Voxel Structure Research Articles

Reliable simulation analysis for high-temperature inrush water hazard based on the digital twin model of tunnel geological environment

In complex mountainous terrains, tunnel construction faces unique challenges from high-temperature water inrush hazards, a systemic risk arising from the interplay of stress, seepage, and temperature fields. Traditional simulation methods, focusing on isolated disaster scenarios, fall short in addressing the multifaceted nature of these risks due to geological ambiguity and data incompleteness. Digital twin technology presents an effective solution to these challenges; however, its core challenge lies in how to utilize digital twin technology for data-model-co-driven simulation analysis of coupled multi-physical fields in situations of incomplete data. This paper introduces a digital twin paradigm for the simulation analysis of water inrush, which significantly enhances efficiency and accuracy through the integration of advanced machine learning and finite element analysis techniques. Specifically, this is achieved by combining a high-precision geological modeling method based on Gaussian Processes (GP) with a parameter calibration method through Gaussian Process-Differential Evolution (GP-DE) back-analysis. Firstly, a voxel structure is utilized to integrate the multi-field attribute features of the tunnel environment. Secondly, through the integration of multi-source advanced geological prediction data, we construct a dynamic digital twin model of the tunnel environment leveraging machine learning techniques. To overcome the issue of low modeling accuracy, the GP is employed, enhancing the exploitation of latent information within multi-source geophysical data. Lastly, we utilize the GP-DE back-analysis method to calibrate the parameters of the tunnel environment, thereby enhancing the precision and reliability of water inrush simulations. The method has been validated through application to a section of an ultra-high-temperature water inrush tunnel in China, featuring a burial depth of 230 meters. The accuracy of the method is corroborated by the monitoring data from the tunnel, supporting dynamic optimization design and safety prevention measures during construction.

The Improvement of Density Peaks Clustering Algorithm and Its Application to Point Cloud Segmentation of LiDAR.

This work focuses on the improvement of the density peaks clustering (DPC) algorithm and its application to point cloud segmentation in LiDAR. The improvement of DPC focuses on avoiding the manual determination of the cut-off distance and the manual selection of cluster centers. And the clustering process of the improved DPC is automatic without manual intervention. The cut-off distance is avoided by forming a voxel structure and using the number of points in the voxel as the local density of the voxel. The automatic selection of cluster centers is realized by selecting the voxels whose gamma values are greater than the gamma value of the inflection point of the fitted γ curve as cluster centers. Finally, a new merging strategy is introduced to overcome the over-segmentation problem and obtain the final clustering result. To verify the effectiveness of the improved DPC, experiments on point cloud segmentation of LiDAR under different scenes were conducted. The basic DPC, K-means, and DBSCAN were introduced for comparison. The experimental results showed that the improved DPC is effective and its application to point cloud segmentation of LiDAR is successful. Compared with the basic DPC, K-means, the improved DPC has better clustering accuracy. And, compared with DBSCAN, the improved DPC has comparable or slightly better clustering accuracy without nontrivial parameters.

VSL-Net: Voxel structure learning for 3D object detection

Current detection methods with single stage generally lack contextual structure information, the classification and location confidence are inconsistent, which are not able to achieve accurate dynamic multi-object detection. Therefore, a VSL-Net method is proposed based on single-stage detection framework, which maps voxels to the point cloud space through voxel structure learning for foreground point segmentation and center estimation. In the voxel feature extraction network, the submanifold sparse convolution is proposed to improve convolution efficiency by reducing operation of null region. In the detection network, a position alignment module is proposed to sample and interpolate in Bird’s Eye View. Characteristics of surrounding points are integrated to further improve the accuracy of detection. The proposed VSL-Net method was compared with other excellent method on the Kitti, Waymo and Nuscene datasets. The vehicle detection accuracy of VSL-Net reached 92.12%. Ablation and accuracy detection experiments have completed on a real physical platform. Experiment results showed that the proposed method had portability, strong generalization ability and high detection accuracy.

