Journal articles: '3D Hilbert's curve'

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Ujang, Uznir, Francois Anton, Suhaibah Azri, Alias Abdul Rahman, and Darka Mioc. "3D Hilbert Space Filling Curves in 3D City Modeling for Faster Spatial Queries." International Journal of 3-D Information Modeling 3, no. 2 (April 2014): 1–18. http://dx.doi.org/10.4018/ij3dim.2014040101.

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The advantages of three dimensional (3D) city models can be seen in various applications including photogrammetry, urban and regional planning, computer games, etc. They expand the visualization and analysis capabilities of Geographic Information Systems on cities, and they can be developed using web standards. However, these 3D city models consume much more storage compared to two dimensional (2 D) spatial data. They involve extra geometrical and topological information together with semantic data. Without a proper spatial data clustering method and its corresponding spatial data access method, retrieving portions of and especially searching these 3D city models, will not be done optimally. Even though current developments are based on an open data model allotted by the Open Geospatial Consortium (OGC) called CityGML, its XML-based structure makes it challenging to cluster the 3D urban objects. In this research, the authors propose an opponent data constellation technique of space-filling curves (3D Hilbert curves) for 3D city model data representation. Unlike previous methods, that try to project 3D or n-dimensional data down to 2D or 3D using Principal Component Analysis (PCA) or Hilbert mappings, in this research, they extend the Hilbert space-filling curve to one higher dimension for 3D city model data implementations. The query performance was tested for single object, nearest neighbor and range search queries using a CityGML dataset of 1,000 building blocks and the results are presented in this paper. The advantages of implementing space-filling curves in 3D city modeling will improve data retrieval time by means of optimized 3D adjacency, nearest neighbor information and 3D indexing. The Hilbert mapping, which maps a sub-interval of the ([0,1]) interval to the corresponding portion of the d-dimensional Hilbert's curve, preserves the Lebesgue measure and is Lipschitz continuous. Depending on the applications, several alternatives are possible in order to cluster spatial data together in the third dimension compared to its clustering in 2 D.

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JIA, Lianyin, Binbin LIANG, Mengjuan LI, Yong LIU, Yinong CHEN, and Jiaman DING. "Efficient 3D Hilbert Curve Encoding and Decoding Algorithms." Chinese Journal of Electronics 31, no. 2 (March 2022): 277–84. http://dx.doi.org/10.1049/cje.2020.00.171.

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Saniman, M. N. F., M. H. M Hashim, K. A. Mohammad, K. A. Abd Wahid, W. M. Wan Muhamad, and N. H. Noor Mohamed. "Tensile Characteristics of Low Density Infill Patterns for Mass Reduction of 3D Printed Polylactic Parts." International Journal of Automotive and Mechanical Engineering 17, no. 2 (July 3, 2020): 7927–34. http://dx.doi.org/10.15282/ijame.17.2.2020.11.0592.

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Various infill patterns are introduced in 3D printing to generate low density objects that leads to reduced cost and fabrication time through mass reduction. However, as a trade-off, the strength of the 3D printed component is uncertain. Confusions arise in determining the infill pattern with highest value of tensile strength since most studies limited only to rectilinear, honeycomb, and concentric infill patterns. As consequences, there are very little information on rarely used infill patterns such as Hilbert curve, Archimedean cord and octagram spiral. Therefore, the purpose of this research is to investigate and compare the tensile strength and strain of all infill patterns in mass reduction of 3D printed components experimentally. Following ASTM D638 type III standard, ten tensile test specimens of each infill patterns with 20% density were printed with an FFF 3D printer and were then tested. It was found that Archimedean cords infill pattern had the highest specific tensile strength of 33.23×103 MPa∙mm3/g which made it as the optimum infill pattern for the mass reduction of 3D printed parts with a high tensile strength. On the other hand, having the highest specific tensile strain of 18.21×103 %∙mm3/g, concentric infill pattern was found to be more suitable for producing lightweight parts with a higher elongation before break. Additionally, Hilbert curve infill was the worst selection for mass reduction since it had the lowest values of specific tensile strength and specific strain of 19.80×103 MPa∙mm3/g and 8.34 %∙mm3/g, respectively. Nevertheless, the trends of tensile strength and strain of all six infill patterns had been obtained, especially for rarely investigated infill patterns of Archimedean cords, octagram spiral, and Hilbert curve. Specifically, the trend from the strongest to the weakest (in % compared to solid) for specific tensile strength is rectilinear (38.57%), Archimedean chords (37.29%), concentric (36.57%), octagram spiral (34.79%), honeycomb (27.84%), and Hilbert curve (22.25%), while for specific strain is concentric (102.6%), octagram spiral (83.94%), rectilinear (78.22%), Archimedean cords (77.99%), honeycomb (54.84%), and Hilbert curve (45.14%).

