Boundary Representation Research Articles

Construction of a 3D Stratum Model Based on a Solid Model

A three-dimensional stratum model stratum model is a useful auxiliary tool for geotechnical engineering and other exploration work. The existing methods for stratum model construction lack complete topological descriptions of entities, so it is difficult to apply them to 3D geological modeling with complex geometric structures and complex topological relationships between modules. To solve the above problem, in this paper, the boundary representation method is used to represent the arbitrarily-shaped geological entities, and the half winged-edge-face structure topological structure is proposed to describe the topological information of the stratum model for a complex entity. The topological structure can record the topological information of the solid stratum model completely, thereby providing the basis for operations with the model and the applications of various algorithms. Based on this topological structure, the construction process for a 3D solid stratum model is proposed. The reliability and effectiveness of the constructed 3D solid stratum model are verified by an engineering case. The solid stratum model not only solves the geological modeling problem with respect to complex geometric and topological relations, but also provides a new method and idea for 3D geological modeling.

Triangle mesh skeletonization using non-deterministic voxel thinning and graph spectrum segmentation

In the context of shape processing, the estimation of the medial axis is relevant for the simplification and re-parameterization of 3D bodies. The currently used methods are based on (1) General fields, (2) Geometric methods and (3) voxel-based thinning. They present shortcomings such as (1) overrepresentation and non-smoothness of the medial axis due to high frequency nodes and (2) biased-skeletons due to skewed thinning. To partially overcome these limitations, this article presents a non-deterministic algorithm for the estimation of the 1D skeleton of triangular B-Reps or voxel-based body representations. Our method articulates (1) a novel randomized thinning algorithm that avoids possible skewings in the final skeletonization, (2) spectral-based segmentation that eliminates short dead-end branches, and (3) a maximal excursion method for reduction of high frequencies. The test results show that the randomized order in the removal of the instantaneous skin of the solid region eliminates bias of the skeleton, thus respecting features of the initial solid. An Alpha Shape-based inversion of the skeleton encoding results in triangular boundary Representations of the original body, which present reasonable quality for fast non-minute scenes. Future work is needed to (a) tune the spectral filtering of high frequencies off the basic skeleton and (b) extend the algorithm to solid regions whose skeletons mix 1D and 2D entities.

Geometry Design Using Function Representation on a Sparse Hierarchical Data Structure

In this study, we introduce new algorithms for efficient function representation (F-rep) based geometric design using the sparse and dynamic voxel data structure Volumetric Dynamic B+ tree (VDB). The level set method is used as the F-rep method. Specifically, we develop the Fast Sweeping Method for boundary points to level set surfaces velocity extension for efficient geometry optimization on such sparse and dynamic data structures. For benchmarking, we developed a level set method in-house, using state of the art algorithms on a dense data structure, which we use as a reference. OpenVDB, which is an open source library, is used to store and modify the sparse and dynamic voxel data. Our results show that the developed method is up to an order of magnitude faster than the reference method, while only consuming a small fraction of the memory. Finally, we apply the level set method using the sparse and dynamic data structure for lattice infill designs, where we show that the sparse F-rep geometry file is more than an order of magnitude smaller in size than a conventional boundary representation (B-rep) formats such as a stereolithography (STL) file.

Boundary Coding Representation for Organ Segmentation in Prostate Cancer Radiotherapy.

Accurate segmentation of the prostate and organs at risk (OARs, e.g., bladder and rectum) in male pelvic CT images is a critical step for prostate cancer radiotherapy. Unfortunately, the unclear organ boundary and large shape variation make the segmentation task very challenging. Previous studies usually used representations defined directly on unclear boundaries as context information to guide segmentation. Those boundary representations may not be so discriminative, resulting in limited performance improvement. To this end, we propose a novel boundary coding network (BCnet) to learn a discriminative representation for organ boundary and use it as the context information to guide the segmentation. Specifically, we design a two-stage learning strategy in the proposed BCnet: 1) Boundary coding representation learning. Two sub-networks under the supervision of the dilation and erosion masks transformed from the manually delineated organ mask are first separately trained to learn the spatial-semantic context near the organ boundary. Then we encode the organ boundary based on the predictions of these two sub-networks and design a multi-atlas based refinement strategy by transferring the knowledge from training data to inference. 2) Organ segmentation. The boundary coding representation as context information, in addition to the image patches, are used to train the final segmentation network. Experimental results on a large and diverse male pelvic CT dataset show that our method achieves superior performance compared with several state-of-the-art methods.