Detecting vertices of building roofs from ALS point cloud data

ABSTRACTRoof vertex information is vital for 3D roof structures. Reconstructing 3D roof structures from point cloud data using traditional methods remains a challenge because their extracted roof vertices are affected by uncertainty and additional errors from roof plane segmentation and supplementary sub-steps for extracting primitives. In this study, instead of segmenting roof planes and then extracting primitives based on them, a flexible rule-based method is proposed to directly detect the vertices of building roofs from point cloud data without the requirement of training data. The point cloud data is first voxelized with a dominant direction-based rotation. Based on the different features of the interior roof points and vertices, rules for voxel filtering and structure line determination are defined to extract the roof vertices. The experimental results on a custom dataset in Trondheim, Norway demonstrate that the proposed method can effectively and accurately extract roof vertices from point cloud data. The comparative experimental results with an unfine-tuned deep learning-based method on custom and benchmark datasets with different point densities further show that the proposed method has good generalization and can adapt to changes of datasets.

Voxel-based structural monitoring model for building structures using terrestrial laser scanning

This study presents a structural monitoring model for building structures using Terrestrial Laser Scanning (TLS). The model includes three phases for data collection, processing, and structural assessment, integrating a voxel-based data processing approach with polynomial regression to estimate structural responses. To investigate the influence of voxel size on estimating responses, several voxel structures were generated, each utilizing a uniform voxel size with voxel sizes ranging from 10 mm to 40 mm. The effectiveness of this proposed model was examined on a large-scale, two-story steel building under gravity and lateral loads. The estimated results demonstrated reasonable agreement with reference data, particularly at higher drift levels. Despite environmental challenges, such as obstacles and blind spots, the regression method effectively mitigated data gaps. This research indicates the viability of TLS as an efficient and effective contactless alternative for structural assessment in terms of speed and accuracy. Future advancements in laser scanning technology could further enhance data density and precision, thus extending the applicability of the model to larger-scale projects.

Multi-material 3D printing of piezoelectric and triboelectric integrated nanogenerators with voxel structure

Flexible and highly filled piezoelectric nanogenerators with excellent performance play an indispensable role in portable electronic devices, while the bottlenecks are hard to improve the polarization efficiency and prepare three-dimensional (3D) amplifying effect structure. Compared with other typical 3D printing technologies, direct ink writing multi-material printing (DIW-M3D), can extrude multiple viscoelastic ink materials with a wide selection of materials, which has the advantage of integrated multi-material processing. However, there are fewer reports on the use of DIW-M3D technology to print functional composite materials. Inspired from Lego block structures, we utilized DIW-M3D technology to prepare fabrications with alternating arrangements of piezoelectric and conductive inks between layers. This voxel-isolated conducting network provided the superior polarization path and uniform distribution of polarization field, which sharply ameliorate the piezoelectric effect and output performance. Owing to this voxel-isolated structure, the VOC and ISC could reach 150 V and 16 µA respectively, with the jumping movements of the forefoot. This work paved a path of scale-up preparing piezoelectric devices with 3D amplification effect structure and enhanced the polarization efficiency of the devices.

A smoothed boundary bidomain model for cardiac simulations in anatomically detailed geometries.

This manuscript presents a novel finite difference method to solve cardiac bidomain equations in anatomical models of the heart. The proposed method employs a smoothed boundary approach that represents the boundaries between the heart and the surrounding medium as a spatially diffuse interface of finite thickness. The bidomain boundary conditions are implicitly implemented in the smoothed boundary bidomain equations presented in the manuscript without the need of a structured mesh that explicitly tracks the heart-torso boundaries. We reported some significant examples assessing the method's accuracy using nontrivial test geometries and demonstrating the applicability of the method to complex anatomically detailed human cardiac geometries. In particular, we showed that our approach could be employed to simulate cardiac defibrillation in a human left ventricle comprising fiber architecture. The main advantage of the proposed method is the possibility of implementing bidomain boundary conditions directly on voxel structures, which makes it attractive for three dimensional, patient specific simulations based on medical images. Moreover, given the ease of implementation, we believe that the proposed method could provide an interesting and feasible alternative to finite element methods, and could find application in future cardiac research guiding electrotherapy with computational models.

