Geometric Queries Research Articles

An interface tracking method with triangle edge cuts

This paper introduces a volume-conserving interface tracking algorithm on unstructured triangle meshes. We propose to discretize the interface via triangle edge cuts which represent the intersections between the interface and the triangle mesh edges using a compact 6 numbers per triangle. This enables an efficient implicit representation of the sub-triangle polygonal material regions without explicitly storing connectivity information. Moreover, we propose an efficient advection algorithm for this interface representation that is based on geometric queries and does not require an optimization process. This advection algorithm is extended via an area correction step that enforces volume-conservation of the materials. We demonstrate the efficacy of our method on a variety of advection problems on a triangle mesh and compare its performance to existing interface tracking methods including VOF and MOF.

User-centric design of a 3D search interface for protein-ligand complexes

In this work, we present the frontend of GeoMine and showcase its application, focusing on the new features of its latest version. GeoMine is a search engine for ligand-bound and predicted empty binding sites in the Protein Data Bank. In addition to its basic text-based search functionalities, GeoMine offers a geometric query type for searching binding sites with a specific relative spatial arrangement of chemical features such as heavy atoms and intermolecular interactions. In contrast to a text search that requires simple and easy-to-formulate user input, a 3D input is more complex, and its specification can be challenging for users. GeoMine’s new version aims to address this issue from the graphical user interface perspective by introducing an additional visualization concept and a new query template type. In its latest version, GeoMine extends its query-building capabilities primarily through input formulation in 2D. The 2D editor is fully synchronized with GeoMine’s 3D editor and provides the same functionality. It enables template-free query generation and template-based query selection directly in 2D pose diagrams. In addition, the query generation with the 3D editor now supports predicted empty binding sites for AlphaFold structures as query templates. GeoMine is freely accessible on the ProteinsPlus web server (https://proteins.plus).

LollipopE: Bi-centered lollipop embedding for complex logic query on knowledge graph

Answering complex First-Order Logic (FOL) query plays a vital role in multi-hop knowledge graph (KG) reasoning. Geometric methods have emerged as a promising category of approaches in this context. However, existing best-performing geometric query embedding (QE) model is still up against three-fold potential problems: (i) underutilization of embedding space, (ii) overreliance on angle information, (iii) uncaptured hierarchy structure. To bridge the gap, we propose a lollipop-like bi-centered query embedding method named LollipopE. To fully utilize embedding space, LollipopE employs learnable centroid positions to represent multiple entities distributed along the same axis. To address the potential overreliance on angular metrics, we design an angular-based and centroid-based metric. This involves calculating both an angular distance and a centroid-based geodesic distance, which empowers the model to make more informed selections of relevant answers from a wider perspective. To effectively capture the hierarchical relationships among entities within the KG, we incorporate dynamic moduli, which allows for the representation of the hierarchical structure among entities. Extensive experiments demonstrate that LollipopE surpasses the state-of-the-art geometric methods. Especially, on more hierarchical datasets, LollipopE achieves the most significant improvement.

Improving Efficiency of Iso-Surface Extraction on Implicit Neural Representations Using Uncertainty Propagation.

Implicit Neural representations (INRs) are widely used for scientific data reduction and visualization by modeling the function that maps a spatial location to a data value. Without any prior knowledge about the spatial distribution of values, we are forced to sample densely from INRs to perform visualization tasks like iso-surface extraction which can be very computationally expensive. Recently, range analysis has shown promising results in improving the efficiency of geometric queries, such as ray casting and hierarchical mesh extraction, on INRs for 3D geometries by using arithmetic rules to bound the output range of the network within a spatial region. However, the analysis bounds are often too conservative for complex scientific data. In this paper, we present an improved technique for range analysis by revisiting the arithmetic rules and analyzing the probability distribution of the network output within a spatial region. We model this distribution efficiently as a Gaussian distribution by applying the central limit theorem. Excluding low probability values, we are able to tighten the output bounds, resulting in a more accurate estimation of the value range, and hence more accurate identification of iso-surface cells and more efficient iso-surface extraction on INRs. Our approach demonstrates superior performance in terms of the iso-surface extraction time on four datasets compared to the original range analysis method and can also be generalized to other geometric query tasks.

