3D printing path planning method and system

Abstract

The invention provides a 3D printing path planning method and system, and belongs to the field of 3D printing. The method comprises the following steps: performing multi-scale geometric feature extraction on a to-be-printed three-dimensional model to obtain a layered feature mapping set; performing adaptive voxelization decomposition on the to-be-printed three-dimensional model based on the hierarchical feature mapping set to obtain a non-uniform voxel grid structure; performing direction field calculation on the non-uniform voxel grid structure to obtain a printing direction tensor field; performing spiral track generation on the non-uniform voxel grid structure based on the printing direction tensor field to obtain a continuous spiral printing path; and controlling a preset printing nozzle to perform material deposition printing based on the continuous spiral printing path. According to the method, the technical problems of uneven filling, excessive supporting structures and surface precision reduction easily occurring in an existing method are effectively solved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of 3D printing, and particularly relates to a 3D printing path planning method and system. BACKGROUND

[0002] The statements in this section merely provide background information related to the present application and do not necessarily constitute the prior art.

[0003] Under the background of rapid development of 3D printing technology, path planning as a key link affecting printing quality and efficiency is attracting more and more researchers' attention. Traditional path planning methods are usually based on uniform slicing and fixed scanning strategy, which is difficult to adapt to the printing needs of complex geometric structure models. Especially when dealing with models with multi-scale features, high curvature or overhanging structures, existing methods are prone to uneven filling, excessive support structure and surface precision decline, which limits the application expansion of 3D printing in high-precision manufacturing field.

[0004] In recent years, although some researches have tried to introduce adaptive voxelization and direction field optimization to improve the intelligence and continuity of the printing path, most of the methods still rely on experience setting parameters, and lack the ability of deep perception of model geometric features. In addition, when dealing with non-uniform material distribution or multi-nozzle collaborative printing scene, the existing algorithms often ignore the collaborative optimization between local details and overall structure, resulting in defects such as stress concentration and insufficient interlayer bonding force in the printing process. Therefore, how to realize efficient and high-quality printing path planning for complex three-dimensional models is still a key challenge in current research. SUMMARY

[0005] In order to overcome the above technical problems of the prior art, the present application provides a 3D printing path planning method and system, which extracts multi-scale geometric features from a three-dimensional model to be printed to obtain a hierarchical feature mapping set, and then performs adaptive voxelization decomposition based on the hierarchical feature mapping set to obtain a non-uniform voxel grid structure. Then, the direction field is calculated to obtain a printing direction tensor field, and then a continuous spiral printing path is generated, and finally the nozzle is controlled to print, thereby solving the technical problems of uneven filling, excessive support structure and surface precision decline in the prior art.

[0006] To achieve the above object, one or more embodiments of the present application provide the following technical solutions: The first aspect of the present application provides a 3D printing path planning method; The 3D printing path planning method comprises: extracting multi-scale geometric features from a three-dimensional model to be printed to obtain a hierarchical feature mapping set; performing adaptive voxelization decomposition on the three-dimensional model to be printed based on the hierarchical feature mapping set to obtain a non-uniform voxel grid structure; perform direction field calculation on the non-uniform voxel grid structure to obtain a printing direction tensor field; perform spiral trajectory generation on the non-uniform voxel grid structure based on the printing direction tensor field to obtain a continuous spiral printing path; control a preset printing nozzle to perform material deposition printing based on the continuous spiral printing path.

[0007] As a further technical solution, the multi-scale geometric feature extraction on the to-be-printed three-dimensional model to obtain a hierarchical feature mapping set comprises: perform shape tensor decomposition on the to-be-printed three-dimensional model to obtain a feature component field, and perform spectral analysis on the feature component field to obtain a multi-scale representation spectrum; perform hierarchical mapping on the multi-scale representation spectrum through manifold embedding to obtain a feature hierarchical graph, and perform connectivity calculation based on the feature hierarchical graph to obtain an inter-layer connection matrix; perform structural feature analysis on the inter-layer connection matrix to obtain the hierarchical feature mapping set.

[0008] As a further technical solution, the adaptive voxelization decomposition on the to-be-printed three-dimensional model based on the hierarchical feature mapping set to obtain a non-uniform voxel grid structure comprises: perform geometric density calculation on the hierarchical feature mapping set to obtain a feature density distribution field, and perform gradient tensor analysis on the feature density distribution field to obtain a voxel scale mapping matrix; perform spatial subdivision on the voxel scale mapping matrix through an octree partitioning method to obtain a multi-level voxel hierarchical tree, and perform boundary refinement processing based on the multi-level voxel hierarchical tree to obtain an adaptive grid topology structure; perform anisotropy analysis on the adaptive grid topology structure to obtain a deformation feature tensor field, and perform grid deformation calculation based on the deformation feature tensor field to obtain a deformed grid element set; perform voxel reconstruction on the to-be-printed three-dimensional model based on the deformed grid element set to obtain the non-uniform voxel grid structure.

[0009] As a further technical solution, the spatial subdivision on the voxel scale mapping matrix through the octree partitioning method to obtain a multi-level voxel hierarchical tree comprises: perform eigenvalue decomposition on the voxel scale mapping matrix to obtain a feature vector group, and perform coordinate axis alignment on the feature vector group to obtain a principal direction component set; perform hierarchical division on the principal direction component set through spatial bisection to obtain a recursive subspace set, and perform boundary node extraction based on the recursive subspace set to obtain a hierarchical boundary table; Perform geometric feature detection on the hierarchical boundary table to obtain a splitting criterion field, and generate a sub-tree from the splitting criterion field by an octree partitioning method to obtain an octree node group; Construct a tree structure based on the octree node group to obtain a multi-level voxel hierarchical tree.