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Memon, Muhammad Usman, Manos M. Tentzeris, and Sungjoon Lim. "Inkjet-printed 3D Hilbert-curve fractal antennas for VHF band." Microwave and Optical Technology Letters 59, no. 7 (May 16, 2017): 1698–704. http://dx.doi.org/10.1002/mop.30613.

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Lopes, L., M. Almeida, and D. Reis. "Influence of 3D microstructure for improving the thermal performance of building façades." IOP Conference Series: Earth and Environmental Science 1196, no. 1 (June 1, 2023): 012064. http://dx.doi.org/10.1088/1755-1315/1196/1/012064.

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Abstract The thermal performance of a building is highly dependent on the heat transmission through the envelope. On the other hand, additive manufacturing has been increasingly used in several industrial applications due to its possibility to produce complex structures. However, most studies of the 3d printing process focused on mechanical performance. This study aims to evaluate how the internal 3D-printed microstructure affects thermal performance. Twelve infill patterns were analysed, including Gyroid, Grid, Hilbert curve, Line, Rectilinear, Stars Triangles, 3D Honeycomb, Honeycomb, Concentric, Cubic, and Octagram spiral. Using fused deposition modelling (FDM), the samples were printed with polyethene terephthalate-glycol (PET-G) thermoplastic filaments. Thermal tests were conducted using a calibrated hotbox, following the recommendations of ASTM C1363-11:2014. The results obtained show a variation of 70% by changing the internal microstructure using fix infill density of 25%. Concentric, Gyroid and Hilbert curve achieved the best thermal insulation properties.

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Nasu, Hirokazu. "The Hilbert Scheme of Space Curves of Degreedand Genus 3d−18." Communications in Algebra 36, no. 11 (November 6, 2008): 4163–85. http://dx.doi.org/10.1080/00927870802175089.

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Eryildiz, Meltem. "The effects of infill patterns on the mechanical properties of 3D printed PLA parts fabricated by FDM." Ukrainian Journal of Mechanical Engineering and Materials Science 7, no. 1-2 (2021): 1–8. http://dx.doi.org/10.23939/ujmems2021.01-02.001.

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The purpose of this study is to analyze the effect of the infill pattern on the mechanical properties of 3D printed PLA parts. Polylactic acid (PLA) parts were fabricated by fused deposition modeling (FDM) at various infill patterns at 30% infill density. Five different infill patterns (stars, 3D honeycomb, honeycomb, gyroid, Hilbert curve) have been investigated. The results have shown that the honeycomb infill pattern exhibited the highest mechanical properties with 29.43 MPa and 2.04 mm elongation due to the improved strength of the strut junctions in this pattern. In the case of the Hilbert curve pattern, compared to the other patterns, though they have the same infill density, tensile strength was lowest because of the presence of large air gaps in the pattern that induced rapid fracture during the test. The optical microscope images of the fracture surfaces were compatible with the tensile strength results. Also considering the build time and the spent filament, it can be said that the honeycomb infill pattern is very promising. Lastly, the results showed that the tensile strength and elongation of 3D printed PLA parts increased 43.4% and 32%, respectively, under optimum infill pattern conditions. The findings of this study will help manufacturing firms and researchers to decide on the appropriate infill pattern, so that FDM parts can be fabricated with minimal production cost and good mechanical properties.

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Papacharalampopoulos, Alexios, Harry Bikas, and Panagiotis Stavropoulos. "Path planning for the infill of 3D printed parts utilizing Hilbert curves." Procedia Manufacturing 21 (2018): 757–64. http://dx.doi.org/10.1016/j.promfg.2018.02.181.