Novel topological method to define scar heterogeneity relates to arrhythmia vulnerability

Abstract Funding Acknowledgements Type of funding sources: Public Institution(s). Main funding source(s): KU Leuven BOF, C14/18/079 Background Healing of myocardial infarction (MI) can result in heterogeneous scar structures, resulting in border zone conduction channels with altered electrophysiological properties, that lead to arrhythmia vulnerability. Identification of scar heterogeneity and potential conduction channels based on contrast enhanced MRI has shown to be viable. However, current methods rely on manual identification and systematic approaches are lacking. Objective To provide a systematic methodology to annotate scar heterogeneity on contrast enhanced MRI and to correlate it to arrhythmia vulnerability. Methods Antero-septal MI was induced in 10 domestic pigs by 120-minute occlusion of the left anterior descending artery followed by reperfusion. Late gadolinium enhanced MR imaging was performed one month after infarction. The endocardium and epicardium of the left ventricle were segmented and the voxels inside the left ventricle (LV) were extracted. All LV voxels with signal intensity above the middle of the myocardial signal intensity range were defined to be infarct voxels and otherwise intact voxels. The infarct voxel structure and intact voxel structure were analyzed using a novel computational cubical homology approach that automatically identifies "holes" in the respective structures. The so called topological "holes" were annotated using a minimal length cycle encircling the hole (see Figure 1). This cycle annotation corresponds with scar heterogeneity as it pinpoints regions of intertwined fibrosis and viable myocardium which can potentially act as functional arrhythmia substrate. Scar heterogeneity, annotated as cycles, was compared against two measures of arrhythmia vulnerability. On one hand, the number of premature ventricular complexes (PVCs) were determined during an incremental isoproterenol infusion protocol (ranging from no infusion to 0.04 µg/kg with increments of 0.01µg/kg each 5 minutes). And on the other hand, the ease of induction is defined as the complementary percentage of the steps of the programmed electrical stimulation (PES) protocol needed to induce a ventricular tachycardia. Results Scar heterogeneity cycles were automatically annotated in all animals. In 7 of the 9 animals a ventricular tachycardia was successfully induced during the PES protocol. The ease of induction correlated with the circumference of the myocardial infarct (r = 0.69, p = 0.040). Furthermore, the ease of induction tended to correlate with the circumference of the largest heterogeneity cycle (r = 0.61, p = 0.083). The total number of PVCs throughout the isoproterenol infusion protocol correlated with the circumference of the heterogeneity cycle (r = 0.72, p = 0.031). Conclusion A novel automated and systematic method to identify scar heterogeneity on contrast enhanced MR imaging is introduced. Furthermore, the presence of large heterogeneous scar structures, potentially adding an arrhythmia substrate, correlated with arrhythmia vulnerability.

Optically functionalization of 3D surfaces via voxel-based hierarchically micro structuralizing, a study case: Patterned optical ID

