Digital line drawing method and device based on three-dimensional model and electronic equipment

Abstract

The application relates to a three-dimensional model-based digital line map drawing method and device and electronic equipment, and belongs to the technical field of three-dimensional geographic information processing, wherein the three-dimensional model-based digital line map drawing method comprises the following steps: extracting multi-scale geometric features of each vertex in a three-dimensional model to be processed, determining a non-ground point set in the vertex based on the multi-scale geometric features; clustering and segmenting the vertex in the non-ground point set, determining a vertex set of each building, and constructing a geometric primitive energy field of each building based on the vertex set; determining discrete boundary points corresponding to each independent boundary of the building based on the geometric primitive energy field, converting the discrete boundary points into smooth vector lines, and drawing a digital line map based on the vector lines. The application can automatically, completely and highly accurately draw a digital line map containing complex topological relations from a three-dimensional model.

Description

Technical Field

[0001] This invention relates to the field of three-dimensional geographic information processing technology, and in particular to a method, apparatus and electronic device for drawing digital line maps based on three-dimensional models. Background Technology

[0002] With the rapid development of oblique photogrammetry, 3D laser scanning, and UAV aerial photography, the acquisition of high-precision 3D models has become increasingly convenient. Efficiently and automatically generating DLG (digital line map) conforming to standards from 3D models has become a pressing problem to be solved in the field of surveying and mapping geographic information.

[0003] In existing technologies, digital line mapping mainly relies on manual stereoscopic observation or semi-automatic interactive vectorization. Manual methods require operators to wear stereoscopic glasses and collect feature outlines one by one from stereoscopic image pairs. This is not only labor-intensive and inefficient, but also suffers from inconsistent results due to subjective differences among operators. Semi-automatic interactive vectorization methods are diverse. Edge detection and vectorization methods based on 2D images are significantly affected by factors such as lighting changes, shadows, occlusion, and texture repetition. Building edges are often broken or confused with vegetation shadows, resulting in discontinuous lines and a high false detection rate. This is especially true in densely built-up areas where the roof edges of adjacent buildings intersect, making it impossible to distinguish their ownership solely based on image grayscale information. Classification and contour extraction methods based on airborne radar point clouds are difficult to apply globally to complex buildings containing recesses, protrusions, and courtyards, easily leading to lost details or false contours.

[0004] It is evident that existing technologies cannot automatically, completely, and with high precision draw digital line diagrams containing complex topological relationships from 3D models. Summary of the Invention

[0005] In view of this, it is necessary to provide a method, apparatus and electronic device for drawing digital line drawings of three-dimensional models, so as to solve the problem that the existing technology cannot automatically, completely and with high precision draw digital line drawings containing complex topological relationships from three-dimensional models.

[0006] To address the aforementioned problems, in a first aspect, the present invention provides a method for drawing digital line drawings based on a three-dimensional model, comprising: Extract multi-scale geometric features of each vertex in the 3D model to be processed, and determine the set of non-ground points in the vertex based on the multi-scale geometric features; Clustering and segmenting the vertices in the non-ground point set to determine the vertex set of each building, and constructing the geometric primitive energy field of each building based on the vertex set; Based on the geometric primitive energy field, the discrete boundary points corresponding to each independent boundary of the building are determined, and the discrete boundary points are transformed into smooth vector lines. Digital line drawings are then drawn based on the vector lines, where the independent boundary is the boundary that belongs exclusively to a single building.

[0007] In one possible implementation, multi-scale geometric features include Gaussian curvature, mean curvature, shape exponent, and curvature variation. Multi-scale geometric features of each vertex in the 3D model to be processed are extracted, including: Anisotropic Laplacian smoothing and denoising are performed on the 3D model to be processed to obtain a smoothed 3D model. Extract the neighborhood principal curvature of each vertex in the smoothed 3D model, and calculate the multi-scale geometric features of each vertex based on the neighborhood principal curvature.

[0008] In one possible implementation, determining the set of non-ground points in a vertex based on multi-scale geometric features includes: The elevation distribution of all vertices in the 3D model is statistically analyzed, and elevation change points are determined based on the elevation distribution. The elevation corresponding to the elevation change points is then used as the distinction threshold. The flatness of the local plane of each vertex is calculated based on multi-scale geometric features, and vertices with elevations below the discrimination threshold and flatnesses greater than the preset flatness threshold are identified as the first ground point. Based on the first ground point, a progressive morphological opening operation is used to determine the second ground point that does not conform to the terrain trend among the remaining vertices whose elevation is below the discrimination threshold. Then, a set of non-ground points is constructed based on the vertices in the 3D model that do not belong to the first ground point or the second ground point.

[0009] In one possible implementation, the vertices in the non-ground point set are clustered and segmented to determine the vertex set of each building, including: The Euclidean distance clustering method with adaptive radius is used to cluster the vertices in the non-ground point set to obtain multiple candidate point clusters; Calculate the plane fitting residual, normal divergence, and elevation change range for each candidate point cluster. Determine the candidate point clusters whose plane fitting residual is less than a preset residual threshold, whose normal divergence is less than a preset divergence threshold, and whose elevation change range is greater than a preset elevation change threshold as building point clusters. Calculate the two-dimensional projection density map of the building point cluster, and use the detection density valleys in the two-dimensional projection density map as dividing lines to segment the building point cluster, thereby obtaining the vertex set of each building.

[0010] In one possible implementation, the geometric primitive energy field of each building is constructed based on the vertex set, including: Based on the vertex set, a pre-defined set of candidate geometric primitives is fitted, and the fitting confidence of each candidate geometric primitive is calculated. Calculate the signed weighted distance from each vertex in the vertex set to each candidate geometric primitive, and construct the geometric primitive energy field of each building by combining the set fitting confidence and the signed weighted distance. The formula for the geometric primitive energy field is:

[0011] in, Let x be the energy field of the geometric primitives corresponding to vertex x, and P be the set of vertices. Let x be the signed weighted distance from point x to the k-th geometric primitive. Let x be the confidence level that vertex x belongs to the k-th geometric primitive. For anisotropic diffusion regularization, , as well as These are adaptive weighting coefficients.