Unbounding discrete oriented polytopes

We propose an efficient algorithm to compute k-sided unbounding discrete oriented polytopes (k-UDOPs) in arbitrary dimensions. These convex polytopes are constructed for a fixed set of directions and a given center point. The interior of k-UDOPs does not intersect the scene geometry. We discuss several types of general geometric queries on these constructs, such as intersection with rays, and provide an empirical investigation on the limit of these shapes as the number of sides increases. In the 2D case, we extend our construction to planar shapes enclosed by arbitrary parametric boundaries with known derivative bounds.

Spelunking the deep

Neural implicit representations, which encode a surface as the level set of a neural network applied to spatial coordinates, have proven to be remarkably effective for optimizing, compressing, and generating 3D geometry. Although these representations are easy to fit, it is not clear how to best evaluate geometric queries on the shape, such as intersecting against a ray or finding a closest point. The predominant approach is to encourage the network to have a signed distance property. However, this property typically holds only approximately, leading to robustness issues, and holds only at the conclusion of training, inhibiting the use of queries in loss functions. Instead, this work presents a new approach to perform queries directly on general neural implicit functions for a wide range of existing architectures. Our key tool is the application of range analysis to neural networks, using automatic arithmetic rules to bound the output of a network over a region; we conduct a study of range analysis on neural networks, and identify variants of affine arithmetic which are highly effective. We use the resulting bounds to develop geometric queries including ray casting, intersection testing, constructing spatial hierarchies, fast mesh extraction, closest-point evaluation, evaluating bulk properties, and more. Our queries can be efficiently evaluated on GPUs, and offer concrete accuracy guarantees even on randomly-initialized networks, enabling their use in training objectives and beyond. We also show a preliminary application to inverse rendering.

Alpha wrapping with an offset

Given an input 3D geometry such as a triangle soup or a point set, we address the problem of generating a watertight and orientable surface triangle mesh that strictly encloses the input. The output mesh is obtained by greedily refining and carving a 3D Delaunay triangulation on an offset surface of the input, while carving with empty balls of radius alpha. The proposed algorithm is controlled via two user-defined parameters: alpha and offset. Alpha controls the size of cavities or holes that cannot be traversed during carving, while offset controls the distance between the vertices of the output mesh and the input. Our algorithm is guaranteed to terminate and to yield a valid and strictly enclosing mesh, even for defect-laden inputs. Genericity is achieved using an abstract interface probing the input, enabling any geometry to be used, provided a few basic geometric queries can be answered. We benchmark the algorithm on large public datasets such as Thingi10k, and compare it to state-of-the-art approaches in terms of robustness, approximation, output complexity, speed, and peak memory consumption. Our implementation is available through the CGAL library.

BFEMP: Interpenetration-free MPM–FEM coupling with barrier contact

This paper introduces BFEMP, a new approach for monolithically coupling the Material Point Method (MPM) with the Finite Element Method (FEM) through barrier energy-based particle–mesh frictional contact using a variational time-stepping formulation. The fully implicit time integration of the coupled system is recast into a barrier-augmented unconstrained nonlinear optimization problem. A modified line-search Newton’s method is adopted to strictly prevent material points from penetrating the FEM domain, ensuring convergence and feasibility regardless of the time step size or the mesh resolutions. The proposed coupling scheme also reduces to a new approach for imposing separable frictional kinematic boundaries for MPM when all nodal displacements in the FEM domain are prescribed with Dirichlet boundary conditions. Compared to standard implicit time integration, the extra algorithmic components associated with the contact treatment only depend on simple point-segment (or point-triangle in 3D) geometric queries which robustly handle arbitrary FEM mesh boundaries represented with codimension-1 simplices. Experiments and analyses are performed to demonstrate the robustness and accuracy of the proposed method.

On the Implicit Equation of Conics and Quadrics Offsets

A new determinantal representation for the implicit equation of offsets to conics and quadrics is derived. It is simple, free of extraneous components and provides a very compact expanded form, these representations being very useful when dealing with geometric queries about offsets such as point positioning or solving intersection purposes. It is based on several classical results in “A Treatise on the Analytic Geometry of Three Dimensions” by G. Salmon for offsets to non-degenerate conics and central quadrics.

