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

Dynamic remeshing and applications

Triangle meshes are a flexible and generally accepted boundary representation for complex geometric shapes. In addition to their geometric qualities such as for instance smoothness, feature sensitivity ,or topological simplicity, intrinsic qualities such as the shape of the triangles, their distribution on the surface and the connectivity is essential for many algorithms working on them. In this thesis we present a flexible and efficient remeshing framework that improves these "intrinsic\u27; properties while keeping the mesh geometrically close to the original surface. We use a particle system approach and combine it with an iterative remeshing process in order to trim the mesh towards the requirements imposed by different applications. The particle system approach distributes the vertices on the mesh with respect to a user-defined scalar-field, whereas the iterative remeshing is done by means of "Dynamic Meshes\u27;, a combination of local topological operators that lead to a good natured connectivity. A dynamic skeleton ensures that our approach is able to preserve surface features, which are particularly important for the visual quality of the mesh. None of the algorithms requires a global parameterization or patch layouting in a preprocessing step, but works with simple local parameterizations instead. In the second part of this work we will show how to apply this remeshing framework in several applications scenarios. In particular we will elaborate on interactive remeshing, dynamic, interactive multiresolution modeling, semiregular remeshing and mesh simplification and we will show how the users can adapt the involved algorithms in a way that the resulting mesh meets their personal requirements

Connectivity Control for Quad-Dominant Meshes

abstract: Quad-dominant (QD) meshes, i.e., three-dimensional, 2-manifold polygonal meshes comprising mostly four-sided faces (i.e., quads), are a popular choice for many applications such as polygonal shape modeling, computer animation, base meshes for spline and subdivision surface, simulation, and architectural design. This thesis investigates the topic of connectivity control, i.e., exploring different choices of mesh connectivity to represent the same 3D shape or surface. One key concept of QD mesh connectivity is the distinction between regular and irregular elements: a vertex with valence 4 is regular; otherwise, it is irregular. In a similar sense, a face with four sides is regular; otherwise, it is irregular. For QD meshes, the placement of irregular elements is especially important since it largely determines the achievable geometric quality of the final mesh. Traditionally, the research on QD meshes focuses on the automatic generation of pure quadrilateral or QD meshes from a given surface. Explicit control of the placement of irregular elements can only be achieved indirectly. To fill this gap, in this thesis, we make the following contributions. First, we formulate the theoretical background about the fundamental combinatorial properties of irregular elements in QD meshes. Second, we develop algorithms for the explicit control of irregular elements and the exhaustive enumeration of QD mesh connectivities. Finally, we demonstrate the importance of connectivity control for QD meshes in a wide range of applications.Dissertation/ThesisDoctoral Dissertation Computer Science 201

Doctor of Philosophy

dissertationOne of the fundamental building blocks of many computational sciences is the construction and use of a discretized, geometric representation of a problem domain, often referred to as a mesh. Such a discretization enables an otherwise complex domain to be represented simply, and computation to be performed over that domain with a finite number of basis elements. As mesh generation techniques have become more sophisticated over the years, focus has largely shifted to quality mesh generation techniques that guarantee or empirically generate numerically well-behaved elements. In this dissertation, the two complementary meshing subproblems of vertex placement and element creation are analyzed, both separately and together. First, a dynamic particle system achieves adaptivity over domains by inferring feature size through a new information passing algorithm. Second, a new tetrahedral algorithm is constructed that carefully combines lattice-based stenciling and mesh warping to produce guaranteed quality meshes on multimaterial volumetric domains. Finally, the ideas of lattice cleaving and dynamic particle systems are merged into a unified framework for producing guaranteed quality, unstructured and adaptive meshing of multimaterial volumetric domains

A framework for hull form reverse engineering and geometry integration into numerical simulations

The thesis presents a ship hull form specific reverse engineering and CAD integration framework. The reverse engineering part proposes three alternative suitable reconstruction approaches namely curves network, direct surface fitting, and triangulated surface reconstruction. The CAD integration part includes surface healing, region identification, and domain preparation strategies which used to adapt the CAD model to downstream application requirements. In general, the developed framework bridges a point cloud and a CAD model obtained from IGES and STL file into downstream applications

3D photogrammetric data modeling and optimization for multipurpose analysis and representation of Cultural Heritage assets

