HexBox: Interactive Box Modeling of Hexahedral Meshes

We introduce HexBox, an intuitive modeling method and interactive tool for creating and editing hexahedral meshes. Hexbox brings the major and widely validated surface modeling paradigm of surface box modeling into the world of hex meshing. The main idea is to allow the user to box-model a volumetric mesh by primarily modifying its surface through a set of topological and geometric operations. We support, in particular, local and global subdivision, various instantiations of extrusion, removal, and cloning of elements, the creation of non-conformal or conformal grids, as well as shape modifications through vertex positioning, including manual editing, automatic smoothing, or, eventually, projection on an externally-provided target surface. At the core of the efficient implementation of the method is the coherent maintenance, at all steps, of two parallel data structures: a hexahedral mesh representing the topology and geometry of the currently modeled shape, and a directed acyclic graph that connects operation nodes to the affected mesh hexahedra. Operations are realized by exploiting recent advancements in grid- based meshing, such as mixing of 3-refinement, 2-refinement, and face-refinement, and using templated topological bridges to enforce on-the-fly mesh conformity across pairs of adjacent elements. A direct manipulation user interface lets users control all operations. The effectiveness of our tool, released as open source to the community, is demonstrated by modeling several complex shapes hard to realize with competing tools and techniques

Developable Quad Meshes

There are different ways to capture the property of a surface being developable, i.e., it can be mapped to a planar domain without stretching or tearing. Contributions range from special parametrizations to discrete-isometric mappings. So far, a local criterion expressing the developability of general quad meshes has been lacking. In this paper, we propose a new and efficient discrete developability criterion that is based on a property well-known from differential geometry, namely a rank-deficient second fundamental form. This criterion is expressed in terms of the canonical checkerboard patterns inscribed in a quad mesh which already was successful in describing discrete-isometric mappings. In combination with standard global optimization procedures, we are able to perform developable lofting, approximation, and design. The meshes we employ are combinatorially regular quad meshes with isolated singularities but are otherwise not required to follow any special curves. They are thus easily embedded into a design workflow involving standard operations like re-meshing, trimming, and merging operations

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

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

Non-smooth developable geometry for interactively animating paper crumpling

International audienceWe present the first method to animate sheets of paper at interactive rates, while automatically generating a plausible set of sharp features when the sheet is crumpled. The key idea is to interleave standard physically-based simulation steps with procedural generation of a piecewise continuous developable surface. The resulting hybrid surface model captures new singular points dynamically appearing during the crumpling process, mimicking the effect of paper fiber fracture. Although the model evolves over time to take these irreversible damages into account, the mesh used for simulation is kept coarse throughout the animation, leading to efficient computations. Meanwhile, the geometric layer ensures that the surface stays almost isometric to its original 2D pattern. We validate our model through measurements and visual comparison with real paper manipulation, and show results on a variety of crumpled paper configurations

Quad Dominant 2-Manifold Mesh Modeling

In this dissertation, I present a modeling framework that provides modeling of 2D smooth meshes in arbitrary topology without any need for subdivision. In the framework, each edge of a quad face is represented by a smooth spline curve, which can be manipulated using edge vertices and additional tangential points. The overall smoothness is achieved by interpolating all four edges of any given quad across the quad surface. The framework consists of simple quad preserving operations that manipulate the principal curves of the smooth model. These operations are all variants of a generic “Curve Split" and its inverse, “Region Collapse". By only using these sets of simple operations, it is possibly to model any desired shape conveniently. I also provide implementation guidelines for these operations. In the results of this dissertation, I present three main applications for this modeling framework. The major application is modeling Mock3D shapes; shapes with well defined interior normals by interpolating the normals at the boundaries of the shape across its surface which can serve as a mock 3D model to mimic a 3D CGI look. As a second application, the framework can be used in origami modeling by allowing assignment of crease patterns across the surface of 2D shapes modelled. Finally, vectorization of reference photos via modeling figures by following their contours is presented as a third application

Discrete Differential Geometry of Thin Materials for Computational Mechanics

Instead of applying numerical methods directly to governing equations, another approach to computation is to discretize the geometric structure specific to the problem first, and then compute with the discrete geometry. This structure-respecting discrete-differential-geometric (DDG) approach often leads to new algorithms that more accurately track the physically behavior of the system with less computational effort. Thin objects, such as pieces of cloth, paper, sheet metal, freeform masonry, and steel-glass structures are particularly rich in geometric structure and so are well-suited for DDG. I show how understanding the geometry of time integration and contact leads to new algorithms, with strong correctness guarantees, for simulating thin elastic objects in contact; how the performance of these algorithms can be dramatically improved without harming the geometric structure, and thus the guarantees, of the original formulation; how the geometry of static equilibrium can be used to efficiently solve design problems related to masonry or glass buildings; and how discrete developable surfaces can be used to model thin sheets undergoing isometric deformation

HexaLab.net: An online viewer for hexahedral meshes

© 2018 Elsevier Ltd We introduce HexaLab: a WebGL application for real time visualization, exploration and assessment of hexahedral meshes. HexaLab can be used by simply opening www.hexalab.net. Our visualization tool targets both users and scholars. Practitioners who employ hexmeshes for Finite Element Analysis, can readily check mesh quality and assess its usability for simulation. Researchers involved in mesh generation may use HexaLab to perform a detailed analysis of the mesh structure, isolating weak points and testing new solutions to improve on the state of the art and generate high quality images. To this end, we support a wide variety of visualization and volume inspection tools. Our system offers also immediate access to a repository containing all the publicly available meshes produced with the most recent techniques for hexmesh generation. We believe HexaLab, providing a common tool for visualizing, assessing and distributing results, will push forward the recent strive for replicability in our scientific community