If two closed polygonal objects with outfacing normals intersect each other there exist one or more lines that intersect these objects at at l east two consecutive front or back fa cing object points. In this work we present a method to efficiently detect these lines us ing depth-peeling and simple fragment operations. Of all polygons only those having an inte rsection with any of these lines ar e potentially colliding. Polygons not intersected by the same line do not intersect each other. We describe ho w to find all potentially colliding polygons and the potentially colliding pairs using a mipmap hierarchy that represents line bundles at ever increasing width. To download onl y potentially colliding polygons to the CPU for polygon-polygon intersection testing, we have developed a general me thod to convert a sparse texture into a packed texture of reduced size. Our method expl oits the intrinsic strength of GPUs to scan convert large sets of polygons and to shade billions of fragm ents at interactive rates. It neither requires a bounding volume hierarchy nor a pre-processing stage, so it can efficiently deal with very large and deforming polygonal models. The particular design makes the method suitable for applications where geometry is modified or even created on the GPU.