Solid modelling for manufacturing: from Voelcker's boundary evaluation to discrete paradigms

Herb Voelcker and his research team laid the foundations of Solid Modelling, on which Computer-Aided Design is based. He founded the ambitious Production Automation Project, that included Constructive Solid Geometry (CSG) as the basic 3D geometric representation. CSG trees were compact and robust, saving a memory space that was scarce in those times. But the main computational problem was Boundary Evaluation: the process of converting CSG trees to Boundary Representations (BReps) with explicit faces, edges and vertices for manufacturing and visualization purposes. This paper presents some glimpses of the history and evolution of some ideas that started with Herb Voelcker. We briefly describe the path from “localization and boundary evaluation” to “localization and printing”, with many intermediate steps driven by hardware, software and new mathematical tools: voxel and volume representations, triangle meshes, and many others, observing also that in some applications, voxel models no longer require Boundary Evaluation. In this last case, we consider the current research challenges and discuss several avenues for further research.Project TIN2017-88515-C2-1-R funded by MCIN/AEI/10.13039/501100011033/FEDER‘‘A way to make Europe’’Peer ReviewedPostprint (published version

Visualization of Tensor Fields in Mechanics

Tensors are used to describe complex physical processes in many applications. Examples include the distribution of stresses in technical materials, acting forces during seismic events, or remodeling of biological tissues. While tensors encode such complex information mathematically precisely, the semantic interpretation of a tensor is challenging. Visualization can be beneficial here and is frequently used by domain experts. Typical strategies include the use of glyphs, color plots, lines, and isosurfaces. However, data complexity is nowadays accompanied by the sheer amount of data produced by large-scale simulations and adds another level of obstruction between user and data. Given the limitations of traditional methods, and the extra cognitive effort of simple methods, more advanced tensor field visualization approaches have been the focus of this work. This survey aims to provide an overview of recent research results with a strong application-oriented focus, targeting applications based on continuum mechanics, namely the fields of structural, bio-, and geomechanics. As such, the survey is complementing and extending previously published surveys. Its utility is twofold: (i) It serves as basis for the visualization community to get an overview of recent visualization techniques. (ii) It emphasizes and explains the necessity for further research for visualizations in this context

Design and Topology Optimisation of Tissue Scaffolds

Tissue restoration by tissue scaffolding is an emerging technique with many potential applications. While it is well-known that the structural properties of tissue scaffolds play a critical role in cell regrowth, it is usually unclear how optimal tissue regeneration can be achieved. This thesis hereby presents a computational investigation of tissue scaffold design and optimisation. This study proposes an isosurface-based characterisation and optimisation technique for the design of microscopic architecture, and a porosity-based approach for the design of macroscopic structure. The goal of this study is to physically define the optimal tissue scaffold construct, and to establish any link between cell viability and scaffold architecture. Single-objective and multi-objective topology optimisation was conducted at both microscopic and macroscopic scales to determine the ideal scaffold design. A high quality isosurface modelling technique was formulated and automated to define the microstructure in stereolithography format. Periodic structures with maximised permeability, and theoretically maximum diffusivity and bulk modulus were found using a modified level set method. Microstructures with specific effective diffusivity were also created by means of inverse homogenisation. Cell viability simulation was subsequently conducted to show that the optimised microstructures offered a more viable environment than those with random microstructure. The cell proliferation outcome in terms of cell number and survival rate was also improved through the optimisation of the macroscopic porosity profile. Additionally artificial vascular systems were created and optimised to enhance diffusive nutrient transport. The formation of vasculature in the optimisation process suggests that natural vascular systems acquire their fractal shapes through self-optimisation

Design and Topology Optimisation of Tissue Scaffolds

Tissue restoration by tissue scaffolding is an emerging technique with many potential applications. While it is well-known that the structural properties of tissue scaffolds play a critical role in cell regrowth, it is usually unclear how optimal tissue regeneration can be achieved. This thesis hereby presents a computational investigation of tissue scaffold design and optimisation. This study proposes an isosurface-based characterisation and optimisation technique for the design of microscopic architecture, and a porosity-based approach for the design of macroscopic structure. The goal of this study is to physically define the optimal tissue scaffold construct, and to establish any link between cell viability and scaffold architecture. Single-objective and multi-objective topology optimisation was conducted at both microscopic and macroscopic scales to determine the ideal scaffold design. A high quality isosurface modelling technique was formulated and automated to define the microstructure in stereolithography format. Periodic structures with maximised permeability, and theoretically maximum diffusivity and bulk modulus were found using a modified level set method. Microstructures with specific effective diffusivity were also created by means of inverse homogenisation. Cell viability simulation was subsequently conducted to show that the optimised microstructures offered a more viable environment than those with random microstructure. The cell proliferation outcome in terms of cell number and survival rate was also improved through the optimisation of the macroscopic porosity profile. Additionally artificial vascular systems were created and optimised to enhance diffusive nutrient transport. The formation of vasculature in the optimisation process suggests that natural vascular systems acquire their fractal shapes through self-optimisation

