A lightweight open-source tool for Meshing within Geosciences

This paper introduces an aircraft wing simulation data set (AWSD) created by an automatic workflow based on creating models, meshing, simulating the wing flight flow field solution, and parameterizing solution results. AWSD is a flexible, independent wing collection of simulations with specific engineering requirements. The data set is applicable to handle computer geometry processing tasks. In contrast to the existing 3D model data set, there are some advantages the scale of this data set is not limited by the collection source, the data files have high quality, no defects, redundancy, and other problems, and the models and simulation are all designed for the specific actual engineering demand. Moreover, AWSD has the characteristics of rich information and a similar model structure, which contributes to the construction of the surrogate model. On the other hand, this data set is suitable for advancing research of data mining in computational geometry graphics. To solve the problem that the CFD flows field results are not intuitive, this paper used the resampling method of surface data to sample the result to the model surface, then segmented the re-sampled 3D mesh surface, and compared with the differences among K-means algorithm, Mini-Batch K-means algorithm, and Spectral Clustering algorithm. AWSD provides 300 sets of models, meshes, CFD simulation results, and parametric results based on ARAP (As-Rigid-As-Possible) and Harmonic mapping for advancing the construction of engineering surrogate models, 3D mesh segmentation, surface resampling, and related geometric processing tasks.

Motion planning for robots operating on 3D rough terrain requires the synergy of various robotic capabilities, from sensing and perception to simulation, planning and prediction. In this paper, we focus on the higher level of this pipeline where by means of physics-based simulation and geometric processing we extract the information that is semantically required for an articulated, tracked robot to optimally traverse 3D terrain. We propose a model that quantifies 3D traversability by accounting for intrinsic robot characteristics and articulating capabilities together with terrain characteristics. By building upon a set of generic cost criteria for a given robot state and 3D terrain patch, we augment the traversability cost estimation by: (i) unifying pose stabilization with traversability cost estimation, (ii) introducing new parameters into the problem that have been previously overlooked and (iii) adapting geometric computations to account for the complete 3D robot body and terrain surface. We apply the proposed model on a state-of-the-art Search and Rescue robot by performing a plurality of tests under varying conditions and demonstrate its efficiency and applicability in real-time.

Quantitative and flexible 3D shape dataset augmentation via latent space embedding and deformation learning

In computer graphics and geometry processing, many traditional problems are now becoming increasingly handled by data-driven methods. In an increasing variety of problem settings, deep networks are state-of-the-art, beating dedicated hand-crafted methods by significant margins. This tutorial gives an organized overview of core theory, practice, and graphics-related applications of deep learning.

Geometry processing has witnessed tremendous development in the last few decades. Starting from acquiring 3D data of real life objects, people have developed practical methods for polishing the raw data usually in the format of point clouds, reconstructing surfaces from the point clouds, cleaning up the surfaces by denoising or fairing, texturing the object surfaces by parametrization to 2D domain, deforming the objects realistically and in real time, and many other advanced tasks. Along with the notable methods is the sophistication of knowledge for working with discrete geometric data, in particular points, triangles, quadrangles and polygons for object representation, with a large body summarized and principled in the field known as discrete differential geometry.
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\nMeanwhile, geometric modeling has come to a new era: unlike the previous industrial practice of spline-based modeling where people tune control points to search for aesthetic shapes, now people want novel ways of interaction. For example, find unknown shapes that are usually characterized to have variational and physical properties of interest. Also user-friendly modeling methods like sketching have gained remarkable attention and advances. We note that many of these surface modeling problems could be regarded as asking for surfaces with special differential geometric properties. To be specific, people find surfaces of minimal area for modeling soap films that are balanced under surface tension; surfaces that if fabricated could stand firmly and are therefore important in real life architectural structures, are described by having homogeneous relative mean curvatures; even for surfaces filling up sketched 3D curves, the significant property of a good filling surface is that the curves follow principal curvature directions of the surface.
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\nThis thesis presents our results in developing effective algorithms for modeling the above mentioned surfaces, by adapting knowledge and techniques in geometry processing, especially from computational and discrete differential geometry. In particular, we extend surface remeshing techniques to model high quality Constant Mean Curvature (CMC) surfaces that are models of soap films and bubbles, use power diagrams and the dual regular triangulations to parametrize and process self-supporting surfaces, and apply direction field modeling and discrete curvature adaptation to surfacing sketch curve networks.