[0012] In one possible implementation, the discrete boundary points corresponding to each independent boundary of the building are determined based on the geometric primitive energy field, including: The local maxima of the gradient magnitude of the geometric primitive energy field are used as candidate boundary points. Based on the density of the initial candidate boundary points in the building, the building is divided into multiple units, and the point with the highest gradient magnitude in each unit is used as the seed point. An adaptive boundary growth strategy based on dynamic step size and direction prediction is adopted to track the discrete boundary points corresponding to each independent boundary in the building, starting from various sub-points.

[0013] In one possible implementation, discrete boundary points are transformed into smooth vector lines, and digital line plots are drawn based on these vector lines, including: The straightness index of each independent boundary is calculated based on the discrete boundary points corresponding to each independent boundary, and the line segment type of the independent boundary is determined based on the straightness index. Based on the line segment type, vector fitting is performed on independent boundaries of different types to obtain smooth vector lines; Construct the topological relationships of vector lines and draw digital line graphs.

[0014] In one possible implementation, vector fitting is performed on independent boundaries of different types based on line segment type to obtain smooth vector lines, including: When the line type is a straight line segment, the least second-level method is used to fit the discrete boundary points to a straight line to obtain a smooth vector line; When the line type is a curve segment, a cubic uniform B-spline fitting is used to obtain a smooth vector line, wherein the number of control points for the cubic uniform B-spline fitting is determined by the curvature of the independent boundary.

[0015] Secondly, the present invention also provides a digital line drawing device based on a three-dimensional model, comprising: The point set acquisition module is used to extract multi-scale geometric features of each vertex in the 3D model to be processed, and to determine the non-ground point set in the vertex based on the multi-scale geometric features. The energy field construction module is used to cluster and segment vertices in the non-ground point set, determine the vertex set of each building, and construct the geometric primitive energy field of each building based on the vertex set. The drawing module is used to determine the discrete boundary points corresponding to each independent boundary of a building based on the geometric primitive energy field, and to convert the discrete boundary points into smooth vector lines. Based on the vector lines, a digital line drawing is drawn, where the independent boundary is the boundary that belongs to a single building.

[0016] Thirdly, the present invention also provides an electronic device, including a data acquisition unit, a memory, and a processor, wherein, A data acquisition device is used to acquire data from the 3D model to be processed. Memory, used to store programs; The processor, coupled to the memory, is used to execute the program stored in the memory to implement the steps in the digital line drawing method based on the three-dimensional model in any of the above implementations.

[0017] The beneficial effects of this invention are as follows: The digital line drawing method based on a 3D model provided by this invention extracts multi-scale geometric features of each vertex in the 3D model to be processed, and determines the set of non-ground points in the vertices based on these multi-scale geometric features. This method can more accurately distinguish between ground points and non-ground points in the 3D model, providing a solid data foundation for the subsequent construction of digital line drawings of buildings. By clustering and segmenting the vertices in the non-ground point set, the vertex set of each building is determined, and the geometric primitive energy field of each building is constructed based on the vertex set. By aggregating and segmenting the non-ground point set, the vertex set of each individual building can be independently extracted from the non-ground point set, effectively separating building groups and providing a more independent point set for the construction of digital line drawings of individual buildings. Then, based on the geometric primitive energy field, the discrete boundary points corresponding to each independent boundary of the building are determined, and the discrete boundary points are transformed into smooth vector lines. Based on the vector lines, digital line drawings are drawn. The geometric primitive energy field embeds high-order geometric knowledge into the boundary positioning, resulting in high boundary accuracy and the ability to handle complex topological relationships between building boundaries, enabling more accurate and complete drawing of digital line drawings. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A flowchart illustrating a method for drawing digital line drawings based on a three-dimensional model, provided in an embodiment of the present invention; Figure 2 A flowchart illustrating a multi-scale geometric feature extraction method provided in an embodiment of the present invention; Figure 3 A flowchart illustrating a method for determining a non-ground point set according to an embodiment of the present invention; Figure 4 This is a flowchart illustrating a building segmentation method provided in an embodiment of the present invention; Figure 5 A flowchart illustrating a discrete boundary point determination method provided in an embodiment of the present invention; Figure 6 This is a flowchart illustrating a method for drawing digital line graphs according to an embodiment of the present invention. Figure 7 This is a schematic diagram of the structure of a digital line drawing device based on a three-dimensional model provided in an embodiment of the present invention; Figure 8 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0020] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0021] In the description of the embodiments of the present invention, unless otherwise stated, "multiple" means two or more. "And / or" describes the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0022] The terms "first," "second," etc., used in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a technical feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.

[0023] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a mutually exclusive, independent, or alternative embodiment. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0024] A specific embodiment of the present invention, such as Figure 1 As shown, a method for drawing digital line drawings based on a three-dimensional model is disclosed, including: S101, extract the multi-scale geometric features of each vertex in the 3D model to be processed, and determine the set of non-ground points in the vertex based on the multi-scale geometric features.

[0025] In this embodiment of the invention, the 3D model to be processed refers to a 3D surface model composed of a large number of vertices. Vertices can form patches through connections, or they can be discrete sets of points without connections. Typical sources include, but are not limited to, triangular mesh models generated by oblique photogrammetry multi-view matching, and point cloud models obtained by airborne or ground-based laser scanning. Multi-scale geometric features refer to a series of local geometric properties obtained by analyzing and calculating different spatial neighborhood ranges at the same vertex. Compared to single-scale features, multi-scale features can not only depict the undulations and orientation of a vertex within a small range, but also reflect its macroscopic structural properties within a larger spatial range, providing rich and robust discrimination information for accurately distinguishing different categories such as ground points, building structure points, and vegetation points.

[0026] Furthermore, based on the fact that ground points typically have approximately vertical normal vectors, small local elevation variances, and relatively low height distributions, appropriate feature thresholds can be set to filter out most ground points. For non-ground points, vegetation points can also be excluded, as vegetation points often exhibit highly discrete normal vector directions and irregular curvature changes at various scales, significantly differing from the regular surfaces of buildings. After the above processing, the obtained non-ground point set mainly consists of the vertices of artificial structures such as building walls and roofs. The specific method for obtaining the non-ground point set will be described in detail later in this invention.