Gelfand transforms and boundary representations of complete Nevanlinna–Pick quotients

The main objects under study are quotients of multiplier algebras of certain complete Nevanlinna–Pick spaces, examples of which include the Drury–Arveson space on the ball and the Dirichlet space on the disc. We are particularly interested in the non-commutative Choquet boundaries for these quotients. Arveson’s notion of hyperrigidity is shown to be detectable through the essential normality of some natural multiplication operators, thus extending previously known results on the Arveson–Douglas conjecture. We also highlight how the non-commutative Choquet boundaries of these quotients are intertwined with their Gelfand transforms being completely isometric. Finally, we isolate analytic and topological conditions on the so-called supports of the underlying ideals that clarify the nature of the non-commutative Choquet boundaries.

SpanBERT: Improving Pre-training by Representing and Predicting Spans

We present SpanBERT, a pre-training method that is designed to better represent and predict spans of text. Our approach extends BERT by (1) masking contiguous random spans, rather than random tokens, and (2) training the span boundary representations to predict the entire content of the masked span, without relying on the individual token representations within it. SpanBERT consistently outperforms BERT and our better-tuned baselines, with substantial gains on span selection tasks such as question answering and coreference resolution. In particular, with the same training data and model size as BERTlarge, our single model obtains 94.6% and 88.7% F1 on SQuAD 1.1 and 2.0 respectively. We also achieve a new state of the art on the OntoNotes coreference resolution task (79.6% F1), strong performance on the TACRED relation extraction benchmark, and even gains on GLUE. 1

Functional optimization of fluidic devices with differentiable stokes flow

We present a method for performance-driven optimization of fluidic devices. In our approach, engineers provide a high-level specification of a device using parametric surfaces for the fluid-solid boundaries. They also specify desired flow properties for inlets and outlets of the device. Our computational approach optimizes the boundary of the fluidic device such that its steady-state flow matches desired flow at outlets. In order to deal with computational challenges of this task, we propose an efficient, differentiable Stokes flow solver. Our solver provides explicit access to gradients of performance metrics with respect to the parametric boundary representation. This key feature allows us to couple the solver with efficient gradient-based optimization methods. We demonstrate the efficacy of this approach on designs of five complex 3D fluidic systems. Our approach makes an important step towards practical computational design tools for high-performance fluidic devices.

A GIS-based Methodology for Assigning a Flux Boundary to a Numerical Groundwater Flow Model and Its Effect on Model Calibration

Abstract Groundwater flow modeling is an important tool for understanding and computing hydrology and water availability of an aquifer zone. However, an accurate representation of boundaries and their initial conditions are vital for simulation of the groundwater flow phenomena. In this study, efforts have been made to develop a GIS based methodology for estimating flux across boundaries of the study area using Darcy flow tool. The spatial maps of topography, bore log, transmissivity, hydraulic conductivity, porosity and groundwater levels for the study area were created in ArcGIS 9.3.1 using krigging method. A buffer zone of 1×1 km2 cell size was created on inner and outer side of the boundaries and Darcy flow model was used to estimate specified flux across boundaries. The groundwater behavior of the study area was simulated with specified flux boundary condition (Neumann boundary condition) and no flow boundary condition to assess importance and estimation accuracy of estimated flux. Darcy model output indicates that flux across the boundaries contributed about 36.20 mm in average annual change in groundwater table depth. With estimated specified flux, simulation accuracy of groundwater flow model (R2) increased to 0.97 from 0.90. The satisfactory level (R2=0.97) of simulation accuracy reveals that developed methodology can be used for estimating flux across boundaries in the absence of physical boundaries.

Development of the PC-based Integrated Interface System of STEP file for CNC Machining Application: Circular Features

STEP is a general data format that observes the international standard ISO 10303-21. STEP means Standard for the Exchange of Product model data. It consists of the 3D geometry of a computer-aided design (CAD) model in the configuration of boundary representation (B-rep). By extracting, refining and decoding the geometric data correctly, the data can be utilized for writing G-code for Computer Numerical Control (CNC) machining application. Usually G-codes can either be manually generated by skilled machinists or automatically generated by computer-aided manufacturing (CAM) software. However, manually generated G-code is inefficient and susceptible to error. Meanwhile automated generation G-code requires significant setup cost. This paper describes the design and development of an integrated interface system, an instrument aimed to be used to analyze STEP files and generate machining tool path based on ISO 6983 format. This developed interface reduces the need for high setup cost as well as eliminates human limitations. The interface at present is able of detecting circular machining features on the workpiece. Circular machining features are created by 3D modelling software and retained as STEP file. The STEP file which contains geometrical data is then uploaded to the interface system as an input file which is structurally analyzed and processed. Finally, the ideal machining tool path in the G Code format is proposed and generated. By bypassing the CAM software and its proprietary post processor, the outcome of this research is important to enhance compatibility between different CNC machine systems

