443 results about "Distance threshold" patented technology

The invention provides an industrial visual anomaly recognition method, system and device based on multi-modal feedback and a medium, and belongs to the technical field of industrial visual detection.The method comprises the steps that a production line video stream is collected in real time, an ROI is automatically segmented, a picture sequence is generated, features of a set dimension are extracted, and the features of the set dimension are extracted; comparing a preset dynamic distance threshold with a feature library, and preliminarily identifying an abnormal image; a cue word of a detection requirement is constructed, the cue word and abnormal related information are input into the multi-modal large model, and a determined abnormal image is output; using the determined abnormal image to construct a data set to train a target detection model, and adjusting the learning rate in the training process; and inputting pictures captured in an industrial scene into the deep learning model, the multi-modal large model and the target detection model in sequence to obtain a recognition result, feeding back the recognition result to a user for confirmation, adding the recognition result to the data set, and optimizing training of the target detection model. According to the invention, accurate identification of abnormal images in industrial production is realized, and the identification efficiency is high.

The invention relates to the technical field of safety monitoring, and particularly discloses an operation safety distance management method based on laser radar point cloud data, and the method comprises the steps: generating a dangerous point cloud set based on an initial three-dimensional point cloud model of a complete field environment; performing coordinate transformation on the point cloud data currently collected by the three-dimensional laser radar equipment based on the rigid body transformation matrix to obtain current point cloud data; registering the current point cloud data with the initial three-dimensional point cloud model and identifying all independent dynamic targets; determining a danger approaching trend of each independent dynamic target based on the motion prediction trajectory of each independent dynamic target; determining a dynamic safety distance threshold value of each dangerous dynamic target based on the danger approaching trend and the response delay of each independent dynamic target and the additional safety distance of the corresponding dangerous source area; triggering a corresponding alarm mechanism based on the dynamic safety distance threshold and the distance between the point cloud set of each independent dynamic target and the dangerous point cloud set; and the overall safety of a working site is improved.

The invention discloses a high-precision plane fitting method for a multi-noise point cloud, and the method comprises the steps: carrying out the plane rough fitting of an original point cloud after down-sampling, taking the longest side of a minimum bounding box of a lower sampling point cloud as a distance threshold value, and calculating the distance weight of each point through a weight mathematical model, then, plane fine fitting is carried out on the weighted down-sampling point cloud, the distance weight of each point is updated after each fitting, plane fitting is carried out on the point cloud of which the weight is updated again, and a fine fitting plane of the down-sampling point cloud is calculated in an iterative manner; and finally, calculating the distance weight of each point in the original point cloud based on the fine fitting plane and the iterated distance threshold value, performing plane fitting on the weighted original point cloud in an iteration mode, and finally obtaining the fine fitting plane of the original point cloud. According to the technical scheme, the method is high in stability and low in calculation amount, can obtain a high-precision fitting plane in a weighted iteration mode under the condition of more noise, and is suitable for different types of point cloud data.

The invention discloses an anomaly detection method based on global reachability density and an adaptive threshold mechanism, which comprises the following steps: collecting single-index historical water quality monitoring data of a target monitoring station, extracting a subsequence with a fixed length through a sliding window mode, constructing a neighbor index structure and extracting neighborhood information, acquiring a k neighbor set of each data point; respectively calculating the local accessibility density of each data point in the local neighborhood of the data point; respectively calculating the global reachability density of each data point; performing statistical summary on GRD values of all data points in the sample set, calculating a mean value and a standard deviation of the GRD values, and defining a dynamically adjusted distance threshold value based on a variable coefficient; and an abnormal score function fusing local and global density features is further constructed, and abnormal point determination is realized according to a distance threshold. The method is suitable for complex time sequence water quality monitoring data, can effectively improve the recognition accuracy of weak anomalies, local drifts and extreme abrupt changes, and has high universality and robustness.

The invention discloses a multi-level hybrid obstacle avoidance control method adaptive to environment complexity, and relates to the technical field of robot control, and the method comprises the steps: obtaining the global map information of an inspection environment, dividing a map into grid units, marking static obstacles, and calculating a global path of an inspection robot from a starting position to a target position through an A * algorithm; position and speed information of a dynamic obstacle is obtained in real time through a laser radar, a gravitational field model and a repulsive force field model are established, a gravitational field is generated by a target point, and a repulsive force field is generated by the detected dynamic obstacle. According to the invention, by establishing an obstacle classification mechanism based on the distance threshold, quantitative evaluation of the threat degree is realized, and the problem of low control efficiency caused by adopting a unified processing strategy for all obstacles in a traditional method is avoided.