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Liu, Jian, Zhou Su, Chenyue Wang, and Zhuofei Xu. "Effect of an Adaptive-Density Filling Structure on the Mechanical Properties of FDM Parts with a Variable Cross-Section." Materials 15, no. 24 (December 7, 2022): 8746. http://dx.doi.org/10.3390/ma15248746.

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Fused deposition modeling (FDM) technique is one of the most popular additive manufacturing techniques. Infill density is a critical factor influencing the mechanical properties of 3D-printed components using the FDM technique. For irregular components with variable cross-sections, to increase their overall mechanical properties while maintaining a lightweight, it is necessary to enhance the local infill density of the thin part while decreasing the infill density of the thick part. However, most current slicing software can only generate a uniform infill throughout one model to be printed and cannot adaptively create a filling structure with a varying infill density according to the dimensional variation of the cross-section. In the present study, to improve the mechanical properties of irregular components with variable cross-sections, an adaptive-density filling structure was proposed, in which Hilbert curve with the same order was used to fill each slice, i.e., the level of the Hilbert curves in each slice is the same, but the side length of the Hilbert curve decreases with the decreasing size of each slice; hence, the infill density of the smaller cross-section is greater than that of the larger cross-section. The ultimate bearing capacity of printed specimens with the adaptive-density filling structure was evaluated by quasi-static compression, three-point bending, and dynamic compression tests, and the printed specimens with uniform filling structure and the same overall infill density were tested for comparison. The results show that the maximum flexural load, the ultimate compression load, and the maximum impact resistance of the printed specimens with the adaptive-density filling structure were increased by 140%, 47%, and 82%, respectively, compared with their counterparts using the uniform filling structure.

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Mohan, Shashi Ranjan, Syed Nizamuddin Khaderi, and Suryakumar Simhambhatla. "3D Printing of Components with Tailored Properties Through Hilbert Curve Filling of a Discretized Domain." 3D Printing and Additive Manufacturing 7, no. 6 (December 1, 2020): 288–99. http://dx.doi.org/10.1089/3dp.2020.0048.

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Wang, Xiaochao, Jianping Hu, Dongbo Zhang, and Hong Qin. "Efficient EMD and Hilbert spectra computation for 3D geometry processing and analysis via space-filling curve." Visual Computer 31, no. 6-8 (April 25, 2015): 1135–45. http://dx.doi.org/10.1007/s00371-015-1100-4.

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Rodriguez-Padilla, Consuelo, Enrique Cuan-Urquizo, Armando Roman-Flores, José L. Gordillo, and Carlos Vázquez-Hurtado. "Algorithm for the Conformal 3D Printing on Non-Planar Tessellated Surfaces: Applicability in Patterns and Lattices." Applied Sciences 11, no. 16 (August 16, 2021): 7509. http://dx.doi.org/10.3390/app11167509.

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In contrast to the traditional 3D printing process, where material is deposited layer-by-layer on horizontal flat surfaces, conformal 3D printing enables users to create structures on non-planar surfaces for different and innovative applications. Translating a 2D pattern to any arbitrary non-planar surface, such as a tessellated one, is challenging because the available software for printing is limited to planar slicing. The present research outlines an easy-to-use mathematical algorithm to project a printing trajectory as a sequence of points through a vector-defined direction on any triangle-tessellated non-planar surface. The algorithm processes the ordered points of the 2D version of the printing trajectory, the tessellated STL files of the target surface, and the projection direction. It then generates the new trajectory lying on the target surface with the G-code instructions for the printer. As a proof of concept, several examples are presented, including a Hilbert curve and lattices printed on curved surfaces, using a conventional fused filament fabrication machine. The algorithm’s effectiveness is further demonstrated by translating a printing trajectory to an analytical surface. The surface is tessellated and fed to the algorithm as an input to compare the results, demonstrating that the error depends on the resolution of the tessellated surface rather than on the algorithm itself.

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Bulavskaya, A., E. Bushmina, A. Grigorieva, I. Miloichikova, and S. Stuchebrov. "X-ray study of the density distribution of FFF-printed samples with different fill patterns." Journal of Instrumentation 19, no. 06 (June 1, 2024): C06013. http://dx.doi.org/10.1088/1748-0221/19/06/c06013.