[0010] As a further technical solution, the direction field calculation on the non-uniform voxel grid structure to obtain a printing direction tensor field includes: Perform stress field analysis on the non-uniform voxel grid structure to obtain a voxel element stress distribution, and perform characteristic decomposition on the voxel element stress distribution to obtain a principal stress direction field; Perform curvature mapping on the principal stress direction field by differential geometry calculation to obtain a curvature tensor field, and perform anisotropy measurement based on the curvature tensor field to obtain a shape feature coefficient table; Perform tensor interpolation operation on the shape feature coefficient table to obtain a continuous direction field, and perform singular point detection based on the continuous direction field to obtain a local singular region set; Perform rotation field calculation on the local singular region set by vector field decomposition to obtain a harmonization direction field, and perform smoothness constraint based on the harmonization direction field to obtain a smoothing tensor field; Perform direction field optimization on the non-uniform voxel grid structure based on the smoothing tensor field to obtain a printing direction tensor field.

[0011] As a further technical solution, the spiral trajectory generation on the non-uniform voxel grid structure based on the printing direction tensor field to obtain a continuous spiral printing path includes: Perform isosurface analysis on the printing direction tensor field to obtain an interlayer equidistant surface sequence, and perform spiral angle mapping on the interlayer equidistant surface sequence to obtain a reference spiral direction field; Perform geometric unfolding on the reference spiral direction field to obtain a planar spiral layout diagram, and perform path density regulation based on the planar spiral layout diagram to obtain a variable-density spiral network; Perform topological connection analysis on the variable-density spiral network to obtain a path connectivity map, and perform transition bridging design based on the path connectivity map to obtain a transition region path set; Perform curvature continuity processing on the transition region path set by geometric optimization to obtain a smoothing transition curve group, and perform path reconstruction based on the smoothing transition curve group to obtain an initial spiral trajectory; Perform path constraint verification on the non-uniform voxel grid structure based on the initial spiral trajectory to obtain a continuous spiral printing path.

[0012] As a further technical solution, the reference spiral direction field is geometrically unfolded to obtain a planar spiral layout diagram, comprising: The reference spiral direction field is subjected to manifold degeneration calculation to obtain a degenerate surface sequence, and the degenerate surface sequence is subjected to topological compression to obtain a simplified topological structure; The simplified topological structure is subjected to geometric flattening through discrete differentiation to obtain an initial planar mapping, and boundary constraint processing is performed based on the initial planar mapping to obtain a constrained planar domain; The constrained planar domain is subjected to equidistant grid division to obtain a regular grid cell set, and spiral interpolation calculation is performed based on the regular grid cell set to obtain a spiral path network; Topological reconnection is performed based on the spiral path network to obtain a planar spiral layout diagram.

[0013] The second aspect of the present application provides a 3D printing path planning system.

[0014] A 3D printing path planning system, comprising: A feature extraction module configured to perform multi-scale geometric feature extraction on a three-dimensional model to be printed to obtain a set of hierarchical feature mappings; A decomposition module configured to perform adaptive voxelization decomposition on the three-dimensional model to be printed based on the set of hierarchical feature mappings to obtain a non-uniform voxel grid structure; A direction field calculation module configured to perform direction field calculation on the non-uniform voxel grid structure to obtain a printing direction tensor field; A printing path generation module configured to generate spiral trajectories based on the printing direction tensor field for the non-uniform voxel grid structure to obtain a continuous spiral printing path; A printing module configured to control a pre-set printing nozzle to perform material deposition printing based on the continuous spiral printing path.

[0015] The third aspect of the present application provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps of a 3D printing path planning method according to the first aspect of the present application.

[0016] The fourth aspect of the present application provides an electronic device comprising a memory, a processor, and a program stored on the memory and executable on the processor, wherein the processor implements the steps of a 3D printing path planning method according to the first aspect of the present application when executing the program.

[0017] The above one or more technical solutions have the following beneficial effects: (1) The present application effectively overcomes the defects of uneven filling, excessive support structure and surface precision reduction in the prior art method by multi-scale geometric feature extraction and adaptive voxelization decomposition, combined with continuous spiral path generation, greatly improving the forming quality of the printed part.

[0018] (2) Multi-scale feature extraction can capture geometric information from macroscopic contour to microscopic detail, and adaptive voxelization can dynamically adjust the voxel scale according to the feature density, while ensuring the printing precision of complex structures (such as high curvature and thin areas), reducing the calculation redundancy of non-critical areas, and balancing precision and efficiency. By calculating the direction field to fuse the stress field and curvature analysis, the generated printing direction tensor field can guide the material to deposit along the optimal direction, reduce the accumulation of internal stress, reduce the risk of deformation and cracking, and enhance the structural strength and stability of the printed part.

[0019] (3) The spiral trajectory is generated by a non-uniform voxel grid structure, and the continuous spiral trajectory is designed by topological connection and fair transition to eliminate path interruption and corner accumulation, strengthen the interlayer bonding force, improve the material utilization rate, and reduce the support structure requirement, which is suitable for efficient manufacturing of complex high-precision components in the fields of aerospace, biomedicine and other fields.

[0020] Advantages of additional aspects of the present application will be given in part in the following description, some will become apparent from the following description, or will be learned by practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0021] The accompanying drawings, which form a part of the specification, are included to provide a further understanding of the application and are incorporated herein by reference. The illustrations are shown for the purpose of explaining the present application, and are not intended to limit the present application.

[0022] Figure 1 The method flowchart of the first embodiment.

[0023] Figure 2 The system structure diagram of the second embodiment. DETAILED DESCRIPTION

[0024] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise indicated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present application belongs.

[0025] It should be noted that the terms used herein are for the purpose of describing the specific embodiments and are not intended to limit the exemplary embodiments according to the present application.

[0026] The embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0027] Embodiment one This embodiment discloses a 3D printing path planning method; like Figure 1 As shown, a 3D printing path planning method includes: Step S1: Perform multi-scale geometric feature extraction on the 3D model to be printed to obtain a hierarchical feature mapping set; Step S2: Based on the hierarchical feature mapping set, perform adaptive voxelization decomposition on the 3D model to be printed to obtain a non-uniform voxel mesh structure. Step S3: Perform orientation field calculation on the non-uniform voxel mesh structure to obtain the printing orientation tensor field; Step S4: Generate a spiral trajectory for the non-uniform voxel mesh structure based on the printing direction tensor field to obtain a continuous spiral printing path; Step S5: Based on the continuous spiral printing path, control the preset printing nozzle to perform material deposition printing.

