Direct rendering of Boolean combinations of self-trimmed surfaces

We explore different semantics for the solid defined by a self-crossing surface (immersed sub-manifold). Specifically, we introduce rules for the interior/exterior classification of the connected components of the complement of a self-crossing surface produced through a continuous deformation process of an initial embedded manifold. We propose efficient GPU algorithms for rendering the boundary of the regularized union of the interior components, which is a subset of the initial surface and is called the trimmed boundary or simply the trim. This classification and rendering process is accomplished in real time through a rasterization process without computing any self-intersection curve, and hence is suited to support animations of self-crossing surfaces. The solid bounded by the trim can be combined with other solids and with half-spaces using Boolean operations and hence may be capped (trimmed by a half-space) or used as a primitive in direct CSG rendering. Being able to render the trim in real time makes it possible to adapt the tessellation of the trim in real time by using view-dependent levels-of-detail or adaptive subdivision.