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Abstract Three-dimensional printing has a wide range of applications in science and technology. Fused filament fabrication (FFF) is a commonly used 3D printing technology, which is now being increasingly employed in radiation physics. In FFF, the internal structure of an object is primarily determined by its fill pattern and selected print modes. Therefore, this study aims to examine the interaction between X-rays and 3D-printed plastic samples with various infill patterns. The 3D-printed objects were produced using FFF with plastic and different infill patterns, including Rectilinear, Grid, Triangles, Stars, Honeycomb, Concentric, Archimedean Chords, Gyroid, and Hilbert Curve. Infill densities of 80% and 90% were utilized. Tomographic methods were applied to analyze the resulting samples. The study provides tomograms of the internal structure for each infill pattern. It was observed that Rectilinear and Grid patterns produced the most homogeneous samples. The findings of this study contribute to understanding of the propagation of X-rays through 3D-printed plastic samples with complex internal structures.

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Davis, Kristofer, and Yaoguo Li. "Efficient 3D inversion of magnetic data via octree-mesh discretization, space-filling curves, and wavelets." GEOPHYSICS 78, no. 5 (September 1, 2013): J61—J73. http://dx.doi.org/10.1190/geo2012-0192.1.

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Airborne magnetic survey data sets can contain from hundreds of thousands to millions of observations and typically cover large areas. The large number of measurements combined with a model mesh to accommodate the survey extent can render an inversion of these data intractable. Faced with this challenge, we have developed a three-step procedure to locally optimize the degree of model discretization and to compress the corresponding sensitivity matrix for the inversion of magnetic data. The mesh optimization is achieved through the use of adaptive octree discretization. The compression is achieved by first reordering the model cells using the Hilbert space filling curve and then applying the one-dimensional wavelet transform to the corresponding sensitivities. The fractal property of the Hilbert curve groups the spatially adjacent cells into algebraically adjacent positions in the reordered model mesh and thereby maximizes the number of zero or near-zero coefficients in the one-dimensional wavelet transform. Winnowing these insignificant coefficients finally leads to a highly sparse representation of the sensitivity matrix, which dramatically reduces the required memory and CPU time in the inversion. As a result, the proposed algorithm is capable of inverting huge data sets ([Formula: see text] measurements) with commensurate model sizes in a short time on a single desktop computer. As a test, we inverted an entire magnetic data set with 170,000 observations from a large uranium exploration program and achieved a reduction in computational cost exceeding 10,000 times.

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Azencott, R., R. Glowinski, J. He, A. Jajoo, Y. Li, A. Martynenko, R. H. W. Hoppe, S. Benzekry, and S. H. Little. "Diffeomorphic Matching and Dynamic Deformable Surfaces in 3d Medical Imaging." Computational Methods in Applied Mathematics 10, no. 3 (2010): 235–74. http://dx.doi.org/10.2478/cmam-2010-0014.

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AbstractWe consider optimal matching of submanifolds such as curves and surfaces by a variational approach based on Hilbert spaces of diffeomorphic transformations. In an abstract setting, the optimal matching is formulated as a minimization problem involving actions of diffeomorphisms on regular Borel measures considered as supporting measures of the reference and the target submanifolds. The objective functional consists of two parts measuring the elastic energy of the dynamically deformed surfaces and the quality of the matching. To make the problem computationally accessible, we use reproducing kernel Hilbert spaces with radial kernels and weighted sums of Dirac measures which gives rise to diffeomorphic point matching and amounts to the solution of a finite dimensional minimization problem. We present a matching algorithm based on the first order necessary optimality conditions which include an initial-value problem for a dynamical system in the trajectories describing the deformation of the surfaces and a final-time problem associated with the adjoint equations. The performance of the algorithm is illustrated by numerical results for examples from medical image analysis.

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Lopes, Lucas, Daniel Reis, Adilson Paula Junior, and Manuela Almeida. "Influence of 3D Microstructure Pattern and Infill Density on the Mechanical and Thermal Properties of PET-G Filaments." Polymers 15, no. 10 (May 11, 2023): 2268. http://dx.doi.org/10.3390/polym15102268.