[0028] Specifically, the above steps also include the following: Step S1: Perform multi-scale geometric feature extraction on the 3D model to be printed to obtain a hierarchical feature mapping set.

[0029] Through multi-level geometric analysis, the geometric information of the 3D model at different scales is systematically captured and expressed, providing a structured feature foundation for subsequent path planning. First, the original 3D model is preprocessed in the form of digital geometry, including surface normal vector calculation, local curvature estimation, and boundary identification. Then, multi-scale analysis algorithms (such as wavelet transform, Gaussian filtering, or Laplacian smoothing) are used to extract features from the model surface at different resolutions, ensuring effective modeling from the overall macroscopic shape to microscopic local details. Based on this, the extracted geometric features are further organized according to scale hierarchy, forming a hierarchical feature mapping set, i.e., a layered feature mapping set.

[0030] Specifically, including: Step S11: Perform shape tensor decomposition on the three-dimensional model to be printed to obtain the feature component field, and perform spectral analysis on the feature component field to obtain the multi-scale characterization spectrum. When performing shape tensor decomposition on the 3D model to be printed, the model surface or volume data is represented as a higher-order tensor form and subjected to spectral decomposition to extract multiple physically meaningful feature components, forming a feature component field. These components typically correspond to the local geometric properties of the model in different directions, such as the principal direction of curvature and boundary strength.

[0031] Specifically, an outer surface of a model to be printed is abstracted as a smooth parametric surface, a first fundamental form and a second fundamental form of the surface are calculated by means of differential geometry tools, a shape operator of a shape tensor of the surface is calculated based on the first fundamental form and the second fundamental form, and the shape operator is as shown in the following formula:

[0032] wherein, is a shape operator; is a first fundamental form; is a second fundamental form.

[0033] By performing spectral decomposition on the shape operator, principal curvatures and principal directions are obtained;

[0034] wherein, is an orthogonal matrix, each column of which is an eigenvector, i.e., a principal curvature direction; is two eigenvalues of the shape operator, i.e., principal curvatures.

[0035] The spectral decomposition result is backfilled into three dimensions to obtain a direction-intensity pair, and a surface feature component field is defined by the direction-intensity pair, as shown in the following formula:

[0036] wherein, is a surface feature component field; is a direction-intensity pair; is a unit normal vector of a surface at p.

[0037] For a volumetric model, a shape tensor is constructed by voxel gradient information, a three-dimensional gradient field is calculated by using voxel data of the volumetric model, a structure tensor is used to describe a local direction distribution feature of a voxel, and a volumetric feature component field is obtained by performing spectral decomposition on the volumetric shape tensor, as shown in the following formula:

[0038] wherein, is a structure tensor; is a Gaussian kernel; is a convolution operation; is a gradient of a volumetric field; is an outer product of a gradient vector. By performing eigen decomposition on an anisotropic dominant direction can be robustly estimated, and a volumetric feature component field is defined based on the anisotropic dominant direction.

[0039] In step S12, the multi-scale representation spectrum is hierarchically mapped by manifold embedding to obtain a feature hierarchical graph, and connectivity calculation is performed based on the feature hierarchical graph to obtain an inter-layer connection matrix. ​By performing pedigree analysis on the feature component field, including continuous scale space solving, wavelet or bandpass energy decomposition and tensor pedigree calculation to extract its energy distribution at different frequencies or scales, a multi-scale characterization spectrum is formed, so that the geometric information of the model can be uniformly described at the macro and micro levels.

[0040] Next, the multi-scale characterization spectrum is hierarchically mapped using a manifold embedding method, embedded into a low-dimensional manifold space, and a feature hierarchical graph is constructed according to the mapping results, thereby realizing hierarchical abstract expression of the original geometric information. On this basis, further connectivity calculation is performed on the feature hierarchical graph to identify the topological association relationship between layers, generating an inter-layer connection matrix to depict the transmission path and dependency relationship between features at different scales.

[0041] Specifically, the manifold embedding method includes taking the sampling points on the model as nodes, and taking the description sub of each point as its local multi-scale spectrum segment:

[0042] wherein, is the multi-scale feature vector of the mth sampling point, containing the feature spectrum value of the point at different scales ; is the spectral operator or feature extraction function at scale ; is the spatial coordinates of the mth sampling point (node) on the model; is the number of scales, that is, how many different scales are taken to represent the point.

[0043] The weight matrix and the degree matrix are obtained by constructing the affinity graph:

[0044]

[0045] wherein, is the weight matrix element, representing the similarity between node m and node n; is the scale parameter (kernel width), controlling the decay rate of the similarity function; represents the norm of the matrix; is the K-nearest neighbor, indicating that connections are established only between the K nearest points; is the degree matrix; is the degree of node m, that is, the sum of the similarity with other points.

[0046] Based on the weight matrix and the degree matrix, the normalized Laplacian is obtained, and the embedding coordinates of the smallest non-trivial features after normalization are taken:

[0047]

[0048] wherein, is a normalized symmetric Laplacian matrix; is a weight matrix; is the d-th eigenvector of at node m; is the embedding coordinate of node m in the low-dimensional manifold space, which is spliced by the components of several eigenvectors.

[0049] Finally, through hierarchical clustering on , a cluster with similar scales and geometries is obtained, a feature hierarchical graph is formed, and an inter-layer connection matrix is obtained by counting the cross-cluster adjacency between layers, as follows:

[0050] wherein, is an element of the inter-layer connection matrix, representing the average connection strength between layer and layer . is the node set of the d-th layer (or cluster); is the node set of the d-th layer (or cluster); is a node pair, indicating whether there is a connection relationship between the m-th node and the n-th node. Step S13, performing structural feature analysis on the inter-layer connection matrix to obtain a hierarchical feature mapping set.

[0051] Based on the inter-layer connection matrix, structural feature analysis is carried out to extract key structural features and their interaction patterns in each layer, and finally integrated into a hierarchical feature mapping set with clear structure and explicit semantics.

[0052] For example, when printing a biological scaffold model containing complex curved surfaces and fine branch structures, this method can extract the overall contour direction under large scale, the main support structure trend under medium scale, and the fine pore edge features under small scale, respectively, so as to ensure that the subsequent path planning can maintain the overall structural stability and also meet the local precision requirements, and finally realize a high-quality, continuous and adaptive 3D printing process.