[0027] S102, cluster and segment the vertices in the non-ground point set to determine the vertex set of each building, and construct the geometric primitive energy field of each building based on the vertex set.

[0028] In this embodiment of the invention, preliminary clustering is first performed based on the spatial proximity between vertices to form multiple spatially continuous clusters. Then, within each cluster, fine segmentation is performed based on the similarity of local geometric attributes to obtain a set of vertices corresponding to independent buildings or independent structural components of buildings. Local geometric attributes may include normal vector direction, curvature magnitude, etc. Through this process, different buildings are separated from each other, and the main body of a single building and its protrusions can also be identified based on geometric discontinuities.

[0029] Furthermore, for the vertex set corresponding to a single building, several geometric primitives constituting the building surface are first extracted. These geometric primitives are typically planar primitives, but in curved building structures, they can also include regular curved surface primitives such as cylindrical and conical surfaces. Then, using vertices as the basic units of the energy field, constraints regarding primitive affiliation and spatial smoothness are defined to form the energy field. The univariate component of this energy field reflects the degree of matching between a vertex and a specific geometric primitive, while the binary component describes the inconsistency cost when adjacent vertices are assigned different primitives. Thus, at the primitive boundaries, the energy field exhibits significant energy gradients or local extrema. The geometric primitive energy field can also be directly implemented in the form of a boundary saliency map, i.e., without explicitly extracting geometric primitives, but by integrating the multi-scale geometric features of each vertex, and directly providing a measure of the probability that each vertex is on the region boundary through factors such as the degree of normal vector mutation, elevation jump amplitude, and curvature extrema, a boundary energy field is formed. In this field, the lines connecting strong response locations correspond to the potential building structural boundaries. Both construction methods can be encompassed within the geometric primitive energy field concept of this invention. The specific construction method of the geometric primitive energy field will be described in detail later in this invention.

[0030] S103. Based on the geometric primitive energy field, determine the discrete boundary points corresponding to each independent boundary of the building, and transform the discrete boundary points into smooth vector lines. Draw a digital line drawing based on the vector lines, where the independent boundary is the boundary that belongs to a single building.

[0031] In this embodiment of the invention, for each ordered subset of discrete boundary points, a polyline simplification process is first performed to eliminate collinear or adjacent redundant points, retaining key inflection points that reflect the boundary shape. Then, parametric curve fitting techniques, such as piecewise spline fitting or Bézier curve fitting, are used to generate continuous and smooth vector contour segments. For right angles or straight line segments that actually exist in the building contour, geometric regularization constraints can be applied before or after smoothing to adjust approximately right angles to an orthogonal state and approximately flush line segments to the same straight line. The multiple smooth vector lines generated for each building are organized according to their building, boundary type, spatial relationship, etc., and assigned corresponding layer attributes and visualization styles, outputting digital line drawing results in a universal vector exchange format. The boundaries of holes and appurtenances inside the building can also be drawn together.

[0032] The present invention provides a method for drawing digital line maps based on 3D models. By extracting multi-scale geometric features from each vertex of the 3D model to be processed, and determining the set of non-ground points within the vertices based on these multi-scale geometric features, the method can more accurately distinguish between ground and non-ground points in the 3D model, providing a solid data foundation for the subsequent construction of digital line maps of buildings. By clustering and segmenting the vertices in the non-ground point set, the vertex set of each building is determined, and the geometric primitive energy field of each building is constructed based on the vertex set. By aggregating and segmenting the non-ground point set, the vertex set of each individual building can be independently extracted from the non-ground point set, effectively separating building groups and providing a more independent point set for the construction of digital line maps of individual buildings. Then, based on the geometric primitive energy field, the discrete boundary points corresponding to each independent boundary of the building are determined, and the discrete boundary points are transformed into smooth vector lines. Based on the vector lines, digital line drawings are drawn. The geometric primitive energy field embeds high-order geometric knowledge into the boundary positioning, resulting in high boundary accuracy and the ability to handle complex topological relationships between building boundaries, enabling more accurate and complete drawing of digital line drawings.

[0033] In some possible embodiments of the present invention, such as Figure 2 As shown, the multi-scale geometric features include Gaussian curvature, mean curvature, shape exponent, and curvature variation. The multi-scale geometric features of each vertex in the 3D model to be processed are extracted, including: S201, perform anisotropic Laplacian smoothing and denoising on the 3D model to be processed to obtain a smoothed 3D model. S202 extracts the neighborhood principal curvature of each vertex in the smoothed 3D model, and calculates the multi-scale geometric features of each vertex based on the neighborhood principal curvature.

[0034] In this embodiment of the invention, the input 3D mesh model undergoes quality enhancement processing, and the multi-scale differential geometric properties of each vertex are calculated to provide basic features for subsequent segmentation and energy field construction. Specifically, the 3D model to be processed can be subjected to anisotropic Laplacian smoothing denoising to obtain a smoothed 3D model. The iterative formula for anisotropic Laplacian smoothing denoising is as follows:

[0035] in, In the three-dimensional mesh model, the first i The new coordinate vector of each vertex after smoothing Distance weights Step size factor In the three-dimensional mesh model, the first i The three-dimensional spatial coordinate vector of each vertex. In the three-dimensional mesh model, the first j The three-dimensional spatial coordinate vector of each vertex. For the first i The set of all neighboring vertices of a vertex.

[0036] Furthermore, multi-scale geometric features, including Gaussian curvature, are calculated for each vertex of the smoothed model. K Mean curvature H Shape index SI and curvature variation Specifically, the calculation formulas for the characteristics of each set are as follows:

[0037]

[0038]

[0039]

[0040] in, and Let be the principal curvature of the neighborhood of the vertex.

[0041] Specifically, the original oblique photogrammetry model contained some noise and small holes due to image matching errors and occlusion. First, anisotropic Laplacian smoothing was performed with 3 iterations, a step size factor λ=0.3, and a neighborhood weight σ=0.05. This smoothed model was smoother while preserving the building's edges. Considering the large number of triangular facets in the model, uniform remeshing was performed to improve subsequent processing speed. The model was remeshed into a uniform triangular mesh with a side length of approximately 0.2m, reducing the number of vertices from 4 million to 1.5 million. For each vertex, the principal curvature within a 0.5m neighborhood radius was calculated, yielding the Gaussian curvature K, mean curvature H, shape index SI, and curvature variation. The curvature gradient is calculated, and finally, the feature vector of each vertex is obtained.

