Methods, devices, equipment and storage media for optimizing the starting point of tile laying

Abstract

This invention provides a method, apparatus, device, and storage medium for optimizing the starting point of tile laying. The method includes: constructing a three-dimensional coordinate system based on the geometric boundary information of the laying area; setting an original starting point; and performing geometric transformation processing based on the original starting point and tile parameters to generate a distribution of gap segments; dividing the laying area into spatial indexes in the three-dimensional coordinate system; determining the overlapping area of ​​floor tiles and wall tiles through collision detection; calculating the intersection line between the wall and the floor based on the overlapping area; determining the coordinates of the intersection point based on the intersection line and the distribution of gap segments; sorting the intersection point coordinates to determine a reference point; calculating the optimal starting point offset based on the reference point; and determining the tile starting point based on the optimal starting point offset and the original starting point. This invention achieves precise alignment of tile gaps through automated geometric calculation, effectively improving design efficiency and reducing human error.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method, apparatus, equipment, and storage medium for optimizing the starting point of tile laying. Background Technology

[0002] Currently, in the field of tile laying design, web-based home decoration design software platforms are widely used as a technical solution. This solution requires users to manually add and configure tile laying elements, manually adjust parameters such as tile thickness, rotation angle, and starting position, and repeatedly coordinate the alignment of the gaps between wall and floor tiles. Users need to handle changes in the associated positions of each tile individually, using clicks and drags to fine-tune the tile layout.

[0003] The main problem with existing technologies is that adjusting the starting position of tiles requires repeated manual operations to associate the tiles, resulting in significantly low design efficiency. Specifically, it cannot automatically handle the joint alignment mechanism, requiring users to coordinate each tile individually, increasing the risk of human error. The root cause of this deficiency is the lack of integrated automation algorithms in the technical structure. After parameter changes, the entire laying system needs to be readjusted, leading to redundant operations and limited flexibility, which seriously affects design quality and user experience. Summary of the Invention

[0004] The main objective of this invention is to solve the technical problems of low efficiency and risk of human error caused by the need for manual and repeated operation to adjust the starting position of existing tiles and the inability to automatically handle the jointing mechanism.

[0005] This invention provides a method for optimizing the starting point of tile laying, the method comprising:

[0006] A three-dimensional coordinate system is constructed based on the geometric boundary information of the paving area, the original starting point is set, and geometric transformation is performed based on the original starting point and tile parameters to generate the distribution of gap line segments;

[0007] The tiling area is spatially indexed and divided in the three-dimensional coordinate system. The overlapping area between the floor tiles and the wall tiles is determined by collision detection, and the intersection line between the wall and the floor is calculated based on the overlapping area.

[0008] The coordinates of the intersection point are determined based on the intersection line and the distribution of the gap segments;

[0009] The coordinates of the intersection points are sorted to determine the reference point, and the optimal starting point offset is calculated based on the reference point. The starting point of the tile is determined according to the optimal starting point offset and the original starting point.

[0010] The present invention also provides a tile starting point optimization device, the tile starting point optimization device comprising:

[0011] The modeling and generation unit is used to construct a three-dimensional coordinate system based on the geometric boundary information of the paving area, set the original starting point, and perform geometric transformation processing based on the original starting point and tile parameters to generate the distribution of gap line segments.

[0012] The index calculation unit is used to divide the tiling area into spatial indexes in the three-dimensional coordinate system, determine the overlapping area of ​​the floor tiles and wall tiles through collision detection, and calculate the intersection line of the wall and the floor based on the overlapping area.

[0013] An intersection point determination unit is used to determine the coordinates of the intersection point based on the intersection line and the distribution of the gap segments;

[0014] The optimization and adjustment unit is used to sort the intersection coordinates to determine the reference point, calculate the optimal starting point offset based on the reference point, and determine the tile starting point according to the optimal starting point offset and the original starting point.

[0015] The present invention also provides a tile starting point optimization device, comprising: a memory and at least one processor, wherein the memory stores instructions, and the memory and the at least one processor are interconnected by a line; the at least one processor invokes the instructions in the memory to cause the tile starting point optimization device to perform the steps of the above-described tile starting point optimization method.

[0016] The present invention also provides a computer-readable storage medium storing instructions that, when executed on a computer, cause the computer to perform the steps of the above-described method for optimizing the starting point of tile laying.

[0017] The aforementioned method, apparatus, equipment, and storage medium for optimizing tile starting points construct a three-dimensional coordinate system based on the geometric boundary information of the paving area, sets an initial starting point, and performs geometric transformation based on the initial starting point and tile parameters to generate a distribution of grout lines. Within the three-dimensional coordinate system, the paving area is spatially indexed and divided. Collision detection determines the overlapping area between floor and wall tiles, and the intersection line between the wall and floor is calculated based on the overlapping area. The intersection point coordinates are determined according to the intersection line and the grout line distribution. The intersection point coordinates are sorted to determine a reference point, and the optimal starting point offset is calculated based on the reference point. The tile starting point is then determined based on the optimal starting point offset and the initial starting point. This invention achieves precise alignment of tile grout lines through automated geometric calculation, effectively improving design efficiency and reducing human error.

[0018] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained in accordance with the structures particularly pointed out in the description, claims and drawings.

[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the first embodiment of the tile starting point optimization method in this invention;

[0021] Figure 2 This is a schematic diagram of a second embodiment of the tile starting point optimization method in this invention;

[0022] Figure 3 This is a schematic diagram of one embodiment of the tile starting point optimization device in this invention;

[0023] Figure 4 This is a schematic diagram of one embodiment of the tile starting point optimization device in this invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] The terms "comprising" and "having," and any variations thereof, used in the embodiments of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not limited to the steps or units listed, but may optionally include other steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or devices.