[0053] Step S2, based on the hierarchical feature mapping set, performing adaptive voxelization decomposition on the three-dimensional model to be printed to obtain a non-uniform voxel grid structure.

[0054] Step S2, based on the hierarchical feature mapping set, performing adaptive voxelization decomposition on the three-dimensional model to be printed to obtain a non-uniform voxel grid structure.

[0055] ​Specifically, the density and distribution of voxel division are guided by using the multi-scale geometric information extracted in step S1, so as to realize the non-uniform discretization modeling of the internal space of the three-dimensional model. In the obtained layered feature mapping set, the geometric features of different levels correspond to the structural importance of the model at different scales, such as curvature change, boundary continuity and local complexity, etc. These information are used to dynamically adjust the size and distribution density of the voxel. For the obtained non-uniform voxel grid structure, in the area with rich geometric features and complex details (such as high curvature area or small branch), the voxel is divided into smaller and denser units to ensure the fidelity of the local structure; while in the area with flat geometric features and stable structure, larger and sparse voxel units are used to reduce the calculation redundancy and improve the processing efficiency. The finally formed non-uniform voxel grid structure can not only more accurately reflect the spatial topological relationship of the original model, but also provide a more adaptive data basis for subsequent direction field calculation and trajectory generation.

[0056] Specifically, comprising: Step S21, performing geometric density calculation on the layered feature mapping set to obtain a feature density distribution field, and performing gradient tensor analysis on the feature density distribution field to obtain a voxel scale mapping matrix, as follows.

[0057]

[0058] Wherein, is a gradient tensor; is a feature density field at a three-dimensional space position x; is a gradient vector of the density field, used to describe the change of the density distribution in each direction; is a local direction distribution tensor; is a Gaussian kernel with a scale parameter is used to convolve and smooth the tensor field to enhance robustness.

[0059] Using the existing geometric information (such as curvature, boundary strength, structural continuity, etc.) in the layered feature mapping set, the geometric density at each position is weighted and calculated to form a feature density distribution field, which reflects the distribution of different regions in terms of geometric importance, for example, the density value is usually high at the edge of the pore or the thin-walled structure. On this basis, gradient tensor analysis is performed on the feature density distribution field, that is, by calculating the gradient direction and amplitude, the direction with the most severe geometric change is identified, and the basis for dynamic adjustment of the voxel scale is provided. The voxel scale mapping matrix obtained in this way can be used as the basic data for subsequent space division.

[0060] In step S22, the voxel scale mapping matrix is spatially divided by an octree partitioning method to obtain a multi-level voxel hierarchical tree, and boundary refinement processing is performed based on the multi-level voxel hierarchical tree to obtain an adaptive grid topology structure. Specifically, the following steps are included. In step S221, eigenvalue decomposition is performed on the voxel scale mapping matrix to obtain a set of eigenvectors, and the set of eigenvectors is aligned with the coordinate axes to obtain a set of principal direction components, as follows.

[0061]

[0062] wherein, is the voxel scale mapping matrix; is an eigenvalue of the matrix, representing the intensity in three principal directions respectively; is a set of eigenvectors, each corresponds to a principal direction; by aligning Q with the global coordinate system, a set of principal direction components can be obtained, which provides a basis for subsequent direction guidance of the printing path.

[0063] By performing eigenvalue decomposition on the voxel scale mapping matrix, the spatial direction information contained therein is extracted; the voxel scale mapping matrix is essentially a field function describing the required voxel scale at each position in the model space. By performing eigenvalue decomposition on the matrix, a set of eigenvectors representing the principal direction of the local space can be obtained. These eigenvectors reflect the main direction of the geometric change of the current region, such as the surface normal direction or the boundary trend. Subsequently, the set of eigenvectors obtained is aligned with the coordinate axes to keep it consistent with the standard Cartesian coordinate system, thereby obtaining a set of principal direction components, which provides a direction reference for subsequent spatial division.

[0064] In step S222, the set of principal direction components is hierarchically divided by spatial bisection to obtain a set of recursive subspaces, and boundary nodes are extracted based on the set of recursive subspaces to obtain a hierarchical boundary table, as follows:

[0065] wherein, is the set of spatial divisions obtained after bisection; is a three-dimensional space along the direction bisection operation is performed; is an eigenvector in the set of principal direction components; the formula represents the bisection operation along the direction The three-dimensional space is divided into two subspaces by bisection operation, and the bisection operation is applied recursively to obtain a set of recursive subspaces. Nodes are extracted on the boundaries of the divided subspaces, i.e., a hierarchical boundary table is obtained, which is used for subsequent path generation and structure constraint.

[0066] The space is divided into several subspaces step by step by using a recursive method based on the set of principal direction components, forming a recursive subspace set. This division method is similar to the traditional KD-Tree structure, but further considers the influence of the local geometric dominant direction, so that the division result is more in line with the actual geometric distribution characteristics of the model. Meanwhile, the boundary nodes of each subspace are extracted during each division process to generate a hierarchical boundary table, which is used to record the boundary point set formed after each division, so as to be used for subsequent boundary refinement and split judgment.

[0067] In step S223, geometric feature detection is performed on the hierarchical boundary table to obtain a split criterion field, and an octree node group is obtained by performing a sub-tree generation on the split criterion field by using an octree division method, as follows:

[0068] wherein, represents a geometric feature function at the boundary node x, which can be curvature, normal change rate or density gradient, etc. is a split threshold; 1 (•) is an indicator function, which takes 1 when the condition is met, and 0 otherwise; constitutes a split criterion field, which marks which boundary region needs to be further subdivided.

[0069] After the space division and boundary information extraction are completed, further geometric feature detection is performed on the hierarchical boundary table to identify geometric mutation points, high curvature regions or weakly connected structures in each boundary region, and a split criterion field is constructed based on the same. The split criterion field is essentially a kind of spatial weight field, which is used to guide whether a region needs to be further subdivided in the octree division process. The gradient modulus, curvature extremum or local density change rate are usually used as the split criterion to ensure that higher precision division details are retained in geometrically complex regions; and in smooth regions, the division level is appropriately simplified, thereby achieving adaptive control. Subsequently, based on the split criterion field, an octree division method is applied to perform a sub-tree generation operation, that is, each spatial unit that does not meet the termination condition is further subdivided into eight sub-cubes, and an octree node corresponding to each sub-cube is established. These nodes not only record their own spatial range, but also carry the geometric feature information (such as split depth, principal direction, boundary attribute, etc.) related thereto, and finally form an octree node group composed of multiple octree nodes.

