Capacity sensing and stacking planning method based on gradient reinforcement learning Delaunay subdivision
Through the combination of gradient reinforcement learning and Delaunay segmentation, the sensitivity of Delaunay segmentation to input data is solved, data uniformity and noise processing are optimized, dynamic update efficiency is improved, and efficient palletization planning is achieved.
Patent Information
- Application Number
- CN202510594512.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-09
- Publication Date
- 2025-08-15
AI Technical Summary
The existing Delaunay triangulation algorithm has high sensitivity to input data, resulting in large differences in the size of the generated triangles, making it difficult to deal with uneven point distribution, complex boundary processing, high computational complexity, large storage overhead, contradiction between local optimization and global optimization, noise sensitivity, non-convex domain processing limitations and isotropic characteristics limitations, and low dynamic update efficiency.
The gradient reinforcement learning method is used to parametric model Delaunay segmentation, point cloud data is obtained through robot laser scanning, star map noise reduction method is used to remove noise, space utilization is optimized through gradient descent, and volume superposition and palletization are combined with Delaunay segmentation.
Improve the uniformity of the input data, reduce noise impact, reduce outliers, optimize the dynamic update efficiency of Delaunay segmentation, and improve space utilization.
Smart Images
Figure CN120495768A_ABST
Abstract
Description
Technical Field
[0001] A capacity perception and palletizing planning method based on gradient reinforcement learning Delaunay decomposition belongs to the field of operations optimization and industrial engineering technology. Background Art
[0002] Delaunay triangulation is a classic algorithm in computational geometry that is used to divide a set of discrete points in a plane into a triangular network that satisfies specific optimization criteria. Its core idea is to improve mesh quality by maximizing the minimum angle of the triangle and avoiding the generation of long and narrow triangles.
[0003] Delaunay triangulation construction algorithms are mainly divided into two categories: incremental insertion method and divide-and-conquer method. The incremental method is the most widely used. However, in practical applications, it also has some significant disadvantages, as follows:
[0004] 1. Sensitivity to input data
[0005] Impact of uneven point distribution: If the input point set is unevenly distributed (e.g., dense in some areas and sparse in others), the resulting triangle sizes may vary significantly. This may require additional processing (e.g., mesh refinement or coarsening) for subsequent applications (e.g., finite element analysis or fluid simulation).
[0006] Boundary handling issues: Standard Delaunay meshing does not automatically preserve the integrity of the input boundary. For example, in geometric modeling, complex non-convex boundaries or internal holes may require the introduction of constrained Delaunay meshing (CDT), but this significantly increases the algorithmic complexity.
[0007] 2. Complexity of high-dimensional expansion
[0008] The computational complexity increases dramatically: In the two-dimensional case, the time complexity of Delaunay decomposition is But in three dimensions and higher, the complexity can reach (dd is the dimension.) For example, the worst-case complexity of three-dimensional Delaunay tetrahedralization is O(n²)O(n²), which makes it difficult to efficiently process large amounts of data.
[0009] High storage overhead: High-dimensional decomposition requires storing a large number of simplexes (such as tetrahedrons and hypertetrahedrons), which leads to a surge in memory usage.
[0010] 3. The contradiction between local optimization and global optimization
[0011] Global Optimization vs. Local Requirements: Delaunay meshing seeks to maximize the global minimum angle, but some applications require specific local conditions (such as anisotropic triangles and directionally aligned structured meshes). In these cases, post-processing (such as mesh optimization) or the use of alternative meshing methods (such as the advancing frontier method) may be necessary.
[0012] 4. Sensitivity to noise and outliers
[0013] Outliers destroy structure: Noise points in the input data can lead to a large number of meaningless, narrow triangles in the segmentation. For example, in point cloud reconstruction, an outlier point far from the main data will generate many low-quality triangles connecting it, which needs to be alleviated through preprocessing (such as outlier filtering).
[0014] 5. Limitations of Non-convex Domain Processing
[0015] Dependence on the convex hull: The standard Delaunay mesh generates triangles based on the convex hull of a point set. For non-convex regions, the generated triangles may extend beyond the actual domain boundary. Constrained edges must be used to enforce the boundary, but the introduction of constraints reduces algorithm efficiency.