Optics is one of the most important applications of functional surfaces enabled by micro-/Nano-structuring. Mass production of optical functional surfaces mainly relies on replication technologies. In optical applications, structural consistency is essential for the precise control of functions such as micro-mirror/lens arrays. A big challenge from the design phase when fabricating functional surfaces is the geometrical constraint, e.g. patterning orient-consistent micromirrors on three-dimensional surfaces. This present paper demonstrates a voxel-based method to indirectly pattern consistently oriented microstructures onto 3D surfaces by creating a hierarchical structure, consisting of the substrate level of a “Minecraft”-like voxel structure and the feature level of micro features machined on the voxels. As a study case, RSA905 injection moulding inserts with 3D functional surfaces for optical encoding are fabricated with diamond machining: a spherical and a sinusoidal sample with a data matrix as an optical ID on each. The encoding is based on the optical contrast generated by the surfaces' directional reflection, which is led by the bevel surfaces of the micro ridge arrays. With the quantified evaluation of the resultant surface quality and functionality, the feasibility of the “Minecraft” method is validated, the surface quality is correlated with its complexity and the process optimization routine is determined. Moreover, by over 15,000 injection moulding cycles, the method is also proved suitable for batch production of 3D functional surfaces by micro injection moulding.

Reprogrammable Mechanical Metamaterials with Heterogeneous Assembly of Soft Shell‐Based Voxels

Mechanical metamaterials are well studied to enable functions that are difficult to achieve in natural materials, in which reprogramming of specific underlying structures targeting different mechanical responses is particularly challenging. Herein, a heterogeneous voxel assembly‐based 2D mechanical metamaterial is purposed, aiming at a reprogrammable design of the mechanical properties and shape‐morphing simultaneously. In particular, each voxel is structured with a bistable soft shell and soft beams, which can be well controlled to achieve various desirable mechanical properties by a parameterized design method. The engineered metamaterial has a periodic arrangement of the voxel structures that can be transformed into an arbitrary aperiodic architecture with low geometrical frustration in the metamaterial plane by manipulating voxels, in which reprogrammable stiffness and Poisson's ratios, as well as deformation sequences and complex surface textures, can be achieved. In addition, the voxelated assembly has two modes allowing for fine or extensive tuning of the stiffness and the optional generation of 1D or 2D textures. Under this design paradigm, the programmability of multiple mechanical responses can support the development of more intelligent mechanical metamaterials with great potentials to soft robotics and active deformable devices.

A Unified Framework Integrating Decision Making and Trajectory Planning Based on Spatio-Temporal Voxels for Highway Autonomous Driving

Intelligent decision making and efficient trajectory planning are closely related in autonomous driving technology, especially in highway environment full of dynamic interactive traffic participants. This work integrates them into a unified hierarchical framework with long-term behavior planning (LTBP) and short-term dynamic planning (STDP) running in two parallel threads with different horizon, consequently forming a closed-loop maneuver and trajectory planning system that can react to the dynamic environment effectively and efficiently. In LTBP, a novel voxel structure and the ‘voxel expansion’ algorithm are proposed for the generation of driving corridors in 3D configuration, which involves the prediction states of surrounding vehicles. By using Dijkstra search, the maneuver with minimal cost is determined in form of voxel sequences, then a quadratic programming (QP) problem is constructed for solving the optimal trajectory. And in STDP, another small-scaled QP problem is performed to track or adjust the reference trajectory from LTBP in response to the dynamic obstacles. Meanwhile, a Responsibility-Sensitive Safety (RSS) Checker keeps running at high frequency for real-time feedback to ensure security. Experiments on real data collected in different highway scenarios demonstrate the effectiveness and efficiency of our work.

Generative Design of Structured Materials for Controlled Frequency Responses.

