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Nowadays, digital 3D models are key components in many industrial and scienti c sectors, such as architecture, geoscience, simulation and obviously computer graphics. Numerous tools propose to build virtual objects, either by construction from scratch, or by reconstruction from acquisition data (point cloud, photos, and so on). However, each application has its own quality requirements that restrict the class of acceptable and supported models [1, 5]. Although 3D modeling is more and more successful, 3D models often correspond to a geometrical representation: either by a set of faces, or (in the best case) by a set of volumes. No additional topological information is available, except the face neighborhood of volumes (according to the used modeler). Hence, the produced objects may still contain inconsistencies, especially interpenetrations between elements of the same dimension (volume to volume, face to face or edge to edge). Although 3D model libraries are increasingly created/published, these objects cannot be used directly. Indeed, a geometrical correction and a dedicated information reconstruction are relevant in most application contexts. Based on previous researches [3, 4, 10, 13], a large survey of model repairing methods is proposed in [5]. More precisely, authors distinguish two main categories for repairing models: global volumetric and surface approaches. Volumetric approaches consist in reconstructing a new valid mesh after transformation of existent mesh into an intermediate mesh. These methods are often too time consuming and relies on chosen intermediate structure. On the contrary, it solves highly inconsistent model in a robust way [5, 14]. Surface approaches work directly on the input mesh, and attempt to repair locally (self-)intersections one by one [3, 14]. Thus, modi cations on original mesh are very limited to inconsistent parts. However, the resolution of intersecting geometry is numerically unstable which may produce artifacts. Finally, above mentioned methods can not respect at same time robustness, accuracy or e ciency properties. Our purpose is clearly di erent, because boolean operations produce, from surface objects (i.e. 2D topological objects with immersions in 3D), a unique volume built from them. In addition, processed volumes must be spatially closed (they have an interior and an exterior) in various simulation as visibility problem in rendering [11]. Thus, our approach keeps all topological volumes called co-re nement (similar to Minkowski sum). In this paper, we present a topological reconstruction method of volumes from soup of polygons in a robust, accurate and e cient way. The main purpose is the direct production of a 3D model with

Reconstruction of Volumes from Soup of Faces with a Formal Topological Approach