Location Privacy-Preserving Task Recommendation With Geometric Range Query in Mobile Crowdsensing

In mobile crowdsensing, location-based task recommendation requires each data requester to submit a task-related geometric range to crowdsensing service providers such that they can match suitable workers within this range. Generally, a trusted server (i.e., database owner) should be deployed to protect location privacy during the process, which is not desirable in practice. In this paper, we propose the location privacy-preserving task recommendation (PPTR) schemes with geometric range query in mobile crowdsensing without the trusted database owner. Specifically, we first propose a PPTR scheme with linear search complexity, named PPTR-L, based on a two-server model. By leveraging techniques of polynomial fitting and randomizable matrix multiplication, PPTR-L enables the service provider to find the workers located in the data requester’s arbitrary geometric query range without disclosing the sensitive location privacy. To further improve query efficiency, we design a novel data structure for task recommendation and propose PPTR-F to achieve faster-than-linear search complexity. Through security analysis, it is shown that our schemes can protect the confidentiality of workers’ locations and data requesters’ queries. Extensive experiments are performed to demonstrate that our schemes can achieve high computational efficiency in terms of geometric range query.

A method of generating depth images for view-based shape retrieval of 3D CAD models from partial point clouds

Laser scanners can easily acquire the geometric data of physical environments in the form of point clouds. Industrial 3D reconstruction processes generally recognize objects from point clouds, which should include both geometric and semantic data. However, the recognition process is often a bottleneck in 3D reconstruction because it is labor intensive and requires expertise in domain knowledge. To address this problem, various methods have been developed to recognize objects by retrieving their corresponding models from a database via input geometric queries. In recent years, geometric data conversion to images and view-based 3D shape retrieval applications have demonstrated high accuracies. Depth images that encode the depth values as pixel intensities are frequently used for view-based 3D shape retrieval. However, geometric data collected from objects are often incomplete owing to occlusions and line-of-sight limitations. Images generated by occluded point clouds lower the view-based 3D object retrieval performance owing to loss of information. In this paper, we propose a viewpoint and image-resolution estimation method for view-based 3D shape retrieval from point cloud queries. Further, automatic selection of viewpoint and image resolution are proposed using the data acquisition rate and density calculations from sampled viewpoints and image resolutions. The retrieval performances for images generated by the proposed method are investigated via experiments and compared for various datasets. Additionally, view-based 3D shape retrieval performance with a deep convolutional neural network was investigated using the proposed method.

LuxGeo: Efficient and Secure Enhanced Geometric Range Queries

As the location-based applications ourishing, we will witness soon the transferring of a prodigious amount of data from the local to a public cloud. The rising demand for outsourced data is moving toward a wider geographical area with arbitrary distribution (i.e., dense or sparse) and query scope (i.e., limited or vast). In terms of cloud risks, the outsourced individual data should be preserved when being queried, especially for location information. Geometric range queries are one of the most fundamental search functions. However, the existed works of secure geometric queries are far from practical usage on efciency and security simultaneously. In this paper, we propose a novel scheme, LuxGeo. Our scheme reaches a constant navigation and a linear sweep, which is tailored for secure and efcient location-lookup. Our experiments over three real-world spatial datasets have shown its practical efciency. For example, it only takes 10.01s with 728 tuples retrieved over 63, 369 ciphertext dataset for a single query. LuxGeo has better performance than the existed solutions for a GSE problem on efciency and security.