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This study aims to evaluate the thermal and mechanical performances of PET-G thermoplastics with different 3D microstructure patterns and infill densities. The production costs were also estimated to identify the most cost-effective solution. A total of 12 infill patterns were analysed, including Gyroid, Grid, Hilbert curve, Line, Rectilinear, Stars, Triangles, 3D Honeycomb, Honeycomb, Concentric, Cubic, and Octagram spiral with a fixed infill density of 25%. Different infill densities ranging from 5% to 20% were also tested to determine the best geometries. Thermal tests were conducted in a hotbox test chamber and mechanical properties were evaluated using a series of three-point bending tests. The study used printing parameters to meet the construction sector’s specific needs, including a larger nozzle diameter and printing speed. The internal microstructures led to variations of up to 70% in thermal performance and up to 300% in mechanical performance. For each geometry, the mechanical and thermal performance was highly correlated with the infill pattern, where higher infill improved thermal and mechanical performances. The economic performance showed that, in most cases, except for the Honeycomb and 3D Honeycomb, there were no significant cost differences between infill geometries. These findings can provide valuable insights for selecting the optimal 3D printing parameters in the construction industry.

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Kim, Ga-In, Seong-Jae Boo, Jang-Wook Lim, Jin-Kyo Chung, and Min-Soo Park. "Texture Modification of 3D-Printed Maltitol Candy by Changing Internal Design." Applied Sciences 12, no. 9 (April 21, 2022): 4189. http://dx.doi.org/10.3390/app12094189.

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The purpose of this study is to show more diverse texture modifications by changing the material of a food 3D-printed structure conducted only with soft materials (in this case, potatoes and chocolate) to a hard material (in this case, maltitol here). However, unlike previous 3D-printed food materials, sweetener materials such as sucrose and maltitol are sensitively caramelized at a high melting temperature. As such, there is no commercialized printing equipment. Therefore, a printing process experiment was conducted first in this case. To do this, a high-temperature syringe pump-based extrusion device was designed, and process tests according to the temperature and environment were conducted. An assessment of the internal structural changes according to the infill patterns and infill percentages was conducted based on the acquired process conditions. The texture strength increased as the infill percentage increased. Depending on the infill patterns, the texture strength increased in the order of the Hilbert curve, honeycomb, and rectilinear samples here. As a result, a change in the texture strength was determined through a change in the internal structure of a hard food material using 3D printing, which showed a wider range of change than in conventional soft food materials.

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Yan, Binpeng, Sanyi Yuan, Shangxu Wang, Yonglin OuYang, Tieyi Wang, and Peidong Shi. "Improved eigenvalue-based coherence algorithm with dip scanning." GEOPHYSICS 82, no. 2 (March 1, 2017): V95—V103. http://dx.doi.org/10.1190/geo2016-0149.1.

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Detection and identification of subsurface anomalous structures are key objectives in seismic exploration. The coherence technique has been successfully used to identify geologic abnormalities and discontinuities, such as faults and unconformities. Based on the classic third eigenvalue-based coherence ([Formula: see text]) algorithm, we make several improvements and develop a new method to construct covariance matrix using the original and Hilbert transformed seismic traces. This new covariance matrix more readily converges to the main effective signal energy on the largest eigenvalue by decreasing all other eigenvalues. Compared with the conventional coherence algorithms, our algorithm has higher resolution and better noise immunity ability. Next, we incorporate this new eigenvalue-based algorithm with time-lag dip scanning to relieve the dip effect and highlight the discontinuities. Application on 2D synthetic data demonstrates that our coherence algorithm favorably alleviates the low-valued artifacts caused by linear and curved dipping strata and clearly reveals the discontinuities. The coherence results of 3D real field data also commendably suppress noise, eliminate the influence of large dipping strata, and highlight small hidden faults. With the advantages of higher resolution and robustness to random noise, our strategy successfully achieves the goal of detecting the distribution of discontinuities.

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Perezhogin, Pavel, Ilya Chernov, and Nikolay Iakovlev. "Advanced parallel implementation of the coupled ocean–ice model FEMAO (version 2.0) with load balancing." Geoscientific Model Development 14, no. 2 (February 5, 2021): 843–57. http://dx.doi.org/10.5194/gmd-14-843-2021.