Multiobjective evolutionary optimization for feature-based simplification of 3D boundary representation models

Boundary representation (B-rep) is one of the most common techniques for representing three-dimensional (3D) shapes. In this method, shapes are described mathematically based on the vertices, edges, and faces present. B-rep models are generated using computer-aided design systems and are employed for various purposes in downstream applications, including computer-aided engineering, manufacturing, and inspection. Therefore, the level of detail of the 3D model should be adjusted based on the purpose of use. In this study, we performed multiobjective optimization for the feature-based simplification of B-rep models. The two objectives of the general model simplification process are to minimize the data size and limit the differences in appearance with respect to the original model. To simultaneously meet these objectives, model simplification was performed to minimize both the difference in the volume and the number of faces with respect to those of the original model. For optimization, we used the simple genetic algorithm (SGA) and the non-dominated sorting genetic algorithm II (NSGA-II). The experimental results confirmed that solution set obtained using NSGA-II was of higher quality as compared with those for SGA and the conventional method.

CAD-driven analysis and beautification of reverse engineered geometric models

Today, it has become more frequent and relatively easy to digitize the surface of 3D objects and then to reconstruct a boundary representation (B-Rep), which is a combination of geometric primitives like planes, cylinders, spheres and cones. However, the obtained results suffer from various inaccuracies, mainly due to noisy data. Moreover, the given reconstruction contains only the geometry, without any information of a semantic nature induced by the design process. In this paper, we present an efficient method to extract absolute references which are not explicitly present in an object, such as the orthogonal coordinate system and alignment planes. These are known as datum references, which are used in the CAD modeling process. Then, we show that datum references can be useful through an application for beautification, which consists in the adjustment of primitive parameters to satisfy relations such as parallelism, orthogonality and concentricity. Our objective is to design a fast and automatic method, which is seldom seen in reverse engineering. We show the efficiency and the robustness of our method through experimental results applied on reverse engineered 3D meshes.

Asymptotic analysis of a contact Hele-Shaw problem in a thin domain

We analyze the contact Hele-Shaw problem with zero surface tension of a free boundary in a thin domain $\Omega^{\varepsilon}(t).$ Under suitable conditions on the given data, the one-valued local classical solvability of the problem for each fixed value of the parameter $\varepsilon$ is proved. Using the multiscale analysis, we study the asymptotic behavior of this problem as $\varepsilon \to 0,$ i.e., when the thin domain $\Omega^{\varepsilon}(t)$ is shrunk into the interval $(0, l).$ Namely, we find exact representation of the free boundary for $t\in[0,T],$ derive the corresponding limit problem $(\varepsilon= 0),$ define other terms of the asymptotic approximation and prove appropriate asymptotic estimates that justify this approach. We also establish the preserving geometry of the free boundary near corner points for $t\in[0,T]$ under assumption that free and fixed boundaries form right angles at the initial time $t=0$.

Remote Sensing for Land Administration

Land administration constitutes the socio-technical systems that govern land tenure, use, value and development within a jurisdiction. The land parcel is the fundamental unit of analysis. Each parcel has identifiable boundaries, associated rights, and linked parties. Spatial information is fundamental. It represents the boundaries between land parcels and is embedded in cadastral sketches, plans, maps and databases. The boundaries are expressed in these records using mathematical or graphical descriptions. They are also expressed physically with monuments or natural features. Ideally, the recorded and physical expressions should align, however, in practice, this may not occur. This means some boundaries may be physically invisible, lacking accurate documentation, or potentially both. Emerging remote sensing tools and techniques offers great potential. Historically, the measurements used to produce recorded boundary representations were generated from ground-based surveying techniques. The approach was, and remains, entirely appropriate in many circumstances, although it can be timely, costly, and may only capture very limited contextual boundary information. Meanwhile, advances in remote sensing and photogrammetry offer improved measurement speeds, reduced costs, higher image resolutions, and enhanced sampling granularity. Applications of unmanned aerial vehicles (UAV), laser scanning, both airborne and terrestrial (LiDAR), radar interferometry, machine learning, and artificial intelligence techniques, all provide examples. Coupled with emergent societal challenges relating to poverty reduction, rapid urbanisation, vertical development, and complex infrastructure management, the contemporary motivation to use these new techniques is high. Fundamentally, they enable more rapid, cost-effective, and tailored approaches to 2D and 3D land data creation, analysis, and maintenance. This Special Issue hosts papers focusing on this intersection of emergent remote sensing tools and techniques, applied to domain of land administration.