A method, computer program product, and computing system for processing a dataset of query-answer pairs. Synthetic variations of queries are generated and each of the synthetic variations of queries are mapped to a corresponding answer from the dataset. An embedding dataset is generated by transforming the synthetic variations into synthetic query embeddings and the queries into query embeddings. A first set of embeddings is defined for storage in a semantic cache and a second set of embeddings are defined and are not stored in the semantic cache. A separate distance threshold is assigned to each embedding of the first set of embeddings and a pairwise distance between each query and the synthetic variations is determined. Distance thresholds for respective pairwise distances between a query and synthetic variations of the query are generated. Subsequent queries are processed using the semantic cache and the distance thresholds.

The invention relates to the technical field of artificial intelligence, can be applied to business scenes of medical health, financial science and technology, leasing and the like, and discloses an operation authenticity verification method, which comprises the following steps: executing operator identity verification, and generating a verification record; starting a countdown mechanism, and monitoring terminal position information; when the initial verification distance accords with a first preset distance threshold value, generating a job permission instruction and receiving task data; acquiring real-time position information of the terminal, and determining a submission verification distance; when the submitted verification distance accords with a second preset distance threshold value, a verification passing timestamp is extracted, and a time effectiveness state is generated; and when the state is valid, storing the task data and the space-time verification information. According to the invention, identity verification and position verification are combined to ensure that an operator executes a task at a target location; the countdown mechanism limits the operable time after identity verification, so that the equipment is prevented from being transferred to others for use; the timeliness verification mechanism ensures that the data submission time is reasonable, and the authenticity and safety of task execution are improved.

The invention discloses an underground mine 4D millimeter wave radar ghosting noise automatic marking method and system. The method comprises the steps that first laser radar point cloud data and first 4D millimeter wave radar point cloud data are aligned at the same time reference through a timestamp nearest neighbor matching method, and a time synchronization data pair is obtained; according to the method, the function of accurately identifying and marking the ghosting noise of the 4D millimeter wave radar by combining the high-precision characteristic of the laser radar is realized, the marking efficiency is greatly improved, the marking cost is reduced, the function of detecting the ghosting noise in a mode of combining a distance threshold method and a clustering analysis method is realized, and the accuracy of the ghosting noise of the 4D millimeter wave radar is improved. The detection speed is guaranteed, the marking precision is improved, various complex conditions in the underground mine environment can be handled without depending on a specific signal model and an environment hypothesis, the safety and stability of a mine automation system are improved, remarkable economic and social benefits are achieved, and the method is suitable for being widely popularized and used.

A wireless transmit receive unit (WTRU) is configured to receive configuration information for reporting Global Navigation Satellite System (GNSS) assistance information (AI). The configuration information comprises a reporting trigger threshold that is at least one of a distance threshold or a time offset threshold. The WTRU determines that the reporting trigger threshold is exceeded and reports GNSS AI. The GNSS AI comprises at least one of a GNSS validity duration or a GNSS acquisition time. The GNSS validity duration comprises an indication of a time duration associated with a validity of a GNSS acquisition, an indication of a time duration associated with expiration of the GNSS acquisition, or a WTRU location associated with the GNSS acquisition. The GNSS acquisition time comprises a time to acquire a GNSS position.

A text processing method, which is executed by means of a computer device. The method comprises: acquiring source text to be processed, wherein the source text comprises a plurality of tokens (S501); on the basis of a relative distance between paired tokens in the source text, determining a relative position code corresponding to the relative distance between the paired tokens, and obtaining position code information comprising the relative position code (S502); acquiring a distance threshold value, determining from the position code information a first relative position code that corresponds to a relative distance exceeding the distance threshold value, and calling a text processing model to map the first relative position code in the position code information to a position code range of the text processing model, so as to obtain mapped position code information (S503); and calling the text processing model to perform semantic understanding on the source text on the basis of the mapped position code information, so as to generate semantically associated text for the source text (S504).

