Polyhedral Objects Research Articles

Triangle-toothed gear occlude-guided universal nanotechnology constructs 3D symmetric DNA polyhedra with high assembly efficiency for precision cancer therapy

Chemotherapy is commonly used to treat malignant tumors. However, conventional chemotherapeutic drugs often cannot distinguish between tumor and healthy cells, resulting in adverse effects and reduced therapeutic efficacy. Therefore, zigzag-shaped gear-occlude-guided cymbal-closing (ZGC) DNA nanotechnology was developed based on the mirror-symmetry principle to efficiently construct symmetric DNA polyhedra. This nanotechnology employed simple mixing steps for efficient sequence design and assembly. A targeting aptamer was installed at a user-defined position using an octahedron as a model structure. Chemotherapeutic drug-loaded polyhedral objects were subsequently delivered into tumor cells. Furthermore, anticancer drug-loaded DNA octahedra were intravenously injected into a HeLa tumor-bearing mouse model. Assembly efficiency was almost 100 %, with no residual building blocks identified. Moreover, this nanotechnology required a few DNA oligonucleotides, even for complex polyhedrons. Symmetric DNA polyhedrons retained their structural integrity for 24 h in complex biological environments, guaranteeing prolonged circulation without drug leakage in the bloodstream and promoting efficient accumulation in tumor tissues. In addition, DNA octahedra were cleared relatively slowly from tumor tissues. Similarly, tumor growth was significantly inhibited in vivo, and a therapeutic outcome comparable to that of conventional gene-chemo combination therapy was observed. Moreover, no systemic toxicity was detected. These findings indicate the potential application of ZGC DNA nanotechnology in precision medicine.

Cycle algebras and polytopes of matroids

Cycle polytopes of matroids have been introduced in combinatorial optimization as a generalization of important classes of polyhedral objects like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here we start an algebraic and geometric investigation of these polytopes by studying their toric algebras, called cycle algebras, and their defining ideals. Several matroid operations are considered which determine faces of cycle polytopes that belong again to this class of polyhedral objects. As a key technique used in this paper, we study certain minors of given matroids which yield algebra retracts on the level of cycle algebras. In particular, that allows us to use a powerful algebraic machinery. As an application, we study highest possible degrees in minimal homogeneous systems of generators of defining ideals of cycle algebras as well as interesting cases of cut polytopes and Eulerian subgraph polytopes.

Optimized Packing Titanium Alloy Powder Particles

To obtain high-quality and durable parts by 3D printing, specific characteristics (porosity and proportion of various sizes of particles) in the mixture used for printing or sintering must be assured. To predict these characteristics, a mathematical model of optimized packing polyhedral objects (particles of titanium alloys) in a cuboidal container is presented, and a solution algorithm is developed. Numerical experiments demonstrate that the results obtained by the algorithm are very close to experimental findings. This justifies using numerical simulation instead of expensive experimentation.

Prediction of difficulty in cryoballoon ablation with a 3D deep learning model using polygonal mesh representation

Abstract Background Cryoballoon ablation (CBA) is a useful treatment for pulmonary vein isolation (PVI). Some cases, however, are difficult to treat and may require multiple freezing procedures and/or touch-up ablation. Although several predictors of CBA difficulty have been reported, no report has been able to assess the spatial location and morphology of the left atrium (LA) and pulmonary veins (PVs). A polygonal mesh is a collection of vertices, edges, and faces that defines the shape of a polyhedral object, and is able to represent a spatial location with a small amount of information. We hypothesized that a deep learning model that learns mesh representation datasets could more accurately detect the CBA difficulty and that we could establish a novel evaluation method in CBA. Purpose The aim of this study was to create a model to predict CBA difficulty with a 3D deep learning model using polygonal mesh representation. Methods and results All the 140 patients who underwent CBA for drug-resistant atrial fibrillation between January 2015 and January 2022 were included. A 28-mm cryoballoon (Arctic Front Advance, Medtronic) was used in all cases. We defined CBA difficulty as requiring a touch-up ablation procedure to create complete PVI. We converted the volume data in DICOM format of the computed tomography images of PVs and LA to obj file format (shown in Figure 1), which supports the definition of the geometry for object surfaces using polygonal meshes. Next, we developed a deep learning model that could learn polygonal meshes and classify whether the CBA required touch-up ablation or not. Only a training dataset is used to train the deep learning model, and finally, a test dataset is used to evaluate the model metrics. The accuracy, area under the ROC curve, recall, precision, and f1-score of the deep learning model using the test dataset was 86.5%, 87.7%, 66.7%, 75.0%, 70.6%, respectively. Conclusions We developed a 3D deep learning model that can detect a difficulty in CBA using polygonal mesh representation. By predicting difficult cases in advance, we will be able to develop strategies to increase the success rate. Funding Acknowledgement Type of funding sources: None.