[0026] To facilitate understanding of this embodiment, a method for optimizing the starting point of tile laying as disclosed in this embodiment of the invention will first be described in detail. For example... Figure 1 As shown, this method includes the following steps:

[0027] 101. Construct a three-dimensional coordinate system based on the geometric boundary information of the paving area, set the original starting point, and perform geometric transformation processing based on the original starting point and tile parameters to generate the distribution of gap line segments;

[0028] In this embodiment, the step of constructing a three-dimensional coordinate system based on the geometric boundary information of the paving area, setting an original starting point, and performing geometric transformation processing based on the original starting point and tile parameters to generate the gap line segment distribution includes: establishing a three-dimensional coordinate system with the lower left corner of the paving area as the origin, performing radian conversion processing on the tile rotation angle to obtain standardized angle parameters; performing two-dimensional rotation matrix transformation calculation on the coordinates of the four vertices of the tile according to the angle parameters to obtain a vertex coordinate set; calculating the maximum and minimum x-values ​​and the maximum and minimum y-values ​​based on the vertex coordinate set, generating an axis-aligned rectangular bounding box and setting the boundary expansion amount to obtain the bounding box boundary; using the set original starting point as the origin of the grid generation, generating horizontal and vertical grid lines according to the tile parameters, and performing clipping processing on the grid lines and the bounding box boundary to extract the line segments on the edge of the bounding box as the gap line segment coordinate distribution.

[0029] Specifically, after enabling design mode, the geometric boundary information of the current tiling area can be obtained, and a three-dimensional coordinate system can then be constructed based on this boundary information. This three-dimensional coordinate system is established with the lower left corner of the tiling area as the origin, the X-axis pointing to the right, the Y-axis pointing upwards, and the Z-axis pointing vertically upwards.

[0030] In addition, the geometric boundary information can also be data from historical design projects, and there are no restrictions on this.

[0031] Understandably, this embodiment can optimize the starting point based on the tile's geometric parameters, such as tile size, rotation angle, and grout width. Compared to traditional manual adjustment methods, which are prone to errors in complex tiling scenarios, this embodiment can utilize automated algorithms based on geometric calculations to optimize the starting point position.

[0032] It should be noted that in this embodiment, the rotation angle range can be set according to preset tile parameters, for example, controlled within the range of -45°≤θ≤45°, to ensure visual aesthetics and construction feasibility. For the input tile rotation angle θ (range 0-360 degrees), it is first converted to radians: Then, a rigid body transformation is performed using a standard two-dimensional rotation matrix. The specific form of this rotation matrix is: The matrix is ​​used to transform and calculate the coordinates of the four vertices of the tile.

[0033] Specifically, for example, when the tile dimensions are length L (e.g., 300mm) and width W (e.g., 300mm), the initial vertex coordinates are (0,0), (L,0), (L,W), (0,W). After matrix multiplication, a new set of vertices is obtained after rotation. This transformation result can be understood as the rotated set of vertex coordinates, providing an accurate geometric basis for subsequent bounding box calculations. It is understood that the geometric transformation based on vertex coordinates in this embodiment is actually a spatial transformation, which involves precise calculation of the current tile geometry.

[0034] The thermal expansion and contraction effect of the tile material also needs to be considered during the transformation process. This transformation process takes into account the coefficient of thermal expansion and contraction of the tile material (typically 5-8 × 10⁻⁶). -6 The calculation incorporates a temperature compensation factor α (°C) to ensure accuracy under varying ambient temperatures (15-35°C). This temperature compensation effectively addresses the impact of ambient temperature changes on tile dimensions, improving the reliability of the calculation results.

[0035] Based on this, the axis-aligned bounding box can be calculated using the transformed vertex coordinates. The specific calculation method is as follows: determine the minimum x-value. Minimum y value Maximum x value Maximum y value The bezel extension is set to 1.2 times the tile thickness to accommodate the adhesive layer thickness (typically 3-6mm), ensuring the bezel completely covers the actual space occupied by the tile.

[0036] Next, using the initial starting point as the origin for grid generation, grid lines are generated based on the tile size and grout width. Specifically, multiple horizontal and vertical lines are generated according to a step distance of L+S in the x-direction and W+S in the y-direction, where S is the grout width (e.g., 3mm). These grid lines form a complete basic framework for tile laying, providing the geometric basis for the generation of grout lines.

[0037] Finally, the Cohen-Sutherland line segment clipping algorithm is used to calculate the geometric intersection of grid lines with the bounding box boundary. This algorithm can accurately detect whether a line segment intersects with the bounding box, retaining the intersecting line segments and filtering out invalid line segments. Through this clipping process, the line segments on the edge of the bounding box are extracted as the coordinate distribution of tile gap line segments. Each gap line segment is represented by its start and end coordinates, with the endpoint coordinate accuracy reaching the 0.01mm level, and the line segment width precisely controlled within the range of 2-5mm, providing a high-precision basic geometric entity for subsequent wall-floor intersection calculations.

[0038] 102. In the three-dimensional coordinate system, the paving area is divided by spatial indexing, the overlapping area of ​​the floor tiles and wall tiles is determined by collision detection, and the intersection line of the wall and the floor is calculated based on the overlapping area.

[0039] In this embodiment, the step of spatially indexing the tiling area in the three-dimensional coordinate system, determining the overlapping area of ​​the floor tiles and wall tiles through collision detection, and calculating the intersection line of the wall and the floor based on the overlapping area includes: recursively spatially dividing the tiling area using a quadtree algorithm in the three-dimensional coordinate system to obtain a multi-level spatial index structure; geometrically overlapping the floor tiles and wall tiles in the spatial index structure using a collision detection algorithm in the three-dimensional coordinate system to determine the boundary coordinates of the overlapping area; and performing projection transformation processing on the vertices of the wall tiles within the overlapping area in the three-dimensional coordinate system, and calculating the intersection line of the wall and the floor based on the projection results.

[0040] In this embodiment, after obtaining the three-dimensional coordinate system, the tiling area can be divided into spatial indexes. This spatial indexing can be based on a quadtree data structure to achieve efficient spatial management.

[0041] In addition, other spatial data structures, such as octrees or KD-trees, can be used for this spatial index partitioning, without any limitation.

