Graph Rotation Systems for Physical Construction of Large Structures

In this dissertation, I present an approach for physical construction of large structures. The approach is based on the graph rotation system framework. I propose two kinds of physical structures to represent the shape of design models. I have developed techniques to generate developable panels from any input polygonal mesh, which can be easily assembled to get the shape of the input polygonal mesh. The first structure is called plain woven structures. I have developed the ?projection method? to convert mathematical weaving cycles on any given polygonal mesh to developable strip panels. The width of weaving strips varies so that the surface of the input model can be covered almost completely. When these strip panels are assembled together, resulting shape resembles to a weaving in 3-space. The second structure is called band decomposition structures. I have developed a method to convert any given polygonal mesh into star-like developable elements, which we call vertex panels. Assembling vertex panels results in band decomposition structures. These band decomposition structures correspond to 2D-thickening of graphs embedded on surfaces. These band decompositions are contractible to their original graph. In a 2D-thickening, each vertex thickens to a polygon and each edge thickens to a band. Within the resulting band decomposition, each polygon corresponds to a vertex and each band corresponds to an edge that connects two vertex polygons. Since the approach is based on graph rotation system framework, the two structures do not have restrictions on design models. The input mesh can be of any genus. The faces in the input mesh can be triangle, quadrilateral, and any polygon. The advantages of this kind of large physical structure construction are low-cost material and prefabrication, easy assemble. Our techniques take the digital fabrication in a new direction and create complex and organic 3D forms. Along the theme of architecture this research has great implication for structure design and makes the more difficult task of construction techniques easier to understand for the fabricator. It has implications to the sculpture world as well as architecture

Multi-Panel Unfolding with Physical Mesh Data Structures

In this thesis, I demonstrate that existing mesh data structures in computer graphics can be used to categorize and construct physical polygonal models. In this work, I present several methods based on mesh data structures for transforming 3D polygonal meshes into developable multi-panels that can be used in physical construction. Using mesh data structures, I developed a system which provides a variety of construction methods. In order to demonstrate that mesh data structures can be used to categorize and construct physical polygonal models, this system visualizes the mathematical theory and generates developable multi-panels that can be printed and assembled to shapes similar to original virtual shapes. The mesh data structures include ones that are orientable: Quad-Edge, Half-Edge, Winged-Edge; and also one that is non-orientable: Extended GRS. The advantages of using mesh data structures as guides for physical construction include: There is no restriction on input design model as long as it is manifold, it can be of any genus with n-sided polygon faces; Different mesh data structures provide more options to better fit the input design while taking the physical constraints and material properties in consideration; Developable panels are easy to obtain from thin planar materials using a laser-cutter; When we use mesh data structures, it is also intuitive to assemble such planar panels using mesh information. Laser-cut developable panels based on mesh data structures provide, therefore, a cost-efficient alternative to 3D printing when dealing with large structures

A Topological Theory of Weaving and Its Applications in Computer Graphics

Recent advances in the computer graphics of woven images on surfaces in 3-space motivate the development of weavings for arbitrary genus surfaces. We present herein a general framework for weaving structures on general surfaces in 3-space, and through it, we demonstrate how weavings on such surfaces are inducible from connected graph imbeddings on the same surfaces. The necessary and sufficient conditions to identify the inducible weavings in our framework are also given. For low genus surfaces, like plane and torus, we extend our framework to the weavings which are inducible from disconnected imbedded graphs. In particular, we show all weavings on a plane are inducible in our framework, including most Celtic Knots. Moreover, we study different weaving structures on general surfaces in 3-space based on our framework. We show that any weaving inducible in our framework can be converted into an alternating weaving by appropriately changing the strand orders at some crossings. By applying a topological surgery operation, called doubling operation, we can refine a weaving or convert certain non-twillable weavings into twillable weavings on the same surfaces. Interestingly, two important subdivision algorithms on graphs imbeddings, the Catmull-Clark and Doo-Sabin algorithms, correspond nicely to our doubling operation on induced weavings. Another technique we used in studying weaving structures is repetitive patterns. A weaving that can be converted into a twillable weaving by our doubling operation has a highly-symmetric structure, which consists of only two repetitive patterns. An extension of the symmetric structure leads to Quad-Pattern Coverable meshes, which can be seamlessly covered with only one periodic pattern. Both of these two topological structures can be represented with simple Permutation Voltage graphs. A considerable advantage of our model is that it is topological. This permits the graphic designer to superimpose strand colors and geometric attributes — distances, angles, and curvatures — that conform to manufacturing or artistic criteria. We also give a software example for plane weaving construction. A benefit of the software is that it supports plane weaving reconstructions from an image of a plane weaving, which could be useful for recording and modifying existing weavings in real life

