We present a method that computes a global potentially visible set for the complete region outside the convex hull of an object. The technique is used to remove invisible parts (triangles) from complex tessellated CAD models. Such optimizations are required to achieve interactive frame rates for the visual exploration of huge data sets on graphics workstations. Our algorithm is subdivided into three stages. At the first step the the tesselated object is rendered with OpenGL from various camera positions to detect visible triangles very fast. A hardware-accelerated hemicube test is applied as the second stage, marking all triangles that can directly exchange energy with an infinitely distant environment. Finally, a Monte Carlo ray tracing pass is applied to each remaining triangle, sampling its visibility with arbitrary accuracy. All invisible triangles are completely removed from the mesh. It is therefore not necessary to store visibility information, allowing the reduced mesh to be...