Diffuse domain method for needle insertion simulations.

We present a new strategy for needle insertion simulations without the necessity of meshing. A diffuse domain approach on a regular grid is applied to overcome the need for an explicit representation of organ boundaries. A phase field function captures the transition of tissue parameters and boundary conditions are imposed implicitly. Uncertainties of a volume segmentation are translated in the width of the phase field, an approach that is novel and overcomes the problem of defining an accurate segmentation boundary. We perform a convergence analysis of the diffuse elastic equation for decreasing phase field width, compare our results to deformation fields received from conforming mesh simulations and analyze the diffuse linear elastic equation for different widths of material interfaces. Then, the approach is applied to computed tomography data of a patient with liver tumors. A three-class U-Net is used to automatically generate tissue probability maps serving as phase field functions for the transition of elastic parameters between different tissues. The needle tissue interaction forces are approximated by the absolute gradient of a phase field function, which eliminates the need for explicit boundary parameterization and collision detection at the needle-tissue interface. The results show that the deformation field of the diffuse domain approach is comparable to the deformation of a conforming mesh simulation. Uncertainties of tissue boundaries are included in the model and the simulation can be directly performed on the automatically generated voxel-based probability maps. Thus, it is possible to perform easily implementable patient-specific elastomechanical simulations directly on voxel data.

A generalized particle in cell method for explicit solid dynamics

Within the framework of the material point method, a generalized particle in cell method for explicit solid dynamics is presented. In this method, the solids are discretized by finite element meshes, and these meshes are embedded in a background Eulerian grid. The external and internal forces of the solids are calculated on their respective finite element meshes and are mapped to the background grid for solving the momentum equation. Two formulations for computing these forces are presented: one using the original configuration of the solids and the other employs the current configuration. Two and three dimensional numerical examples, covering massive tensile, compressive elastic and plastic deformation, demonstrate that the former formulation performs much better for extremely large deformation problems. Compared with previous material point methods, the proposed method offers these advantages: (i) better representation of solid boundaries, (ii) seamless enforcement of Dirichlet and Neumann boundary conditions, (iii) seamless treatment of material interfaces and (iv) higher efficiency. All of these are achieved with the introduction of a finite element mesh in a supposedly meshfree method.

CMGC: a CAD to Monte Carlo geometry conversion code

Automatic conversion from a computer-aided design (CAD) model to Monte Carlo geometry is one of the most effective methods for large-scale and detailed Monte Carlo modeling. The CAD to Monte Carlo geometry converter (CMGC) is a newly developed conversion code based on the boundary representation to constructive solid geometry (BRep → CSG) conversion method. The goal of the conversion process in the CMGC is to generate an appropriate CSG representation to achieve highly efficient Monte Carlo simulations. We designed a complete solid decomposition scheme to split a complex solid into as few nonoverlapping simple sub-solids as possible. In the complete solid decomposition scheme, the complex solid is successively split by so-called direct, indirect, and auxiliary splitting surfaces. We defined the splitting edge and designed a method for determining the direct splitting surface based on the splitting edge, then provided a method for determining indirect and auxiliary splitting surfaces based on solid vertices. Only the sub-solids that contain concave boundary faces need to be supplemented with auxiliary surfaces because the solid is completely decomposed, which will reduce the redundancy in the CSG expression. After decomposition, these sub-solids are located on only one side of their natural and auxiliary surfaces; thus, each sub-solid can be described by the intersections of a series of half-spaces or geometrical primitives. The CMGC has a friendly graphical user interface and can convert a CAD model into geometry input files for several Monte Carlo codes. The reliability of the CMGC was evaluated by converting several complex models and calculating the relative volume errors. Moreover, JMCT was used to test the efficiency of the Monte Carlo simulation. The results showed that the converted models performed well in particle transport calculations.

