Self-adaptive path planning method for automatic paving curved surface of fiber reinforced composite material

Abstract

The invention belongs to the technical field of preparation and processing of fiber reinforced composites, and particularly relates to a self-adaptive path planning method for an automatic pavement curved surface of a fiber reinforced composite. According to the curved surface adaptive path planning method, a variable-angle initial path is generated through a unit direction vector obtained through pavement angle calculation; and the bottom layer paving path and the rest paths are sequentially generated, so that the self-adaptive generation of the fiber reinforced composite material paving path is realized. The curved surface adaptive path planning method comprises the following steps: obtaining a space triangular grid corresponding to the surface of a curved surface of a to-be-paved area; grid topology data is obtained; projecting the spatial triangular grid, and determining a projection area range; establishing a mapping relationship between the planar triangular mesh and the spatial triangular mesh; constructing a linear parameter equation where the initial path is located, and obtaining the initial path in the plane; generating a plurality of plane paths in the projection area range; a bottom layer paving path is obtained; and performing layer-by-layer offset to obtain a paving path of each layer.

Description

Technical Field

[0001] The present invention belongs to the technical field of the preparation and processing of fiber-reinforced composites, and particularly relates to an automated paving curved surface adaptive path planning method for fiber-reinforced composites. Background Art

[0002] Fiber Reinforced Polymer (FRP), as a new type of composite material, is specifically processed by winding, molding or pultrusion and other forming processes from reinforcing fibers and matrix materials; according to the different types of reinforcing fibers used, common fiber-reinforced composites can be divided into glass fiber-reinforced composites (GFRP), carbon fiber-reinforced composites (CFRP), and aramid fiber-reinforced composites (AFRP), etc. Since fiber-reinforced composites can meet the requirements of large spans, heavy loads, light weight and high strength for various complex structures, and at the same time adapt to different harsh working conditions. Therefore, this type of fiber-reinforced composites has shown broad application prospects and significant market value in many technical fields such as bridge construction, building construction, and ocean engineering.

[0003] Among them, in order to further improve the response speed of the automated paving of fiber-reinforced composites and realize the adaptive generation of complex curved surface paths, technicians have carried out a lot of research and innovation on the path planning direction of fiber-reinforced composites. For example: In 2018, Huang Dangming proposed a "natural path" trajectory planning algorithm based on the geodesic numerical method. Its principle is to plan the starting laying point, calculate the direction vector according to the laying angle to generate a geodesic, and then move along the geodesic according to the reference step length to obtain an initial path with adjustable angles. In 2019, Hu Jun developed a ply path generation technology based on the isometric line method. On the basis of obtaining the initial path, according to the data sampling interpolation principle, a space circular arc approximation method is used with the ply spacing R as the radius to generate a ply path with adjustable spacing. In 2019, Chen Chuanxun et al. used the Catmull-Clark subdivision surface method to perform grid subdivision on the large curvature surface of the wind turbine blade mold, obtained the projection initial path according to the Newton iteration method interpolation, and inserted the measured offset distance on-site into the initial path function, and finally generated a complete paving path.

[0004] However, the inventor found after further research that although the above method can adjust the laying angle and width, the curvature change of the model surface it depends on is gentle and cannot fully adapt to the geometric features of the existing complex structures, resulting in a cumbersome and lengthy path generation process. The generated results still require a large amount of manual intervention and correction, thus limiting the improvement of the laying efficiency of fiber-reinforced composites. Therefore, it is urgent for those skilled in the art to provide a new method for automatically planning the adaptive path of the fiber-reinforced composite material laying surface to improve the accuracy and efficiency of the automatic laying of fiber-reinforced composites. Summary of the Invention

[0005] The present invention provides a method for automatically planning the adaptive path of the fiber-reinforced composite material laying surface. The adaptive path planning method for the surface generates an initial path with variable angles through the unit direction vector calculated by the laying angle. Then, in combination with the thickness of the fiber-reinforced composite material cloth, the bottom layer laying path and the remaining paths of each layer are generated in sequence, realizing the adaptive generation of the fiber-reinforced composite material laying path and providing an efficient solution for the automatic laying of fiber-reinforced composites in the process of forming complex structures.