[0042] Understandably, this embodiment can perform spatial management of floor and wall tiles based on a quadtree algorithm, such as tile location, size, and geometric attributes. Compared to the traditional global traversal method, which is computationally inefficient when there are many tiles, this embodiment can utilize a local retrieval algorithm based on spatial indexing to quickly locate relevant tile areas.

[0043] It should be noted that in this embodiment, the depth of the quadtree hierarchy can be dynamically adjusted according to the tile density. For example, a 4-layer structure is used when the tile density is less than 50 tiles / m², and an 8-layer structure is used when the density exceeds 200 tiles / m². The recursive partitioning rule of the quadtree is as follows: the maximum depth of each node is set to 5 layers, and the minimum leaf node size is 0.5m × 0.5m; when a node contains more than 50 tile objects or its size is larger than the minimum unit, it is automatically subdivided into four equal subquadrants. This partitioning result can be understood as a multi-level spatial index structure. For example, in a paving area of ​​5m × 4m, the root node covers the entire area, and multiple child nodes are formed through recursive partitioning. It can be understood that the spatial partitioning based on the quadtree in this embodiment is actually a hierarchical management, which is an orderly organization of the current paving area.

[0044] During the construction phase, tile objects are inserted one by one. The bounding box coordinates of each tile are calculated, and it is assigned to the corresponding quadtree node based on the center point position. At the same time, the tile ID and geometric attributes are stored. Each leaf node stores the complete spatial coordinate information of 10-50 tiles, including the center point coordinates, rotation angle, size parameters, and material properties.

[0045] Based on this, a collision detection algorithm can be used to determine the geometric overlap between floor tiles and wall tiles in the spatial index structure. Specifically, for example, for a target tile (e.g., floor tile A), starting from the root node, traverse downwards to the leaf node level, retrieving the set of all tiles (including wall tiles) belonging to its own node and its 8 nearest neighbors. Then, the axis-aligned bounding box (AABB) detection algorithm is applied to compare the boundary coordinates (e.g., position) of the target tile. , )to( , The function retrieves the geometric data of tiles within the set, and marks overlapping areas as such if they exist.

[0046] Precise bounding box collision detection is performed using the Separating Axis Theorem (SAT), achieving an accuracy of 0.01mm. A two-stage strategy employing AABB pre-screening and OBB (Directed Bounding Box) precise detection quickly locates areas geometrically overlapping with wall tiles, reducing unnecessary calculations by over 90% while maintaining a 99.9% detection accuracy. Determining the boundary coordinates of the overlapping areas provides an accurate spatial range for subsequent projection transformations.

[0047] Next, a projection transformation is performed on the vertices of the wall tiles within the overlapping area. The projection process uses orthogonal projection transformation to accurately map the geometric information of the wall tiles in 3D space to the XY plane. The projection transformation matrix considers the actual tilt angle of the wall (typically within the range of 89-91°) and fits the wall plane equation using the least squares method to ensure projection accuracy.

[0048] Specifically, for example, the vertex coordinates of the wall tiles (based on a 3D coordinate system, with tile dimensions of 300mm × 600mm) are projected onto a horizontal reference plane (such as the xy plane, z=0), ignoring the z-axis value and retaining the x and y coordinate point set. An improved Delaunay triangulation algorithm is used to generate continuous line segments. This algorithm employs an incremental insertion strategy and local optimization techniques to ensure that the generated triangular mesh satisfies the Delaunay criterion.

[0049] Finally, an improved Iterative Closest Point (ICP) algorithm was used to perform sequence matching calculations between the edge point set of the floor tiles and the projected line segments of the wall. This algorithm integrates a point-to-plane distance metric, normal vector constraints, and a weight adaptive mechanism. The convergence criterion is set at a root mean square error variation of less than 0.001 mm over three consecutive iterations. The geometric accuracy of the precise intersection line L between the wall and floor tiles output by the algorithm reaches ±0.05 mm, meeting the quality requirements of high-end decoration projects and providing a reliable geometric basis for subsequent intersection point calculations.

[0050] Furthermore, the step of performing projection transformation processing on the vertices of the wall tiles within the overlapping area in the three-dimensional coordinate system, and calculating the intersection line between the wall and the ground based on the projection results, includes: performing orthogonal projection transformation on the vertices of the wall tiles within the overlapping area to map the three-dimensional coordinates to a horizontal reference plane, obtaining a set of projection points; processing the set of projection points using the Delaunay triangulation algorithm to generate continuous line segments; determining the boundary range of the ground tiles based on the overlapping area, and extracting the edge point set of the ground tiles using an edge detection algorithm; and performing sequence matching calculation between the edge point set of the ground tiles and the continuous line segments using an iterative nearest point algorithm to obtain the intersection line between the wall and the ground.

[0051] Specifically, the orthogonal projection transformation of the wall tile vertices maps the geometric information of the wall tile in three-dimensional space to a two-dimensional plane. Once the overlapping area is determined, the three-dimensional vertex coordinate data of all wall tiles within that area are obtained. Assuming the wall tile size is 300mm × 600mm, its vertex coordinates are imported from the CAD system. The projection process maps these three-dimensional coordinates to a horizontal reference plane. Typically, the xy plane is chosen as the projection target plane, ignoring the z-axis coordinate value and retaining the x and y coordinate components, forming a two-dimensional projection point set.

[0052] The mathematical principle of projection transformation is based on the calculation of the wall plane equation. In actual construction, the wall surface may have a slight tilt angle. By fitting the wall plane using the least squares method, accurate plane equation parameters are obtained. This fitting process avoids the accumulation of calculation errors caused by wall tilt, ensuring the geometric accuracy of the projection transformation.

[0053] After obtaining the projection point set, the Delaunay triangulation algorithm is used for processing. This algorithm can generate high-quality triangular meshes and avoids producing narrow and elongated triangles. In its implementation, an incremental insertion strategy is used to add projection points one by one. Each time a new point is inserted, adjacent triangles are adjusted through local optimization techniques to ensure that all triangles satisfy the Delaunay criterion. A constraint edge processing mechanism is introduced in this process to ensure the integrity and continuity of the wall tile boundaries. The resulting continuous line segments accurately reflect the geometric contours of the wall tiles.