MGOS: A library for molecular geometry and its operating system

The geometry of atomic arrangement underpins the structural understanding of molecules in many fields. However, no general framework of mathematical/computational theory for the geometry of atomic arrangement exists. Here we present “Molecular Geometry (MG)” as a theoretical framework accompanied by “MG Operating System (MGOS)” which consists of callable functions implementing the MG theory. MG allows researchers to model complicated molecular structure problems in terms of elementary yet standard notions of volume, area, etc. and MGOS frees them from the hard and tedious task of developing/implementing geometric algorithms so that they can focus more on their primary research issues. MG facilitates simpler modeling of molecular structure problems; MGOS functions can be conveniently embedded in application programs for the efficient and accurate solution of geometric queries involving atomic arrangements. The use of MGOS in problems involving spherical entities is akin to the use of math libraries in general purpose programming languages in science and engineering. Program summaryProgram Title: Molecular Geometry Operating System (MGOS)Program Files doi:http://dx.doi.org/10.17632/hp2wmvxsfz.1Licensing provisions: CC By 4.0Programming language: C++Supplementary material: (1) Supplementary Video 1, (2) Supplementary Video 2, (3) Supplementary Video 3, (4) Supplementary Video 4, (5) MGOS manual, and (6) 300 test PDB structure filesNature of problem: For both organic and inorganic molecules, structure determines molecular function and molecular structure is highly correlated with molecular shape or geometry. Hence, many studies were conducted for the analysis and evaluation of the geometry of atomic arrangement. However, most studies were based on Monte Carlo, grid-counting, or approximation methods and a high-quality solution requires heavy computational resources, not to mention its dependency on computation environment. In this paper, we introduce a unified framework of computational library, Molecular Geometry Operating System (MGOS), based on an analytic method for the molecular geometry of atomic arrangements. We believe that the powerful MGOS application programming interface (API) functions will free scientists from developing and implementing complicated geometric algorithms and let them focus on more important scientific problems.Solution method: Molecular Geometry (MG) is a general framework of mathematical/computational methods for solving molecular structure problems using a geometry-priority philosophy and is implemented by MGOS which is a library of callable C++ API functions. MGOS is developed based on the Voronoi diagram of three-dimensional spheres and its two derivative constructs called the quasi-triangulation and beta-complex. Note that this Voronoi diagram is different from the ordinary Voronoi diagram of points where the points are atom centers. Being an analytic method, the solutions of many geometric queries on atomic arrangement, if not all, are obtained correctly and quickly. The MGOS architecture is carefully designed in a three-tier architecture so that future modifications and/or improvements can be reflected in the application programs with no additional programming by users.

SEMANTIC ENRICHMENT OF ROUTING ENGINES USING LINKED DATA: A CASE STUDY USING GRAPHHOPPER

Abstract. Traveling is a basic part of our daily life, whenever a person wants to travel e.g. from home to workplace, the essential question that rises is which route to follow. The choice of a route also varies based on traveler’s interest e.g. visiting hospital on way back to home or traveling on a greener route. This varied route planning may be easy for any person in his local neighborhood, however in a new neighborhood and increasing number of options e.g. possible restaurant options to visit, a guiding system is required that suggests an optimal route according to traveler’s interests i.e. answering semantic queries. Most of the existing routing engines only answer geometric queries e.g. shortest route due to lack of data semantics and adding semantics to a routing graph requires a semantic data source. Geo-semantics can be added through combination of GIS and semantic web. Semantic web is an extension of World Wide Web (WWW) where the content is maintained and structured in a standard way that is understandable by machines; hence providing linked data as a way for semantic enrichment, in this study the semantic enrichment of routing dataset. To use this semantically enriched routing network a routing application needs to be developed that can answer the semantic queries. This research serves as a proof of concept for how linked data can be used for semantic enrichment of routing networks and proposes a prototype routing framework and application designed using open source technologies along with use cases where semantic routing queries are addressed. It also highlights the challenges of this approach and future research perspectives.

Exact Representations and Geometric Queries for Lattice Structures with Quador Beams

Objects with architected internal structure often consist of a lattice of beams that are interconnected at nodes. Compared to the conventional cylindrical and conical beams, quador-beams are bounded by quadrics-of-revolution. We decompose the lattice into an assembly of hubs, wherein a hub is the union of a node (ball) with the half-beams incident upon it. In this paper, we propose (1) a hybrid representation of a quador-hub (hub with quador half-beams) consisting of exact CSG + CST + Boundary models, (2) a compact data structure and associated operators to work with the hybrid representation, and (3) algorithms to perform fundamental geometric queries on the hub. We provide the operators to query the half-beams of the hub, to inquire the trimming planes of a surface, or to traverse the faces, edges and vertices of the hub. We suggest efficient algorithms, that take advantage of the hybrid representation, for geometric queries such as point membership classification, planar slicing, surface meshing, and area/volume computation. We outline a possible approach for computing exact answers to all tests that are required for computing the exact topology of the proposed representation of the hub. Finally, we show that the simplified geometry of quador hubs leads to smaller data sizes and improved performance in a commercial modeler.