[0006] To solve the above technical problems, the present invention adopts the following technical solutions: The present invention provides a method for automatically planning the adaptive path of the fiber-reinforced composite material laying surface, including the following steps: Step 1: Determine the three-dimensional model of the target structure; extract the surface of the area to be laid, and perform closed meshing on it to obtain the spatial triangular mesh corresponding to the surface of the area to be laid. Step 2: Reconstruct the mesh topological relationship of the spatial triangular mesh to obtain mesh topological data. Step 3: Project the spatial triangular mesh to determine the range of its projection area. Step 4: Establish the mapping relationship between the planar triangular mesh and the spatial triangular mesh. Step 5: Determine the initial point of the initial path; according to the laying angle of the fiber-reinforced composite material, construct the linear parameter equation of the line where the initial path is located. Based on the boundary of the projection area range, sequentially generate initial path points on the line at a set step length within the boundary to obtain the initial path in the plane. Step 6: Perform equidistant offset on the initial path to obtain the laying path points covering the entire projection area range, thereby generating multiple planar paths in the projection area range. Step 7: Sort the multiple planar paths obtained in Step 6 in the positive direction of the X-axis or Z-axis according to the laying angle of the fiber-reinforced composite material. Step 8: Convert the laying path points of the multiple planar paths into spatial path points to obtain the bottom layer laying path.

[0007] More preferably, the following steps are further included: Step 9: Offset all the spatial path points of the bottom paving path by the thickness of a fiber-reinforced composite material cloth along the normal vector of the spatial triangle where they are located to obtain the second-layer paving path; And so on, offset layer by layer to obtain the paving paths of each layer.

[0008] More preferably, the specific steps of step 5 are as follows: Step 5.1: Select the point at the minimum Z-axis coordinate and at a distance of half the width w / 2 of the fiber-reinforced composite material cloth from the boundary of the projection area range as the initial point A(x a ,z a ); Determine the unit direction vector from the paving angle , and construct the linear parameter equation of the straight line where the initial path is located, satisfying: Equation (1); In equation (1), k is the parameter to be solved, is the paving angle of the fiber-reinforced composite material; Step 5.2: Based on the grid topology data, extract the vertex coordinates P n (x n ,z n ) of all the vertices on the boundary of the two-dimensional plane region; Connect all the vertices in sequence into line segments, satisfying: Equation (2); In equation (2), t is the parameter to be solved and t ∈ [0, 1]; Simultaneously solve equations (1) and (2) to calculate the parameter t1; If t1 ∈ [0, 1], then there is an intersection point P I (x i ,z i ) between the straight line where the initial path is located constructed by equation (1) and the line segment of equation (2), satisfying: Equation (3); Step 5.3: Sort the obtained intersection points according to the direction vector N1; at the set step size , sequentially generate initial path points on the straight line between the minimum intersection point and the maximum intersection point; Arrange the above initial path points in order to obtain the initial path in the plane.

[0009] More preferably, the specific steps of step 8 are as follows: Step 8.1: Query the paving path point P(xp , z p ) of the three vertices A(x a , z a )、B(x b , z b )、C(x c , z c ) of the plane triangular mesh ABC; According to the vector cross product method, calculate the areas of the triangles in the plane triangular mesh, respectively satisfying: Equation (4); Equation (5); Equation (6); Equation (7); Among them, the centroid coordinates W(u, v, w) of the paving path point P(x p , z p ) in the plane triangular mesh ABC satisfy: Equation (8); Step 8.2: Query the corresponding space triangular mesh of the plane triangular mesh ABC; among them, the three vertex coordinates of the space triangular mesh are A K (x ak , y ak , z ak ), B K (a bk , y bk , z bk ), C K (z ck , y ck , z ck ); Interpolate the space path point P K (x pk , y pk , z pk ) according to the centroid coordinates W(u, v, w); among them, the space path point P K , satisfies: Equation (9).

[0010] The present invention provides an automatic laying curved surface adaptive path planning method for fiber reinforced composite materials. The curved surface adaptive path planning method includes the following steps: determining the three-dimensional model of the target structure to obtain the spatial triangular mesh corresponding to the surface of the area to be laid; reconstructing the mesh topological relationship of the spatial triangular mesh to obtain mesh topological data; projecting the spatial triangular mesh to determine the range of its projection area; establishing the mapping relationship between the planar triangular mesh and the spatial triangular mesh; determining the initial point of the initial path, constructing the linear parameter equation of the straight line where the initial path is located, and obtaining the initial path in the plane; generating multiple planar paths within the projection area range; sorting the multiple planar paths in the positive direction of the X-axis or Z-axis; performing spatial path point conversion on the laying path points of the multiple planar paths to obtain the bottom layer laying path.