[0054] The extraction of the edge point set of the floor tiles is based on the range information of the overlapping area. First, the boundary range of the floor tiles to be processed is determined. Using the previously generated gap segment distribution data, the geometric boundary of the floor tiles is accurately located. Next, a multi-scale edge detection algorithm is used to process the floor tile boundary. This algorithm first performs preprocessing with a Gaussian filter, with the filter parameter σ set to 0.5mm, to smooth out noise interference at the tile boundary. Then, the Canny edge detection operator is applied to extract sub-pixel level edge feature points. These edge points constitute the edge point set of the floor tiles.

[0055] During edge detection, the distance threshold δ is set to ≤0.1mm to ensure that only truly close edge points are included in subsequent calculations. This high-precision edge detection obtains a set of point data that accurately reflects the boundary characteristics of the floor tiles, providing a geometric basis for subsequent matching calculations.

[0056] The Iterative Closest Point (ICP) algorithm performs sequence matching calculations to find the optimal matching relationship between the set of edge points of the floor tiles and the continuous line segments of the wall projection. The improved ICP algorithm integrates multiple optimization mechanisms: a point-to-plane distance metric ensures the geometric rationality of the matching, a normal vector constraint mechanism avoids erroneous matching correspondences, and a weight adaptive mechanism dynamically adjusts the influence weight of points in the optimization process based on their reliability.

[0057] The ICP algorithm employs a convergence control strategy during its iterative process. The convergence criteria are: the root mean square error change over three consecutive iterations is less than 0.001 mm, or the number of iterations reaches a preset upper limit of 50. This dual convergence condition ensures computational accuracy and avoids wasting computational resources due to excessive iteration. After iterative optimization, the algorithm outputs a precise intersection line L between the wall and floor tiles, achieving a high geometric accuracy of ±0.05 mm. This meets the requirements for gap alignment in high-end decoration projects and provides geometric foundation data for subsequent intersection point calculations and starting point optimization based on the intersection line.

[0058] Throughout the intersection calculation process, data transfer between various algorithm modules employs a standardized interface design to ensure the integrity and consistency of geometric data. The continuous line segments generated by wall projection maintain a consistent data format with the point set data obtained from ground edge detection, facilitating efficient matching calculations by the ICP algorithm.

[0059] 103. Determine the coordinates of the intersection point based on the intersection line and the distribution of the gap segments;

[0060] In this embodiment, determining the intersection coordinates based on the distribution of the intersection line and the gap line segments includes: using vector cross product operation to perform intersection judgment calculation on the intersection line and the gap line segments to identify the geometric relationship between the line segments; calculating the intersection coordinates of the intersection line and the gap line segments based on the intersection judgment result, and filtering duplicate intersection points to obtain valid intersection coordinates.

[0061] In this embodiment, the process of determining the coordinates of the intersection point between the intersection line and the distribution of gap segments employs a precise geometric calculation method. First, the intersection of the intersection line and the gap segments is determined by the vector cross product operation. This operation can accurately identify geometric relationships such as intersection, overlap, and parallelism between the segments.

[0062] Specifically, for a given intersection line L and a set of gap segments, a vector cross product algorithm is used to check the positional relationship between each gap segment and the intersection line. Assuming the intersection line L is defined by points P1(x1,y1) and P2(x2,y2), and the gap segments are defined by points Q1(x3,y3) and Q2(x4,y4), the relative positions of the segments are determined by calculating the cross product of vectors P1P2 and Q1Q2. When the cross product is zero, it indicates that the two segments are collinear or parallel; when the cross product values ​​have different signs, it indicates that the segments intersect.

[0063] Based on the intersection determination results, the precise coordinates of the intersection points are calculated for the determined intersecting line segments. A parametric equation solution method is used, representing the intersection line as L(t) = P1 + t(P2-P1) and the gap segment as S(s) = Q1 + s(Q2-Q1), where t and s are parameters. The parameter values ​​are obtained by solving a system of linear equations, and then the precise coordinates of the intersection points are calculated. Considering numerical precision, double-precision floating-point arithmetic is used to ensure coordinate accuracy reaches the 0.001mm level.

[0064] After the intersection point calculation is completed, duplicate intersection points need to be filtered. Since the endpoints of the gap segments may overlap or nearly overlap, very close duplicate intersection points may occur. The filtering algorithm sets a distance threshold of 0.5mm. When the Euclidean distance between two intersection points is less than this threshold, they are considered duplicate intersection points and are merged. The merging strategy uses the coordinate average method, meaning the final coordinates of the duplicate intersection point are the arithmetic mean of the coordinates of all duplicate points.

[0065] The filtering process also includes a verification step for boundary intersections. Since false intersections may occur on the extension lines of line segments during the calculation, it is necessary to verify whether the intersections are truly located within the original line segment range. The verification method is to check whether both parameters t and s are within the interval [0,1]. Only intersections that meet this condition are considered valid intersections.

[0066] After three steps—vector cross product judgment, intersection point calculation, and duplicate filtering—a valid set of intersection point coordinates is obtained. This set contains the true intersection points of the intersection line with all relevant gap segments, and each intersection point has a clear two-dimensional coordinate representation. This intersection point coordinate data provides a complete geometric information foundation for subsequent sorting and reference point selection, ensuring that the starting point optimization algorithm can perform calculations based on accurate spatial relationships.

[0067] The entire intersection point determination process employs an efficient computational strategy, reducing unnecessary computation by pre-screening obviously non-intersecting line segment pairs, while maintaining the accuracy and reliability of the algorithm.

[0068] 104. Sort the coordinates of the intersection points to determine the reference point, calculate the optimal starting point offset based on the reference point, and determine the tile starting point according to the optimal starting point offset and the original starting point.