Satin Non-Woven Fabrics for Designing of Self-Regulating Breathable Building Skins

In this paper, we introduce the concept of 2-way 2-fold genus-1 non-woven fabrics that can be used to design self-regulating breathable building skins. The advantage of non-woven structures over woven structures for breathable skin design is that they can completely be closed to stop air exchange. We have developed a theoretical framework for such non-woven structures starting from the mathematical theory of biaxial 2-fold Genus-1 woven fabrics. By re-purposing a mathematical notation that is used to describe 2-fold 2-way 2-fold genus-1 woven fabrics, we identify and classify non-woven fabrics. Within this classification, we have identified a special subset that corresponds to satin woven fabrics and allows for maximum air exchange. Any other subset of non-woven structures that correspond to other classical 2-way 2-fold genus-1 fabrics, such as plain or twill, will allow for less air exchange. We also show that there exists another subset of satin non-woven fabrics that can provide the biggest openings.Comment: 10 page

Stability-aware simplification of curve networks

La conception de réseaux de courbes nécessite la considération de plusieurs facteurs: la stabilité de la structure, l'efficience matérielle, et l'aspect esthétique - des objectifs complexes et interdépendants rendant la conception manuelle difficile. Nous présentons une nouvelle méthode permettant de simplifier des réseaux de courbes destinés à la fabrication. Pour un ensemble de courbes 3D donné, notre algorithme en sélectionne un sous-ensemble stable. Bien que la stabilité soit traditionnellement mesurée par l'ordre de grandeur des déformations entraînées par des charges prédéfinies, une telle approche peut s'avérer limitante. Elle ne tient ni compte des effets de vibration pour les structures de grandes tailles, ni des multiples possibilités de forces appliquées pour les structures et objets de plus petite taille. Ainsi, nous optimisons directement pour une déformation minimale avec la charge dans le pire des cas (de l'anglais "worst-case"). Notre contribution technique est une nouvelle formulation de la simplification de réseaux de courbes pour la stabilité dans le pire des cas. Celle-ci mène à un problème d'optimisation semi-définie positive en nombres entiers (MI-SDP). Malgré que résoudre ce problème MI-SDP directement est irréaliste dans la plupart des cas, une intuition physique nous mène à un algorithme vorace efficace. Enfin, nous démontrons le potentiel de notre approache à l'aide plusieurs réseaux de courbes et validons l'efficacité de notre méthode en la comparant de façon quantitative à des approaches plus simples.Designing curve networks for fabrication requires simultaneous consideration of structural stability, cost effectiveness, and visual appeal - complex, interrelated objectives that make manual design a difficult and tedious task. We present a novel method for fabrication-aware simplification of curve networks, algorithmically selecting a stable subset of given 3D curves. While traditionally, stability is measured as the magnitude of deformation induced by a set of predefined loads, predicting applied forces for common day objects can be challenging. Instead, we directly optimize for minimal deformation under the worst-case load. Our technical contribution is a novel formulation of 3D curve network simplification for worst-case stability, leading to a mixed-integer semi-definite programming problem (MI-SDP). We show that while solving MI-SDP directly is impractical, a physical insight suggests an efficient greedy heuristic algorithm. We demonstrate the potential of our approach on a variety of curve network designs and validate its effectiveness compared to simpler alternatives using numerical experiments

7th International Meshing Roundtable '98

The goal of the 7th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the past, the Roundtable has enjoyed significant participation from each of these groups from a wide variety of countries