Hydrogel actuators with complex 3D initial shapes show numerous important applications, but it remains challenging to fabricate such actuators. This article describes a polyelectrolyte-based strategy for modulating small-scale internal stresses within hydrogels to construct complex actuators with tailored 3D initial shapes. Introducing polyelectrolytes into precursor solutions significantly enhances the volume shrinkage of hydrogel networks during polymerization, allowing us to modulate internal stresses. Photopolymerization of these polyelectrolyte-containing solutions through a mask produces mechanically strong hydrogel sheets with large patterned internal stresses. Consequently, these hydrogel sheets attain complex 3D initial shapes at equilibrium, in contrast to the planar initial configuration of 2D actuators. We demonstrate that these 3D actuators can reversibly transform into other 3D shapes (i.e., 3D-to-3D shape transformations) in response to external stimuli. Additionally, we develop a predictive model based on the Flory-Rehner theory to analyze the polyelectrolyte-mediated shrinking behaviors of hydrogel networks during polymerization, allowing precise modulation of shrinkage and internal stress. This polyelectrolyte-boosted shrinking mechanism paves a route to the fabrication of high-performance 3D hydrogel actuators.

Virtual Un-manufacturing of Fibre-steered Preforms for Complex Geometry Composites

This research explores how to incorporate physical quantities such as mass distributions, internal deformation energies, damping, and forces into the T-spline geometric substrate and its related geometric processing algorithms. The research is inspired by the successful physics-based design paradigm of dynamic non-uniform rational B-splines (D-NURBS) and T-spline technology. D-NURBS introduce physical quantities into the NURBS geometric formulation through the application of Lagrangian mechanics and provide a new design paradigm that integrates standard geometric design and physics-based design. However, there exist serious weaknesses within the D-NURBS scheme. D-NURBS do not support local refinement which is very important in geometric design and engineering computation, D-NURBS generally do not have closed-form solutions and need numerical methods, and currently D-NURBS lack very effective surface editing tools. T-splines are a free-form surface technology that solve most of the limitations inherent in NURBS representation. In particular, T-splines allow local refinement and are well-suited for geometric modeling, and engineering computation and analysis. Therefore, it is tempting to develop physically-based dynamic T-splines (or PD-T-splines) and related algorithms to overcome the weaknesses of D-NURBS. In this thesis, we first present the formulation of PD-T-splines. The dynamic equation that governs the motion of the PD-T-splines is
\nderived based on the work-energy version of Lagrangian Dynamics. The highly non-linear equation motivates us to further propose Efficient PD-T-splines (or E-PD-T-splines) by freezing the weights, whose dynamic equation becomes a linear ordinary differential equations (ODE). A closed form solution is derived based on the physical point of view that a vibration system can be viewed as a coupling of individual vibrant modes. Based on this physical insight, a modal reduction technique is developed to reduce computational complexity. We also consider incorporating the local refinement property of T-splines into PD-T-splines, which means the change of the generalized coordinates as well as the dynamic equation. We present an efficient method to achieve local update of these physical matrices along with local refinement. Second, we present a new modeling tool based on general curve handles. Curve based modeling techniques become prevalent and are shown more effective than point based. We propose to deform the T-spline surface by adjusting the sketched curve handles on the surface. The curve handle is defined by the composition between a 2D domain curve and the incident T-spline surface. To facilitate the adjustment of the composite curve, physically based dynamic composite (PBDC) curve is developed directly based on the composite representation, which supports arbitrary type of 2D domain curves. To avoid the possible rank deficiency of its dynamic equation, we carefully examine the relation between the dimension of the composite blending functions and the rank of their corresponding construction matrix. We present an approach to identify a basis for the vector space spanned by those blending functions, and compute their dependency. After filtering out the deficient DOFs, we obtain a regularized PBDC curve, which serves as the main tool to adjust the general curve handle on the surface. Finally, the surface deformation is achieved through introducing the curve force into PD-T-splines, which connects the handle curve and the 3D target curve in space. Third, to explore geometric processing of PD-T-Splines such as morphing and rendering, we consider the problem of constrained mapping. We reveal the relation between a smooth mapping and its induced transformation and propose a refinement strategy based on the longest edge bisection to guarantee that the induced transformation is locally foldover free if the smooth mapping is locally bijective. To make the RBF-based mapping locally bijective, we propose to find non-intersecting trajectories to guide the warping and derive a bound for the warping stepsize. Furthermore, to make the warping process more effective, we derive the truly foldover free condition for the induced transformation. Based on this condition and the bound for the local bijective smooth mapping, we determine whether we perform local mesh refinement or warping and the actual warping stepsize as well. Integrating all these technical components provides a constrained mesh warping algorithm that is effective, provably foldover free, able to handle a large number of constraints, and able to output a visually pleasing result without extra smoothing optimization. Fourth, we present a novel solution to the T-spline morphing problem. It is well known that morphing involves two basic steps: vertex correspondence and vertex path. We solve the vertex correspondence problem by consistent approximation technique, which aligns important feature points using our proposed constrained mapping technique and approximates the two input surfaces using the same preimage of control T-mesh. Observing that PD-T-splines naturally produce the dynamic evolution from one pose to another, the vertex path problem can be readily solved by introducing PD-T-splines into morphing. In this case, we impose the boundary conditions into the ODE, which is also analytically solvable. Furthermore, we also introduce extra DOFs into the physical model to enable speed control. Finally, we consider the rendering of the dynamic evolution in both modeling and morphing. We present an efficient method to map a static image onto the evolution sequence. Here we would like to achieve dynamic rendering in realtime along with dynamic evolution. Rather than applying the technique on every frame separately, we propose to establish the constrained map making use of the existing map. We first compute a satisfactory map for the initial frame. Then we generate the subsequent maps from the first map, which only involves the calculation of the barycentric coordinates. In this way, the proposed method can render the dynamic evolution in realtime.