[0070] In step S224, a tree structure is constructed based on the octree node group to obtain a multi-level voxel hierarchical tree, as follows:

[0071] wherein, for the final constructed multi-level voxel hierarchy tree; for representing a node in the tree, comprising: for the octree cell (spatial center and scale information) corresponding to the node, and for a set of its child nodes (generated by octree partitioning); by recursively organizing all octree node groups, a tree hierarchy from coarse to fine is obtained; the hierarchical tree provides multi-level voxel indexing and local geometric constraints for subsequent path planning.

[0072] Based on the octree node group, a tree structure is constructed, and all nodes are organized into a complete multi-level voxel hierarchy tree according to the parent-child relationship. The tree structure not only clearly expresses the scale change rule of the model from the whole to the local, but also provides efficient data access interface and spatial index support for subsequent boundary refinement, mesh deformation and path planning. At the same time, through the guidance of the main direction alignment and the splitting criterion, the voxel division direction is consistent with the main stress direction of the scaffold structure, avoiding the distortion problem caused by the misalignment of the division direction, thereby significantly improving the accuracy and stability of the printing path on the premise of ensuring the modeling efficiency.

[0073] Step S23, anisotropy analysis is performed on the adaptive mesh topology structure to obtain a deformation characteristic tensor field, and mesh deformation calculation is performed based on the deformation characteristic tensor field to obtain a set of deformed mesh cells.

[0074] Anisotropy analysis is performed on the adaptive mesh topology structure to identify the deformation trend of each voxel cell in different directions, and a deformation characteristic tensor field is constructed accordingly; the tensor field describes the stretching or compression direction that each voxel cell may occur during the stress or material deposition process, which helps to reasonably adjust the voxel shape during subsequent mesh deformation calculation, so that it better fits the actual geometric shape. Then, based on the deformation characteristic tensor field, mesh deformation calculation is carried out, and an elastic mechanics model or a finite element analysis method is used to apply corresponding deformation constraints to each voxel cell, and finally a set of optimized deformed mesh cells is generated, so that each voxel not only adapts to the local geometric features in size, but also matches the original model in shape.

[0075] Step S24, based on the set of deformed mesh cells, voxel reconstruction is performed on the three-dimensional model to be printed to obtain a non-uniform voxel mesh structure.

[0076] Based on the deformed mesh cells, voxel reconstruction is performed on the original three-dimensional model, that is, the model surface or volume information is projected onto these deformed meshes to form a complete non-uniform voxel mesh structure. This structure not only retains the key geometric features of the model, but also provides a high-quality spatial discrete basis for subsequent direction field calculation and spiral trajectory generation.

[0077] Through the boundary refinement and mesh deformation calculation, the geometric distortion problem caused by voxel misplacement or shape mismatch can be effectively avoided, ensuring the accurate fitting of the printing path on the microstructure and the continuous and smooth flow on the macrostructure, thereby significantly improving the quality and functionality of the final formed part.

[0078] Step S3, direction field calculation is performed on the non-uniform voxel grid structure to obtain a printing direction tensor field.

[0079] Specifically, based on the constructed non-uniform voxel grid, combined with the local geometric features of the model and the printing process constraints, a tensor with direction information is calculated on each voxel unit to describe the optimal printing material deposition direction of the region. Specifically, it includes: Step S31, stress field analysis is performed on the non-uniform voxel grid structure to obtain the stress distribution of the voxel unit, and the stress distribution of the voxel unit is decomposed to obtain the principal stress direction field.

[0080] Based on the non-uniform voxel grid structure, stress field analysis is carried out, which usually uses finite element simulation or elastic mechanics model to map the internal stress distribution that may be generated during material deposition to each voxel unit, thereby obtaining the stress distribution of the voxel unit; then the stress distribution is decomposed (such as principal component analysis or tensor diagonalization), and the main stress direction of each voxel unit is extracted, i.e. the principal stress direction field, which reflects the natural flow trend and stress dominant direction of the material at this position during deposition, providing a physical basis for subsequent direction field construction.

[0081] Step S32, curvature mapping is performed on the principal stress direction field through differential geometry calculation to obtain a curvature tensor field, and anisotropy measurement is performed based on the curvature tensor field to obtain a shape feature coefficient table.

[0082] The curvature mapping process is performed on the principal stress direction field using the surface differential operator in differential geometry, and the curvature tensor field of the region where each voxel unit is located is calculated. This tensor field not only contains information about the local surface curvature, but also reflects the degree of change in direction.

[0083] On this basis, further combined with the anisotropy measurement method, the direction consistency of each voxel unit is quantitatively evaluated, and a shape feature coefficient table is generated. This table records the comprehensive features of each voxel in terms of direction stability and curvature intensity, which helps in the weight distribution in the subsequent direction field interpolation and optimization process.

[0084] Step S33, tensor interpolation operation is performed on the shape feature coefficient table to obtain a continuous direction field, and based on the continuous direction field, singular point detection is performed to obtain a local singular region set, as follows:

[0085] wherein, represents the continuous orientation field obtained at spatial position x; is the local tensor (orientation information) in the shape feature coefficient table; is the interpolation weight function, usually a Gaussian kernel or a distance-based weighting function, used to ensure the smoothness and continuity of the orientation field; through this tensor interpolation, a continuous orientation distribution can be constructed in the entire voxel space; in this orientation field, if there are positions with ×F(x) or ·F(x) abnormal mutations, i.e., singular points are determined; clustering these singular point regions gives a set of local singular regions, which are regions that need to be avoided or specially treated during path optimization.

[0086] The shape feature coefficient table is subjected to tensor interpolation operation, which extends the discrete orientation information distributed in each voxel to a continuous spatial orientation field, so that the orientation field remains smooth in space.