[0016] 6. Limitations of Isotropic Properties
[0017] Unsuitable for anisotropic problems: The isotropic nature of the Delaunay mesh (i.e., no directional preference) can be a disadvantage in some scenarios. For example, when simulating physical fields with directional characteristics (such as fluid boundary layers), anisotropic meshes may be required, and Delaunay has difficulty directly generating such structures.
[0018] 7. Efficiency issues of dynamic updates
[0019] The cost of incremental updates: In scenarios where points need to be added and deleted dynamically (such as real-time simulation), traditional Delaunay decomposition incremental algorithms (such as Bowyer-Watson) are feasible, but frequent local reconstruction may lead to performance degradation, especially in high-dimensional situations. Summary of the Invention
[0020] The technical problem to be solved by the present invention is: to overcome the shortcomings of the existing technology and provide a capacity perception and stacking planning method based on gradient reinforcement learning Delaunay decomposition, which improves the uniformity of input data, effectively reduces noise, reduces outliers, and solves the problem of Delaunay decomposition sensitivity to input data.
[0021] The technical solution adopted by the present invention to solve the technical problem is: the capacity perception and palletizing planning method based on gradient reinforcement learning Delaunay decomposition includes the following steps:
[0022] S1. Set up the initial reinforcement learning dataset and obtain the truck cargo point cloud data map and truck location information through the robot laser scanning sensor and ultra-wideband technology;
[0023] S2: Use the star map denoising method to correct the edges of the point cloud data to remove noise and delete useless areas;
[0024] S3: Delaunay segmentation is performed on the corrected point cloud image, and the triangular prism formed by the convex hull projection of the N triangular facets is volume superimposed to obtain the required sample;
[0025] S4: Use different stacking methods for N convex hull areas, continuously optimize the initial data set of reinforcement learning through gradient descent, update the optimal strategy, and obtain the optimal space utilization;
[0026] S5: The convex hull area stacking method with the best space utilization is the optimal stacking planning strategy, and the optimal stacking quantity is calculated.
[0027] Furthermore, the specific steps for train location and capacity perception and cargo matching are as follows:
[0028] Given a dataset S = (C, V, U, Q) of reinforcement learning state representation, where S consists of a four-tuple, C represents the capacity of the truck compartment, V represents the volume of a single cargo, U represents the space utilization, and Q represents the number of cargoes carried by the truck;
[0029] Define the robot state action space V k =(mode,L c ), different palletizing modes on the truck and truck positions L c The output corresponding to the short-term optimal strategy U′;
[0030] The truck location information and truck capacity point cloud data map were obtained, and the reinforcement learning initial state data set was set.
[0031] Furthermore, if the robot's state at time t is k and the action taken at this time is recorded as a, then the expected value function of the cumulative reward at this time is defined as:
[0032] f(k, a) rewards =E U (w t |K t =k, A t =a)
[0033] Where w t is the cumulative return, K t 、A t is the state and action at time t, EU is the expected value of cumulative return.
[0034] Furthermore, we set the reward function R in the action space reward To determine the optimal quantity planning of goods, in the process of taking different actions to update data in different states, if the cumulative return expected value function f(k, a) rewards The larger the R reward The larger the value, the more it encourages the short-term optimal strategy U′ to update the state data set S = (C, V, U, Q);
[0035] R reward The calculation formula is as follows:
[0036]
[0037] Where, is the valuation reward of state k at time t, k t+1 is the state at the next moment, K t =k, A t =a, π is the cumulative reward after starting from state k and executing action a using strategy U′.
[0038] Furthermore, the point cloud data of the truck and cargo consists of three parts: the identified target, the identified background, and the image noise, which are represented by the following model:
[0039] g(m,n)=o(m,n)+c(m,n)+l(m,n)
[0040] Where g(m, n) is the grayscale value of the pixel (m, n) in the point cloud data, o(m, n) is the brightening of the identified target, c(m, n) is the grayscale value of the identified background, and l(m, n) is the image noise signal.
[0041] Furthermore, the background grayscale value of each data point is identified according to the following expanded definition:
[0042] c′(m,n)=c(m+1,n+1)+c(m-1,m-1)
[0043] g(m+1,n+1)=2c(m,n)
[0044] Where c(m, n) is the grayscale value of the identified background, g(m+1, n+1) is the grayscale value of the cloud data pixel (m+1, n+1), and c(m+1, n+1) and c(m-1, n-1) are the grayscale values before and after (m, n).