One of the fundamental problems of computer vision is to extract 3D shape and motion from images. This can be achieved when a scene or object is observed from different viewpoints or over a period of time. There is a wide range of applications, ranging from digitizing cultural heritage to vision-based autonomous robot navigation. This talk will present several approaches to solve this problem. First, we’ll discuss techniques for 3D shape recovery for static objects and scenes. One particular case is the 3D mapping and localization in large environments from images, e.g. urban 3D reconstruction from vehicleborne cameras or localization from cell-phone images. Next, we’ll shift our focus to modeling dynamic scenes, e.g. people who are moving around. In addition to explicitly 3D modeling an event, we'll consider the possibility to perform video-based rendering from casually captured videos. Speaker Bio-Sketch: Marc Pollefeys is a full professor in the Dept. of Computer Science of ETH Zurich since 2007 where he is the head of the Institute for Visual Computing and leads the Computer Vision and Geometry lab. He currently also remains associated with the Dept. of Computer Science of the University of North Carolina at Chapel Hill where he started as an assistant professor in 2002 and became an associate professor in 2005. Before this he was a postdoctoral researcher at the Katholieke Universiteit Leuven in Belgium, where he also received his M.S. and Ph.D. degrees in 1994 and 1999, respectively. His main area of research is computer vision. One of his main research goals is to develop flexible approaches to capture visual representations of real world objects, scenes and events. Dr. Pollefeys has received several prizes for his research, including a Marr prize, an NSF CAREER award, a Packard Fellowship and a European Research Council Starting Grant. He is the author or co-author of more than 130 peer-reviewed publications. He is the General Chair for the European Conference on Computer Vision 2014 (ECCV), was a Program Co-Chair for the IEEE Conference on Computer Vision and Pattern Recognition 2009 (CVPR), was general/program co-chair of the Third Symposium on 3D Data Processing, Visualization and Transmission and has organized workshops and courses at major vision and graphics conferences and has served on the program committees of many conferences. Prof. Pollefeys is/was on the Editorial Board of the IEEE Transactions on Pattern Analysis and Machine Intelligence and the International Journal of Computer Vision as well as several other journals in computer vision, graphics and robotics.

