NURBS-models. We show how a NURBS-model given as a set of trimmed NURBS patches can be approximated with position dependent approximation errors by a discrete multiresolution model. This model consists of a coarse initial triangle net, a set of vertices, and a rule on how to insert these vertices into the initial triangulation in order to get different levels of detail (LOD). Furthermore, we show how the triangle nets of the different LODs can be adapted to changes of the viewing parameters. In our new approach the main idea is to compute different LODs, instead of using special data structures to store them. This way we trade off storage capacity and storage access time against computing power. In addition only a few points of the actual triangle net have to be removed or inserted in order to switch between different LODs. The algorithm is easy to implement and fast enough to achieve real-time updates for the visualization of usual CAD models. Examples from real data illustrate the power of this approach.