[0042] This invention provides a data foundation for subsequent processing by extracting multi-scale geometric features of each vertex in a 3D model.

[0043] In some possible embodiments of the present invention, such as Figure 3 As shown, determining the set of non-ground points in a vertex based on multi-scale geometric features includes: S301, Statistically analyze the elevation distribution of all vertices in the 3D model, determine elevation change points based on the elevation distribution, and determine the elevation corresponding to the elevation change points as the distinction threshold; S302, calculate the flatness of the local plane of each vertex based on multi-scale geometric features, and determine the vertex with an elevation lower than the distinction threshold and a flatness greater than the preset flatness threshold as the first ground point; S303, based on the first ground point, a progressive morphological opening operation is used to determine the second ground point that does not conform to the terrain trend among the remaining vertices whose elevation is below the distinction threshold, and a non-ground point set is constructed based on the vertices in the 3D model that do not belong to the first ground point and the second ground point.

[0044] In this embodiment of the invention, a global statistical analysis of the elevation distribution of all vertices in the 3D model is performed. Since the 3D model to be processed typically covers the ground and various terrain features, the vertex elevations extend upwards from the ground reference plane to heights such as the top of buildings, and the overall elevation distribution exhibits a certain regularity. By analyzing this elevation distribution, abrupt changes in elevation values ​​can be automatically identified. These abrupt changes often correspond to the junction where the ground area and the building facade begin to rise. Therefore, the elevation values ​​corresponding to these abrupt changes are determined as preliminary thresholds to distinguish between ground and non-ground areas. The purpose of this threshold is to separate prominent building facades and rooftop high points from low-lying areas that may belong to the ground, thereby avoiding misclassifying building structures as ground and eliminating the need to rely on manually setting fixed elevation thresholds, thus enhancing scene adaptability.

[0045] Subsequently, using the multi-scale geometric features extracted in the preceding steps, the flatness of the local plane at each vertex is calculated. Flatness is a geometric property that measures how close a local surface is to an ideal plane; the higher the value, the flatter the local area where the vertex is located. For vertices with elevations below the aforementioned distinction threshold, their flatness is examined one by one. If the flatness of a vertex is greater than the preset flatness threshold, it indicates that the point is on a very flat local surface, possessing typical ground features, and is therefore identified as the first ground point. The first ground point constitutes the most reliable core part of the ground area, typically corresponding to an open and flat plaza, road surface, or bare soil surface.

[0046] However, relying solely on a flatness threshold to determine the first ground point may not fully cover areas of terrain that have some undulations but are essentially still ground, such as gentle slopes, the edges of low flower beds, or slightly rough grassland. While the elevation of these areas may be below the distinction threshold, their flatness may not meet the preset standard. Directly classifying them as non-ground points would result in omissions in the ground point set. Morphological opening is a process that erodes and then dilates a spatial set based on structuring elements, often used in ground filtering to simulate terrain trend surfaces. Progressive morphological opening means that the size of the structuring element gradually increases during the operation. Specifically, an initial ground surface is constructed using the first ground point, and the size of the structuring element is gradually increased. Opening operations are performed at each size level, and the result represents the allowable terrain undulation envelope at the corresponding scale. When the position of a point among the remaining vertices is significantly higher than the local topographic trend reflected by the envelope surface, it indicates that the point exhibits an uncoordinated prominence or isolation characteristic relative to the surrounding continuous topography, and is likely a low-lying feature or noise attached to the ground; conversely, if the point can be reasonably enveloped by the topographic trend surface, it is determined to be a second ground point that conforms to the topographic trend.

[0047] For example, calculating the elevation histogram of all vertices revealed two main peaks in the elevation distribution: the first peak corresponds to the ground level, approximately 40-45m, and the second peak corresponds to the base of buildings, above approximately 45.5m. The valley floor between the two peaks, corresponding to an elevation of 43.5m, was taken as the initial threshold. Simultaneously, the local flatness of each vertex was calculated, and principal component analysis was performed on the neighborhood within a 0.5m radius. Points with elevations below 45m and flatness greater than 0.8 were marked as ground candidate points. A progressive morphological filter was then applied using circular structuring elements with radii of 1m, 2m, and 4m. Opening operations were performed, and points whose elevation decreased by more than 0.5m after each opening operation were marked as non-ground points. Ultimately, approximately 350,000 ground points and approximately 1,150,000 non-ground points were extracted.

[0048] The embodiments of the present invention can effectively capture ground points that are not completely flat in some areas but conform to the continuous trend of terrain changes in the whole, making up for the shortcomings of simply relying on flatness judgment. The non-ground point set eliminates the interference of various ground points and centrally retains the surface vertices of non-ground features such as building walls, roofs, and independent structures, providing a clean and reliable data foundation for subsequent building clustering and individual segmentation.

[0049] In some possible embodiments of the present invention, such as Figure 4 As shown, clustering and segmentation are performed on the vertices in the non-ground point set to determine the vertex set of each building, including: S401 uses the Euclidean distance clustering method with adaptive radius to cluster vertices in the non-ground point set, resulting in multiple candidate point clusters; S402, calculate the plane fitting residual, normal divergence and elevation change range of each candidate point cluster, and determine the candidate point clusters whose plane fitting residual is less than the preset residual threshold, whose normal divergence is less than the preset divergence threshold, and whose elevation change range is greater than the preset elevation change threshold as building point clusters. S403, calculate the two-dimensional projection density map of the building point cluster, and use the detection density valleys in the two-dimensional projection density map as dividing lines to segment the building point cluster, thereby obtaining the vertex set of each building.

[0050] In this embodiment of the invention, an improved Euclidean distance clustering method is used for the non-ground point set to separate independent targets such as buildings and trees. Due to the uneven density of the building point cloud, an adaptive radius variant of DBSCAN is used, employing a smaller radius for areas with high local point density and a larger radius for areas with low density. The radius calculation formula is as follows:

[0051] in, For local point density, and For the maximum and minimum values ​​of the radius, Let be the initial radius.