The invention discloses a distance measurement method and device based on target width and electronic equipment, and relates to the field of automatic driving, and the method comprises the steps: collecting an image in front of a vehicle, and recognizing a target in the image; determining a first target distance corresponding to the image; when the first target distance is smaller than a distance threshold value, judging that the first target distance is an estimated distance corresponding to each frame of image, and determining a target measurement width corresponding to each frame of image according to the first target distance, the focal length and the pixel width of the vehicle tail; performing fusion updating on the target measurement width corresponding to the current frame image and the previous frame image to obtain the updated target measurement width; when the updating frequency is greater than a frequency threshold and a first target distance corresponding to the subsequent frame image is greater than a distance threshold, determining a second target distance corresponding to the subsequent frame image; and fusing the first target distance and the second target distance corresponding to the subsequent frame image to obtain an estimated distance corresponding to the target in the subsequent frame image. According to the method, the inter-vehicle distance measurement precision is improved.

Aspects of the present disclosure are directed to triggering object transitions between near-field and far-field regions in an artificial reality environment. For example, the near-field region can be within arm's length for the user, while the far-field region can be greater than arm's length from the user. Objects can be displayed within these regions such that the user can interact with the objects in the artificial reality environment. A field manager can cause a displayed object to transition from the near-field region to the far-field region and / or from the far-field region to the near-field region. The field manager can compare sensed user movements to one or more trigger criteria (e.g., distance threshold(s), velocity threshold(s), etc.) to trigger transition of an object between field regions.

The invention relates to a method and a device for generating a video with a body and electronic equipment. The method comprises the following steps: analyzing a task instruction and initial environment observation data, generating a key operation step sequence and an associated object set thereof, and constructing a three-dimensional physical constraint graph; generating an initial action video sequence based on the coding condition; in response to single-frame action execution, calculating a spatial error index, and if the object contact distance deviation, the trajectory collision probability or the physical constraint violation value exceeds a preset threshold, triggering the space-time diffusion model to generate a correction frame based on the current physical constraint graph; in response to the completion of the key operation steps, verifying the semantic matching degree of the generated result and the task target, and if the key object attribute loss or the operation logic error is detected, regenerating the task operation step sequence and the physical constraint graph; and updating the object position, the distance threshold and the motion feasible region in the physical constraint graph, and inputting the space-time diffusion model. According to the method, the problems of physical consistency deficiency, error accumulation and semantic understanding splitting are solved.

The invention discloses a method for detecting gluing defects and a storage medium thereof, and relates to the technical field of gluing detection.The method comprises the following steps that S10, a line laser sensor scans a gluing workpiece to obtain a gluing workpiece point cloud, and scans an unglued standard workpiece to obtain a standard template workpiece point cloud; s20, fitting to obtain a reference plane of a workpiece point cloud of a gluing workpiece point cloud standard template, and intercepting a gluing to-be-detected area point cloud and a template to-be-detected area point cloud; s30, point cloud registration is carried out on the point cloud of the gluing to-be-detected area and the point cloud of the template to-be-detected area; s40, performing point distance threshold judgment on the point cloud of the to-be-detected gluing area after registration, and performing separation to obtain a pure colloid point cloud; and S50, judging that the point cloud of the pure colloid in the region is unqualified according to the fact that the cross section width and the cross section area of the point cloud of the pure colloid are smaller than a preset threshold value. According to the invention, the gluing defect can be detected more accurately, and the efficiency is high.

The present application relates to the field of information retrieval, and in particular relates to a data processing method, an electronic device, a readable storage medium, and a program product. In the method, when a query result of a query vector needs to be searched in a constructed graph index, neighbor nodes of at least some nodes among multiple nodes included in the graph index satisfy at least one of the following: the included angle between two vectors obtained by subtracting a node from any two neighbor nodes of the node is greater than or equal to a first angle threshold value, the distance between any two neighbor nodes of the node is greater than or equal to a first distance threshold value, and the number of neighbor nodes of the node within a preset space range is smaller than a first number. Thus, the neighbor nodes of the nodes in the constructed graph index are relatively dispersed in space, and the problem that a query result falls into a local optimum due to being unable to find nodes at a certain portion of space during a node-based neighbor node search process, because the nodes are densely distributed at a certain position, is avoided.

