Partial differential equations can be solved on general polygonal and polyhedral meshes, through Polytopal Element Methods (PEMs). Unfortunately, the relation between geometry and analysis is still unknown and subject to ongoing research in order to identify weaker shape-regularity criteria under which PEMs can reliably work. We propose PEMesh, a graphical framework to support the analysis of the relation between the geometric properties of polygonal meshes and the numerical performances of PEM solvers. PEMesh allows the design of polygonal meshes that increasingly stress some geometric properties, by exploiting any external PEM solver, and supports the study of the correlation between the performances of such a solver and geometric properties of the input mesh. Furthermore, it is highly modular, customisable, easy to use, and provides the possibility to export analysis results both as numerical values and graphical plots. PEMesh has a potential practical impact on ongoing and future research activities related to PEM methods, polygonal mesh generation and processing.
Estimating the differential properties of a signal sampled on a surface is of paramount importance in many fields of applied sciences. In the common practice, the surface is discretized with a polygonal mesh, the signal is sampled at its vertices and extended linearly over the triangles. This means that the polyhedral metric is assumed over the surface; the first derivatives of the signal become discontinuous across edges; and the second derivatives vanish. We present a new method based on surface fitting, which efficiently estimates the metric tensor, and the first and second order Riemannian differential operators at any point on the surface. All our differential operators are smooth within each triangle and continuous across the edges, providing a much better estimate of differential quantities on the - yet unknown - underlying smooth manifold.
The following paper proposes the study, the design and the preliminary development of a solution for supporting users without programming experience in creating stories in a Mixed Reality environment. We focus on a Mixed Reality interface split into two parts: the creation and observation phases. During the creation phase, the end user can build his/her own story in the immersive mode of the Mixed Reality experience. The user can also enjoy the stories that other users have designed by seeing the characters appear in their surrounding environment.
In this paper, we discuss the problem of converting a 3D mesh into an assembly of LEGO blocks. The major challenge of this task is how to aggregate the voxels derived by the shape discretization into a set of standard bricks guaranteeing global connectivity. Weproposean outside-in priority-based heuristic method based on the analysis of the critical regions that are more likely to cause the creation of a legal assembly to fail. We show that our graph-building heuristic provides relevant advantages, making it easier to obtain a connected graph with good properties with respect to the layer-based or random aggregation strategies applied in most of the optimization approaches. We also propose BRICKS, a novel dataset for the evaluation of aggregation strategies. It includes voxelizations at 3 different resolutions of 33 shapes and allows the easy comparison of different voxel aggregation strategies independently of the shape discretization step and also considering their scalability. We use it to evaluate our approach with respect to graph-based connectivity measures, showing the advantages of the proposed strategy.
Shape matching is a central problem in geometry processing applications, ranging from texture transfer to statistical shape analysis. The functional maps framework provides a compact representation of correspondences between discrete surfaces, which is then converted into point-wise maps required by real-world applications. The vast majority of methods based on functional maps involve the eigenfunctions of the Laplace-Beltrami Operator (LB) as the functional basis. A primary drawback of the LB basis is that its energy does not uniformly cover the surface. This fact gives rise to regions where the estimated correspondences are inaccurate, typically at tiny parts and protrusions. For this reason, state-of-the-art procedures to convert the functional maps (represented in the LB basis) into point-wise correspondences are often error-prone. We propose PC-G AU , a new functional basis whose energy spreads on the whole shape more evenly than LB. As such, PC-G AU can replace the LB basis in existing shape matching pipelines. PC-G AU consists of the principal vectors obtained by applying Principal Component Analysis (PCA) to a dictionary of sparse Gaussian functions scattered on the surfaces. Through experimental evaluation of established benchmarks, we show that our basis produces more accurate point-wise maps — compared to LB — when employed in the same shape-matching pipeline
To fully understand a Natural System, the representation of an environmental variable’s distribution in 3D space is a mandatory and complex task. The challenge derives from a scarcity of samples number in the survey domain (e.g., logs in a reservoir, soil samples, fixed acquisition sampling stations) or an implicit difficulty in the in-situ measurement of parameters. Field or lab measurements are generally considered error-free, although not so. That aspect, combined with conceptual and numerical approximations used to model phenomena, makes the results intrinsically less performing, fading the interpretation. In this context, we design a computational infrastructure to evaluate spatial uncertainty in a multi-scenario application in Environment survey and protection, such as in environmental geochemistry, coastal oceanography, or infrastructure engineering. Our Research aims to expand the operative knowledge by developing an open-source stochastic tool, named MUSE, the acronym for Modeling Uncertainty as a Support for Environment. At this stage, the methodology mainly includes the definition of a flexible environmental data format, a geometry processing module to discretize the space, and geostatistics tools to evaluate the spatial continuity of sampled parameters, predicting random variable distribution. The implementation of the uncertainty module and the development of a graphic interface for ad-hoc visualization will be integrated as the next step. The poster summarizes research purposes, and MUSE computational code structure developed so far.