[0052] For each candidate point cluster, the following geometric characteristics are calculated: plane fitting residual (root mean square error of fitting the points within the cluster to the optimal plane), normal divergence (average angle between the normals of all points within the cluster), and elevation variation range. Building point clouds exhibit small plane fitting residuals (typically <0.05m), small normal divergence (normals concentrated on the main walls), and large elevation variations (reflecting height); vegetation point clouds exhibit large plane fitting residuals, large normal divergence, and moderate elevation variations, but lack regular planes. A threshold is set: if the plane fitting residual is <0.1m and the normal divergence is <30°, it is marked as a building cluster; otherwise, it is marked as vegetation or other land features.

[0053] Furthermore, for large clusters labeled as buildings, if a single cluster corresponds to multiple clearly separated buildings (e.g., two independent buildings that are close but not completely separated), a secondary segmentation based on normal variation and skeleton analysis is adopted. The two-dimensional projected density map of the cluster is calculated, and density valleys are detected as dividing lines; at the same time, combined with the location of normal abrupt changes, the minimum cut graph algorithm is used to decompose the cluster into independent instances, and finally the vertex set of each building instance is obtained.

[0054] For example, DBSCAN clustering with adaptive radius can be used for non-ground point sets. Local point density. Cluster radius is estimated by counting points within a 1m radius:

[0055] The minimum neighborhood number was set to 15, resulting in 247 initial clusters. Buildings and vegetation were distinguished based on flatness and normal consistency. For each cluster, the least squares method was used to fit the plane, and the residual RMS was calculated. Simultaneously, the normals of all points within the cluster were calculated, and the average angle between normals was statistically analyzed. Typical values ​​were: RMS < 0.03m and normal divergence < 25° for building wall clusters; and RMS > 0.15m and normal divergence > 50° for vegetation clusters. Clusters with RMS < 0.08m and normal divergence < 35° were designated as building clusters. A total of 187 building clusters were selected, with the remainder being vegetation and other land features. Examining the 187 building clusters, three clusters covered two clearly separated buildings with a spacing < 1m, which prevented DBSCAN from separating them. For these clusters, a 0.2m resolution density grid was generated in the XY plane, and density troughs were detected as dividing lines, such as five consecutive grid densities < 1 / 3 of the average density. Simultaneously, the normal change was calculated. Abrupt changes in the normal occurred near low-density regions, with a change >30°, further confirming the segmentation location. A graph cut algorithm was used to segment the cluster into independent sub-clusters, ultimately resulting in 192 building instances, each containing an average of approximately 6000 vertices.

[0056] This invention, through clustering and segmenting non-ground points, can accurately isolate the point set of each detached building, ensuring the accuracy of detached building boundary extraction.

[0057] In some possible embodiments of the present invention, the geometric primitive energy field of each building is constructed based on the vertex set, including: Based on the vertex set, a pre-defined set of candidate geometric primitives is fitted, and the fitting confidence of each candidate geometric primitive is calculated. Calculate the signed weighted distance from each vertex in the vertex set to each candidate geometric primitive, and construct the geometric primitive energy field of each building by combining the set fitting confidence and the signed weighted distance. The formula for the geometric primitive energy field is:

[0058] in, Let x be the energy field of the geometric primitives corresponding to vertex x, and P be the set of vertices. Let x be the signed weighted distance from point x to the k-th geometric primitive. Let x be the confidence level that vertex x belongs to the k-th geometric primitive. For anisotropic diffusion regularization, , as well as These are adaptive weighting coefficients.

[0059] In this embodiment of the invention, for each building instance, a set of possible geometric primitive types P = {plane, cylinder, sphere, cone, freeform surface} is defined. For each instance, candidate geometric primitives are first fitted, and then an energy field function is constructed such that the local minimum line of the energy field corresponds to the true geometric boundary of the feature. For all vertices contained in the current instance, the RANSAC (Random Sample Consensus) method is used to fit the parameters of the plane, cylinder, sphere, and cone respectively, and the fitting confidence of each primitive is calculated. The plane fitting uses the least squares method, and the cylinder fitting first estimates the axis and then performs circular fitting. For residual regions that cannot be represented by basic quadratic surfaces, they are marked as freeform surfaces and locally represented using moving least squares surfaces. Within the axis-aligned bounding box of the instance, a regular grid is established at a certain resolution (e.g., 0.2m). For each grid point x, the signed weighted distance to all candidate geometric primitives is calculated, and the energy function is defined:

[0060] Where is the energy field of the geometric primitive corresponding to vertex x, and is the signed weighted distance from point x to the k-th geometric primitive. For cylindrical primitives... (a,p 0 ,r) , , a p0 is the unit vector along the axis of the cylinder; p0 is the coordinate vector of any point on the axis of the cylinder; r is the radius (scalar) of the cylinder.

[0061] The normalized confidence score for point x belonging to the k-th geometric primitive is calculated based on the consistency between the normal at point x and the theoretical normal of the primitive:

[0062] in For point x The neighborhood normal, Let x be the theoretical normal of the projection point of the primitive onto x.

[0063] Esmooth(x) The anisotropic diffusion regularization term is defined as: Esmooth(x) = div(g( Φ) Φ) Where g(s)=1 / (1+s2) is the edge stopping function, which can protect the boundary while smoothing.

[0064] , , The adaptive weighting coefficients are dynamically adjusted based on the point cloud density and noise level within the instance. A typical setting range is... ∈[0.3,0.6], ∈[0.2,0.4], ∈[0.1,0.3].

[0065] The calculated Φ(x) The values ​​are stored as scalar fields on a regular grid and linearly normalized to the [0,1] interval for subsequent boundary tracking.

[0066] The energy field construction process is illustrated using a typical commercial building as an example. This building has a rectangular main body with a decorative conical top structure. First, geometric primitives are fitted to all vertices (approximately 23,000) of this instance. RANSAC plane fitting yields four main wall surfaces and one top plane; conical fitting yields the top cone, with a fitting confidence level of 0.92. No obvious cylindrical or spherical surfaces were found. Then, within the axis-aligned bounding box of this instance, a three-dimensional regular mesh (approximately 80×40×60 grid size) is established at 0.2m intervals. For each grid point x, the distance to each candidate primitive and the confidence level are calculated. Using ω1=0.5, ω2=0.3, and ω3=0.2, the energy value is calculated using the formula. After anisotropic diffusion smoothing, a continuous energy field is obtained.