QUADOR: QUADric-Of-Revolution beams for lattices

Objects with designed internal structure often consist a lattice of beams, in which the surface of each beam smoothly connects two spheres, possibly of different radii. We propose a geometric model for these beams that provides a compromise between shape flexibility and ease of computation: each beam is either a single quadric of revolution (“quador”), or two smoothly connected ones (“biquador”). Quador and biquador beams can be specified using easily adjustable parameters. They simplify and accelerate several common geometric queries, including point classification, ray casting, planar slicing, and boundary evaluation. We compare quadors and biquadors with other possible beam shapes, and show that these alternatives have either reduced flexibility or increased computational cost. We advocate decomposing the lattice into an assembly of hubs, each hub defined as the union of a sphere with the half-beams (stumps) that connect to it. We describe approaches for computing an exact polyhedral Constructive Solid Trimming expression of each face and the exact edges and vertices of the hub.

Particle tracking acceleration via signed distance fields in direct-accelerated geometry Monte Carlo

Abstract Computer-aided design (CAD)-based Monte Carlo radiation transport is of value to the nuclear engineering community for its ability to conduct transport on high-fidelity models of nuclear systems, but it is more computationally expensive than native geometry representations. This work describes the adaptation of a rendering data structure, the signed distance field, as a geometric query tool for accelerating CAD-based transport in the direct-accelerated geometry Monte Carlo toolkit. Demonstrations of its effectiveness are shown for several problems. The beginnings of a predictive model for the data structure's utilization based on various problem parameters is also introduced.

The Façade of Paolo Soleri’s Solimene Factory

A simple geometric query provides us with the opportunity to review a symbolic work of modern architecture, the Solimene Ceramics factory by Paolo Soleri, built in 1954. A question that is perhaps marginal in some contexts, becomes fundamental when it is a matter of executing elaborate technical and project drawings that accurately describe the project. Well beyond the necessities of descriptive geometry, a study of the configuration provides knowledge about it was built, at times highlighting variances that required corrections in the course of the works and the hypothetical area of generated stress. In the specific case, it explains the origin of the ‘flare’ that occurs at mid-height in the forms that compose the facade, a characteristic that paradoxically has never been considered in the technical drawings or discussed in numerous studies. The aim of this research is to explain why the forms of the facade are shaped the way they are.

Design an Efficient Top-K Query Retrieval Technique for GIQ problems

In a given geometric objects, set of objects are retrieved as results for the given query. The problem is defined as geometric query intersection problem. The problem defines that, for the given user query, all the relevant results which are intersected by the query are showed as output. Because of the large number results, it occupies the huge memory space. For that here we propose a solution that we show the top-k results as the output where k is the integer. This paper gives a general technique to solve any top-k GIQ problem efficiently. The technique relies only on the availability of an efficient solution for the underlying (non-top-k) GIQ problem, which is often the case. Using this, asymptotically efficient solutions are derived for several top-k GIQ problems, including top-k orthogonal and circular range search, point enclosure search, half space range search, etc. Implementations of some of these solutions, using practical data structures, show that they are quite efficient in practice. This paper also does a formal investigation of the hardness of the top-k GIQ problem, which reveals interesting connections between the top-k GIQ problem and the underlying (non-top-k) GIQ problem. In our proposed system we are going to perform multiple query processing. Because in the existing approach it can able to process only one query at the time. But in our proposed work we process multiple queries at the time.

Toward better surface tracking for fluid simulation.

Representing moving surfaces as polygonal meshes offers a unique set of advantages as well as challenges. In his dissertation, the author attempted to address several of the difficulties traditionally associated with explicit surface tracking. In later research, he and his colleagues sought to address one of the main challenges in incorporating an explicit surface tracker into an existing Eulerian fluid simulation system: the potential for resolution mismatch between the surface and the simulation. This article discusses issues of numerical robustness in geometric queries when dealing with moving explicit surfaces and summarizes the work by other researchers that has been undertaken concurrently and subsequently to the author's dissertation work.