[0045] Furthermore, by coinciding the center point of the truck and cargo point cloud data with the center position of the Gaussian filter, and setting the parameters of the pooling layer and convolution layer, a convolution operation is performed to obtain a grayscale image of the data sample point close to the center position of the Gaussian filter. Assuming that the distance from any grayscale point in the grayscale image to the center position of the Gaussian filter is x, y, the processing coefficient of the Gaussian filter and the δ neighborhood of the center point are:
[0046]
[0047] Where x and y are the distances between the grayscale point and the center of the Gaussian filter, and σ is the standard deviation of the Gaussian filter. When σ is small, the sample points vary significantly, and the point cloud becomes more compact and clear.
[0048] Furthermore, the median of the neighborhood of the Gaussian filter center point δ is used instead of the difference calculation formula:
[0049]
[0050] c′(m,n)=g(m+p,n+q)-C(m+1,n+1)
[0051] Where G(m+1, n+1) is the grayscale value of g(m+p, n+q) after data expansion and median processing of the δ neighborhood, c′(m, n) is the grayscale value of the final output, N is the median value of the δ neighborhood of the center point, and g(m+p, n+q) is the grayscale value of the pixel (m+p, n+q) in the point cloud data map.
[0052] Compared with the prior art, the present invention has the following beneficial effects:
[0053] The present invention combines the gradient reinforcement learning method with the Delaunay partitioning method, and directly performs parameterized modeling on the data required for the Delaunay partitioning through gradient optimization, thereby greatly improving the uniformity of the input data, effectively reducing noise and outliers, and solving the Delaunay y The sensitivity of the segmentation to the input data is solved. At the same time, the local reconstruction pressure is reduced through gradient reinforcement learning, and the Delauna y Dynamic update efficiency of segmentation. BRIEF DESCRIPTION OF THE DRAWINGS
[0054] Figure 1 It is a structured block diagram of the present invention;
[0055] Figure 2 This is the point cloud data map of the noise concentration area;
[0056] Figure 3 is the grayscale image of the noise concentration area;
[0057] Figure 4 This is the point cloud data map of the truck;
[0058] Figure 5 Correct the map for the point cloud;
[0059] Figure 6 This is the plane section drawing of the carriage;
[0060] Figure 7 This is a simulation diagram of volume error. DETAILED DESCRIPTION
[0061] Figures 1 to 7 The best embodiment of the present invention is shown below in conjunction with the attached Figures 1 to 7 The present invention is further described.
[0062] The present invention will be further described below in conjunction with specific embodiments. However, people familiar with the art should understand that the detailed description given here in conjunction with the drawings is for better explanation, and the structure of the present invention necessarily exceeds these limited embodiments. For some equivalent replacement solutions or common means, they will not be described in detail herein, but they still fall within the scope of protection of this application.
[0063] Refer to the attached Figure 1-Figure 7 The capacity perception and palletizing planning method based on gradient reinforcement learning Delaunay decomposition of the present invention includes the following steps:
[0064] S1. Set up the initial reinforcement learning dataset and obtain the truck cargo point cloud data map and truck location information through the robot laser scanning sensor and ultra-wideband technology;
[0065] S2: Use the star map denoising method to correct the edges of the point cloud data to remove noise and delete useless areas;
[0066] S3: Delaunay segmentation is performed on the corrected point cloud image, and the triangular prism formed by the convex hull projection of the N triangular facets is volume superimposed to obtain the required sample;
[0067] S4: Use different stacking methods for N convex hull areas, continuously optimize the initial data set of reinforcement learning through gradient descent, update the optimal strategy, and obtain the optimal space utilization;
[0068] S5: The convex hull area stacking method with the best space utilization is the optimal stacking planning strategy, and the optimal stacking quantity is calculated. Figure 1 A structural diagram of the problem.