[0011] The automatic laying curved surface adaptive path planning method for fiber reinforced composite materials with the above step characteristics has at least the following technical advantages compared with the prior art: (1) The automatic laying curved surface adaptive path planning method for fiber reinforced composite materials provided by the present invention realizes the precise regulation of the direction vector and path spacing of the laying path by integrating parameters such as the width and laying angle of the fiber reinforced composite material, and ensures the coordinated cooperation of the laying angle and path width. (2) The automatic laying curved surface adaptive path planning method for fiber reinforced composite materials provided by the present invention realizes the offset processing of the bottom layer path by combining the thickness parameter of the fiber reinforced composite material, and then realizes the gapless and continuous curved surface adaptive multi-layer path intelligent planning for complex geometric structure features, significantly reducing the waste of fiber reinforced composite materials and manual intervention, and providing a new solution for the automatic laying of fiber reinforced composite materials. Description of the Drawings

[0012] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the present invention, and do not constitute a limitation to the present invention. In the following drawings: Figure 1 is a schematic flow chart of an automatic laying curved surface adaptive path planning method for fiber reinforced composite materials provided by the present invention; Figure 2 is a schematic diagram of the three-dimensional model of a wind turbine blade; Figure 3 is a schematic image diagram of the surface of the area to be laid of a wind turbine blade; Figure 4 is a schematic diagram of the laying of fiber reinforced composite materials; Figure 5 is a schematic trajectory diagram of the generated bottom layer laying path; Figure 6 Schematic diagram of the trajectories of the generated paving paths for each layer. Detailed implementation manner

[0013] The present invention provides a method for automatically paving the curved surface of a fiber-reinforced composite material with an adaptive path planning. Through the unit direction vector calculated by the paving angle, the variable-angle initial path is generated; then, in combination with the thickness of the fiber-reinforced composite material cloth, the bottom-layer paving path and the remaining paths for each layer are generated in sequence, realizing the adaptive generation of the paving path of the fiber-reinforced composite material and providing an efficient solution for the automatic paving of the fiber-reinforced composite material in the forming process of complex structures.

[0014] The present invention provides a method for automatically paving the curved surface of a fiber-reinforced composite material with an adaptive path planning, as Figure 1 shown, including the following steps: Step 1: Determine the three-dimensional model of the target structure. Extract the curved surface of the area to be paved, and perform closed meshing on it to obtain the spatial triangular mesh corresponding to the curved surface of the area to be paved.

[0015] To facilitate the understanding of the present invention by those skilled in the art, here, taking the paving of the fiber-reinforced composite material in the area near the tip of the wind turbine blade of a 5KW wind turbine as an example for introduction. Among them, the three-dimensional model of the wind turbine blade of this wind turbine is as Figure 2 shown; the curved surface of the area to be paved of the wind turbine blade of this wind turbine is referred to as Figure 3 shown. Specifically, use existing engineering software (such as Magics software) to perform meshing on the curved surface of the area to be paved, so as to process it into a closed spatial triangular mesh.

[0016] Step 2: Reconstruct the mesh topology relationship of the spatial triangular mesh to obtain the mesh topology data.

[0017] On the basis of completing Step 1, further implement Step 2. As an alternative implementation manner, first store all the triangular vertex data in the spatial triangular mesh into the initial set in sequence; then traverse the vertices of all the triangles in the initial set, establish a vertex set without duplicate data, and mark the vertices belonging to the same triangular mesh; then establish a new triangle set for the marks of the vertices and mark the serial numbers in sequence, and the reconstruction of the mesh topology relationship of the spatial triangular mesh can be completed.

[0018] Step 3: Project the spatial triangular mesh to determine the range of its projection area.

[0019] On the basis of completing Step 2, further implement Step 3 to project the above-mentioned spatial triangular mesh. Taking Figure 2Taking the three-dimensional model of the wind turbine blade of a 5KW wind turbine shown as an example, the direction from the root to the tip of the blade is defined as the positive direction of the Z-axis, and the direction from the leading edge to the trailing edge in the transverse direction is defined as the positive direction of the X-axis (refer to Figure 3 as shown). Read the grid topology data, obtain the vertex spatial coordinates of all spatial triangular grids on the surface of the surface of the area to be paved, and project them onto the XZ plane: obtain the vertex plane coordinates of all spatial triangular grids after projection, and respectively find the extreme value coordinates on the X and Z axes of the two-dimensional plane, so as to obtain the projection area range.