Macro-mechanical modelling and simulation of textile fabric and clothing with S-FEM

Tese de Doutoramento Programa Doutoral em Engenharia TêxtilEsta tese propõe um método de elementos finitos, designado por S-FEM (Smoothed Finite Element Method), para modelação e análise mecânica de estruturas têxteis planas. Neste enquadramento teórico, supõe-se que a estrutura têxtil não-tecida é um material isotrópico elástico, enquanto a estrutura têxtil tecida é um material elástico com anisotropia ortotrópica, para os quais as leis constitutivas utilizam propriedades mecânicas de baixa pressão (low stress) com base na Medição Objetiva de Tecidos (FOM - Fabric Objective Measurement). As formulações de elementos finitos de baixa ordem baseadas em deslocamento quando aplicadas a elementos finitos de placas (plate/shell) quadriláteras de 4 nós, incluindo campos de tensão de cisalhamento transversal, baseiam-se nas contribuições de Raymond Mindlin e por Eric Reissner, no que agora se designa teoria de deformação por cisalhamento de primeira ordem (first-order shear deformation, do inglês, ou FSDT de forma abreviada), ou simplesmente teoria de Mindlin-Reissner, e nas abordagens MITC (Mixed Interpolation of Tensorial Components), são nesta tese combinadas com a técnica de suavização do/da gradiente/tensão nos termos dos modelos S-FEM por forma a mitigar problemas como são o caso da distorção de elementos finitos, da granularidade grosseira da malha, bem como dos bem conhecidos fenómenos de bloqueio. As malhas de quadriláteros são utilizadas nesta tese devido à sua capacidade de representar geometrias complexas de tecidos em resultado de deformações mecânicas como são os casos da recuperação face à pressão planar, flexão, deformação, vibração, drapejamento, etc. Refira-se que foi desenvolvido e implementado em Matlab um software para os novos modelos de elementos finitos, em grande medida devido à inexistência de modelos S-FEM em softwares de análise de elementos finitos (finite element analysis ou FEA), lacuna esta que ocorre quer em softwares comerciais, quer não comerciais, e até em códigos abertos. Exemplos numéricos para as aplicações básicas de engenharia no que respeita à modelação mecânica de folhas de tecido fino e de folhas de tecido de espessura média em estudos de casos típicos, como é o caso da recuperação face a pressão planar, flexão, deformação e comportamento livre de vibrações, indicam que os elementos finitos (plate/shell) desenvolvidos com a técnica de suavização de tensão e MITC acabam por aliviar os efeitos de distorção dos elementos, a granularidade grosseira da malha e efeito de bloqueio na modelação e análise mecânica de tecidos muito finos e até mesmo de tecidos de espessura média. Os modelos de elementos finitos de placas (plate/shell) desenvolvidos durante o trajeto desta tese, bem como as suas propriedades mecânicas de baixa tensão em termos de FOM, são, portanto, bem adaptados à modelação e análise numérica de deformação macro-mecânica de folhas de tecido muito fino e de folhas de tecido de espessura média, incluindo ao mesmo tempo análise de deformação mecânica simples e complexa.An S-FEM (Smoothed Finite Element Method) for mechanical analysis and modelling of the textile fabrics is proposed. In this theoretical framework, one assumes that the non-woven fabric is an elastic isotropic material, while the woven fabric is an elastic with orthotropic anisotropy for which the constitutive laws formulated are using low-stress mechanical properties based on FOM (Fabric Objective Measurement). The displacement-based low-order finite element formulations for four-node quadrilateral plate/shell finite element, including assumed transverse shear strain fields, are based on the contributions of Raymond Mindlin and by Eric Reissner as FSDT (first-order shear deformation theory and so-called the Mindlin-Reissner theory) together with MITC (Mixed Interpolation of Tensorial Components) approaches, which are combined with the gradient/strain smoothing technique in terms of S-FEM models contributed by G. R. Liu et al. in order to mitigate problems as element distortion, mesh coarseness as well as the well-known locking phenomena. Quadrilateral meshes are used due to ability to represent complicated geometries of complex mechanical deformation of the fabric such as plane stress recovery, bending, buckling, vibration, draping behavior, etc. The finite element computer codes were developed in MATLAB for the new formulated plate/shell finite element models due to the lack of FEM (Finite Element Method) packages for S-FEM models in both commercial and non-commercial FEA (Finite Element Analysis) computer applications, and even from open-source platforms. Numerical examples for the basic engineering applications of mechanical modelling of thin to moderately thick fabric sheet in the typical case studies such as in-plane stress recovery, bending, buckling and free-vibration behavior, indicate that the developed plate/shell finite elements with assumed strain smoothing technique and MITC, do alleviate element distortion, mesh coarseness, and locking effect even for mechanical analysis and modelling very thin to moderately thick fabric. The developed plate/shell finite element models and low-stress mechanic properties in terms of FOM are, therefore, well adapted for numerical analysis and modelling of macro-mechanical deformation of the thin to moderately thick fabric sheet including both simple and complex mechanical deformation analysis.EMECW L12 MOBILITY GRANT AWARD CONTRACT BTG_559 Grant agreement n 2009/1661-001 001EC