[0069] The specific steps for truck location and capacity perception and cargo matching are as follows:
[0070] Given a dataset S = (C, V, U, Q) representing the state of reinforcement learning, where S consists of a four-tuple, C represents the capacity of the truck compartment, V represents the volume of a single cargo, U represents the space utilization, and Q represents the number of cargoes carried by the truck. Each time the state transitions, the dataset S updates its internal data. If the space utilization reward value obtained each time satisfies U′≥U, then the new U′ is used as the maximum space utilization reward value for this state transition and is recorded as the short-term optimal strategy. In the search for the optimal strategy, the cumulative return expectation function corresponding to the strategy is maximized as much as possible. If the robot's state at time t is k and the action taken at this time is recorded as a, then the cumulative return expectation function at this time is defined as:
[0071] f(k, a) rewards =E U (w t |K t =k, A t =a)
[0072] Where w t is the cumulative return, K t 、A t is the state and action at time t, E U is the expected value of cumulative return.
[0073] Define the robot state action space V k =(mode, L c ), different palletizing modes on the truck and truck positions L c The output of the short-term optimal strategy U′ corresponds to the output of the short-term optimal strategy U′. Here, the truck space can be divided into discrete cells or continuous regions, each cell or region represents a different palletizing method. Obviously, the size of the action space depends on the short-term optimal strategy U′, different palletizing methods and the size of the truck. Set the reward function R in the action space reward To determine the optimal quantity planning of goods. In the process of taking different actions to update data in different states, if the cumulative return expected value function f(k, a) rewards The larger the R reward The larger the value, the more it encourages the short-term optimal strategy U' to update the state data set S = (C, V, U, Q). reward The calculation formula is as follows:
[0074]
[0075] Where, is the valuation reward of state k at time t, k t+1 is the state at the next moment, K t =k, A t =a, π is the cumulative reward after starting from state k and executing action a using strategy U′.
[0076] The robot laser scanning sensor is a hardware device carried by the robot, through which its target point cloud data map can be indirectly obtained. The detailed principle of this sensor will not be explained here.
[0077] The truck location information and truck capacity point cloud data map were obtained, and the reinforcement learning initial state data set was set to facilitate subsequent research.
[0078] After obtaining the point cloud data of the truck and individual cargo through the laser scanning sensor of the robot hardware equipment, the star map denoising method is used to process the point cloud data containing a large number of points, thereby achieving the purpose of edge correction, noise removal, and deletion of useless areas to facilitate subsequent calculations and processing. The star map denoising method is to achieve preliminary processing through Gaussian filtering of data expansion, and use the median value in the neighborhood of the Gaussian filter center point δ as the standard value. The points in the area with a large difference in grayscale value from the standard value are replaced and deleted with the median value. In this way, the overall difference of the neighborhood area of the processed point cloud data is significantly reduced, reducing the error in data acquisition and avoiding the impact on subsequent segmentation calculations. Figure 2 This is the cargo point cloud data in half space.
[0079] The point cloud data of a truck and its cargo consists of three parts: the identified target, the identified background, and the image noise. These data can be represented by the following model:
[0080] g(m,n)=o(m,n)+c(m,n)+l(m,n)
[0081] Where g(m, n) is the grayscale value of the pixel (m, n) in the point cloud data, o(m, n) is the brightening of the identified target, c(m, n) is the grayscale value of the identified background, and l(m, n) is the image noise signal.
[0082] Data expansion removes noise concentrations in areas with significant differences by expanding the grayscale image segmentation region to identify the background. The background grayscale value of each data point follows the following expansion definition:
[0083] c′(m,n)=c(m+1,n+1)+c(m-1,n-1)
[0084] g(m+1,n+1)=2c(m,n)
[0085] In the formula, c(m, n) is the gray value of the identified background, g(m+1, n+1) is the gray value of the cloud data pixel (m+1, n+1), c(m+1, n+1) and c(m-1, n-1) are the gray values before and after (m, n). Figure 3 shown.
[0086] After the grayscale segmentation area is expanded, the center point of the identified target in the truck and cargo point cloud data map is overlapped with the center position of the Gaussian filter. The pooling layer and convolution layer parameters are set to perform the overlap convolution operation, thereby obtaining a grayscale image with the data sample point close to the center position of the Gaussian filter. This makes it easier to compare the difference between points in different areas. Assuming the distance from any grayscale point in the grayscale image to the center position of the Gaussian filter is x, y, the processing coefficient of the Gaussian filter and the δ neighborhood of the center point are:
[0087]
[0088] Where x and y are the distances between the grayscale point and the center of the Gaussian filter, and σ is the standard deviation of the Gaussian filter. When σ is small, the sample points vary significantly, and the point cloud becomes more compact and clear.