Rigid impacts of three-dimensional rocking structures

Studies of rocking motion aim to explain the remarkable earthquake resistance of rocking structures. State-of-the-art assessment methods are mostly based on planar models, despite ongoing efforts to understand the significance of three-dimensionality. Impacts are essential components of rocking motion. We present experimental measurements of free-rocking blocks on a rigid surface, focusing on extreme sensitivity of impacts to geometric imperfections, unpredictability, and the emergence of three-dimensional motion via spontaneous symmetry breaking. These results inspire the development of new impact models of three-dimensional facet and edge impacts of polyhedral objects. Our model is a natural generalization of existing planar models based on the seminal work of George W. Housner. Model parameters are estimated empirically for rectangular blocks. Finally, new perspectives in earthquake assessment of rocking structures are discussed.

Comparison of Two Parallel Offsetting Algorithms Free from Conflicts Between Threads

Offset computation for expanding a polyhedral object by an offset radius is a fundamental geometric process frequently used in manufacturing applications. This process combined with the triple-dexel representation solid model has become popular because of its robustness and compatibility with parallel processing using a graphics processing unit (GPU). In parallel geometric processing, conflicts between threads must be avoided. Thus, we propose a novel parallel offsetting algorithm free from conflicts between threads. The triple-dexel model is a combination of x-, y-, and z-axis-aligned dexel models. Each dexel model is defined based on an orthogonal grid given on a coordinate plane. We subdivide the grid into several sub-grids of a fixed size in advance. For each sub-grid, a block of GPU threads is assigned. As each GPU thread always processes different dexel elements from the other threads in this method, no conflict occurs. Our research group has previously presented a parallel offset computation algorithm for a polyhedral solid model that also uses a triple-dexel representation model and a GPU. In the previous algorithm, the surface polygons of the model are classified into several groups in advance. The parallel offset computation of multiple polygon groups is realized by selecting groups of polygon in which the offset processing of the polygons does not affect one another. This selection process is time-consuming. Computational experiments were performed to analyze the performance difference between the current algorithm and our previous algorithm. In our experiments, the current algorithm achieved speedups of 1.4 times to 3.2 times compared to our previous offsetting algorithm.

Immobilizing Caging Grasps of Convex Polyhedrons With a Four-Pin Gripper

This letter converts one high-dimensional caging configuration into several lower-dimensional cage sets in the translation space and rotation space, through which analysis of grasping can be carried out more efficiently. A caging set detection method is introduced based on the constraint region. It is found that a caging on a high-dimensional convex constraint region can be converted into a caging set in low-dimensional sub-region. An efficient method to compute the caging of a polyhedral object using a one-parameter four-pin industrial gripper is then presented. Several simulations and real experiments are conducted to show the efficacy of the proposed methods.

Polyhedral-based Modeling and Algorithms for Tolerancing Analysis

The cumulative stack-up of geometric variations in mechanical systems can be modeled summing and intersecting sets of constraints. These constraints derive from tolerance zones or from contact restrictions between parts. The advantage of this approach is its robustness for treating any kind of mechanisms, including the over-constrained ones. However, the sum of constraints, which must be computed when simulating the accumulation of defects in serial joints, is a very time-consuming operation. In previous papers, we proposed to virtually limit the degrees of freedom of the toleranced features and joints turning the polyhedra into polytopes to avoid manipulating unbounded objects. Even though this approach enables to process the whole mechanism, it also introduces bounding or cap facets which increase the complexity of the operand sets after each operation until becoming far too significant. In this work, we introduce algorithms summing, intersecting and testing inclusions. As they operate on sets of constraints using unbounded polyhedral objects, we identify the smaller sub-space in which the projection of these operands are bounded sets. Calculating the sum in this sub-space allows reducing the operands complexity significantly and consequently the computational time. Then, checking the final inclusion informs us not only about the compliance of the mechanism tolerances with respect to the functional specification but also to quantify how far we are from this target. Finally prismatic polyhedra integrate ISO and contacts specifications in a very natural way and are able to perform a full kinematic analysis of the mechanism. After presenting the geometric properties on which this approach rely, we demonstrate it on an industrial case. Then we compare the computation times, prove the robustness of the new method and show how to quantify the functional condition compliance with respect to a given set of tolerances.