Representing complex shapes with simple primitives in high accuracy is\nimportant for a variety of applications in computer graphics and geometry\nprocessing. Existing solutions may produce suboptimal samples or are complex to\nimplement. We present methods to approximate given shapes with user-tunable\nnumber of spheres to balance between accuracy and simplicity: touching\nmedial/scale-axis polar balls and k-means smallest enclosing circles. Our\nmethods are easy to implement, run efficiently, and can approach quality\nsimilar to manual construction.\n

Finding distortion-minimizing homeomorphisms between surfaces of arbitrary genus is a fundamental task in computer graphics and geometry processing. We propose a simple method utilizing intrinsic triangulations, operating directly on the original surfaces without going through any intermediate domains such as a plane or a sphere. Given two models A and B as triangle meshes, our algorithm constructs a Compatible Intrinsic Triangulation (CIT), a pair of intrinsic triangulations over A and B with full correspondences in their vertices, edges and faces. Such a tessellation allows us to establish consistent images of edges and faces of A's input mesh over B (and vice versa) by tracing piecewise-geodesic paths over A and B. Our algorithm for constructing CITs, primarily consisting of carefully designed edge flipping schemes, is empirical in nature without any guarantee of success, but turns out to be robust enough to be used within a similar second-order optimization framework as was used previously in the literature. The utility of our method is demonstrated through comparisons and evaluation on a standard benchmark dataset.

The efficient and practical representation and processing of geometrically or topologically complex shapes often demands a partitioning into simpler patches. Possibilities range from unstructured arrangements of arbitrarily shaped patches on the one end, to highly structured conforming networks of all‐quadrilateral patches on the other end of the spectrum. Due to its regularity, this latter extreme of conforming partitions with quadrilateral patches, called quad layouts, is most beneficial in many application scenarios, for instance enabling the use of tensor‐product representations based on splines or Bézier patches, grid‐based multi‐resolution techniques and discrete pixel‐based map representations. However, this type of partition is also most complicated to create due to the strict inherent structural restrictions. Traditionally often performed manually in a tedious and demanding process, research in computer graphics and geometry processing has led to a number of computer‐assisted, semi‐automatic, as well as fully automatic approaches to address this problem more efficiently. This survey provides a detailed discussion of this range of methods, treats their strengths and weaknesses and outlines open problems in this field of research.

Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal parameterizations of the surfaces. In this paper, we propose a novel algorithm for the conformal parameterization of a simply-connected open surface onto the unit disk, which significantly speeds up the computation, enhances the conformality and stability, and guarantees the bijectivity. The conformality distortions at the inner region and on the boundary are corrected by two steps, with the aid of an iterative scheme using quasi-conformal theories. Experimental results demonstrate the effectiveness of our proposed method.

Direction fields and vector fields play an increasingly important role in computer graphics and geometry processing. The synthesis of directional fields on surfaces, or other spatial domains, is a fundamental step in numerous applications, such as mesh generation, deformation, texture mapping, and many more. The wide range of applications resulted in definitions for many types of directional fields: from vector and tensor fields, over line and cross fields, to frame and vector-set fields. Depending on the application at hand, researchers have used various notions of objectives and constraints to synthesize such fields. These notions are defined in terms of fairness, feature alignment, symmetry, or field topology, to mention just a few. To facilitate these objectives, various representations, discretizations, and optimization strategies have been developed. These choices come with varying strengths and weaknesses. This course provides a systematic overview of directional field synthesis for graphics applications, the challenges it poses, and the methods developed in recent years to address these challenges.

This paper presents an accurate method of calculating design sensitivities of behaviour variables, such as displacements and stress, in FE structural shape optimisation problems. Its applicability to unstructured meshes is emphasised. The semi-analytical method is applied to the determination of the design sensitivities of behaviour variables in structural shape optimisation. It is shown how the computation of the geometric sensitivities (i.e. the sensitivity of internal points in the problem domain to boundary perturbations) is a primary task to carry out the sensitivity analysis. A BEM based pointtracking method, which is particularly applicable to unstructured meshes, is developed and used, in conjunction with FT) approximation, to determine these geometric sensitivities. Three benchmark examples, with unstructured meshes, are used to show the application of the method and results from these show that the geometric sensitivity calculations are easily carried out using the BEM point tracking approach. Design sensitivities calculated compare favourably with analytical solutions.