Spatially varying material properties allow the dynamic response of structural systems to be almost arbitrarily tailored, far beyond the first or fundamental natural frequency. Continuing advances in manufacturing technology are making it possible to achieve the necessary range of stiffness and density variations, but the design of these property distributions is a challenging task because of the complex multidimensional nature of the problem. Generative design methods based on evolutionary optimization algorithms have been successfully used to obtain solutions based on multi-material distributions. However, the applicability of these solutions is limited by their reliance on multi-material additive manufacturing (AM), which currently only offers digitally mixed acrylic polymer options that are generally unsuitable to produce functional parts. A novel structured material solution is proposed here, in which the problem domain is divided into several volume elements (voxels), each of which contains a structure whose geometrical form is altered to adjust its effective properties to desired values. The single material structural solution will be amenable for ready fabrication by the powder-based selective laser sintering and melting processes with real engineering polymer and metal systems, thereby allowing for the realization of the benefits in real-world applications. The resulting continuous design spaces are searched using a modern evolutionary algorithm, the covariance matrix adaptation evolution strategy (CMA-ES). A MATLAB implementation of this evolutionary design method, in conjunction with finite element simulations for fitness evaluation, showed good convergence for several different cantilever beam test cases when tested against several different sets of target natural frequencies. Correlations with the multi-material solutions show that the single structured material approach is on par or even better in some cases, even though the test domain was discretized into 80% fewer voxels than for the multi-material case. Furthermore, the voxel structures can be realized using current AM technologies.

Radiometric enhancement of full-waveform airborne laser scanner data for volumetric representation in environmental applications

The scientific investigation of forest ecosystems requires precise information on the three-dimensional structure of trees. Full-waveform airborne laser scanner data contain very valuable information on the biophysical structure in forest stands. Beyond 3D point cloud representations obtained from full-waveform decomposition techniques, volumetric representations of full-waveform laser scanner data (i.e. 3D voxel spaces) form a valuable basis for various scientific analysis ranging from biomass determination (or biomass change determination) over habitat analysis to meteorological gas exchange investigations. In order to achieve volumetric forest stand representations of high geometric and radiometric quality, the raw measurement data have to be prepared for the transformation into the voxel structure. The preparation of the full-waveform airborne laser scanner data comprises on the one hand the reconstruction of the differential backscatter cross section. On the other hand, we have to apply a radiometric correction on the reconstructed differential backscatter cross section, since each individual laser pulse echo is significantly affected by attenuation effects caused by partial reflections in higher regions of the crown during the laser pulse propagation through the vegetation. As a result, the structure in the lower parts of the vegetation is underrepresented in the digitized waveform and consequently also in the volumetric reconstruction.In this paper, we present novel methods for the radiometric enhancement of full-waveform airborne laser scanner data for volumetric representations in environmental applications. Our approach allows the numerically stable reconstruction of the effective differential backscatter cross section using appropriate deconvolution and regularization techniques. Moreover, we developed a correction method, which compensates for the loss of signal strength caused by partial reflections on the path of a laser pulse through the canopy. The correction term is derived from the differential backscatter cross section directly via a waveform history analysis. The basic idea of the correction method is a stepwise increase of the signal amplitudes depending on the individual history of each laser pulse. Therefore, the procedure is also referred to as pulse history correction.Our novel methods contribute to an improved access to the information on vegetation structure contained in full-waveform laser scanner data. Furthermore, they allow to overcome limitations of existing approaches, which are mainly based on the extraction of discrete maxima.

Real-time ground filtering algorithm of cloud points acquired using Terrestrial Laser Scanner (TLS)

3D modeling based on point clouds requires ground-filtering algorithms that separate ground from non-ground objects. This study presents two ground filtering algorithms. The first one is based on normal vectors. It has two variants depending on the procedure to compute the k-nearest neighbors. The second algorithm is based on transforming the cloud points into a voxel structure. To evaluate them, the two algorithms are compared according to their execution time, effectiveness and efficiency. Results show that the ground filtering algorithm based on the voxel structure is faster in terms of execution time, effectiveness, and efficiency than the normal vector ground filtering.