The invention provides a belt tearing detection method and device based on three-dimensional vision. The method comprises the steps of calculating a spatial distance value between each target point and an adjacent point in three-dimensional point cloud data in a direction perpendicular to a tangential direction of a laser arc, screening points of which the spatial distance values exceed a preset distance threshold value, forming an initial candidate point set, starting from each point, expanding a space through a breadth-first search algorithm, and obtaining a target candidate point set, calculating the length and depth of each connected domain; and taking the connected domain meeting the threshold condition as a corresponding potential crack, forming a potential crack set by the spatial position information of all the potential cracks, and generating a belt tearing detection result containing the spatial position information of the real crack and the corresponding alarm level. According to the technical scheme provided by the invention, high-precision dynamic identification and alarm of the surface crack of the belt are realized, the false detection rate is effectively reduced, and the industrial safety monitoring efficiency is improved.

A method of updating, by a user equipment (UE), a reference location based on non-terrestrial networks (NTN) in a wireless communication system may include acquiring reference location related information from a base station; as an operation of determining whether a distance between the UE and a reference location is less than a distance threshold based on the reference location related information, not performing measurement for cell reselection if the distance between the UE and the reference location, and performing the measurement for the cell reselection if the distance between the UE and the reference location is greater than the distance threshold; and performing reference location update based on a reference location related timer if the distance between the UE and the reference location is less than the distance threshold.

The invention provides a GIS buffer generation method and system based on fuzzy semantics and geographic constraints, and belongs to the technical field of geographic information systems.The method comprises the steps that fuzzy descriptors, membership values and geographic entity types are input into a pre-trained language-space mapping model, and basic distance parameters are obtained; querying a spatial database based on the geographic entity keywords, obtaining geometric features associated with the geographic entities, and calculating feature lengths corresponding to the geometric features; correcting the basic distance parameter based on the intention direction, the membership value, the geographic entity type and the feature length expressed by the fuzzy description word to obtain a geographic distance threshold; generating an initial two-dimensional buffer polygon based on the geographic distance threshold and the spatial geometric features of the geographic entity; and querying a digital elevation model to obtain topographic data based on the initial two-dimensional buffer region polygon, and generating a three-dimensional buffer region curved surface through a gradient sensitive interpolation algorithm. According to the invention, the accuracy of generating the GIS buffer area is improved.

The invention discloses a multi-unmanned aerial vehicle target tracking method based on cross-view collaboration, which is suitable for robust target monitoring in a dynamic scene. The method comprises the following steps: firstly, establishing a spatial mapping relation among visual angles of multiple unmanned aerial vehicles through feature point matching and projection transformation; after each unmanned aerial vehicle node independently executes deep learning-based target detection, converting a detection frame center point coordinate of an auxiliary view angle into a main view angle coordinate system, and calculating an Euclidean distance between the detection frame center point coordinate and a main view angle detection result; a main visual angle potential leak detection area is identified by setting a dynamic distance threshold value, and a local high-sensitivity re-detection module is triggered based on leak detection confidence; and finally, realizing space-time tracking of observation data by adopting a single-view target tracking algorithm. According to the invention, the problem of leak detection caused by single-view-angle shielding is effectively solved through a cooperative verification mechanism of a cross-view-angle detection frame center point space relationship, and the continuity and reliability of target tracking in an unmanned aerial vehicle view angle complex environment are remarkably improved while the real-time performance is ensured.

The invention particularly relates to a radar and AIS track association method based on an adaptive dynamic threshold. The method comprises the following steps: acquiring radar and AIS data and analyzing target information; based on the radar target information, least square fitting of a sliding window is adopted for a radar track, and the radar course is solved based on the radar track; calculating an adaptive dynamic threshold based on the distance of the radar target, the size of the AIS target and the measurement error of the sensor; determining an initial correlation quality factor based on the time initial correlation threshold value and the adaptive dynamic threshold value, and when the initial correlation quality factor meets the initial correlation quality threshold value, performing track initial correlation on the radar target and the AIS target; and establishing a fuzzy factor set based on the Euclidean distance, the navigational speed, the course and the orientation between the radar target and the AIS target, determining a fuzzy correlation quality factor based on the fuzzy factor set, and performing track correlation on the radar target and the AIS target when the fuzzy correlation quality factor meets a fuzzy correlation quality threshold. According to the method, the problems of missed association and wrong association caused by a fixed distance threshold are solved.