A stratified process for the perception of objects: From optical transformations to 3D relief structure to 3D similarity structure to slant or aspect ratio

Previously, we developed a stratified process for slant perception. First, optical transformations in structure-from-motion (SFM) and stereo were used to derive 3D relief structure (where depth scaling remains arbitrary). Second, with sufficient continuous perspective change (≥45°), a bootstrap process derived 3D similarity structure. Third, the perceived slant was derived. As predicted by theoretical work on SFM, small visual angle (<5°) viewing requires non-coplanar points. Slanted surfaces with small 3D cuboids or tetrahedrons yielded accurate judgment while planar surfaces did not. Normally, object perception entails non-coplanar points. Now, we apply the stratified process to object perception where, after deriving similarity structure, alternative metric properties of the object can be derived (e.g. slant of the top surface or width-to-depth aspect ratio). First, we tested slant judgments of the smooth planar tops of three different polyhedral objects. We tested rectangular, hexagonal, and asymmetric pentagonal surfaces, finding that symmetry was required to determine the direction of slant (AP&P, 2019, https://doi.org/10.3758/s13414-019-01859-5). Our current results replicated the previous findings. Second, we tested judgments of aspect ratios, finding accurate performance only for symmetric objects. Results from this study suggest that, first, trackable non-coplanar points can be attained in the form of 3D objects. Second, symmetry is necessary to constrain slant and aspect ratio perception. Finally, deriving 3D similarity structure precedes estimating object properties, such as slant or aspect ratio. Together, evidence presented here supports the stratified bootstrap process for 3D object perception. Statement of significancePlanning interactions with objects in the surrounding environment entails the perception of 3D shape and slant. Studying ways through which 3D metric shape and slant can be perceived accurately by moving observers not only sheds light on how the visual system works, but also provides understanding that can be applied to other fields, like machine vision or remote sensing. The current study is a logical extension of previous studies by the same authors and explores the roles of large continuous perspective changes, relief structure, and symmetry in a stratified process for object perception.

Algorithmic Perception of Vertices in Sketched Drawings of Polyhedral Shapes

In this article, visual perception principles were used to build an artificial perception model aimed at developing an algorithm for detecting junctions in line drawings of polyhedral objects that are vectorized from hand-drawn sketches. The detection is performed in two dimensions (2D), before any 3D model is available and minimal information about the shape depicted by the sketch is used. The goal of this approach is to not only detect junctions in careful sketches created by skilled engineers and designers but also detect junctions when skilled people draw casually to quickly convey rough ideas. Current approaches for extracting junctions from digital images are mostly incomplete, as they simply merge endpoints that are near each other, thus ignoring the fact that different vertices may be represented by different (but close) junctions and that the endpoints of lines that depict edges that share a common vertex may not necessarily be close to each other, particularly in quickly sketched drawings. We describe and validate a new algorithm that uses these perceptual findings to merge tips of line segments into 2D junctions that are assumed to depict 3D vertices.

Self‐Assembly of Wireframe DNA Nanostructures from Junction Motifs

AbstractWireframe frameworks have been investigated for the construction of complex nanostructures from a scaffolded DNA origami approach; however, a similar framework is yet to be fully explored in a scaffold‐free “LEGO” approach. Herein, we describe a general design scheme to construct wireframe DNA nanostructures entirely from short synthetic strands. A typical edge of the resulting structures in this study is composed of two parallel duplexes with crossovers on both ends, and three, four, or five edges radiate out from a certain vertex. By using such a self‐assembly scheme, we produced planar lattices and polyhedral objects.

Self-Assembly of Wireframe DNA Nanostructures from Junction Motifs.