[0067] In this embodiment of the invention, the geometric primitive energy field embeds high-order geometric knowledge into the boundary positioning, resulting in high boundary accuracy; the unique topology-preserving progressive tracking algorithm automatically handles complex topologies such as T-shapes and cross-shapes.

[0068] In some possible embodiments of the present invention, such as Figure 5 As shown, the discrete boundary points corresponding to each independent boundary of a building are determined based on the geometric primitive energy field, including: S501 uses the local maxima of the gradient magnitude of the geometric primitive energy field as candidate boundary points, divides the building into multiple units based on the density of the initial candidate boundary points in the building, and uses the point with the highest gradient magnitude in each unit as the seed point. S502 employs an adaptive boundary growth strategy based on dynamic step size and direction prediction to track discrete boundary points corresponding to each independent boundary in a building, starting from various sub-points.

[0069] In this embodiment of the invention, the gradient magnitude map of the energy field is calculated. G(x) = || Φ(x)||Non-maximum suppression (NMS) is applied to extract local maxima of gradient magnitude as initial candidate boundary points. To ensure that each independent boundary can be traced, a Voronoi diagram partitioning strategy is adopted: within each instance region, Voronoi units are divided according to the candidate point density, and the point with the highest gradient magnitude within each unit is retained as a seed point.

[0070] From each seed Starting from a point, establish a boundary linked list. Initially included Set the current direction. For each step, based on the current position curvature (, Calculate the adaptive step size:

[0071] in Use the base step size (e.g., 0.5 times the grid spacing). This is the curvature sensitivity coefficient (usually set to 2.0). The step size decreases when the curvature is large to accommodate sharp turns.

[0072] Furthermore, predict the next direction of movement, and combine the historical directions with the energy gradient direction to solve for the optimal direction angle:

[0073] in, This is the directional smoothing coefficient (usually set to 0.1~0.5). The analytical solution to this optimization problem can be obtained by searching over the candidate direction set (e.g., discretized into 8 or 16 directions).

[0074] Update location, If Φ(xt+1) < Φ(xt) τ (τ is the energy decrease threshold) indicates that the true boundary may be exceeded, in which case the growth is reversed and terminated; if If the number of tracked points is greater than the minimum length, then it is marked as closed.

[0075] Real-world terrain features often exhibit complex topologies such as T-junctions and Y-bifurcations. To address this, a topological constraint function is introduced. When a boundary growth encounters an existing boundary, the saddle point structure of the energy field is first analyzed within the local neighborhood. The energy value at a saddle point lies between two minima, typically corresponding to multiple boundary intersections. The Hessian matrix is ​​used to determine the saddle point location, and then the current boundary, existing boundaries, and predicted new branches are reconnected to this saddle point to form the correct topological network. For intersections, the algorithm automatically generates branch lines, each of which is independently traced until it closes or encounters the next intersection. For all traced boundary lines, noise segments shorter than a threshold are removed. For closely spaced parallel boundaries, those with higher confidence are retained based on their energy values, resulting in discrete boundary points corresponding to each independent boundary.

[0076] For example, boundary tracing is performed for each instance. First, the energy field gradient magnitude is calculated, and approximately 1200 initial candidate points are extracted using NMS. After Voronoi filtering, 85 seed points are retained.

[0077] Adaptive boundary growth is performed starting from each seed point. The parameters are set as follows: basic step size δ0 = 0.15m (slightly smaller than the grid spacing to ensure tracking accuracy), curvature sensitivity coefficient α = 2.0, directional smoothness coefficient β = 0.3, and minimum boundary length Lmin = 1.0m.

[0078] The following situations were encountered during the tracking process: (1) For an external contour seed point, the tracking direction moves along the energy valley and automatically closes after about 80 steps to obtain a complete external polygon contour.

[0079] (2) For the rooftop antenna base, a closed small rectangle with a length of about 2m×2m is traced.

[0080] (3) At the southeast corner of the building, the boundaries of two different primitives (wall and roof) meet to form an L-shaped corner. The algorithm automatically detects the saddle point and connects them correctly.

[0081] At the connection between the main building and the podium, a T-shaped topology appears. The algorithm identifies that the podium boundary terminates at the main building wall, determines the intersection point through saddle point analysis, and correctly generates three boundary lines (the main building outline continues to extend, and the podium boundary terminates and connects). The entire tracking process generates a total of 152 boundary line fragments, which are merged into 105 independent boundaries (including closed outline lines and internal structural lines) after topology post-processing.

[0082] In some possible embodiments of the present invention, such as Figure 6 As shown, discrete boundary points are transformed into smooth vector lines, and digital line plots are drawn based on these vector lines, including: S601, calculate the straightness index of each independent boundary based on the discrete boundary points corresponding to each independent boundary, and determine the line segment type of the independent boundary based on the straightness index; S602, based on line segment type, performs vector fitting on independent boundaries of different types to obtain smooth vector lines; S603, construct the topological relationships of vector lines and draw digital line graphs.

[0083] In this embodiment of the invention, the traced discrete point boundary lines are vectorized. First, the straightness of each boundary is calculated. For most building outlines, the straightness S is less than 0.015, and is determined to be a straight segment; for the intersection lines of the top cone, a slight curve is observed, and is determined to be a curved segment. Different fitting methods are used for vector lines with different linearities.

[0084] Specifically, based on the line segment type, vector fitting is performed on independent boundaries of different types to obtain smooth vector lines, including: When the line type is a straight line segment, the least second-level method is used to fit the discrete boundary points to a straight line to obtain a smooth vector line; When the line type is a curve segment, a cubic uniform B-spline fitting is used to obtain a smooth vector line, wherein the number of control points for the cubic uniform B-spline fitting is determined by the curvature of the independent boundary.