[0087] In order to ensure the topological rationality of the orientation field, singular point detection is also needed for the continuous orientation field to identify local singular regions where the orientation is mutated or cannot be defined, such as key structural parts such as pore intersections or thin-walled turning points, thereby forming a set of local singular regions.

[0088] In step S34, the set of local singular regions is subjected to rotation field calculation through vector field decomposition to obtain a coordinated orientation field, and based on the coordinated orientation field, smoothness constraint is performed to obtain a smoothing tensor field as follows:

[0089] wherein, represents the original orientation field within the set of local singular regions; is the gradient part of the orientation field, which describes the irrotational component; is the rotation part (curl field) of the orientation field, which is used to describe the rotation characteristics around the singular points; through this vector field decomposition, the rotation component can be extracted separately, thereby constructing a coordinated orientation field; on this basis, smoothness constraint is further applied to the orientation field to obtain a globally consistent and continuous smoothing tensor field; the smoothing tensor field provides smooth and singular-free orientation guidance for subsequent path generation.

[0090] In order to eliminate the direction conflict caused by these singular regions, the vector field decomposition method is used to calculate the rotation field of the local singular region set, that is, through local coordinate transformation and rotation matrix adjustment, the direction field of the adjacent region is adjusted to be consistent, so as to construct a coordinated direction field; On this basis, a smoothing constraint mechanism is also introduced, and the harmonic field optimization or minimum energy functional method is usually used to perform overall smoothing processing on the coordinated direction field, so as to ensure that the direction field not only has consistency in the local region, but also maintains continuity and integrability in the global range, and finally obtains the smoothing tensor field.

[0091] Step S35, based on the smoothing tensor field, the direction field of the non-uniform voxel grid structure is optimized to obtain a printing direction tensor field.

[0092] Based on the smoothing tensor field, the direction field of the original non-uniform voxel grid structure is optimized, that is, the optimized direction information is remapped to each voxel unit, so that it presents a more reasonable direction distribution characteristic in space, and then a printing direction tensor field for subsequent spiral trajectory generation is generated. This tensor field not only accurately reflects the direction trend of the model surface and internal structure, but also effectively avoids the problems of direction mutation and path breakage existing in traditional path planning, thereby significantly improving the continuity and fit degree of the printing path.

[0093] Step S4, based on the printing direction tensor field, the non-uniform voxel grid structure is subjected to spiral trajectory generation to obtain a continuous spiral printing path.

[0094] Using the constructed printing direction tensor field as a direction guide, combined with the spatial distribution characteristics of the non-uniform voxel grid, under the premise of ensuring the continuity and consistency of the path, an efficient and high-quality spiral printing trajectory suitable for 3D printing is generated.

[0095] In the specific implementation process, first, each voxel in the non-uniform voxel grid is taken as a basic operation unit, the material deposition trend of the region is determined according to the main direction information of the corresponding position in the printing direction tensor field, and the path is gradually extended along the direction through integral curve or streamline tracking algorithm; On this basis, a spiral topological structure is introduced, so that the path presents a smooth transition and natural rotation trend in the process of layer-by-layer accumulation, thereby avoiding the problems of path interruption, corner accumulation and layer misalignment commonly existing in traditional scanning paths. Specifically, it includes: Step S41, performing isosurface analysis on the printing direction tensor field to obtain a sequence of interlayer equidistant surfaces, and performing spiral angle mapping on the sequence of interlayer equidistant surfaces to obtain a reference spiral direction field.

[0096] Firstly, the printing direction tensor field is analyzed by isosurface analysis, and a plurality of interlayer equidistant surfaces maintaining a certain distance from the model surface are extracted to form an interlayer equidistant surface sequence; the distance between the equidistant surfaces can be set to 0.1-0.3 mm according to the printing layer thickness, so as to ensure that each layer can be accurately covered.

[0097] The interlayer equidistant surface sequence is subjected to spiral angle mapping operation, that is, the direction vector on each equidistant surface is subjected to angle transformation along the preset rotation axis (usually the Z axis of the model) to make it show a certain spiral trend, and finally a reference spiral direction field is generated; the direction field not only inherits the spatial direction characteristics of the original direction tensor field, but also introduces the geometric characteristics of spiral rising, thereby providing a direction basis for subsequent path expansion.

[0098] In step S42, the reference spiral direction field is subjected to geometric expansion to obtain a planar spiral layout graph, and path density regulation is performed based on the planar spiral layout graph to obtain a variable-density spiral network.

[0099] The reference spiral direction field is subjected to geometric expansion processing and is projected onto a two-dimensional plane to form a planar spiral layout graph; this process is similar to "flattening" a three-dimensional spiral structure into a two-dimensional curve, so that path planning can be performed in a more intuitive space.

[0100] On this basis, the planar spiral layout graph is subjected to path density regulation according to the geometric complexity and material requirements of each region to generate a variable-density spiral network; for example, the path density is automatically increased to 2-3 lines per millimeter at the edge of the pore or the thin-walled region, and reduced to 1 line per millimeter in the stable structure region, so as to realize the balance between local reinforcement and overall efficiency of material deposition.

[0101] In step S421, the reference spiral direction field is subjected to manifold degeneration calculation to obtain a degenerate surface sequence, and the degenerate surface sequence is subjected to topological compression to obtain a simplified topological structure.

[0102] The reference spiral direction field is subjected to manifold degeneration calculation, that is, the spiral direction information originally embedded in the three-dimensional curved surface space is gradually simplified to extract a degenerate surface sequence capable of representing the main characteristics of the original direction field; the degenerate surfaces are usually obtained by main direction projection and local curvature constraint from the original model surface, and the number thereof can be set to 5-15 layers according to the model complexity, so as to ensure that the geometric details are retained and the redundant calculation burden is not increased.

[0103] The degenerate surface sequence is subjected to topological compression processing, and repeated or highly similar topological units are identified and merged, so as to obtain a simplified topological structure which is more concise in structure but can reflect the overall geometric trend.

[0104] Step S422, geometrically flatten the simplified topological structure by discrete differentiation to obtain an initial planar mapping, and perform boundary constraint processing based on the initial planar mapping to obtain a constrained planar domain.