Influence of SLM-process parameters on the formation of the boundaries of parts of heat-resistant nickel alloy Inconel 718

We consider the improvement is considered of the modes of selective laser melting technology based on the design model to reduce the level of residual stresses and prevent deviations in the geometry of the part. Simulation results are presented on a universal voxel structure and a simplified object to predict metal behavior depending on the specific energy density in the region of the boundaries of a metal part made of Inconel 718. An experiment was carried out to study the influence of different strategies and process modes on the curvature of parts as a result of the effect of residual stresses in order to minimize them. Printing was carried out on a 3-D printer "Alfa-150" (LLC "ALT Ukraine") at constant power (P, W) and distance between tracks (d, mm) in each zone (up-skin, down-skin, in - skin) with a change in the speed (V, mm / s) of the laser beam movement, as well as a different pattern of sample growth by 3-D printing with 67 degrees rotation of each new layer relative to the previous one. To identify defects and deviations from the original model to the solid (sample), metallographic analysis was performed using optical microscopy (Carl Zeiss AXIOVERT 200M). It was found that the simulation of printing processes, performed on the Magics platform by breaking the model into a voxel structure, allows an analytical assessment of stresses and strains. Analysis of the appearance of the prototypes showed that the best down-skin indicators are formed at a power of 80 W and a specific energy density (40 ... 38 J / mm3). By using the 67 degrees staggered printing strategy at the optimum specific energy density, it is possible to minimize the residual internal stresses leading to distortion of the product. In the future, the results can be supplemented by studies of the effect of residual stresses of compressive forces when exposed to a laser beam at constant applied power. Using a computational model that allows calculating the residual stresses during the deposition of the next layer, depending on the speed of the laser, the power and the distance between the applied tracks, it is possible to obtain high-precision parts with specified properties. The adaptation of the model, which allows us to obtain a quantitative estimate of the residual thermal stresses depending on the speed of movement and the laser power for the Inconel 718 heat-resistant alloy, has been carried out. Optimal modes have been determined to minimize these stresses and reduce the curvature of the part.

Approximate Intrinsic Voxel Structure for Point Cloud Simplification.

A point cloud as an information-intensive 3D representation usually requires a large amount of transmission, storage and computing resources, which seriously hinder its usage in many emerging fields. In this paper, we propose a novel point cloud simplification method, Approximate Intrinsic Voxel Structure (AIVS), to meet the diverse demands in real-world application scenarios. The method includes point cloud pre-processing (denoising and down-sampling), AIVS-based realization for isotropic simplification and flexible simplification with intrinsic control of point distance. To demonstrate the effectiveness of the proposed AIVS-based method, we conducted extensive experiments by comparing it with several relevant point cloud simplification methods on three public datasets, including Stanford, SHREC, and RGB-D scene models. The experimental results indicate that AIVS has great advantages over peers in terms of moving least squares (MLS) surface approximation quality, curvature-sensitive sampling, sharp-feature keeping and processing speed. The source code of the proposed method is publicly available. (https://github.com/vvvwo/AIVS-project).

Solid rocket motor propellant grain burnback simulation based on fast minimum distance function calculation and improved marching tetrahedron method

To efficiently compute arbitrary propellant grain evolution of the burning surface with uniform and non-uniform burning rate for solid rocket motor, a unified framework of burning surface regression simulation has been developed based on minimum distance function. In order to speed up the computation of the mini-mum distance between grid nodes of grain and the triangular mesh of burning surface, a fast distance querying method based on the equal size cube voxel structure was employed. An improved marching tetrahedron method based on piecewise linear approximation was carried out on second-order tetrahedral elements, achieved high-efficiency and adequate accuracy of burning surface extraction simultaneously. The cases of star grain, finocyl grain, and non-uniform tube grain were studied to verify the proposed method. The observed result indicates that the grain burnback computation method could realize the accurate simulation on unstructured tetrahedral mesh with a desirable performance on computational time.