[0085] Straight line segments were fitted using constrained least squares fitting, with the vertical constraint strength set to 10.0 and the parallel constraint strength to 5.0 in the global constraint optimization. After optimization, adjacent wall surfaces that originally had slight angular deviations (such as 89.5° and 90.2°) were forcibly corrected to an exact 90°, and the angular differences between adjacent parallel boundaries were eliminated. The deviation between the output coordinates and the original model boundary was less than 0.03m, meeting the accuracy requirements for 1:500 scale mapping. Curve segments were fitted using cubic B-spline fitting with 6-10 control points.

[0086] The generated vector lines are divided into three layers: (1) Building outline layer: bottom and top outlines of 192 instances (384 polygons in total) (2) Building structural layer: including ridge line, parapet line, decorative line, etc., totaling about 530 lines. (3) Road edge layer: Roads were detected by ground point areas (using morphological skeleton extraction and boundary tracing), and a total of about 12.6 km of road edges were obtained. The output is in DXF and SHP files. In the DXF file, each line feature includes extended data (XData) recording information such as semantic type, instance ID, and geometric precision. The entire processing time is as follows: preprocessing 12 minutes (CPU multi-threading), segmentation and clustering 8 minutes, energy field construction and boundary tracing 9 minutes, vectorization and output 3 minutes, totaling approximately 32 minutes. Compared to traditional manual data collection (approximately 8 hours), this represents an efficiency improvement of more than 15 times.

[0087] The entire process of this invention uses only deterministic algorithms such as geometric calculation, traditional clustering, RANSAC fitting, and level set tracking, without requiring a large amount of labeled data for training. It is more adaptable to the input model. The geometric primitive energy field embeds high-order geometric knowledge into the boundary positioning, resulting in high boundary accuracy. The unique topology-preserving progressive tracking algorithm automatically handles complex topologies such as T-shapes and cross-shapes. The global constraint optimization in the vectorization stage ensures the geometric regularity of the building outline, such as straightness, perpendicularity, and parallelism. It has good anti-interference ability against model noise and missing data, and is suitable for various building forms.

[0088] To better implement the digital line drawing method based on a three-dimensional model in this invention, based on the digital line drawing method based on a three-dimensional model, the corresponding method is as follows: Figure 7 As shown, this embodiment of the invention also provides a digital line drawing device based on a three-dimensional model. The digital line drawing device 700 based on a three-dimensional model includes: The point set acquisition module 701 is used to extract the multi-scale geometric features of each vertex in the 3D model to be processed, and to determine the non-ground point set in the vertex based on the multi-scale geometric features. The energy field construction module 702 is used to cluster and segment the vertices in the non-ground point set, determine the vertex set of each building, and construct the geometric primitive energy field of each building based on the vertex set. The drawing module 703 is used to determine the discrete boundary points corresponding to each independent boundary of a building based on the geometric primitive energy field, and to convert the discrete boundary points into smooth vector lines. Based on the vector lines, a digital line drawing is drawn, where the independent boundary is the boundary that belongs to a single building.

[0089] The digital line drawing device 700 based on a three-dimensional model provided in the above embodiments can realize the technical solutions described in the embodiments of the digital line drawing method based on a three-dimensional model. The specific implementation principles of each module or unit can be found in the corresponding content in the embodiments of the digital line drawing method based on a three-dimensional model, and will not be repeated here.

[0090] like Figure 8As shown, the present invention also provides an electronic device 800. The electronic device 800 includes a processor 801, a memory 802, and a data acquisition unit 803. Figure 8 Only some components of the electronic device 800 are shown, but it should be understood that it is not required to implement all the components shown, and more or fewer components may be implemented instead.

[0091] In some embodiments, processor 801 may be a central processing unit (CPU), a microprocessor, or other data processing chip, used to run program code stored in memory 802 or process data, such as the digital line drawing method based on a three-dimensional model in this invention.

[0092] In some embodiments, processor 801 may be a single server or a group of servers. The server group may be centralized or distributed. In some embodiments, processor 801 may be local or remote. In some embodiments, processor 801 may be implemented on a cloud platform. In some embodiments, the cloud platform may include private cloud, public cloud, hybrid cloud, community cloud, distributed cloud, internal cloud, multi-cloud, etc., or any combination thereof.

[0093] In some embodiments, memory 802 may be an internal storage unit of electronic device 800, such as a hard disk or memory of electronic device 800. In other embodiments, memory 802 may also be an external storage device of electronic device 800, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on electronic device 800.

[0094] Furthermore, the memory 802 may include both internal storage units of the electronic device 800 and external storage devices. The memory 802 is used to store application software and various types of data installed on the electronic device 800.

[0095] In some embodiments, the data acquisition device 803 includes lidar, oblique photography device, and drone aerial photography device.

[0096] In some embodiments, when the processor 801 executes a digital line drawing program based on a three-dimensional model stored in the memory 802, the following steps may be performed: Extract multi-scale geometric features of each vertex in the 3D model to be processed, and determine the set of non-ground points in the vertex based on the multi-scale geometric features; Clustering and segmenting the vertices in the non-ground point set to determine the vertex set of each building, and constructing the geometric primitive energy field of each building based on the vertex set; Based on the geometric primitive energy field, the discrete boundary points corresponding to each independent boundary of the building are determined, and the discrete boundary points are transformed into smooth vector lines. Digital line drawings are then drawn based on the vector lines, where the independent boundary is the boundary that belongs exclusively to a single building.

[0097] It should be understood that when the processor 801 executes the digital line drawing program based on the three-dimensional model in the memory 802, in addition to the functions mentioned above, it can also perform other functions, as can be found in the description of the corresponding method embodiments above.

[0098] Furthermore, this embodiment of the invention does not specifically limit the type of electronic device 800 mentioned. Electronic device 800 can be a mobile phone, tablet computer, personal digital assistant (PDA), wearable device, laptop computer, or other portable electronic device. Exemplary embodiments of portable electronic devices include, but are not limited to, portable electronic devices running iOS, Android, Microsoft, or other operating systems. The aforementioned portable electronic device can also be other portable electronic devices, such as a laptop computer with a touch-sensitive surface (e.g., a touch panel). It should also be understood that in some other embodiments of the invention, electronic device 800 may not be a portable electronic device, but rather a desktop computer with a touch-sensitive surface (e.g., a touch panel).

