Geometric Surface Processing and Virtual Modeling

In this work we focus on two main topics "Geometric Surface Processing" and "Virtual Modeling". The inspiration and coordination for most of the research work contained in the thesis has been driven by the project New Interactive and Innovative Technologies for CAD (NIIT4CAD), funded by the European Eurostars Programme. NIIT4CAD has the ambitious aim of overcoming the limitations of the traditional approach to surface modeling of current 3D CAD systems by introducing new methodologies and technologies based on subdivision surfaces in a new virtual modeling framework. These innovations will allow designers and engineers to transform quickly and intuitively an idea of shape in a high-quality geometrical model suited for engineering and manufacturing purposes. One of the objective of the thesis is indeed the reconstruction and modeling of surfaces, representing arbitrary topology objects, starting from 3D irregular curve networks acquired through an ad-hoc smart-pen device. The thesis is organized in two main parts: "Geometric Surface Processing" and "Virtual Modeling". During the development of the geometric pipeline in our Virtual Modeling system, we faced many challenges that captured our interest and opened new areas of research and experimentation. In the first part, we present these theories and some applications to Geometric Surface Processing. This allowed us to better formalize and give a broader understanding on some of the techniques used in our latest advancements on virtual modeling and surface reconstruction. The research on both topics led to important results that have been published and presented in articles and conferences of international relevance

Feature preserving noise removal for binary voxel volumes using 3D surface skeletons

Skeletons are well-known descriptors that capture the geometry and topology of 2D and 3D shapes. We leverage these properties by using surface skeletons to remove noise from 3D shapes. For this, we extend an existing method that removes noise, but keeps important (salient) corners for 2D shapes. Our method detects and removes large-scale, complex, and dense multiscale noise patterns that contaminate virtually the entire surface of a given 3D shape, while recovering its main (salient) edges and corners. Our method can treat any (voxelized) 3D shapes and surface-noise types, is computationally scalable, and has one easy-to-set parameter. We demonstrate the added-value of our approach by comparing our results with several known 3D shape denoising methods

Geometric surface processing via normal maps

technical reportThe generalization of signal and image processing to surfaces entails filtering the normals of the surface, rather than filtering the positions of points on a mesh. Using a variational framework, smooth surfaces minimize the norm of the derivative of the surface normals? i.e. total curvature. Penalty functions on the surface normals are computed using geometrybased shape metrics and minimized using gradient descent. This produces a set of partial differential equations (PDE). In this paper, we introduce a novel framework for implementing geometric processing tools for surfaces using a two step algorithm: (i) operating on the normal map of a surface, and (ii) manipulating the surface to fit the processed normals. The computational approach uses level set surface models; therefore, the processing does not depend on any underlying parameterization. Iterating this two-step process, we can implement geometric fourth-order flows efficiently by solving a set of coupled second-order PDEs. This paper will demonstrate that the framework provides for a wide range of surface processing operations, including edge-preserving smoothing and high-boost filtering. Furthermore, the generality of the implementation makes it appropriate for very complex surface models, e.g. those constructed directly from measured data

Segmentation Based Mesh Denoising

Feature-preserving mesh denoising has received noticeable attention recently. Many methods often design great weighting for anisotropic surfaces and small weighting for isotropic surfaces, to preserve sharp features. However, they often disregard the fact that small weights still pose negative impacts to the denoising outcomes. Furthermore, it may increase the difficulty in parameter tuning, especially for users without any background knowledge. In this paper, we propose a novel clustering method for mesh denoising, which can avoid the disturbance of anisotropic information and be easily embedded into commonly-used mesh denoising frameworks. Extensive experiments have been conducted to validate our method, and demonstrate that it can enhance the denoising results of some existing methods remarkably both visually and quantitatively. It also largely relaxes the parameter tuning procedure for users, in terms of increasing stability for existing mesh denoising methods

Surface-Only Simulation of Fluids

Surface-only simulation methods for fluid dynamics are those that perform computation only on a surface representation, without relying on any volumetric discretization. Such methods have superior asymptotic complexity in time and memory than the traditional volumetric discretization approaches, and thus are more tractable for simulation of complex fluid phenomena. Although for most computer graphics applications and many engineering applications, the interior flow inside the fluid phases is typically not of interest, the vast majority of existing numerical techniques still rely on discretization of the volumetric domain. My research first tackles the mesh-based surface tracking problem in the multimaterial setting, and then proposes surface-only simulation solutions for two scenarios: the soap-films and bubbles, and the general 3D liquids. Throughout these simulation approaches, all computation takes place on the surface, and volumetric discretization is entirely eliminated