In metal 3D printing, and in particular in the production of dental implants and prosthodontics, a careful geometric analysis of the parts is key to maximize the overall throughput and minimize fabrication costs. Herewith we describe the main results obtained within the European Project DIGITBrain/ProMED, whose objective is to optimize the production of customized metal medical devices. ProMED delivers a digital twin of an existing production pipeline and allows for the quick simulation of a large number of fabrication scenarios. This is achieved thanks to a clever geometric analysis driving the optimal orientation of the part in the platform combined with a geometry-based process simulator that makes it possible to estimate fabrication time, material consumption, human labour, and other useful information that greatly supports users in the task of optimizing the overall fabrication performances from many meaningful points of view. Compared to standard simulation software provided by printer vendors, our approach can be orders of magnitude faster: this makes it possible to analyze and compare a great number of scenarios to support companies in their day-by-day decisions for real productions.
We present a novel visualization technique for geometry-based visualization of vector fields. Our approach generalizes and combines several existing approaches in a flexible framework using a scalable GPU-accelerated implementation. We map characteristic lines to a variety of glyphs. The user can define multiple cross-sectional shapes that will be used for extrusion. Our system interpolates between these shapes as requested, either based on attributes of the vector field and the characteristic lines or using global user-controlled parameters. Thus, a single characteristic line can use different cross-sectional shapes in different parts to aid the visualization of different phenomena. Transitions can be smooth or discrete and we support highlighting of silhouettes. Additionally, we track and visualize the rotation in the vector field and offer full control of the color mapping, the opacity and the radii along the characteristic lines. Texture-based approaches such as 3D line integral convolution (3D LIC) offer another avenue to vector field visualization. In 3D, they typically rely on sparsely placed seed points. We emulate their appearance with our geometry-based approach through an approximation of the volume integral within our glyphs. Combined with fast order-independent transparency, our GPU implementation achieves fast rendering, even at high resolutions, while keeping the memory footprint moderate. CCS Concepts • Human-centered computing → Visualization systems and tools;
The recent studies on GAN achieved impressive results in image synthesis. However, they are still not so perfect that output images may contain unnatural regions. We propose a tuning method for generator networks trained by GAN to improve their results by interactively removing unexpected objects and textures or changing the object colors. Our method could find and ablate those units in the generator networks that are highly related to the specific regions or their colors. Compared to the related studies, our proposed method can tune pre-trained generator networks without relying on any additional information like segmentation-based networks. We built the interactive system based on our method, capable of tuning the generator networks to make the resulting images as expected. The experiments show that our method could remove only unexpected objects and textures. It could change the selected area color as well. The method also gives us some hints to discuss the properties of generator networks which layers and units are associated with objects, textures, or colors.
Integer Grid Maps (IGM) are a class of mappings characterized by integer isolines that align up to unit translations and rotations of multiples of 90 degrees. They are widely used in the context of remeshing, to lay a quadrilateral grid onto the mapped surface. Computing an IGM is notoriously a challenging task, because it requires to solve a numerical problem with mixed discrete and continuous variables which is known to be NP-Hard. As a result, state of the art methods rely on heuristics that may occasionally fail to produce a valid quadrilateral mesh. Existing pipelines incorporate a final sanitization step which attempts to fix such defects, but no guaranteees can be given in this regard. In this paper we propose a simple topological construction that allows to reduce the problem of computing an IGM to the one of mapping a topological disk to a convex domain. This is a much easier problem to deal with, because it does not endow integer translational and rotational constraints, permitting to obtain a parameterization that is guaranteed to incorporate all the correct integer transitions and to not contain degenerate or inverted elements. Despite provably correct, the so generated maps contain a considerable amount of geometric distortion and a poor quad connectivity, making this technique more suitable for a robust initialization rather than for the computation of an application-ready IGM. In the article we present the details of our construction, also analyzing its geometric and topological properties.
The use of elastic deformation of straight or flat structural components for achieving complex 3D shapes has acquired attention from recent computational design works, particularly in architectural geometry. The so-called bending-active structures are built by deforming and restraining the components mutually to form a stable configuration. While the manufacturing of components from flat raw material and their assembly are simple and inexpensive, the complexity lies in the design phase, in which computational tools are required to predict the deformation and forces under a prescribed form-finding load or displacement. Currently, there is a scarcity of open and efficient tools that hinder the design of bending-active structures. This paper proposes and validates an open-source computational tool for predicting the static equilibrium of general bending-active structures in the form of a network of elements using the dynamic relaxation method. We apply our tool to various real-world examples and compare the results to a commercial FEM solver. The proposed tool shows accuracy and good time performance, making it a significant addition to the available open-source structural engineering toolkit.