Remote sensing data fusion as a tool for biomass prediction in extensive grasslands invaded by L. polyphyllus

AbstractRemote sensing data fusion is a powerful tool to gain information of quantitative and qualitative vegetation properties on field level. The aim of this study was to develop prediction models from sensor data fusion for fresh and dry matter yield (FMY/DMY) in extensively managed grasslands with variable degree of invasion by Lupinus polyphyllus. Therefore, a terrestrial 3d laser scanner (TLS) and a drone‐based hyperspectral camera was used to collect high resolution 3d point clouds and hyperspectral aerial orthomosaics of four extremely heterogenous grasslands. From 3d point clouds multiple features (vegetation height, sum of voxel, point density and surface structure) were extracted and combined with hyperspectral data to develop an optimized biomass model from random forest regression algorithm to predict FMY and DMY (ntrain = 130, ntest = 33). Models from hyperspectral data solitarily had the lowest prediction performance (FMY: R2 = 0.61, nRMSEr = 17.14; DMY: R2 = 0.59, nRMSEr = 19.37). Higher performance was gained by models derived from 3d laser data (FMY: R2 = 0. 76, nRMSEr = 13.3; DMY: R2 = 0. 74, nRMSEr = 15.1). A fusion of both sensor systems increased the FMY prediction performance up to R2 = 0.8; nRMSEr = 12.02 and the DMY prediction performance to R2 = 0.81 and nRMSEr = 12.06. The fusion of complementary sensor systems can increase the power to predict biomass yields of heterogenous and extensively managed grasslands. It is a novel alternative to labour‐intensive, traditional biomass prediction methods and to remote sensing methods using only single sensor data.

UV‐free Texturing using Sparse Voxel DAGs

AbstractAn application may have to load an unknown 3D model and, for enhanced realistic rendering, precompute values over the surface domain, such as light maps, ambient occlusion, or other global‐illumination parameters. High‐quality uv‐unwrapping has several problems, such as seams, distortions, and wasted texture space. Additionally, procedurally generated scene content, perhaps on the fly, can make manual uv unwrapping impossible. Even when artist manipulation is feasible, good uv layouts can require expertise and be highly labor intensive.This paper investigates how to use Sparse Voxel DAGs (or DAGs for short) as one alternative to avoid uv mapping. The result is an algorithm enabling high compression ratios of both voxel structure and colors, which can be important for a baked scene to fit in GPU memory. Specifically, we enable practical usage for an automatic system by targeting efficient real‐time mipmap filtering using compressed textures and adding support for individual mesh voxelizations and resolutions in the same DAG. Furthermore, the latter increases the texture‐compression ratios by up to 32% compared to using one global voxelization, DAG compression by 10 – 15% compared to using a DAG per mesh, and reduces color‐bleeding problems for large mipmap filter sizes.The voxel‐filtering is more costly than standard hardware 2D‐texture filtering. However, for full HD with deferred shading, it is optimized down to 2.5 ± 0.5 ms for a custom multisampling filtering (e.g., targeted for minification of low‐frequency textures) and 5 ± 2 ms for quad‐linear mipmap filtering (e.g., for high‐frequency textures). Multiple textures sharing voxelization can amortize the majority of this cost. Hence, these numbers involve 1–3 textures per pixel (Fig. 1c).

Space-time cluster detection with cross-space-time relative risk functions

ABSTRACTSpace-time kernel density estimation (STKDE) commonly is used for space-time cluster detection. But, this technique might be limited because it does not take into account an underlying population at risk for observed events. A space-time relative risk function (STRRF) can help overcome this limitation by allowing a comparison of each kernel density of observations with that of controls. This paper proposes a cross-STRRF to identify spatio-temporal locations that experience statistically significant changes in their density of events. With events organized in a space-time voxel structure, the cross-STRRF evaluates space-time patterns by comparing event occurrences at a spatial location in a previous time period with ones in its future as well as with its spatial neighbors in its contemporaneous time period. The test statistics of the cross-STRRF values in each voxel are obtained with a permutation test in which cases and controls are shuffled within each time period to maintain the space-time envelope of events. An application to assault crime incidents in the city of Plano, Texas between 2008 and 2012 illustrates that the cross-STRRF and its significance test results emphasize spatio-temporal changes in event density rather than constantly focusing on high density regions, which STKDE does.