[0020] Step 4: Establish the mapping relationship between the planar triangular grid and the spatial triangular grid.

[0021] On the basis of completing Step 3, further implement Step 4. Specifically, the vertices of the spatial triangular grid are put into one-to-one correspondence with the vertices of the planar triangular grid after its projection. Among them, according to the set of spatial triangular grids and their serial numbers, determine the set of corresponding planar triangular grids (through one-to-one correspondence of serial numbers), complete the construction of the topological relationship of the planar triangular grid, and realize the mapping relationship between the planar triangular grid and the spatial triangular grid.

[0022] Step 5: Determine the initial point of the initial path; construct the linear parameter equation of the straight line where the initial path is located according to the paving angle of the fiber-reinforced composite material.

[0023] Based on the boundary of the projection area range, sequentially generate initial path points on the straight line at a set step length within the boundary to obtain the initial path in the plane.

[0024] On the basis of completing Step 4, further implement Step 5. As a relatively preferred implementation manner of the present invention, this Step 5 specifically includes the following steps: Step 5.1: Select the point at the minimum Z-axis coordinate and at a distance of half the width w / 2 of the fiber-reinforced composite material cloth from the boundary of the projection area range as the initial point A(x a , z a ).

[0025] From the paving angle , determine the unit direction vector , and construct the linear parameter equation of the straight line where the initial path is located, satisfying: Equation (1); In Equation (1) thereof, k is the parameter to be obtained, is the paving angle of the fiber-reinforced composite material. It should be noted that the paving angle of the fiber-reinforced composite material is a known quantity, and it can refer to the paving schematic diagram of the fiber-reinforced composite material as shown in Figure 4 .

[0026] Step 5.2: Based on the grid topology data, extract all the vertex coordinates P on the boundary of the two-dimensional planar region n (x n , z n ).

[0027] Connect all the vertices into line segments in sequence, satisfying: Equation (2); In the equation (2), t is the parameter to be solved and t ∈ [0, 1].

[0028] Combine equation (1) and equation (2) to calculate the parameter t1.

[0029] If t1 ∈ [0, 1], there is an intersection point P I (x i , z i ) between the straight line where the initial path is constructed by equation (1) and the line segment of equation (2), satisfying: Equation (3).

[0030] Step 5.3: Sort the obtained intersection points according to the direction vector N1. Generate initial path points in sequence on the straight line between the minimum intersection point and the maximum intersection point according to the set step size . Arrange the above initial path points in order to obtain the initial path in the plane.

[0031] Step 6: Perform an equidistant offset on the initial path to obtain paving path points covering the entire projection area range, so as to generate multiple planar paths in the projection area range.

[0032] On the basis of completing Step 5, further implement Step 6. Specifically, here choose to perform an equidistant offset on the initial path based on the width of the uniaxial fabric of the fiber-reinforced composite material; that is, in the direction perpendicular to the direction vector N1, offset the path line by the width of one fabric in sequence. After offsetting, obtain the paving path points covering the entire projection area range, so as to obtain multiple planar paths within the projection area range.

[0033] Step 7: Sort the multiple planar paths obtained in Step 6 in the positive direction of the X-axis or Z-axis according to the paving angle of the fiber-reinforced composite material.

[0034] On the basis of completing Step 6, further implement Step 7. Specifically, based on the paving angle of the fiber-reinforced composite material, perform a sorting process on each path obtained in Step 6 in the positive direction of the X-axis or Z-axis.

[0035] Step 8: Convert the paving path points of the multiple planar paths into spatial path points to obtain the underlying paving path.

[0036] On the basis of completing Step 7, Step 8 is further implemented. As a relatively preferred implementation manner of the present invention, Step 8 specifically includes the following steps: Step 8.1: Query the three vertices A(x p , z p )), B(x a , z a ), and C(x b , z b ) of the plane triangular grid ABC where the paving path point P(x c , z c ) is located.

[0037] According to the vector cross product method, calculate the areas of the triangles in the plane triangular grid, respectively satisfying: Equation (4); Equation (5); Equation (6); Equation (7).