Large Model Visualization : Techniques and Applications

The size of datasets in scientific computing is rapidly increasing. This increase is caused by a boost of processing power in the past years, which in turn was invested in an increase of the accuracy and the size of the models. A similar trend enabled a significant improvement of medical scanners; more than 1000 slices of a resolution of 512x512 can be generated by modern scanners in daily practice. Even in computer-aided engineering typical models eas-ily contain several million polygons. Unfortunately, the data complexity is growing faster than the rendering performance of modern computer systems. This is not only due to the slower growing graphics performance of the graphics subsystems, but in particular because of the significantly slower growing memory bandwidth for the transfer of the geometry and image data from the main memory to the graphics accelerator. Large model visualization addresses this growing divide between data complexity and rendering performance. Most methods focus on the reduction of the geometric or pixel complexity, and hence also the memory bandwidth requirements are reduced. In this dissertation, we discuss new approaches from three different research areas. All approaches target at the reduction of the processing complexity to achieve an interactive visualization of large datasets. In the second part, we introduce applications of the presented ap-proaches. Specifically, we introduce the new VIVENDI system for the interactive virtual endoscopy and other applications from mechanical engineering, scientific computing, and architecture.The size of datasets in scientific computing is rapidly increasing. This increase is caused by a boost of processing power in the past years, which in turn was invested in an increase of the accuracy and the size of the models. A similar trend enabled a significant improvement of medical scanners; more than 1000 slices of a resolution of 512x512 can be generated by modern scanners in daily practice. Even in computer-aided engineering typical models eas-ily contain several million polygons. Unfortunately, the data complexity is growing faster than the rendering performance of modern computer systems. This is not only due to the slower growing graphics performance of the graphics subsystems, but in particular because of the significantly slower growing memory bandwidth for the transfer of the geometry and image data from the main memory to the graphics accelerator. Large model visualization addresses this growing divide between data complexity and rendering performance. Most methods focus on the reduction of the geometric or pixel complexity, and hence also the memory bandwidth requirements are reduced. In this dissertation, we discuss new approaches from three different research areas. All approaches target at the reduction of the processing complexity to achieve an interactive visualization of large datasets. In the second part, we introduce applications of the presented ap-proaches. Specifically, we introduce the new VIVENDI system for the interactive virtual endoscopy and other applications from mechanical engineering, scientific computing, and architecture

3D printing porous proxies as a new tool for laboratory and numerical analyses of sedimentary rocks

The study of geological processes at the pore-scale has significant implications to understanding many real-world phenomena related to flow in porous media (e.g., hydrogeology, petroleum geology and engineering, CO2 sequestration). While numerical and experimental analyses of sedimentary-rock pore systems have advanced to the characterization of nanometer-scale features, correlation of data across multiple scales of investigation (e.g., between seismic data, core samples, thin-section images, and SEM images) is still challenging. The differences arise in petrophysical properties (e.g., permeability) calculated on the same pore network under varying experimental conditions (e.g., pressure, temperature). 3D printing is a rapidly evolving technology that enables the manufacture of intricate 3D pore-network models (defined in this research as proxies) that can be investigated experimentally and compared to numerical simulations repeatedly. The main objective of my Ph.D. research has been to improve our understanding of the accuracy of 3D-printed pore networks in comparison to natural rocks. In addition, the researched aimed at: 1) the improvement of building and post-processing workflows for accurate geometric replication of pore networks by each 3D printing technique; 2) the establishment and enhancement of validation workflows to test transport properties of rock proxies (e.g., porosity and permeability); and 3) the characterization of artifacts related to 3D printing, post-processing, and validation methods for several common 3D printing methods. While all 3D printers build models layer-by-layer, the physical and chemical properties of build materials, the build process itself, and post-processing methods vary widely. My research results provide the extent to which major 3D printing techniques (binder jet, polyjet, stereolithography, and fused depositional modelling) and associated materials (powders, polymers, resins, and plastics) can generate useful proxies of common porous sandstones (Idaho gray, Berea, and Fontainebleau) that can be tested in the laboratory as natural porous rocks. The accuracy and resolution of each technique was evaluated by testing the 3D printers with simple pore proxies (built from simple numerical models) and natural rock proxies (built from computed tomography data of natural porous rocks). With future advances in 3D printer resolution and materials, the fidelity with which we can reproduce natural rock pore systems should improve