Wireframe frameworks have been investigated for the construction of complex nanostructures from a scaffolded DNA origami approach; however, a similar framework is yet to be fully explored in a scaffold-free "LEGO" approach. Herein, we describe a general design scheme to construct wireframe DNA nanostructures entirely from short synthetic strands. A typical edge of the resulting structures in this study is composed of two parallel duplexes with crossovers on both ends, and three, four, or five edges radiate out from a certain vertex. By using such a self-assembly scheme, we produced planar lattices and polyhedral objects.

Large continuous perspective change with noncoplanar points enables accurate slant perception.

Perceived slant has often been characterized as a component of 3D shape perception for polyhedral objects. Like 3D shape, slant is often perceived inaccurately. Lind, Lee, Mazanowski, Kountouriotis, and Bingham (2014) found that 3D shape was perceived accurately with perspective changes ≥ 45°. We now similarly tested perception of 3D slant. To account for their results, Lind et al. (2014) developed a bootstrap model based on the assumption that optical information yields perception of 3D relief structure then used with large perspective changes to bootstrap to perception of 3D Euclidean structure. However, slant perception usually entails planar surfaces and structure-from-motion fails in the absence of noncoplanar points. Nevertheless, the displays in Lind et al. (2014) included stereomotion in addition to monocular optical flow. Because stereomotion is higher order, the bootstrap model might apply in the case of strictly planar surfaces. We investigated whether stereomotion, monocular structure-from-motion (SFM), or the combination of the two would yield accurate 3D slant perception with large continuous perspective change. In Experiment 1, we found that judgments of slant were inaccurate in all information conditions. In Experiment 2, we added noncoplanar structure to the surfaces. We found that judgments in the monocular SFM and combined conditions now became correct once perspective changes were ≥ 45°, replicating the results of Lind et al. (2014) and supporting the bootstrap model. In short, we found that noncoplanar structure was required to enable accurate perception of 3D slant with sufficiently large perspective changes. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Segmentation of Laser Point Clouds in Urban Areas by a Modified Normalized Cut Method.

Normalized Cut is a well-established divisive image segmentation method, which we adapt in this paper for the segmentation of laser point clouds in urban areas. Our focus is on polyhedral objects with planar surfaces. Due to its target function, Normalized Cut favours cuts with "short cut lines" or "small cut surfaces", which is a drawback for our application. We therefore modify the target function, weighting the similarity measures with distance-dependent weights. We call the induced minimization problem "Distance-weighted Cut" (DWCut). The new target function leads to a generalized eigenvalue problem, which is slightly more complicated than the corresponding problem for the Normalized Cut; on the other hand, the new target function is easier to interpret and avoids some drawbacks of the Normalized Cut. We point out an efficient method for the numerical solution of the eigenvalue problem which is based on a Krylov subspace method. DWCut can be beneficially combined with an aggregation in order to reduce the computational effort and to avoid shortcomings due to insufficient plane parameters. We present examples for the successful application of the Distance-weighted Cut principle and evaluate its results by comparison with the results of corresponding manual segmentations.

Automatic 3D reconstruction of a polyhedral object from a single line drawing under perspective projection

A novel method is proposed to automatically recover a 3D polyhedral object from a single 2D line drawing in perspective projection. In the algorithm, a camera calibration based on partial orthogonality is performed in order to retrieve multiple pinhole cameras. Then, 3D orientations of edge lines are estimated by a factor graph inference. Finally, 3D reconstruction is conducted through hybrid optimization by combining beam search with simulated annealing. Parameterization based on inverse depths is proposed to reduce the dimension of variables in optimization. Experimental results show that the algorithm proposed in the study can reconstruct reasonable 3D objects from perspective-projected line drawings, which cannot be handled by existing approaches. Qualitative and quantitative comparisons are provided to illustrate the advantages of the proposed method.