The invention discloses a proxy model auxiliary evolution method based on two-stage adaptive switching and Voronoi niche. The method comprises the steps of generating an initial sample by adopting optimal Latin hypercube sampling, obtaining a real fitness value through simulation, constructing an initial training data set, and setting an initial iteration counter k and an evaluation budget threshold value; training a proxy model based on the current data set, and executing evolutionary algorithm optimization by using the proxy model to obtain a current optimal individual; judging two stages according to an iteration counter k and a distance threshold value; the development execution stage comprises the following steps: evaluating the real fitness and updating a data set; the exploration execution stage comprises the steps of multi-modal approximate detection, Voronoi niche division, multi-modal collaborative search, real fitness evaluation and data set updating; judging a termination condition and outputting a result; according to the method, three core technologies of an adaptive stage switching mechanism, multi-modal approximate detection and Voronoi niche division and multi-extremum collaborative filling are creatively integrated, so that the defects of insufficient global exploration, low local development precision and poor convergence efficiency of a traditional method in a high-dimensional multi-modal expensive optimization problem are effectively overcome; and the solving efficiency and reliability of a complex and expensive optimization problem are remarkably improved.

The invention relates to the technical field of cloud computing and information security services, and particularly discloses a network security and data hosting integrated cloud service system and method, and the method comprises the steps: obtaining a multi-dimensional behavior data flow of a user, and generating a user feature vector; inputting the user feature vector into an incremental clustering algorithm, calculating the distance between the feature vector and a clustering center, performing user classification according to a distance threshold, and generating a user type tag; calculating a user reputation score based on the historical behavior statistical data of the category to which the user belongs; a sliding window algorithm is adopted to collect a data packet arrival time interval sequence, a jitter value in a window is calculated, a jitter value at the next moment is predicted, the number of packet loss in the window is counted, and a packet loss rate estimation value is calculated; and inputting the user type label, the reputation score, the jitter prediction value and the packet loss rate estimation value into a QoS decision engine. According to the invention, the problem of poor high-value user experience caused by unreasonable resource allocation is solved.

The invention relates to the technical field of intelligent blasting, and discloses an automatic blasthole arrangement method for a slow slope deep hole step and related equipment, and the method comprises the following steps: obtaining topographic data of a target step, and determining an initial blasthole layout for the target step according to the topographic data; determining whether a first included angle between the designed slope bottom line of the target step and the natural slope surface line is within a preset range or not; in response to the first included angle within the preset range, determining that the slope surface of the target step is a gentle slope surface; a main blast hole closest to the gentle slope in the initial blast hole layout is determined, a first intersection point of the main blast hole and a designed slope bottom line and a second intersection point of the natural slope surface line and the designed slope bottom line are determined, and the resistance line distance between the first intersection point and the second intersection point is calculated; whether the resistance line distance exceeds a preset distance threshold value or not is determined, and it is determined that a supplementary blast hole is additionally formed between the main blast hole and the natural slope line in response to the fact that the resistance line distance exceeds the preset distance threshold value. Therefore, it can be guaranteed that the blasting effect is better.

A neighboring cell measurement method is performed by a terminal, and includes: receiving configuration information sent by a network device, wherein the configuration information includes at least one piece of reference point information and a distance threshold corresponding to every one of the at least one piece of reference point information, and at least one of every piece of reference point information or the distance threshold corresponding to the every piece of reference point information is associated with at least one frequency; and performing a neighboring cell measurement based on the at least one piece of reference point information and the distance threshold corresponding to the every piece of reference point information.

The invention provides an object contour minimum bounding box generation method and device, a storage medium and equipment, and is applied to the technical field of computers. The method comprises the following steps: screening out a maximum distance point and an angular point of a target point cloud cluster, and determining a pre-selected long edge of the target point cloud cluster; performing linear fitting on at least one long side point cloud in the target point cloud cluster, wherein the linear distance between the long side point cloud and the pre-selected long side point cloud is within a preset distance threshold value to obtain a course angle; and according to a rotation matrix constructed by the course angle, carrying out translation and rotation transformation on the target point cloud cluster, then calculating the contour size and the center point of the point cloud cluster, and generating an object contour minimum bounding box of the target point cloud cluster. The method determines the pre-selected long edge by screening the maximum distance point and the angular point, improves the course angle precision by combining the threshold filtering point cloud and straight line fitting, and performs coordinate transformation on the point cloud based on the rotation matrix to generate the minimum bounding box closely fitting the object contour, thereby improving the course detection and bounding box precision, and improving the course detection precision. And more reliable environment information is provided for intelligent driving perception.