Target acquisition is a basic task that is part of almost any high-level interaction in 3D environments. Therefore, providing accurate selection is a necessity for most applications and games. When targets are small and scenes are cluttered, selection becomes inaccurate. This may lead to selecting the wrong elements which, apart from the time consumed, may become a frustrating experience. Besides the unintentional tremor, the button/trigger press for effectively selecting an element further reduces our stability, increasing the probability of an incorrect target acquisition. In this paper, we focus on molecular visualization and address the problem of selecting atoms, which are rendered as small spheres. We build upon previous progressive selection algorithms and present two alternatives that accelerate the selection of neighbors after an initial selection. We have implemented and analyzed such techniques through a formal user study and found that they were highly appreciated by the users. These selection methods may be suitable for other crowded environments beyond molecular visualization. (see https://www.acm.org/publications/class-2012)
We propose a physically-based, multispectral simulation to render underwater scenarios in real time, which also takes into account the RGB response curve of arbitrary sensors. Underwater illumination is mostly governed by multiple scattering, where light is scattered a number of times between particles before reaching the sensor. This phenomenon is therefore very low frequency and can be modeled as a function of depth and wavelength. Our approximation to multiple scattering is based on the measurable coefficient of diffuse downwelling attenuation. We show examples simulating underwater appearance under different scattering, absorption and downwelling coefficients of the Jerlov water types.
Nowadays, a high-fidelity 3d model representation can be obtained easily by means of handheld optical scanners, which offer a good level of reconstruction quality, portability, and low latency in scan-to-data. However, it is well known that the tracking process can be critical for such devices: sub-optimal lighting conditions, smooth surfaces in the scene, or occluded views and repetitive patterns are all sources of error. In this scenario, recent disruptive technologies such as sparse convolutional neural networks have been tailored to address common problems in 3D vision and analysis. Our work aims to integrate the most promising solutions into an operating framework which can then be used to achieve compelling results in 3D real-time reconstruction. Several scenes from a dataset containing dense views of objects are tested using our proposed pipeline and compared with the current state-of-the-art of online reconstruction. CCS Concepts • Computing methodologies → Reconstruction; 3D imaging; Tracking; Artificial intelligence; • Hardware → Emerging tools
Microfacet models suffer from a significant limitation: they only simulate a single interaction between light and surface, ignoring the subsequent scattering across the microfacets. As a consequence, the BSDF is not energy preserving, resulting in an unexpected darkening of rough specular surfaces. Energy compensation methods face this limitation by adding to the BSDF a secondary component accounting for multiple scattering contributions. While these methods are fast, robust and can be added to a renderer with relatively minor modifications, they involve the computation of the directional albedo. This quantity is expressed as an integral that does not have a closed-form solution, but it needs to be precomputed and stored in tables. These look-up tables are notoriously cumbersome to use, in particular on GPUs. This work obviates the need of look-up tables by fitting an analytic approximation of the directional albedo, which is a more practical solution. We propose a 2D rational polynomial of degree three to fit conductors and a 3D rational polynomial of degree three to fit dielectrics and materials composed of a specular layer on top of a diffuse one, such as plastics. We enforce energy preservation by rescaling the specular albedo, thus maintaining the same lobe shape. We validated our results via the furnace test, highlighting that materials rendered using our analytic approximations match almost exactly the behaviour of the ones rendered with the use of look-up tables, resulting in an energy-preserving model even at maximum roughness. The software we use to fit coefficients is open-source and can be used to fit other BSDF models as well.
Computational methods to compute similarities between floor plans can help architects explore floor plans in large datasets to avoid duplication of designs and to search for existing plans that satisfy their needs. Recently, LayoutGMN delivered state-of-the-art performance for computing similarity scores between floor plans. However, the high computational costs of LayoutGMN make it unsuitable for the aforementioned applications. In this paper, we significantly reduced the times needed to query results computed by LayoutGMN by projecting the floor plans into a common low-dimensional (e.g., three) data space. The projection is done by optimizing for coordinates of floor plans with Euclidean distances mimicking their similarity scores originally calculated by LayoutGMN. Quantitative and qualitative evaluations show that our results match the distributions of the original LayoutGMN similarity scores. User study shows that our similarity results largely match human expectations.
We propose a computational approach to find a minimal set of 360-degree camera placements that together sufficiently cover an indoor environment for the building documentation problem in the architecture, engineering, and construction (AEC) industries. Our approach, based on a simple integer programming (IP) problem formulation, solves very efficiently and globally optimally. We conducted a study of using panoramas to capture the appearances of a real-world indoor environment, in which we found that our computed solutions are better than human solutions decided by both non-professional and professional users.
In this paper, we introduce a new approach for retrieval and classification of 3D models that directly performs in the Computer-Aided Design (CAD) format without any conversion to other representations like point clouds or meshes, thus avoiding any loss of information. Among the various CAD formats, we consider the widely used STEP extension, which represents a standard for product manufacturing information. This particular format represents a 3D model as a set of primitive elements such as surfaces and vertices linked together. In our approach, we exploit the linked structure of STEP files to create a graph in which the nodes are the primitive elements and the arcs are the connections between them. We then use Graph Neural Networks (GNNs) to solve the problem of model classification. Finally, we created two datasets of 3D models in native CAD format, respectively, by collecting data from the Traceparts model library and from the Configurators software modeling company. We used these datasets to test and compare our approach with respect to state-of-the-art methods that consider other 3D formats. Our code is available at https://github.com/divanoLetto/3D_STEP_Classification