RASTERIZATION AND VOXELIZATION OF TWO- AND THREE-DIMENSIONAL SPACE PARTITIONINGS

Abstract. The paper presents a very straightforward and effective algorithm to convert a space partitioning, made up of polyhedral objects, into a 3D block of voxels, which is fully occupied, i.e. in which every voxel has a value. In addition to walls, floors, etc. there are 'air' voxels, which in turn may be distinguished as indoor and outdoor air. The method is a 3D extension of a 2D polygon-to-raster conversion algorithm. The input of the algorithm is a set of non-overlapping, closed polyhedra, which can be nested or touching. The air volume is not necessarily represented explicitly as a polyhedron (it can be treated as 'background', leading to the 'default' voxel value). The approach consists of two stages, the first being object (boundary) based, the second scan-line based. In addition to planar faces, other primitives, such as ellipsoids, can be accommodated in the first stage without affecting the second.

RASTERIZATION AND VOXELIZATION OF TWO- AND THREE-DIMENSIONAL SPACE PARTITIONINGS

The paper presents a very straightforward and effective algorithm to convert a space partitioning, made up of polyhedral objects, into a 3D block of voxels, which is fully occupied, i.e. in which every voxel has a value. In addition to walls, floors, etc. there are 'air' voxels, which in turn may be distinguished as indoor and outdoor air. The method is a 3D extension of a 2D polygon-to-raster conversion algorithm. The input of the algorithm is a set of non-overlapping, closed polyhedra, which can be nested or touching. The air volume is not necessarily represented explicitly as a polyhedron (it can be treated as 'background', leading to the 'default' voxel value). The approach consists of two stages, the first being object (boundary) based, the second scan-line based. In addition to planar faces, other primitives, such as ellipsoids, can be accommodated in the first stage without affecting the second.

Modeling a 3D City Model and Its Levels of Detail as a True 4D Model

The various levels of detail (LODs) of a 3D city model are often stored independently, without links between the representations of the same object, causing inconsistencies, as well as update and maintenance problems. One solution to this problem is to model the LOD as an extra geometric dimension perpendicular to the three spatial ones, resulting in a true 4D model in which a single 4D object (a polychoron) represents a 3D polyhedral object (e.g., a building) at all of its LODs and a multiple-LOD 3D city model is modeled as a 4D cell complex. While such an approach has been discussed before at a conceptual level, our objective in this paper is to describe how it can be realized by appropriately linking existing 3D models of the same object at different LODs. We first present our general methodology to construct such a 4D model, which consists of three steps: (1) finding corresponding 0D–3D cells; (2) creating 1D–4D cells connecting them; and (3) constructing the 4D model. Because of the complex relationships between the objects in different LODs, the creation of the connecting cells can become difficult. We therefore describe four different alternatives to do this, and we discuss the advantages and disadvantages of each in terms of their feasibility in practice and the properties that the resulting 4D model has. We show how the different linking schemes result in objects with different characteristics in several use cases. We also show how our linking method works in practice by implementing the linking of matching cells to construct a 4D model.

Thickness and clearance visualization based on distance field of 3D objects

Abstract This paper proposes a novel method for visualizing the thickness and clearance of 3D objects in a polyhedral representation. The proposed method uses the distance field of the objects in the visualization. A parallel algorithm is developed for constructing the distance field of polyhedral objects using the GPU. The distance between a voxel and the surface polygons of the model is computed many times in the distance field construction. Similar sets of polygons are usually selected as close polygons for close voxels. By using this spatial coherence, a parallel algorithm is designed to compute the distances between a cluster of close voxels and the polygons selected by the culling operation so that the fast shared memory mechanism of the GPU can be fully utilized. The thickness/clearance of the objects is visualized by distributing points on the visible surfaces of the objects and painting them with a unique color corresponding to the thickness/clearance values at those points. A modified ray casting method is developed for computing the thickness/clearance using the distance field of the objects. A system based on these algorithms can compute the distance field of complex objects within a few minutes for most cases. After the distance field construction, thickness/clearance visualization at a near interactive rate is achieved.

Progressive 3D Reconstruction of Planar-Faced Manifold Objects with DRF-Based Line Drawing Decomposition.

This paper presents an approach for reconstructing polyhedral objects from single-view line drawings. Our approach separates a complex line drawing representing a manifold object into a series of simpler line drawings, based on the degree of reconstruction freedom (DRF). We then progressively reconstruct a complete 3D model from these simpler line drawings. Our experiments show that our decomposition algorithm is able to handle complex drawings which are challenging for the state of the art. The advantages of the presented progressive 3D reconstruction method over the existing reconstruction methods in terms of both robustness and efficiency are also demonstrated.