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Abstract. In this paper, we present a parallel version of the finite-element model of the Arctic Ocean (FEMAO) configured for the White Sea and based on MPI technology. This model consists of two main parts: an ocean dynamics model and a surface ice dynamics model. These parts are very different in terms of the number of computations because the complexity of the ocean part depends on the bottom depth, while that of the sea-ice component does not. In the first step, we decided to locate both submodels on the same CPU cores with a common horizontal partition of the computational domain. The model domain is divided into small blocks, which are distributed over the CPU cores using Hilbert-curve balancing. Partitioning of the model domain is static (i.e., computed during the initialization stage). There are three baseline options: a single block per core, balancing of 2D computations, and balancing of 3D computations. After showing parallel acceleration for particular ocean and ice procedures, we construct the common partition, which minimizes joint imbalance in both submodels. Our novelty is using arrays shared by all blocks that belong to a CPU core instead of allocating separate arrays for each block, as is usually done. Computations on a CPU core are restricted by the masks of non-land grid nodes and block–core correspondence. This approach allows us to implement parallel computations into the model that are as simple as when the usual decomposition to squares is used, though with advances in load balancing. We provide parallel acceleration of up to 996 cores for the model with a resolution of 500×500×39 in the ocean component and 43 sea-ice scalars, and we carry out a detailed analysis of different partitions on the model runtime.

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Narasimhadhan, A. V., and Kasi Rajgopal. "FDK-Type Algorithms with No Backprojection Weight for Circular and Helical Scan CT." International Journal of Biomedical Imaging 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/969432.

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We develop two Feldkamp-type reconstruction algorithms with no backprojection weight for circular and helical trajectory with planar detector geometry. Advances in solid-state electronic detector technologies lend importance to CT systems with the equispaced linear array, the planar (flat panel) detectors, and the corresponding algorithms. We derive two exact Hilbert filtered backprojection (FBP) reconstruction algorithms with no backprojection weight for 2D fan-beam equispace linear array detector geometry (complement of the equi-angular curved array detector). Based on these algorithms, the Feldkamp-type algorithms with no backprojection weight for 3D reconstruction are developed using the standard heuristic extension of the divergent beam FBP algorithm. The simulation results show that the axial intensity drop in the reconstructed image using the FDK algorithms with no backprojection weight with circular trajectory is similar to that obtained by using Hu's and T-FDK, algorithms. Further, we present efficient algorithms to reduce the axial intensity drop encountered in the standard FDK reconstructions in circular cone-beam CT. The proposed algorithms consist of mainly two steps: reconstruction of the object using FDK algorithm with no backprojection weight and estimation of the missing term. The efficient algorithms are compared with the FDK algorithm, Hu's algorithm, T-FDK, and Zhu et al.'s algorithm in terms of axial intensity drop and noise. Simulation shows that the efficient algorithms give similar performance in axial intensity drop as that of Zhu et al.'s algorithm while one of the efficient algorithms outperforms Zhu et al.'s algorithm in terms of computational complexity.

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Wang, Lu, Nan Xu, and Jiangdian Song. "Decoding intra-tumoral spatial heterogeneity on radiological images using the Hilbert curve." Insights into Imaging 12, no. 1 (October 30, 2021). http://dx.doi.org/10.1186/s13244-021-01100-8.

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Abstract Background Current intra-tumoral heterogeneous feature extraction in radiology is limited to the use of a single slice or the region of interest within a few context-associated slices, and the decoding of intra-tumoral spatial heterogeneity using whole tumor samples is rare. We aim to propose a mathematical model of space-filling curve-based spatial correspondence mapping to interpret intra-tumoral spatial locality and heterogeneity. Methods A Hilbert curve-based approach was employed to decode and visualize intra-tumoral spatial heterogeneity by expanding the tumor volume to a two-dimensional (2D) matrix in voxels while preserving the spatial locality of the neighboring voxels. The proposed method was validated using three-dimensional (3D) volumes constructed from lung nodules from the LIDC-IDRI dataset, regular axial plane images, and 3D blocks. Results Dimensionality reduction of the Hilbert volume with a single regular axial plane image showed a sparse and scattered pixel distribution on the corresponding 2D matrix. However, for 3D blocks and lung tumor inside the volume, the dimensionality reduction to the 2D matrix indicated regular and concentrated squares and rectangles. For classification into benign and malignant masses using lung nodules from the LIDC-IDRI dataset, the Inception-V4 indicated that the Hilbert matrix images improved accuracy (85.54% vs. 73.22%, p < 0.001) compared to the original CT images of the test dataset. Conclusions Our study indicates that Hilbert curve-based spatial correspondence mapping is promising for decoding intra-tumoral spatial heterogeneity of partial or whole tumor samples on radiological images. This spatial-locality-preserving approach for voxel expansion enables existing radiomics and convolution neural networks to filter structured and spatially correlated high-dimensional intra-tumoral heterogeneity.