[0099] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for drawing digital line drawings based on a three-dimensional model, characterized in that, include: Extract multi-scale geometric features of each vertex in the 3D model to be processed, and determine the set of non-ground points in the vertex based on the multi-scale geometric features; Clustering and segmenting the vertices in the non-ground point set to determine the vertex set of each building, and constructing the geometric primitive energy field of each building based on the vertex set; Based on the geometric primitive energy field, the discrete boundary points corresponding to each independent boundary of the building are determined, and the discrete boundary points are transformed into smooth vector lines. A digital line drawing is then drawn based on the vector lines, wherein the independent boundary is a boundary belonging exclusively to a single building.

2. The method for drawing digital line drawings based on a three-dimensional model according to claim 1, characterized in that, The multi-scale geometric features include Gaussian curvature, average curvature, shape exponent, and curvature variation. The extraction of multi-scale geometric features from each vertex of the 3D model to be processed includes: Anisotropic Laplacian smoothing and denoising are performed on the 3D model to be processed to obtain a smoothed 3D model. Extract the principal curvature of the neighborhood of each vertex in the smoothed 3D model, and calculate the multi-scale geometric features of each vertex based on the principal curvature of the neighborhood.

3. The method for drawing digital line drawings based on a three-dimensional model according to claim 2, characterized in that, Determining the set of non-ground points in the vertex based on the multi-scale geometric features includes: The elevation distribution of all vertices in the three-dimensional model is statistically analyzed, and elevation change points are determined based on the elevation distribution. The elevation corresponding to the elevation change points is then determined as the distinction threshold. Based on the multi-scale geometric features, the flatness of the local plane of each vertex is calculated, and the vertex with an elevation lower than the discrimination threshold and a flatness greater than the preset flatness threshold is determined as the first ground point; Based on the first ground point, a progressive morphological opening operation is used to determine a second ground point that does not conform to the terrain trend among the remaining vertices whose elevation is lower than the discrimination threshold, and a non-ground point set is constructed based on the vertices in the three-dimensional model that do not belong to the first ground point and the second ground point.

4. The method for drawing digital line drawings based on a three-dimensional model according to claim 1, characterized in that, The process of clustering and segmenting the vertices in the non-ground point set to determine the vertex set of each building includes: The vertices in the non-ground point set are clustered using the Euclidean distance clustering method with adaptive radius to obtain multiple candidate point clusters; Calculate the plane fitting residual, normal divergence, and elevation change range for each candidate point cluster. Determine the candidate point clusters whose plane fitting residual is less than a preset residual threshold, whose normal divergence is less than a preset divergence threshold, and whose elevation change range is greater than a preset elevation change threshold as building point clusters. Calculate the two-dimensional projection density map of the building point cluster, and use the detected density valleys in the two-dimensional projection density map as dividing lines to segment the building point cluster, thereby obtaining the vertex set of each building.

5. The method for drawing digital line drawings based on a three-dimensional model according to claim 4, characterized in that, The construction of the geometric primitive energy field for each building based on the vertex set includes: Based on the vertex set, a preset candidate geometric primitive is fitted, and the fitting confidence of each candidate geometric primitive is calculated. Calculate the signed weighted distance from each vertex in the vertex set to each of the candidate geometric primitives, and construct the geometric primitive energy field of each building by combining the fitting confidence and the signed weighted distance. The formula for the geometric primitive energy field is: in, Let x be the energy field of the geometric primitives corresponding to vertex x, and P be the set of vertices. Let x be the signed weighted distance from point x to the k-th geometric primitive. Let x be the confidence level that vertex x belongs to the k-th geometric primitive. For anisotropic diffusion regularization, , as well as These are adaptive weighting coefficients.

6. The method for drawing digital line drawings based on a three-dimensional model according to claim 5, characterized in that, The step of determining the discrete boundary points corresponding to each independent boundary of the building based on the geometric primitive energy field includes: The local maxima of the gradient magnitude of the geometric primitive energy field are used as candidate boundary points, and the building is divided into multiple units based on the density of the initial candidate boundary points in the building. The point with the highest gradient magnitude in each unit is used as the seed point. An adaptive boundary growth strategy based on dynamic step size and direction prediction is adopted to trace the discrete boundary points corresponding to each independent boundary in the building, starting from each of the seed points.

7. The method for drawing digital line drawings based on a three-dimensional model according to claim 6, characterized in that, The discrete boundary points are transformed into smooth vector lines, and a digital line drawing is generated based on the vector lines, including: The straightness index of each independent boundary is calculated based on the discrete boundary points corresponding to each independent boundary, and the line segment type of the independent boundary is determined based on the straightness index. Based on the line segment type, vector fitting is performed on different types of independent boundaries to obtain smooth vector lines; Construct the topological relationships of the vector lines and draw a digital line graph.

8. The method for drawing digital line drawings based on a three-dimensional model according to claim 7, characterized in that, The step of performing vector fitting on independent boundaries of different types based on the line segment type to obtain smooth vector lines includes: When the line type is a straight line segment, the least second-order method is used to fit the discrete boundary points to a straight line to obtain a smooth vector line; When the line type is a curve segment, a cubic uniform B-spline fitting is used to obtain a smooth vector line, wherein the number of control points for the cubic uniform B-spline fitting is determined by the curvature of the independent boundary.

9. A digital line drawing device based on a three-dimensional model, characterized in that, include: The point set acquisition module is used to extract multi-scale geometric features of each vertex in the 3D model to be processed, and determine the non-ground point set in the vertex based on the multi-scale geometric features. The energy field construction module is used to cluster and segment the vertices in the non-ground point set, determine the vertex set of each building, and construct the geometric primitive energy field of each building based on the vertex set. The drawing module is used to determine the discrete boundary points corresponding to each independent boundary of the building based on the geometric primitive energy field, and to convert the discrete boundary points into smooth vector lines, and to draw a digital line drawing based on the vector lines, wherein the independent boundary is the boundary that belongs to a single building.

10. An electronic device, characterized in that, Includes a data acquisition unit, memory, and processor, among which, The data acquisition device is used to acquire the 3D model to be processed; The memory is used to store programs; The processor, coupled to the memory, is used to execute the program stored in the memory to implement the steps in the digital line drawing method based on a three-dimensional model as described in any one of claims 1 to 8.

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