We present a fully automatic technique which converts an inconsistent input mesh into an output mesh that is guaranteed to be a clean and consistent mesh representing the closed manifold surface of a solid object. The algorithm removes all typical mesh artifacts such as degenerate triangles, incompatible face orientation, non-manifold vertices and edges, overlapping and penetrating polygons, internal redundant geometry, as well as gaps and holes up to a user-defined maximum size ρ. Moreover, the output mesh always stays within a prescribed tolerance ε to the input mesh. Due to the effective use of a hierarchical octree data structure, the algorithm achieves high voxel resolution (up to 4096 3 on a 2GB PC) and processing times of just a few minutes for moderately complex objects. We demonstrate our technique on various architectural CAD models to show its robustness and reliability.

We present the new procedural modeling language G 2 (Generalized Grammar), which adapts various concepts from general purpose programming languages to provide high descriptive power with well-defined semantics and a simple syntax which is easily readable even by non-programmers. The term 'Generalized' reflects two kinds of generalization. On the one hand, we extend the scope of previous architectural modeling languages by allowing for multiple types of non-terminal objects with domain-specific operators and attributes. On the other hand, the language accepts non-terminal symbols as parameters in modeling rules and thus enables the definition of abstract structure templates for flexible re-use within the grammar. By deriving G 2 from the well-established programming language Python, we can make sure that our modeling language has a well-defined semantics. For illustration, we apply G 2 to architectural as well as plant modeling to demonstrate its descriptive power with some complex examples.

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We present a new algorithm for the efficient and reliable generation of offset surfaces for polygonal meshes. The algorithm is robust with respect to degenerate configurations and computes (self-)intersection free offsets that do not miss small and thin components. The results are correct within a prescribed ε-tolerance. This is achieved by using a volumetric approach where the offset surface is defined as the union of a set of spheres, cylinders, and prisms instead of surface-based approaches that generally construct an offset surface by shifting the input mesh in normal direction. Since we are using the unsigned distance field, we can handle any type of topological inconsistencies including non-manifold configurations and degenerate triangles. A simple but effective mesh operation allows us to detect and include sharp features (shocks) into the output mesh and to preserve them during post-processing (decimation and smoothing). We discretize the distance function by an efficient multi-level scheme on an adaptive octree data structure. The problem of limited voxel resolutions inherent to every volumetric approach is avoided by breaking the bounding volume into smaller tiles and processing them independently. This allows for almost arbitrarily high voxel resolutions on a commodity PC while keeping the output mesh complexity low. The quality and performance of our algorithm is demonstrated for a number of challenging examples.

In this paper, we present a novel method to compute Boolean operations on polygonal meshes. Given a Boolean expression over an arbitrary number of input meshes we reliably and efficiently compute an output mesh which faithfully preserves the existing sharp features and precisely reconstructs the new features appearing along the intersections of the input meshes. The term "hybrid" applies to our method in two ways: First, our algorithm operates on a hybrid data structure which stores the original input polygons (surface data) in an adaptively refined octree (volume data). By this we combine the robustness of volumetric techniques with the accuracy of surfaceoriented techniques. Second, we generate a new triangulation only in a close vicinity around the intersections of the input meshes and thus preserve as much of the original mesh structure as possible (hybrid mesh). Since the actual processing of the Boolean operation is confined to a very small region around the intersections of the input meshes, we can achieve very high adaptive refinement resolutions and hence very high precision. We demonstrate our method on a number of challenging examples.