[0089] Next, we can process the point cloud using an extended Gaussian filter. When the grayscale value difference between the extended cloud data point c′(m, n) and the standard point in the δ neighborhood is large, it is the area point we want to focus on. For cloud data points c′(m, n) with large differences, we use the median value in the δ neighborhood of the Gaussian filter center point to replace and delete them, thereby achieving the purpose of reducing this difference. The formula for replacing the difference with the median value in the δ neighborhood of the Gaussian filter center point is:
[0090]
[0091] c′(m,n)=g(m+p,n+q)-C(m+1,n+1)
[0092] Where G(m+1, n+1) is the grayscale value of g(m+p, n+q) after data expansion and median processing of the δ neighborhood, c′(m, n) is the grayscale value of the final output, N is the median value of the δ neighborhood of the center point, and g(m+p, n+q) is the grayscale value of the pixel (m+p, n+q) in the point cloud data map.
[0093] Based on the above, we first perform star image denoising on the point cloud model. Using the median value within the δ neighborhood of the Gaussian filter center point as the standard value, we replace and delete any points in the area where the grayscale value differs significantly from the standard value with the median value. This significantly reduces the overall difference in the neighborhood area of the processed point cloud data, reducing data acquisition errors and avoiding any impact on subsequent segmentation calculations. Figure 4 To obtain the point cloud data, Figure 5 Corrected image for point cloud.
[0094] Based on the corrected point cloud image, a triangulated network of point cloud data containing N triangular facet convex hulls is established. The steps to establish the triangulated network are as follows:
[0095] S31. Set the α1 plane layer, find the maximum inscribed circle for the defined triangular element convex hull region set, and rotate the triangular element convex hull around any vertex (x, y);
[0096] S32, setting the α2 plane layer, inserting the data point P1, and finding all circumscribed circles containing the data point P1, and removing the cavity areas formed between the circumscribed circles;
[0097] S33, performing lofting processing on the convex hull region set of the triangular elements of the α1 plane layer and the data point P1 of the α2 plane layer to form a new triangular network;
[0098] S34. The new triangulated network is filled and the corresponding point cloud data is deleted. Step (2) is repeated until all point cloud data are traversed and inserted, and finally a triangulated network of point cloud data containing N triangular facet convex hulls is formed. At the same time, projection is performed and a volume superposition operation is performed on the projected geometry. Figure 6 Figure 2 is a plane section diagram of a truck box.
[0099] When the corrected point cloud data is segmented to calculate the capacity, the error is significantly reduced as the volume increases, making the calculation of truck capacity more realistic and accurate. Figure 7 shown.
[0100] By superimposing the volumes, the original volume of the target in the point cloud data image is obtained, i.e., the truck's capacity. Different palletizing strategies are applied to the different triangular convex hull regions of the truck. Gradient descent is used to update the change in regional space utilization, and an optimal strategy is found to update the palletizing strategy for the entire truck. This results in an optimal palletizing planning method, solving the cargo planning problem. Compared to traditional palletizing planning methods, this technique offers higher space utilization and is a viable solution.
[0101] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other manner. Any person skilled in the art may utilize the above-disclosed technical content to modify or modify the present invention into equivalent embodiments. However, any simple modifications, equivalent variations, and modifications to the above embodiments that do not depart from the technical content of the present invention and are based on the technical essence of the present invention remain within the scope of protection of the present invention.
Claims
1. A capacity perception and palletizing planning method based on gradient reinforcement learning Delaunay decomposition, characterized by: The steps include: S1. Set up the initial reinforcement learning dataset and obtain the truck cargo point cloud data map and truck location information through the robot laser scanning sensor and ultra-wideband technology; S2: Use the star map denoising method to correct the edges of the point cloud data to remove noise and delete useless areas; S3: Delaunay segmentation is performed on the corrected point cloud image, and the triangular prism formed by the convex hull projection of the N triangular facets is volume superimposed to obtain the required sample; S4: Use different stacking methods for N convex hull areas, continuously optimize the initial data set of reinforcement learning through gradient descent, update the optimal strategy, and obtain the optimal space utilization; S5: The convex hull area stacking method with the best space utilization is the optimal stacking planning strategy, and the optimal stacking quantity is calculated.