[0105] The simplified topological structure is geometrically flattened by a discrete differentiation method to be "flattened" from a three-dimensional space to a two-dimensional planar space to form an initial planar mapping; the mapping process adopts an angle-preserving transformation strategy, that is, the mapping is performed under the premise of maintaining the original angle relationship as much as possible, so as to ensure that the spiral path still has good directional consistency in the two-dimensional space. On this basis, further boundary constraint processing is performed on the initial planar mapping, and according to the contour boundary information of the original model under two-dimensional projection, an effective printing area range is delimited to form a constrained planar domain; for example, in the projection of a biological stent model, the constrained planar domain can be an elliptical region with a diameter of about 30mm-50mm, which ensures that all paths are located within the effective printing range and avoids exceeding the nozzle movement limit.

[0106] Step S423, equally divide the constrained planar domain into a regular grid cell set, and perform spiral interpolation calculation based on the regular grid cell set to obtain a spiral path network.

[0107] The constrained planar domain is equally divided into a regular grid cell set; these grid cells are usually set as square lattices with a side length of 0.5mm-1mm to balance path accuracy and calculation efficiency; each grid cell records a spiral direction vector at the corresponding position, which is used for subsequent interpolation calculation.

[0108] A spiral path network is generated by carrying out spiral interpolation calculation, that is, according to the direction information of adjacent grid cells, a bilinear interpolation or spline interpolation method is used to generate a spiral path network that penetrates the entire planar domain; the network presents a form of gradually rotating and expanding from the center, similar to an Archimedes spiral curve, and the pitch (i.e., the radial distance between adjacent turns) can be controlled between 1mm-3mm to match different scale printing requirements.

[0109] Step S424, topological reconnection based on the spiral path network to obtain a planar spiral layout map.

[0110] Local adjustment is performed on the path intersection points, breakpoints or direction mutation regions to ensure that the entire path has good connectivity and non-self-intersection characteristics in the two-dimensional plane; for example, when two paths are too close or even intersect in a certain region, a transition section is automatically inserted or the local path direction is adjusted, so that the planar spiral layout map formed finally not only has visual continuity, but also meets the physical feasibility requirements of the actual printing path.

[0111] Step S43: Perform topology connection analysis on the variable density spiral network to obtain a path connectivity graph, and design a transition bridging based on the path connectivity graph to obtain a path set for the transition region.

[0112] A topology connection analysis was performed on the variable density spiral network to identify the connection relationships between each spiral segment and to construct a path connectivity graph. This graph records the adjacency information between all path segments and is used to guide the subsequent transition and bridging design.

[0113] Step S44: Perform curvature continuity processing on the path set of the transition region through geometric optimization to obtain a smooth transition curve set, and reconstruct the path based on the smooth transition curve set to obtain the initial spiral trajectory.

[0114] Transition path sets are designed for path breakpoints or abrupt directional changes. Smooth bridging curves are inserted to achieve seamless connections between adjacent path segments. The length of these transition paths is typically controlled between 0.5mm and 2mm to avoid material buildup due to excessive length, while ensuring path continuity and stability. To improve the overall smoothness of the path, the transition path sets undergo geometric optimization, focusing on curvature continuity adjustment. This involves local fitting and interpolation of key points on the path to eliminate sharp changes at path corners, achieving a smoother transition. The continuity standard ultimately forms a set of smooth transition curves. The continuity standard refers to the fact that two curves not only coincide in position at the splicing point ( ), tangent direction is consistent ( More importantly, its curvature also remains continuously changing (the second derivative is continuous). This ensures that the curvature of the printing path at the inflection point is smoothly transitioned, fundamentally eliminating abrupt changes in curvature. As a result, the print head does not need to experience a sharp change in acceleration when passing through the point, ultimately achieving the technical effects of effectively suppressing equipment vibration, avoiding material accumulation, and significantly improving the surface finish of the printed parts.

[0115] Subsequently, the path was reconstructed based on these smooth curve groups, and all segments were reintegrated into a complete initial spiral trajectory. This trajectory presents a natural spiral ascent in space and is geometrically highly consistent with the model surface.

[0116] Step S45: Based on the initial spiral trajectory, perform path constraint verification on the non-uniform voxel mesh structure to obtain a continuous spiral printing path.

[0117] Based on the initial spiral trajectory, the non-uniform voxel mesh structure is subjected to path constraint verification to determine whether the path conflicts with or is missing from the model boundary, and whether it meets the minimum radius of curvature requirement (usually greater than or equal to 1.5 mm) for nozzle movement. If non-compliant areas are found, they are locally corrected until all path segments meet the process constraints, and finally a continuous spiral printing path is output.

[0118] Step S5: Based on the continuous spiral printing path, control the preset printing nozzle to perform material deposition printing.

[0119] The generated continuous spiral printing path is converted into actual executable motion commands, which drive the preset printing nozzle to perform high-precision, continuous material deposition operations in three-dimensional space according to the path.

[0120] In practice, the continuous spiral printing path is first input into the 3D printing control system in the form of CNC code (such as G-code). The system calculates the nozzle's motion trajectory, speed curve, and material extrusion rate in real time based on the path data, and coordinates with the lifting and lowering movements of the printing platform to ensure that each layer of material is precisely laid along the set spiral direction. Based on this, and considering the rheological properties and curing behavior of the printing material, process parameters such as nozzle temperature and extrusion pressure are dynamically adjusted to ensure the stability of material deposition and the quality of interlayer bonding. For example, when printing a biological scaffold model with complex pore structures and thin-walled features, this step ensures that the printing nozzle runs smoothly along the spiral path, avoiding material accumulation or breakage problems caused by sudden path changes or frequent start-stop cycles, thereby achieving high-precision, high-strength, and high-surface-quality integrated printing of the biological scaffold.