The invention relates to the technical field of path planning, and discloses a mechanical arm path planning method and system based on RRT *, and the method comprises the steps: sampling in a map space to obtain a sampling point, finding a node closest to the current sampling point from an expansion tree, determining the generation direction of a new node in combination with an artificial potential field method, and expanding to generate the new node; judging whether the new node collides with an obstacle or not, if not, adding the new node into the extension tree, and otherwise, re-sampling; constructing a father node according to whether collision occurs or not, performing rewiring, judging whether the distance between a new node and a target node in the extension tree is smaller than a preset distance threshold value or not and whether collision does not occur on a connection path between the two points or not, if yes, ending generation of the new node, and if not, performing resampling; and connecting the initial node, all the new nodes and the target node to obtain an initial planning path, removing redundant nodes in the initial planning path, and performing smoothing processing to obtain a final planning path. According to the invention, environment adaptability, efficiency and path quality can be improved.

This disclosure relates generally to coding and decoding of 3-dimensional (3D) mesh and specifically to merging of boundary vertexes in a symmetric mesh. The disclosure particularly provides methods, systems, and devices for determining whether true boundary vertices are present near a symmetry cut plane during symmetric coding of the 3D mesh, for determining an adaptive distance threshold for merging of boundary vertices, and for determining a list of true boundary vertices in order to reduce incorrect merging of these vertices, thereby reducing cracking artifact near the symmetry plane while preserving true boundaries in the reconstructed mesh

The invention provides a target detection result post-processing method and a computer program product, and relates to the technical field of target detection, and the method comprises the steps: obtaining a target detection result detected by a sensor; wherein the target detection result comprises bounding boxes and attribute information of a plurality of targets; dividing the plurality of targets into one or more target clusters based on a preset combination condition and the bounding boxes of the plurality of targets; wherein the merging condition comprises that the distance between the bounding boxes is smaller than a preset distance threshold value, or an inclusion relation exists between the bounding boxes; the two targets meeting the combination condition belong to the same target cluster; screening out the bounding box of one target from the bounding boxes of the targets in the target cluster as the bounding box of the combined targets; based on the attribute information of the targets in the target cluster, determining the attribute information of the combined targets; wherein the target clusters are in one-to-one correspondence with the combined targets. The calculation amount can be reduced, and the accuracy of the merging result is improved.

The invention relates to an address processing method and device, computer equipment, a computer readable storage medium and a computer program product. The method comprises the steps of obtaining a positioning address corresponding to a positioning coordinate; if the first text similarity value of the positioning address and the order address is smaller than a similarity threshold value, searching a plurality of candidate positions, wherein the distances between the candidate positions and the positioning coordinates are smaller than a first distance threshold value; obtaining a candidate address corresponding to each candidate position; according to the second text similarity value of each candidate address and the order address, determining a plurality of recommendation addresses in each candidate address, and displaying each recommendation address; and in response to the selection operation, determining a target address in each recommended address. By adopting the method, the auditing difficulty of authenticity verification through field evidence collection can be reduced, and the labor cost is saved.

The invention provides a point cloud data plane detection method and apparatus, an electronic device and a readable storage medium. The method comprises the steps of obtaining a to-be-merged plane pair in point cloud data; if the two planes in the plane pair are determined to have a significant adjacent relationship, judging whether the two planes are effectively separated by an adjacent straight line between the two planes or not, otherwise, judging whether the two planes can be combined or not according to the adjacent points of the two planes; if not, the two planes are combined, and otherwise, the distance between the two planes is calculated; if the distance is smaller than a preset distance threshold value, combining the two planes, otherwise, determining interference points between the two planes and judging whether the number of the interference points meets a preset condition or not; wherein the preset condition is that the ratio of the number of the interference points to the length of the adjacent straight line is smaller than a preset proportion or the number of the interference points is smaller than a preset point number threshold; and if not, combining the two planes, otherwise, not processing. The plane detection efficiency and accuracy can be improved, and the method is suitable for point cloud data with extremely narrow planes.