[0038] Among them, the barycentric coordinates W(u, v, w) of the paving path point P(x p , z p ) in the plane triangular grid ABC satisfy: Equation (8).

[0039] Step 8.2: Query the spatial triangular grid corresponding to the plane triangular grid ABC. Among them, the three vertex coordinates of the spatial triangular grid are A K (x ak , y ak , z ak ), B K (a bk , y bk , z bk ), and C K (z ck , y ck , z ck ).

[0040] Interpolate to obtain the spatial path point P K (x pk , y pk , z pk ) according to the barycentric coordinates W(u, v, w); among them, the spatial path point P K satisfies: Equation (9).

[0041] It should be added that based on the mapping relationship between the planar triangular mesh and the spatial triangular mesh established in step 4, the corresponding spatial triangular mesh of the planar triangular mesh can be found. Then, by combining the vertex coordinates of the spatial triangular mesh and the spatial path points corresponding to all the planar paving path points obtained by barycentric coordinate interpolation, the fiber-reinforced composite material automatic paving surface adaptive path planning method provided by the present invention finally obtains the bottom layer paving path. Among them, the bottom layer paving path can be applied to the gapless paving of the wind turbine blade near the tip region of a 5KW wind turbine with as the paving angle of the fiber-reinforced composite material and w as the width of the fiber-reinforced composite material cloth, as shown in Figure 5 .

[0042] On the other hand, as a fiber-reinforced composite material automatic paving surface adaptive path planning method provided by the present invention, preferably, it further includes the following steps: Step 9: Offset all the spatial path points of the bottom layer paving path by a fiber-reinforced composite material cloth thickness along the normal vector of the spatial triangle where they are located to obtain the second layer paving path. By analogy, each layer of paving path is offset layer by layer.

[0043] On the basis of completing step 8, step 9 is further implemented. Specifically, offsetting all the spatial path points of the above-mentioned bottom layer paving path by a fiber-reinforced composite material cloth thickness along the normal vector of the spatial triangle where they are located can obtain the second layer paving path; on the basis of obtaining the second layer paving path, further offsetting by a fiber-reinforced composite material cloth thickness along the normal vector of the spatial triangle where it is located can obtain the third layer paving path, and so on to offset each layer of paving path. The visualization trajectory of each layer of paving path can be referred to as Figure 6 shown; among them, the 45° trajectory is the bottom layer paving path, and the 90° trajectory is the paving path of the second layer and other layers.

[0044] So far, a fiber-reinforced composite material automatic paving surface adaptive path planning method provided by the present invention generates a variable-angle initial path through the unit direction vector calculated by the paving angle; then, according to the cloth width, a planar path covering the entire projection area range is obtained; then, in combination with the cloth thickness, the bottom layer paving path and each layer of paving path are obtained; thus, the adaptive path planning process for the fiber-reinforced composite material automatic paving surface is realized.

[0045] The present invention provides an automatic paving surface adaptive path planning method for fiber reinforced composites. The surface adaptive path planning method includes the following steps: determining a three-dimensional model of a target structure to obtain a spatial triangular mesh corresponding to the surface of the area to be paved; reconstructing the mesh topology relationship of the spatial triangular mesh to obtain mesh topology data; projecting the spatial triangular mesh to determine the range of its projection area; establishing a mapping relationship between the planar triangular mesh and the spatial triangular mesh; determining the initial point of the initial path, constructing the linear parameter equation of the line where the initial path is located, and obtaining the initial path in the plane; generating multiple planar paths within the projection area range; sorting the multiple planar paths in the positive direction of the X-axis or Z-axis; performing a spatial path point conversion on the paving path points of the multiple planar paths to obtain the bottom layer paving path.

[0046] The automatic paving surface adaptive path planning method for fiber reinforced composites with the above step features, compared with the prior art, at least has the following technical advantages: (1) The automatic paving surface adaptive path planning method for fiber reinforced composites provided by the present invention realizes precise control of the direction vector and path spacing of the ply path by integrating parameters such as the width and paving angle of the fiber reinforced composites, and ensures the coordinated cooperation of the paving angle and path width. (2) The automatic paving surface adaptive path planning method for fiber reinforced composites provided by the present invention realizes the offset processing of the bottom layer path by combining the ply thickness parameter of the fiber reinforced composites, and further realizes the gapless and continuous surface adaptive multi-layer path intelligent planning for complex geometric structure features, significantly reducing the waste of fiber reinforced composites and manual intervention, and providing a new solution for the automatic paving of fiber reinforced composites.