Doctor of Philosophy

dissertationVolumetric parameterization is an emerging field in computer graphics, where volumetric representations that have a semi-regular tensor-product structure are desired in applications such as three-dimensional (3D) texture mapping and physically-based simulation. At the same time, volumetric parameterization is also needed in the Isogeometric Analysis (IA) paradigm, which uses the same parametric space for representing geometry, simulation attributes and solutions. One of the main advantages of the IA framework is that the user gets feedback directly as attributes of the NURBS model representation, which can represent geometry exactly, avoiding both the need to generate a finite element mesh and the need to reverse engineer the simulation results from the finite element mesh back into the model. Research in this area has largely been concerned with issues of the quality of the analysis and simulation results assuming the existence of a high quality volumetric NURBS model that is appropriate for simulation. However, there are currently no generally applicable approaches to generating such a model or visualizing the higher order smooth isosurfaces of the simulation attributes, either as a part of current Computer Aided Design or Reverse Engineering systems and methodologies. Furthermore, even though the mesh generation pipeline is circumvented in the concept of IA, the quality of the model still significantly influences the analysis result. This work presents a pipeline to create, analyze and visualize NURBS geometries. Based on the concept of analysis-aware modeling, this work focusses in particular on methodologies to decompose a volumetric domain into simpler pieces based on appropriate midstructures by respecting other relevant interior material attributes. The domain is decomposed such that a tensor-product style parameterization can be established on the subvolumes, where the parameterization matches along subvolume boundaries. The volumetric parameterization is optimized using gradient-based nonlinear optimization algorithms and datafitting methods are introduced to fit trivariate B-splines to the parameterized subvolumes with guaranteed order of accuracy. Then, a visualization method is proposed allowing to directly inspect isosurfaces of attributes, such as the results of analysis, embedded in the NURBS geometry. Finally, the various methodologies proposed in this work are demonstrated on complex representations arising in practice and research

Reverse Engineering of Materials Using Surfacelet-Based Methods for CAD-Material Integration

To integrate material information into CAD systems, geometric features of material microstructure must be recognized and represented, which is the focus of this paper. Linear microstructure features, such as fibers or grain boundaries, can be found computationally from microstructure images using surfacelet based methods, which include the Radon or Radon-like transform followed by a wavelet transform. By finding peaks in the transform results, linear features can be recognized and characterized by length, orientation, and position. The challenge is that often a feature will be imprecisely represented in the transformed parameter space. In this paper, we demonstrate surfacelet-based methods to recognize microstructure features in parts fabricated by additive manufacturing. We will provide an explicit mathematical method to recognize and to quantify linear geometric features from an image.Mechanical Engineerin

Simplifying The Non-Manifold Topology Of Multi-Partitioning Surface Networks

In bio-medical imaging, multi-partitioning surface networks: MPSNs) are very useful to model complex organs with multiple anatomical regions, such as a mouse brain. However, MPSNs are usually constructed from image data and might contain complex geometric and topological features. There has been much research on reducing the geometric complexity of a general surface: non-manifold or not) and the topological complexity of a closed, manifold surface. But there has been no attempt so far to reduce redundant topological features which are unique to non-manifold surfaces, such as curves and points where multiple sheets of surfaces join. In this thesis, we design interactive and automated means for removing redundant non-manifold topological features in MPSNs, which is a special class of non-manifold surfaces. The core of our approach is a mesh surgery operator that can effectively simplify the non-manifold topology while preserving the validity of the MPSN. The operator is implemented in an interactive user interface, allowing user-guided simplification of the input. We further develop an automatic algorithm that invokes the operator following a greedy heuristic. The algorithm is based on a novel, abstract representation of a non-manifold surface as a graph, which allows efficient discovery and scoring of possible surgery operations without the need for explicitly performing the surgeries on the mesh geometry