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Weissenböck, Johannes, Bernhard Fröhler, Eduard Gröller, Jonathan Sanctorum, Jan De Beenhouwer, Jan Sijbers, Santhosh Ayalur Karunakaran, Helmuth Hoeller, Johann Kastner, and Christoph Heinzl. "An Interactive Visual Comparison Tool for 3D Volume Datasets represented by Nonlinearly Scaled 1D Line Plots through Space-filling Curves." e-Journal of Nondestructive Testing 24, no. 3 (March 2019). http://dx.doi.org/10.58286/23675.

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The comparison of many 3D volumes to find subtle differences is tedious, time-consuming and error-prone. Previously we presented Dynamic Volume Lines [1], a novel tool for the interactive visual analysis and comparison of ensembles of 3D volumes, which are linearized using Hilbert spacing-filling curve and represented as 1D line plots. In this paper we further demonstrate the usefulness and capabilities of our method by conducting a detailed visual analysis and evaluation of an artificial specimen from simulated 3D X-Ray Computed Tomography (XCT) and a real-world XCT titanium alloy specimen.

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Garner, Niklas, and Oscar Kivinen. "Generalized Affine Springer Theory and Hilbert Schemes on Planar Curves." International Mathematics Research Notices, March 2, 2022. http://dx.doi.org/10.1093/imrn/rnac038.

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Abstract We show that Hilbert schemes of planar curve singularities and their parabolic variants can be interpreted as certain generalized affine Springer fibers for $GL_n$, as defined by Goresky–Kottwitz–MacPherson. Using a generalization of affine Springer theory for Braverman–Finkelberg–Nakajima’s Coulomb branch algebras, we construct a rational Cherednik algebra action on the homology of the Hilbert schemes and compute it in examples. Along the way, we generalize to the parahoric setting the recent construction of Hilburn–Kamnitzer–Weekes, which may be of independent interest. In the spherical case, we make our computations explicit through a new general localization formula for Coulomb branches. Via results of Hogancamp–Mellit, we also show the rational Cherednik algebra acts on the HOMFLY-PT homologies of torus knots. This work was inspired in part by a construction in 3D ${\mathcal {N}}=4$ gauge theory.

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Pfeifer, Wolfgang G., Chao-Min Huang, Michael G. Poirier, Gaurav Arya, and Carlos E. Castro. "Versatile computer-aided design of free-form DNA nanostructures and assemblies." Science Advances 9, no. 30 (July 28, 2023). http://dx.doi.org/10.1126/sciadv.adi0697.

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Recent advances in structural DNA nanotechnology have been facilitated by design tools that continue to push the limits of structural complexity while simplifying an often-tedious design process. We recently introduced the software MagicDNA, which enables design of complex 3D DNA assemblies with many components; however, the design of structures with free-form features like vertices or curvature still required iterative design guided by simulation feedback and user intuition. Here, we present an updated design tool, MagicDNA 2.0, that automates the design of free-form 3D geometries, leveraging design models informed by coarse-grained molecular dynamics simulations. Our GUI-based, stepwise design approach integrates a high level of automation with versatile control over assembly and subcomponent design parameters. We experimentally validated this approach by fabricating a range of DNA origami assemblies with complex free-form geometries, including a 3D Nozzle, G-clef, and Hilbert and Trifolium curves, confirming excellent agreement between design input, simulation, and structure formation.