[0047] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claimed rights.

Claims

1. An automated paving curved surface adaptive path planning method for fiber-reinforced composite materials, characterized in that It includes the following steps: Step 1: Determine the three-dimensional model of the target structure; extract the curved surface of the area to be paved, perform closed meshing on it to obtain the spatial triangular mesh corresponding to the curved surface of the area to be paved; Step 2: Reconstruct the mesh topological relationship of the spatial triangular mesh to obtain mesh topological data; Step 3: Project the spatial triangular mesh to determine the range of its projection area; Step 4: Establish the mapping relationship between the planar triangular mesh and the spatial triangular mesh; Step 5: Determine the initial point of the initial path; According to the paving angle of the fiber-reinforced composite material, construct the linear parameter equation where the initial path lies; Based on the boundary of the projection area range, sequentially generate initial path points on the line at a set step length within the boundary to obtain the initial path in the plane; Step 6: Perform equidistant offset on the initial path to obtain paving path points covering the entire projection area range, thereby generating multiple planar paths in the projection area range; Step 7: Based on the paving angle of the fiber-reinforced composite material, sort the multiple planar paths obtained in Step 6 in the positive direction of the X-axis or Z-axis; Step 8: Convert the paving path points of the multiple planar paths into spatial path points to obtain the bottom layer paving path.

2. The automatic paving curved surface adaptive path planning method for a fiber-reinforced composite material according to claim 1, wherein It also includes the following steps: Step 9: Offset all the spatial path points of the bottom layer paving path along the normal vector of the spatial triangle where they are located by the thickness of the fiber-reinforced composite material cloth to obtain the second layer paving path; And so on, layer by layer offset to obtain the paving paths of each layer.

3. The automatic paving curved surface adaptive path planning method for a fiber reinforced composite material according to claim 1, wherein, The specific steps of Step 5 include the following steps: Step 5.1: Select the point at the minimum Z-axis coordinate that is half the width w / 2 of the fiber-reinforced composite fabric away from the boundary of the projection area range as the initial point A(x a , z a ); Determine the unit direction vector from the paving angle , and construct the linear parametric equation of the initial path, satisfying: Formula (1); In the formula (1), k is the parameter to be determined, is the paving angle of the fiber reinforced composite material; Step 5.2: Based on the grid topology data, extract all vertex coordinates P on the boundary of the two-dimensional planar region n (x n , z n ); Connect all the vertices into line segments in sequence, satisfying: Formula (2); In formula (2) thereof, t is the parameter to be solved and t ∈ [0, 1]; Combine formula (1) and formula (2) to calculate and obtain the parameter t1; If \(t_1\in[0,1]\), there is an intersection point \(P\) between the line where the initial path is constructed by Equation (1) and the line segment of Equation (2). I (x i ,z i ), satisfying: Formula (3); Step 5.3: Sort the obtained intersection points according to the direction vector N1; at the set step size , successively generate initial path points on the straight line between the minimum intersection point and the maximum intersection point; Arrange the above initial path points in order to obtain the initial path in the plane.

4. The automatic paving surface adaptive path planning method for a fiber reinforced composite material according to claim 1, characterized in that, The specific steps of Step 8 include the following steps: Step 8.1: Query the three vertices A(x p , z p ), B(x a , z a ), and C(x b , z b ) of the planar triangular mesh ABC where the paving path point P(x c , z c ) is located; According to the vector cross product method, calculate the areas of the triangles in the planar triangular mesh, respectively satisfying: Formula (4); Formula (5); Formula (6); Formula (7); Among them, the barycentric coordinates W(u, v, w) of the paving path point P(x p , z p ) in the plane triangular mesh ABC satisfy: Formula (8); Step 8.2: Query the spatial triangular mesh corresponding to the planar triangular mesh ABC; among them, the three vertex coordinates of the spatial triangular mesh are A K (x ak , y ak , z ak ), B K (a bk , y bk , z bk ), C K (z ck , y ck , z ck ); Spatial path point P interpolated according to the barycentric coordinates W(u, v, w) K (x pk , y pk , z pk ); where the spatial path point P K , satisfies: Formula (9).

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