[0069] In this embodiment, the quicksort algorithm is used to sort the intersection coordinates, arranging all valid intersections in ascending order of their X-coordinates. The sorting process first extracts the X-axis coordinates of all points in the intersection set and constructs a coordinate array for sorting. The quicksort algorithm has a time complexity of O(nlogn) and a space complexity of O(logn). When the number of intersections exceeds 1000, the algorithm automatically switches to an external sorting strategy to ensure stability in large-scale data processing.

[0070] After sorting, the intersection point with the smallest X-coordinate is selected as the benchmark point pmin. The selection of the benchmark point considers not only the minimum coordinate value but also a comprehensive evaluation of visual saliency, construction convenience, and structural stability. A multi-objective optimization model is used for the specific evaluation: visual saliency is weighted at 0.4, construction convenience at 0.35, and structural stability at 0.25. This weighted scoring mechanism ensures that the benchmark point selection is highly consistent with the actual engineering requirements, achieving a decision accuracy rate of over 98%.

[0071] After the reference point is determined, the optimal starting point offset is calculated. Using the reference point pmin as the origin, an optimization model is established with the gap alignment as the objective function. This model considers the distribution characteristics of the intersection point coordinate sequence, and the objective function is the weighted sum of squares of the gap alignment.

[0072] The gradient descent optimization algorithm is used to iteratively optimize the offset parameters. The algorithm sets the learning rate to 0.01 and the convergence threshold to 0.001 mm. By optimizing the objective function through gradient descent, the optimal offset parameter values ​​are gradually approximated.

[0073] During the optimization process, the offset range is constrained and controlled. Based on statistical data from engineering practice, the offset dx in the X direction is strictly limited to ≤50mm, and the offset dy in the Y direction is limited to ≤30mm. These limits are derived from a large amount of statistical data from engineering practice, ensuring alignment while avoiding visual inconsistencies caused by over-adjustment.

[0074] After convergence, the algorithm outputs the offset values ​​in the X and Y directions, forming the optimal translation vector V = (dx, dy). Convergence is determined based on the magnitude of change in the objective function value during continuous iterations; the algorithm terminates when the change is less than the convergence threshold.

[0075] The final starting point for tile laying was determined using a coordinate transformation method. The original starting point coordinates were added to the optimal offset using a vector addition operation to obtain the adjusted starting point position. This coordinate transformation process ensured precise adjustment of the starting point position, enabling the tiles to achieve optimal alignment with the wall surface during installation.

[0076] The offset calculation also takes into account constraints such as standard tile dimensions, gap allowance, and allowable deviation range. By comprehensively considering these engineering parameters, it is ensured that the calculation results meet actual construction requirements and quality standards.

[0077] The entire calculation process employs a closed-loop optimization control mechanism, using feedback verification to ensure that the final determined tile starting point meets engineering quality requirements. During algorithm execution, the calculation accuracy and convergence status are monitored in real time to guarantee the reliability and stability of the optimization results.

[0078] In this embodiment, a three-dimensional coordinate system is constructed based on the geometric boundary information of the paving area. An initial starting point is set, and geometric transformation is performed based on the initial starting point and tile parameters to generate a distribution of grout lines. The paving area is spatially indexed within the three-dimensional coordinate system. Collision detection determines the overlapping area between the floor tiles and wall tiles, and the intersection line between the wall and floor is calculated based on the overlapping area. The intersection point coordinates are determined according to the intersection line and the grout line distribution. The intersection point coordinates are sorted to determine a reference point, and the optimal starting point offset is calculated based on the reference point. The tile starting point is then determined based on the optimal starting point offset and the initial starting point. This invention achieves precise alignment of tile grout lines through automated geometric calculation, effectively improving design efficiency and reducing human error.

[0079] Please see Figure 2 Another embodiment of the tile starting point optimization method in this application includes:

[0080] 201. Construct a three-dimensional coordinate system based on the geometric boundary information of the paving area, set the original starting point, and perform geometric transformation processing based on the original starting point and tile parameters to generate the distribution of gap line segments;

[0081] 202. In the three-dimensional coordinate system, the tiling area is divided by spatial indexing, the overlapping area of ​​the floor tiles and wall tiles is determined by collision detection, and the intersection line of the wall and the floor is calculated based on the overlapping area.

[0082] 203. Determine the coordinates of the intersection point based on the intersection line and the distribution of the gap segments;

[0083] In this embodiment, steps 201-203 are similar to steps 101-103 in the first embodiment, and will not be described again here.

[0084] 204. Sort the intersection point coordinates in ascending order of X coordinate, and select the intersection point with the smallest X coordinate as the reference point;

[0085] In this embodiment, the sorting of intersection coordinates is implemented using a dedicated sorting component. This component, as a dedicated module in the CAD system, first receives input data, including coordinate system information of the wall and floor association group, coordinates of the endpoints of the gap line segments, and intersection equation data.

[0086] Specifically, the sorting component traverses all potential intersections of the gap segments and the intersecting lines, using a segment intersection algorithm to calculate the coordinates of each intersection point. The calculation process records the intersection point positions in a two-dimensional Cartesian coordinate system with an accuracy controlled to the level of 0.01 millimeters, ensuring the accuracy of subsequent sorting and selection operations. Each intersection point contains complete coordinate values ​​(x, y), providing the necessary data foundation for the sorting algorithm.

[0087] The sorting algorithm employs the quicksort strategy, specifically for ascending order of X-axis coordinate values. The algorithm first extracts all X-axis coordinate values ​​from the intersection set, constructing a numerical array for sorting. The sorting process uses standard quicksort implementation, employing a recursive divide-and-conquer strategy to decompose the large intersection set into smaller subsets, gradually completing the overall sorting.

[0088] After sorting, the algorithm identifies and marks the first element in the sorted list, i.e., the intersection point with the smallest X-axis coordinate value, as the reference point. This selection strategy is based on the principle of geometric optimization; the point with the smallest X-coordinate is usually located near the starting boundary of the tiling area, facilitating reference positioning for subsequent offset calculations. After the reference point is selected, its three-dimensional coordinates are stored in a designated memory buffer for direct use by the subsequent offset calculation component.