This research deals with the issues concerning the processing, managing, representation for further dissemination of the big amount of 3D data today achievable and storable with the modern geomatic techniques of 3D metric survey. In particular, this thesis is focused on the optimization process applied to 3D photogrammetric data of Cultural Heritage assets. Modern Geomatic techniques enable the acquisition and storage of a big amount of data, with high metric and radiometric accuracy and precision, also in the very close range field, and to process very detailed 3D textured models. Nowadays, the photogrammetric pipeline has well-established potentialities and it is considered one of the principal technique to produce, at low cost, detailed 3D textured models. The potentialities offered by high resolution and textured 3D models is today well-known and such representations are a powerful tool for many multidisciplinary purposes, at different scales and resolutions, from documentation, conservation and restoration to visualization and education. For example, their sub-millimetric precision makes them suitable for scientific studies applied to the geometry and materials (i.e. for structural and static tests, for planning restoration activities or for historical sources); their high fidelity to the real object and their navigability makes them optimal for web-based visualization and dissemination applications. Thanks to the improvement made in new visualization standard, they can be easily used as visualization interface linking different kinds of information in a highly intuitive way. Furthermore, many museums look today for more interactive exhibitions that may increase the visitors’ emotions and many recent applications make use of 3D contents (i.e. in virtual or augmented reality applications and through virtual museums). What all of these applications have to deal with concerns the issue deriving from the difficult of managing the big amount of data that have to be represented and navigated. Indeed, reality based models have very heavy file sizes (also tens of GB) that makes them difficult to be handled by common and portable devices, published on the internet or managed in real time applications. Even though recent advances produce more and more sophisticated and capable hardware and internet standards, empowering the ability to easily handle, visualize and share such contents, other researches aim at define a common pipeline for the generation and optimization of 3D models with a reduced number of polygons, however able to satisfy detailed radiometric and geometric requests. iii This thesis is inserted in this scenario and focuses on the 3D modeling process of photogrammetric data aimed at their easy sharing and visualization. In particular, this research tested a 3D models optimization, a process which aims at the generation of Low Polygons models, with very low byte file size, processed starting from the data of High Poly ones, that nevertheless offer a level of detail comparable to the original models. To do this, several tools borrowed from the game industry and game engine have been used. For this test, three case studies have been chosen, a modern sculpture of a contemporary Italian artist, a roman marble statue, preserved in the Civic Archaeological Museum of Torino, and the frieze of the Augustus arch preserved in the city of Susa (Piedmont- Italy). All the test cases have been surveyed by means of a close range photogrammetric acquisition and three high detailed 3D models have been generated by means of a Structure from Motion and image matching pipeline. On the final High Poly models generated, different optimization and decimation tools have been tested with the final aim to evaluate the quality of the information that can be extracted by the final optimized models, in comparison to those of the original High Polygon one. This study showed how tools borrowed from the Computer Graphic offer great potentialities also in the Cultural Heritage field. This application, in fact, may meet the needs of multipurpose and multiscale studies, using different levels of optimization, and this procedure could be applied to different kind of objects, with a variety of different sizes and shapes, also on multiscale and multisensor data, such as buildings, architectural complexes, data from UAV surveys and so on

Accurate geometry reconstruction of vascular structures using implicit splines

3-D visualization of blood vessel from standard medical datasets (e.g. CT or MRI) play an important role in many clinical situations, including the diagnosis of vessel stenosis, virtual angioscopy, vascular surgery planning and computer aided vascular surgery. However, unlike other human organs, the vasculature system is a very complex network of vessel, which makes it a very challenging task to perform its 3-D visualization. Conventional techniques of medical volume data visualization are in general not well-suited for the above-mentioned tasks. This problem can be solved by reconstructing vascular geometry. Although various methods have been proposed for reconstructing vascular structures, most of these approaches are model-based, and are usually too ideal to correctly represent the actual variation presented by the cross-sections of a vascular structure. In addition, the underlying shape is usually expressed as polygonal meshes or in parametric forms, which is very inconvenient for implementing ramification of branching. As a result, the reconstructed geometries are not suitable for computer aided diagnosis and computer guided minimally invasive vascular surgery. In this research, we develop a set of techniques associated with the geometry reconstruction of vasculatures, including segmentation, modelling, reconstruction, exploration and rendering of vascular structures. The reconstructed geometry can not only help to greatly enhance the visual quality of 3-D vascular structures, but also provide an actual geometric representation of vasculatures, which can provide various benefits. The key findings of this research are as follows: 1. A localized hybrid level-set method of segmentation has been developed to extract the vascular structures from 3-D medical datasets. 2. A skeleton-based implicit modelling technique has been proposed and applied to the reconstruction of vasculatures, which can achieve an accurate geometric reconstruction of the vascular structures as implicit surfaces in an analytical form. 3. An accelerating technique using modern GPU (Graphics Processing Unit) is devised and applied to rendering the implicitly represented vasculatures. 4. The implicitly modelled vasculature is investigated for the application of virtual angioscopy