Generative Mesh Modeling

Generative Modeling is an alternative approach for the description of three-dimensional shape. The basic idea is to represent a model not as usual by an agglomeration of geometric primitives (triangles, point clouds, NURBS patches), but by functions. The paradigm change from objects to operations allows for a procedural representation of procedural shapes, such as most man-made objects. Instead of storing only the result of a 3D construction, the construction process itself is stored in a model file. The generative approach opens truly new perspectives in many ways, among others also for 3D knowledge management. It permits for instance to resort to a repository of already solved modeling problems, in order to re-use this knowledge also in different, slightly varied situations. The construction knowledge can be collected in digital libraries containing domain-specific parametric modeling tools. A concrete realization of this approach is a new general description language for 3D models, the "Generative Modeling Language" GML. As a Turing-complete "shape programming language" it is a basis of existing, primitv based 3D model formats. Together with its Runtime engine the GML permits - to store highly complex 3D models in a compact form, - to evaluate the description within fractions of a second, - to adaptively tesselate and to interactively display the model, - and even to change the models high-level parameters at runtime.Die generative Modellierung ist ein alternativer Ansatz zur Beschreibung von dreidimensionaler Form. Zugrunde liegt die Idee, ein Modell nicht wie üblich durch eine Ansammlung geometrischer Primitive (Dreiecke, Punkte, NURBS-Patches) zu beschreiben, sondern durch Funktionen. Der Paradigmenwechsel von Objekten zu Geometrie-erzeugenden Operationen ermöglicht es, prozedurale Modelle auch prozedural zu repräsentieren. Statt das Resultat eines 3D-Konstruktionsprozesses zu speichern, kann so der Konstruktionsprozess selber repräsentiert werden. Der generative Ansatz eröffnet unter anderem gänzlich neue Perspektiven für das Wissensmanagement im 3D-Bereich. Er ermöglicht etwa, auf einen Fundus bereits gelöster Konstruktions-Aufgaben zurückzugreifen, um sie in ähnlichen, aber leicht variierten Situationen wiederverwenden zu können. Das Konstruktions-Wissen kann dazu in Form von Bibliotheken parametrisierter, Domänen-spezifischer Modellier-Werkzeuge gesammelt werden. Konkret wird dazu eine neue allgemeine Modell-Beschreibungs-Sprache vorgeschlagen, die "Generative Modeling Language" GML. Als Turing-mächtige "Programmiersprache für Form" stellt sie eine echte Verallgemeinerung existierender Primitiv-basierter 3D-Modellformate dar. Zusammen mit ihrer Runtime-Engine erlaubt die GML, - hochkomplexe 3D-Objekte extrem kompakt zu beschreiben, - die Beschreibung innerhalb von Sekundenbruchteilen auszuwerten, - das Modell adaptiv darzustellen und interaktiv zu betrachten, - und die Modell-Parameter interaktiv zu verändern