[0089] To ensure processing efficiency, the sorting component operates in real-time mode. The component's runtime cycle is designed for continuous response, enabling it to process new intersection data inputs instantly. In terms of hardware configuration, the component relies on an embedded ARM Cortex-A53 processor for computation. This processor supports single-precision floating-point operations, ensuring both efficiency and accuracy requirements for sorting calculations.

[0090] During data processing, the sorting component also integrates data validation functionality. It performs validity checks on the input intersection coordinates, filtering out potentially outlier data points. Validation rules include coordinate value range checks and numerical validity verification, ensuring that all intersection data used in the sorting process meets geometric calculation requirements.

[0091] Once the reference point is determined, the component generates a standardized data output format. The output information includes the precise coordinates of the reference point, a sorted list of complete intersection points, and relevant geometric parameter information. This data provides complete input parameters for subsequent offset calculation steps, ensuring the continuity and data consistency of the entire starting point optimization process.

[0092] The entire sorting and benchmark selection process employs a modular design, offering excellent scalability and maintainability. Component interface design adheres to standardized specifications, facilitating data exchange and collaborative work with other computing modules.

[0093] 205. Using the aforementioned reference point as the origin, an optimization algorithm is employed to calculate the optimal starting point offsets in the X and Y directions;

[0094] In this embodiment, the step of calculating the optimal starting point offset in the X and Y directions using an optimization algorithm with the reference point as the origin includes: establishing an optimization model with gap alignment as the objective function based on the intersection coordinate sequence with the reference point as the origin; iteratively calculating the offset parameters in the optimization model using a gradient descent algorithm to obtain the optimal starting point offset that optimizes the gap alignment; outputting the optimal starting point offset in the X and Y directions, and verifying that the optimal starting point offset is within a preset reasonable range.

[0095] Specifically, the starting point offset calculation module performs precise calculations based on the sorted list of intersection points. This module reads the input sequence of intersection points, each containing coordinate values ​​(x, y), and simultaneously obtains the key parameters required for offset calculation. These parameters include the standard tile size (e.g., 300mm × 600mm), the pre-set gap allowance (standard 2mm), and the allowable deviation range (±5mm), providing constraints for subsequent optimization calculations.

[0096] The optimization model is built using a reference point as the origin and the intersection point coordinate sequence as input data. The model employs gap alignment as the objective function, which measures the degree of matching between the tile gap and the wall intersection line. Mathematical relationships are established by fitting the intersection point coordinates to a linear model. A typical form of the linear model is y = kx + b, where k and b are parameters to be determined, and their values ​​are obtained through least squares fitting.

[0097] The gradient descent algorithm employs an iterative optimization strategy. During initialization, the learning rate is set to 0.01, and the convergence threshold is 0.001 mm. During iteration, the algorithm calculates the gradient of the objective function with respect to the offset parameters, determining the parameter update direction and step size. Each iteration evaluates the objective function value with respect to the current parameters, adjusting the offset parameters based on the gradient information to gradually approach the optimal solution.

[0098] The offset parameter is calculated for each tile's starting point. Taking the bottom left corner of a tile as an example, the algorithm calculates the offset coordinates (Δx, Δy) of that point to minimize the gap between tiles while meeting the geometric requirements for joint alignment. The calculation process considers the actual size constraints of the tiles and the limitations of the construction process to ensure that the offset result is within the feasible range for the project.

[0099] The module is implemented using the Python scripting language and the NumPy library for matrix calculations and data processing. The NumPy library provides efficient numerical computation capabilities, supporting large-scale matrix operations and complex mathematical function calculations. Batch intersection processing is achieved through matrix operations, significantly improving computational efficiency and accuracy.

[0100] The convergence of the iterative computation is determined based on the trend of the objective function value. When the change in the function value after multiple consecutive iterations is less than the convergence threshold, the algorithm considers it to have reached convergence and terminates the iteration. The algorithm also sets a maximum limit on the number of iterations to prevent infinite loops in special cases.

[0101] The offset output includes two values: an offset of Δx in the X direction and an offset of Δy in the Y direction. These two offsets constitute a complete two-dimensional translation vector, used to adjust the original starting point position. The accuracy of the output values ​​is maintained at the 0.001mm level, meeting the requirements of high-precision decoration projects.

[0102] The offset verification step checks whether the calculation results are within a preset reasonable range. Based on engineering experience, the offset in the X direction should be controlled within 50mm, and the offset in the Y direction should be controlled within 30mm. When the calculated offset exceeds these ranges, the system will issue a warning and suggest readjusting the input parameters or optimizing the strategy.

[0103] After completing the automatic alignment operation, the module generates a configuration file for the bricklaying scheme. This configuration file contains information such as the starting point coordinates, gap adjustment values, and layout direction parameters, and is output in JSON format for easy subsequent system calls. Through an API request interface, the configuration information is transmitted to the bricklaying control system, achieving automated closed-loop control of the entire optimization process.

[0104] The entire offset calculation process adopts a modular design, which has good scalability and parameter adjustability. Users can flexibly adjust algorithm parameters and constraints according to different tile specifications and construction requirements to achieve personalized starting point optimization effects.

[0105] 206. Adjust the position of the original starting point according to the optimal starting point offset to determine the starting point of the tile.

[0106] In this embodiment, the final determination of the tile starting point is achieved through a coordinate transformation method to adjust the position. This process first obtains the optimal starting point offset calculated in the previous step, including the offset Δx in the X direction and the offset Δy in the Y direction, as well as the original coordinate position (x0, y0) of the starting point.

[0107] The position adjustment process employs vector addition for coordinate transformation. This coordinate transformation ensures precise adjustment of the starting point position, achieving a translational transformation from the initial position to the optimal position.

[0108] The adjustment process requires verifying the rationality of the calculation results. The system checks whether the adjusted starting point is still within the valid tiling area to prevent the starting point from exceeding the design boundary due to excessive offset. Simultaneously, it verifies the alignment between the adjusted starting point and the tile grid to ensure that the new starting position can generate a regular tile laying pattern.