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Sharma, Deepti, Binod Kumar Kanaujia, Vikrant Kaim, Raj Mittra, Ravi Kumar Arya, and Ladislau Matekovits. "Design and implementation of compact dual-band conformal antenna for leadless cardiac pacemaker system." Scientific Reports 12, no. 1 (February 24, 2022). http://dx.doi.org/10.1038/s41598-022-06904-2.

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AbstractThe leadless cardiac pacemaker is a pioneering device for heart patients. Its rising success requires the design of compact implantable antennas. In this paper, we describe a circularly polarized Hilbert curve inspired loop antenna. The proposed antenna works in the WMTS (Wireless Medical Telemetry Services) 1.4 GHz and ISM (Industrial, Scientific, and Medical) 2.45 GHz bands. High dielectric constant material Rogers RT/Duroid 6010 LM ($${\epsilon }_{r}$$ ϵ r =10) and fractal geometry helps to design the antenna with a small footprint of 9.1 mm3 (6 mm × 6 mm × 0.254 mm). The designed antenna has a conformal shape that fits inside a leadless pacemaker’s capsule is surrounded by IC models and battery, which are tightly packed in the device enclosure. Subsequently, the integrated prototype is simulated deep inside at the center of the multi-layer canonical heart model. To verify experimentally, we have put dummy electronics (IC and battery) inside the 3D printed pacemaker’s capsule and surfaced the fabricated conformal antenna around the inner curved body of the TCP (Transcatheter Pacing) capsule. Furthermore, we have tested the TCP capsule by inserting it in a ballistic gel phantom and minced pork. The measured impedance bandwidths at 1.4 GHz and 2.45 GHz are 250 MHz and 430 MHz, whereas measured gains are − 33.2 dBi, and − 28.5 dBi, respectively.

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Lu, Yue, Gang Wang, Zhuangdian Liang, Jian Sun, Yu Gu, and Zhiyong Tang. "Fractal Reactor in Micro-Scale for Process Intensification." International Journal of Chemical Reactor Engineering 17, no. 1 (September 29, 2018). http://dx.doi.org/10.1515/ijcre-2017-0225.

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AbstractFractal theory, with its novel architectures inspired by nature, provides some novel concepts for smart reactor design. Here, researches on the applications of fractal theory to micro-reactor design are reviewed, in term of its high surface area-to-volume ratio, rapid and direct numbering-up, safety, and precise control. In addition, two designs of fractal micro-reactor are introduced as typical examples. First, the H-type fractal structure is considered in the context of the design of a double-plate micro-reactor, which is used for photocatalytic reactions of CO2. Second, applications of fractal Hilbert curves are considered in the design of channel structures for gas-liquid reactions. These two fractal micro-reactors can be fabricated via 3D printing technology and used for CO2conversion under mild conditions.

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Zhang, Zhiqiang, Peng Lin, and Dayong Hu. "Crashworthiness analysis and optimization of brain-coral-inspired multilayer sandwich structures under axial crushing." Journal of Sandwich Structures & Materials, May 29, 2024. http://dx.doi.org/10.1177/10996362241257789.

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Inspired by brain corals and cuttlebone, this study employed 3D printing technology to fabricate a novel bio-inspired multilayer sandwich structure based on the Hilbert space-filling curve (named BHSS). The mechanical behavior and deformation process of the BHSS were compared through quasi-static axial crushing experiments and finite element (FE) simulations. The energy absorbing characteristics of the BHSS with different layers were compared through FE simulations, and the results indicated that the 4-layer BHSS displayed superior crashworthiness. Then, parametric studies were conducted to investigate the influence of layer-height gradient and wall-thickness gradient on the energy absorption performance and deformation modes of the BHSS. It was confirmed that the double gradient designs significantly reduced the initial peak force and improved the specific energy absorption of the BHSS. Finally, the multi-objectives optimization based on response surface method and the non-dominated sorting genetic algorithm (NSGA-II) was employed to optimize the geometric parameters of the BHSS, aiming at the optimal configuration for better crashworthiness. Compared to the original design structure, the SEA of the optimized knee point structure was increased by 21.8% and the IPF was reduced by 72.6%. These findings provided valuable guidelines for the brain-coral-inspired design of multilayer sandwich structures with superior energy-absorbing performance.

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Journal articles on the topic '3D Hilbert's curve'

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