2. The capacity perception and palletizing planning method based on gradient reinforcement learning Delaunay decomposition according to claim 1 is characterized in that: The specific steps for train location and capacity perception and cargo matching are as follows: Given a dataset S = (C, V, U, Q) of reinforcement learning state representation, where S consists of a four-tuple, C represents the capacity of the truck compartment, V represents the volume of a single cargo, U represents the space utilization, and Q represents the number of cargoes carried by the truck; Define the robot state action space V k =(mode,L c ), different palletizing modes on the truck and truck positions L c The output corresponding to the short-term optimal strategy U′; The truck location information and truck capacity point cloud data map were obtained, and the reinforcement learning initial state data set was set.
3. The capacity perception and palletizing planning method based on gradient reinforcement learning Delaunay decomposition according to claim 2 is characterized in that: If the robot's state at time t is k, and the action taken at this time is recorded as a, then the expected value function of the cumulative return at this time is defined as: f(k,a) rewards =E U (w t |K t =k,A t =a) Where w t is the cumulative return, K t 、A t is the state and action at time t, E U is the expected value of cumulative return.
4. The capacity perception and palletizing planning method based on gradient reinforcement learning Delaunay decomposition according to claim 3 is characterized by: Set the reward function R in the action space reward To determine the optimal quantity planning of goods, in the process of taking different actions to update data in different states, if the cumulative return expected value function f(k, a) rewards The larger the R reward The larger the value, the more it encourages the short-term optimal strategy U′ to update the state data set S = (C, V, U, Q); R reward The calculation formula is as follows: Where, is the valuation reward of state k at time t, k t+1 is the state at the next moment, K t =k, A t =a, π is the cumulative reward after starting from state k and executing action a using strategy U′.
5. The capacity perception and palletizing planning method based on gradient reinforcement learning Delaunay decomposition according to claim 2 is characterized in that: The point cloud data of the truck and its cargo consists of three parts: the identified target, the identified background, and the image noise, which are represented by the following model: g(m,n)=o(m,n)+c(m,n)+l(m,n) Where g(m, n) is the grayscale value of the pixel (m, n) in the point cloud data, o(m, n) is the brightening of the identified target, c(m, n) is the grayscale value of the identified background, and l(m, n) is the image noise signal.
6. The capacity perception and palletizing planning method based on gradient reinforcement learning Delaunay decomposition according to claim 5 is characterized by: Identify the background grayscale value of each data point according to the following expanded definition: c′(m,n)=c(m+1,n+1)+c(m-1,-1) g(m+1,n+1)=2c(m,n) Where c(m, n) is the grayscale value of the identified background, g(m+1, n+1) is the grayscale value of the cloud data pixel (m+1, n+1), and c(m+1, n+1) and c(m-1, n-1) are the grayscale values before and after (m, n).
7. The capacity perception and palletizing planning method based on gradient reinforcement learning Delaunay decomposition according to claim 2 is characterized by: By coinciding the center point of the truck and cargo point cloud data with the center position of the Gaussian filter, setting the parameters of the pooling layer and convolution layer, and performing coincidence processing convolution operation, a grayscale image of the data sample point close to the center position of the Gaussian filter is obtained. Assuming the distance from any grayscale point in the grayscale image to the center position of the Gaussian filter is x, y, the processing coefficient of the Gaussian filter and the center point δ neighborhood are: Where x and y are the distances between the grayscale point and the center of the Gaussian filter, and σ is the standard deviation of the Gaussian filter. When σ is small, the sample points vary significantly, and the point cloud becomes more compact and clear.
8. The capacity perception and palletizing planning method based on gradient reinforcement learning Delaunay decomposition according to claim 7 is characterized in that: The median of the δ neighborhood of the Gaussian filter center point replaces the difference calculation formula: c′(m,n)=g(m+p,n+q)-C(m+1,n+1) Where G(m+1, n+1) is the grayscale value of g(m+p, n+q) after data expansion and median processing of the δ neighborhood, c′(m, n) is the grayscale value of the final output, N is the median value of the δ neighborhood of the center point, and g(m+p, n+q) is the grayscale value of the pixel (m+p, n+q) in the point cloud data map.