[0109] To ensure calculation accuracy, double-precision floating-point arithmetic was used for position adjustment. Coordinate calculation accuracy was controlled to the 0.01mm level, meeting the construction requirements of high-precision decoration projects. The impact of numerical rounding errors was also considered during the calculation process, and appropriate rounding strategies were employed to ensure the accuracy of the final coordinates.

[0110] After determining the starting point for tile laying, the system generates a complete configuration of laying parameters. This configuration information includes the precise coordinates of the optimal starting point, a comparison of the positions before and after adjustment, and records of offset values. This information is stored in a standardized format for easy subsequent construction guidance and quality verification.

[0111] The final coordinates of the tile starting point serve as the output of the entire optimization algorithm, providing an accurate positioning benchmark for actual construction. This automated position adjustment process effectively solves the inefficiencies and error risks inherent in traditional manual adjustment methods, achieving precise alignment between the tiles and wall grout lines, and improving the overall quality and construction efficiency of the decoration project.

[0112] The entire position adjustment process adopts a closed-loop verification mechanism, which ensures that the final determined tile starting point meets geometric constraints, engineering requirements and quality standards through multiple checks, providing reliable technical support for subsequent tile laying construction.

[0113] In this embodiment, a three-dimensional coordinate system is constructed based on the geometric boundary information of the paving area. An initial starting point is set, and geometric transformation is performed based on the initial starting point and tile parameters to generate a distribution of grout lines. The paving area is spatially indexed within the three-dimensional coordinate system. Collision detection determines the overlapping area between the floor tiles and wall tiles, and the intersection line between the wall and floor is calculated based on the overlapping area. The intersection point coordinates are determined according to the intersection line and the grout line distribution. The intersection point coordinates are sorted to determine a reference point, and the optimal starting point offset is calculated based on the reference point. The tile starting point is then determined based on the optimal starting point offset and the initial starting point. This invention achieves precise alignment of tile grout lines through automated geometric calculation, effectively improving design efficiency and reducing human error.

[0114] The above describes the method for optimizing the starting point of tile laying in the embodiments of the present invention. The following describes the device for optimizing the starting point of tile laying in the embodiments of the present invention. Please refer to [link to device description] for details. Figure 3 One embodiment of the tile starting point optimization device in this invention includes:

[0115] The modeling and generation unit 301 is used to construct a three-dimensional coordinate system based on the geometric boundary information of the paving area, set the original starting point, and perform geometric transformation processing based on the original starting point and tile parameters to generate the distribution of gap line segments.

[0116] The index calculation unit 302 is used to perform spatial indexing of the paving area in the three-dimensional coordinate system, determine the overlapping area of ​​the floor tiles and wall tiles through collision detection, and calculate the intersection line of the wall and the floor based on the overlapping area.

[0117] The intersection point determination unit 303 is used to determine the intersection point coordinates based on the intersection line and the distribution of the gap line segments;

[0118] The optimization and adjustment unit 304 is used to sort the intersection coordinates to determine the reference point, calculate the optimal starting point offset based on the reference point, and determine the tile starting point according to the optimal starting point offset and the original starting point.

[0119] In this embodiment of the invention, the tile starting point optimization device operates the aforementioned tile starting point optimization method. The device constructs a three-dimensional coordinate system based on the geometric boundary information of the paving area, sets an initial starting point, and performs geometric transformation based on the initial starting point and tile parameters to generate a grout line distribution. Within the three-dimensional coordinate system, the paving area is spatially indexed and divided. Collision detection is used to determine the overlapping area between the floor tiles and wall tiles, and the intersection line between the wall and floor is calculated based on the overlapping area. The intersection point coordinates are determined according to the intersection line and the grout line distribution. The intersection point coordinates are sorted to determine a reference point, and the optimal starting point offset is calculated based on the reference point. Finally, the tile starting point is determined based on the optimal starting point offset and the initial starting point. This invention achieves precise alignment of tile grout lines through automated geometric calculation, effectively improving design efficiency and reducing human error.

[0120] above Figure 3 The tile starting point optimization device in this embodiment of the invention will be described in detail from the perspective of unitized functional entities. The tile starting point optimization device in this embodiment of the invention will be described in detail from the perspective of hardware processing.

[0121] Figure 4 This is a schematic diagram of the structure of a tile starting point optimization device 400 provided in an embodiment of the present invention. The tile starting point optimization device 400 can vary significantly due to different configurations or performance. It may include one or more central processing units (CPUs) 410 (e.g., one or more processors) and a memory 420, and one or more storage media 430 (e.g., one or more mass storage devices) storing application programs 433 or data 432. The memory 420 and storage media 430 can be temporary or persistent storage. The program stored in the storage media 430 may include one or more units (not shown in the diagram), each unit may include a series of instruction operations on the tile starting point optimization device 400. Furthermore, the processor 410 may be configured to communicate with the storage media 430 and execute the series of instruction operations in the storage media 430 on the tile starting point optimization device 400 to implement the steps of the aforementioned tile starting point optimization method.

[0122] The tile starting point optimization device 400 may also include one or more power supplies 440, one or more wired or wireless network interfaces 450, one or more input / output interfaces 460, and / or one or more operating systems 431, such as Windows Server, Mac OS X, Unix, Linux, FreeBSD, etc. Those skilled in the art will understand that... Figure 4The illustrated structure of the tile starting point optimization device does not constitute a limitation on the tile starting point optimization device provided by the present invention. It may include more or fewer components than illustrated, or combine certain components, or have different component arrangements.

[0123] The present invention also provides a computer-readable storage medium, which may be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when executed on a computer, cause the computer to perform the steps of the tile starting point optimization method.