Simultaneous Shape and Permittivity Reconstruction in ECT With Sparse Representation: Two-Phase Distribution Imaging

Electrical capacitance tomography (ECT) is a technique to visualize the permittivity distribution inside a domain from the interelectrode mutual capacitances on the domain boundary. The potential applications of ECT in nondestructive testing (NDT) depend on accurate and stable image reconstruction. To improve image quality, this article presents a reconstruction framework with the sparse representation of phase boundaries in two-phase distributions. By adopting a sparsity-promoting basis, i.e., radial basis functions, the reconstruction problem is transformed into searching for the optimal phase boundaries and real-permittivity values of inclusions by formulating an optimization problem accordingly. This can reduce the number of unknowns significantly and has a strong ability to accommodate to the topology changes of inclusion geometries, which can improve the reconstruction accuracy and robustness. Both simulation and phantom experiments are performed to investigate the reconstruction performance, especially regarding the antinoise ability and robustness against choices of model parameters. Compared with typical conventional methods, our method can not only provide significantly improved image quality but also accurately estimate the real-permittivity values of inclusions. This would enable ECT to be applied in challenging NDT applications.

Surface shape-based clustering for B-rep models

Matching, clustering, and retrieving 3D CAD models of mechanical components based on their shape are useful for many CAD/CAM applications such as design reuse, variant process planning and group technology. Surfaces are the prominent elements of the B-Rep (Boundary Representation) CAD model, but the current methods of similarity assessment are not centered on the surfaces and lack an accurate description of their geometric features. In order to solve the problem of retrieval and clustering of B-Rep models more efficiently, the concept of “most crucial surface” is proposed and its corresponding characteristics are studied in detail. The contribution of our approach is that surfaces are the major shape determinants of the B-Rep model, and the distribution of Carosati curvatures is the optimum shape features of surfaces. First, the surface elements are extracted from the STEP (Standard for Exchange of Product Model) files of the B-rep models, and the distribution of minimum, Gauss and Carosati surface curvatures are converted into the shape feature space by the wavelet transform, the Fourier transform, and the grouping calculation. Thus we characterize the B-Rep model as a histogram with surfaces as bins, and then compare and cluster the B-Rep models by the bipartite matching algorithm or the earth mover’s distance. The surface-based methods are evaluated with the four effectiveness indices in the clustering experiment of the NDR (National Design Reservoir) data, and the results indicated that the grouping method for the surface Carosati curvatures has a highly competent matching and clustering performance.

Towards untrimmed NURBS: CAD embedded reparameterization of trimmed B-rep geometry using frame-field guided global parameterization

The boundary representation or B-rep is the prevalent geometry description in computer aided design (CAD). It combines aspects from explicit and implicit geometry and is incompatible with many downstream applications such as finite element analysis (FEA) and computer aided manufacturing (CAM). We develop a semi-automatic frame-field guided parameterization approach that converts trimmed B-rep geometry to conforming, watertight analysis-suitable NURBS. The resulting geometry description is simultaneously suitable for design as well as analysis and therefore avoids the need for further meshing and geometry-processing. While existing frame-field based global parameterization methods offer the high quality necessary in our application, they suffer from several robustness issues. Current challenges mainly stem from the lack of integrability of the frame-field which causes the computed parameterization to fold-over, particularly near parameterization singularities. We propose specialized constraints that incorporate properties of an analytical solution that resolve the poor behavior near singularities. Furthermore, we present a convenient and efficient solution framework that directly incorporates such constraints into a reduced basis. Improved behavior around parameterization singularities simplifies the extraction of a quadrilateral layout. This layout is subsequently fitted with C0 NURBS to yield a conforming watertight model that is analysis suitable. The latter is illustrated by performing isogeometric shell modal analysis on several geometric models.

Who is the Counterpublic? Bromance-as-Masquerade in Chinese Online Drama—S.C.I. Mystery

This articles examines the representation of the blurred boundary between bromance and romance in the Chinese drama, S.C.I. Mystery (2018) and how it can be interpreted in Chinese gender discourse because it is the unique boys’ love fanfiction being adapted for an online drama in mainland China. We use the term bromance-as-masquerade to denote a representational strategy of depicting male–male romance under the guise of homosocial bromance. Bromance-as-masquerade facilitates the promotion of male intimacy cultivated by the leading actors themselves and the production team in the marketing process. Their actions demonstrate a proactive engagement in the counterpublic discourse; however, this article argues that the self-censored modification of the plot-setting represents a refusal and exclusion of boys’ love subculture, which places the notion of the counterpublic in question.