[0124] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the system, device, or unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0125] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0126] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing the starting point of tile laying, characterized in that, The method for optimizing the starting point of tile laying includes: A three-dimensional coordinate system is constructed based on the geometric boundary information of the paving area, the original starting point is set, and geometric transformation is performed based on the original starting point and tile parameters to generate the distribution of gap line segments; The tiling area is spatially indexed and divided in the three-dimensional coordinate system. The overlapping area between the floor tiles and the wall tiles is determined by collision detection, and the intersection line between the wall and the floor is calculated based on the overlapping area. The intersection of the intersection line and the gap segment is determined by the cross product operation of vectors, and the geometric relationship between the segments is identified. Based on the intersection determination result, the coordinates of the intersection point of the intersection line and the gap segment are calculated, and duplicate intersection points are filtered to obtain the valid intersection point coordinates. The coordinates of the intersection points are sorted to determine the reference point, and the optimal starting point offset is calculated based on the reference point. The starting point of the tile is determined according to the optimal starting point offset and the original starting point.

2. The method for optimizing the starting point of tile laying according to claim 1, characterized in that, The process of constructing a three-dimensional coordinate system based on the geometric boundary information of the paving area, setting the original starting point, and performing geometric transformation based on the original starting point and tile parameters to generate the distribution of gap lines includes: A three-dimensional coordinate system is established with the lower left corner of the paving area as the origin. The rotation angle of the tile is converted into radians to obtain standardized angle parameters. Based on the angle parameters, a two-dimensional rotation matrix transformation is performed on the coordinates of the four vertices of the tile to obtain a set of vertex coordinates; Based on the vertex coordinate set, calculate the maximum and minimum x values ​​and the maximum and minimum y values, generate an axis-aligned rectangular bounding box, and set the boundary expansion amount to obtain the bounding box boundary; Using the set original starting point as the origin of the grid generation, horizontal and vertical grid segments are generated according to the tile parameters. The grid segments and the boundary of the bounding box are then trimmed, and the segments on the edge of the bounding box are extracted as the coordinate distribution of the gap segments.

3. The method for optimizing the starting point of tile laying according to claim 1, characterized in that, The step of spatially indexing the tiling area in the three-dimensional coordinate system, determining the overlapping area of ​​the floor tiles and wall tiles through collision detection, and calculating the intersection line of the wall and floor based on the overlapping area includes: In the three-dimensional coordinate system, a quadtree algorithm is used to recursively divide the tiling area into multiple levels of spatial index structure. In the three-dimensional coordinate system, a collision detection algorithm is used to determine the geometric overlap between the floor tiles and wall tiles in the spatial index structure, and to determine the boundary coordinates of the overlapping area. In the three-dimensional coordinate system, the vertices of the wall tiles in the overlapping area are subjected to projection transformation, and the intersection of the wall and the ground is calculated based on the projection results.

4. The method for optimizing the starting point of tile laying according to claim 3, characterized in that, The step of performing projection transformation on the vertices of the wall tiles within the overlapping area in the three-dimensional coordinate system, and calculating the intersection line between the wall and the ground based on the projection results, includes: An orthogonal projection transformation is performed on the vertices of the wall tiles within the overlapping area to map the three-dimensional coordinates to a horizontal reference plane, thereby obtaining a set of projection points. The Delaunay triangulation algorithm is used to process the projection point set to generate continuous line segments; The boundary range of the ground tiles is determined based on the overlapping area, and the edge detection algorithm is used to extract the set of edge points of the ground tiles; The iterative nearest point algorithm is used to perform sequence matching calculations on the edge point set of the ground tiles and the continuous line segments to obtain the intersection line of the wall and the ground.

5. The method for optimizing the starting point of tile laying according to claim 1, characterized in that, The process of sorting the intersection coordinates to determine the reference point, calculating the optimal starting point offset based on the reference point, and determining the tile starting point based on the optimal starting point offset and the original starting point includes: The intersection point coordinates are sorted in ascending order of X coordinate, and the intersection point with the smallest X coordinate is selected as the reference point; Using the reference point as the origin, an optimization algorithm is used to calculate the optimal starting point offset in the X and Y directions; The original starting point is adjusted according to the optimal starting point offset to determine the starting point of the tile.

6. The method for optimizing the starting point of tile laying according to claim 5, characterized in that, The calculation of the optimal starting point offset in the X and Y directions using an optimization algorithm with the reference point as the origin includes: Using the aforementioned reference point as the origin, an optimization model with gap alignment as the objective function is established based on the intersection point coordinate sequence. The gradient descent algorithm is used to iteratively calculate the offset parameters in the optimization model to obtain the optimal starting point offset that maximizes the gap alignment. Output the optimal starting point offset in the X and Y directions, and verify that the optimal starting point offset is within the preset reasonable range.

7. A device for optimizing the starting point of tile laying, characterized in that, The tile starting point optimization device includes: The modeling and generation unit is used to construct a three-dimensional coordinate system based on the geometric boundary information of the paving area, set the original starting point, and perform geometric transformation processing based on the original starting point and tile parameters to generate the distribution of gap line segments. The index calculation unit is used to divide the tiling area into spatial indexes in the three-dimensional coordinate system, determine the overlapping area of ​​the floor tiles and wall tiles through collision detection, and calculate the intersection line of the wall and the floor based on the overlapping area. The intersection point determination unit is used to perform intersection judgment calculation on the intersection line and the gap line segment using vector cross product operation, and identify the geometric relationship between the line segments; calculate the intersection point coordinates of the intersection line and the gap line segment based on the intersection judgment result, and filter duplicate intersection points to obtain valid intersection point coordinates; The optimization and adjustment unit is used to sort the intersection coordinates to determine the reference point, calculate the optimal starting point offset based on the reference point, and determine the tile starting point according to the optimal starting point offset and the original starting point.

8. A device for optimizing the starting point of tile laying, characterized in that, The tile starting point optimization device includes: a memory and at least one processor, wherein the memory stores instructions; The at least one processor invokes the instructions in the memory to cause the tile starting point optimization device to perform the steps of the tile starting point optimization method as described in any one of claims 1-6.

9. A computer-readable storage medium storing instructions thereon, characterized in that, When the instruction is executed by the processor, it implements the steps of the tile starting point optimization method as described in any one of claims 1-6.

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