[0121] Example 2 This embodiment discloses a 3D printing path planning system; like Figure 2 As shown, a 3D printing path planning system includes: A 3D printing path planning system, comprising: The feature extraction module is configured to perform multi-scale geometric feature extraction on the 3D model to be printed, and obtain a hierarchical feature mapping set. The decomposition module is configured to: perform adaptive voxelization decomposition on the 3D model to be printed based on the hierarchical feature mapping set to obtain a non-uniform voxel mesh structure. The orientation field calculation module is configured to perform orientation field calculations on the non-uniform voxel mesh structure to obtain the printing orientation tensor field. The printing path generation module is configured to generate a spiral trajectory for the non-uniform voxel mesh structure based on the printing direction tensor field to obtain a continuous spiral printing path. The printing module is configured to control a preset printing nozzle to perform material deposition printing based on the continuous spiral printing path.

[0122] Embodiment three An object of the present embodiment is to provide a computer-readable storage medium.

[0123] A computer-readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the 3D printing path planning method of embodiment one.

[0124] Embodiment four An object of the present embodiment is to provide an electronic device.

[0125] An electronic device comprising a memory, a processor, and a program stored on the memory and executable on the processor, wherein the processor, when executing the program, implements the steps of the 3D printing path planning method of embodiment one.

[0126] The steps and methods of the above embodiments two, three and four correspond to those of embodiment one, and the specific embodiments can be understood with reference to the relevant description of embodiment one. The term "computer-readable storage medium" should be understood to include a single medium or multiple media of one or more instruction sets; it should also be understood to include any medium capable of storing, encoding or carrying a set of instructions for execution by a processor and causing the processor to perform any of the methods of the present application.

[0127] Those skilled in the art should understand that the above-mentioned modules or steps of the present application can be implemented by a general computer device, alternatively, they can be implemented by program codes executable by a computing device, so that they can be stored in a storage device for execution by a computing device, or they can be made into individual integrated circuit modules, or a plurality of modules or steps can be made into a single integrated circuit module. The present application is not limited to any specific combination of hardware and software.

[0128] The above describes the specific embodiments of the present application in conjunction with the accompanying drawings, but is not a limitation on the scope of protection of the present application. Those skilled in the art should understand that various modifications or variations made by those skilled in the art on the basis of the technical solutions of the present application without inventive labor are still within the scope of protection of the present application.

Claims

1. A 3D printing path planning method, characterized in that, The method comprises the following steps: multi-scale geometric feature extraction is performed on a three-dimensional model to be printed to obtain a hierarchical feature mapping set; adaptive voxelization decomposition is performed on the three-dimensional model to be printed based on the hierarchical feature mapping set to obtain a non-uniform voxel grid structure; direction field calculation is performed on the non-uniform voxel grid structure to obtain a printing direction tensor field; spiral trajectory generation is performed on the non-uniform voxel grid structure based on the printing direction tensor field to obtain a continuous spiral printing path; material deposition printing is performed on a preset printing nozzle based on the continuous spiral printing path.

2. The 3D printing path planning method of claim 1, wherein, The multi-scale geometric feature extraction on the three-dimensional model to be printed to obtain the hierarchical feature mapping set comprises the following steps: shape tensor decomposition is performed on the three-dimensional model to be printed to obtain a feature component field, and spectral analysis is performed on the feature component field to obtain a multi-scale representation spectrum; hierarchical mapping is performed on the multi-scale representation spectrum through manifold embedding to obtain a feature hierarchical graph, and connectivity calculation is performed based on the feature hierarchical graph to obtain an inter-layer connection matrix; structure feature analysis is performed on the inter-layer connection matrix to obtain the hierarchical feature mapping set.

3. The method of claim 1, wherein, The adaptive voxelization decomposition on the three-dimensional model to be printed based on the hierarchical feature mapping set to obtain the non-uniform voxel grid structure comprises the following steps: geometric density calculation is performed on the hierarchical feature mapping set to obtain a feature density distribution field, and gradient tensor analysis is performed on the feature density distribution field to obtain a voxel scale mapping matrix; space subdivision is performed on the voxel scale mapping matrix through an octree partitioning method to obtain a multi-level voxel hierarchical tree, and boundary refinement processing is performed based on the multi-level voxel hierarchical tree to obtain an adaptive grid topology structure; anisotropy analysis is performed on the adaptive grid topology structure to obtain a deformation feature tensor field, and grid deformation calculation is performed based on the deformation feature tensor field to obtain a deformed grid element set; voxel reconstruction is performed on the three-dimensional model to be printed based on the deformed grid element set to obtain the non-uniform voxel grid structure.

4. The 3D printing path planning method of claim 3, wherein, The space subdivision on the voxel scale mapping matrix through the octree partitioning method to obtain the multi-level voxel hierarchical tree comprises the following steps: eigenvalue decomposition is performed on the voxel scale mapping matrix to obtain a feature vector group, and coordinate axis alignment is performed on the feature vector group to obtain a principal direction component set; hierarchical division is performed on the principal direction component set through space bisection to obtain a recursive subspace set, and boundary node extraction is performed based on the recursive subspace set to obtain a hierarchical boundary table; geometric feature detection is performed on the hierarchical boundary table to obtain a splitting criterion field, and sub-tree generation is performed on the splitting criterion field through the octree partitioning method to obtain an octree node group; tree structure construction is performed based on the octree node group to obtain the multi-level voxel hierarchical tree.

5. The 3D printing path planning method of claim 1, wherein, The direction field calculation on the non-uniform voxel grid structure to obtain the printing direction tensor field comprises the following steps: stress field analysis is performed on the non-uniform voxel grid structure to obtain a voxel element stress distribution, and feature decomposition is performed on the voxel element stress distribution to obtain a principal stress direction field; The curvature tensor field is obtained by curvature mapping of the principal stress direction field through differential geometry calculation, and anisotropy measurement is performed based on the curvature tensor field to obtain a shape feature coefficient table; The continuous direction field is obtained by performing tensor interpolation operation on the shape feature coefficient table, and the local singular region set is obtained by performing singular point detection based on the continuous direction field; The rotation field calculation is performed on the local singular region set through vector field decomposition to obtain a harmonization direction field, and the smoothing tensor field is obtained by performing smoothness constraint based on the harmonization direction field; The direction field optimization is performed on the non-uniform voxel grid structure based on the smoothing tensor field to obtain a printing direction tensor field.

6. The 3D printing path planning method of claim 1, wherein, The spiral trajectory generation is performed on the non-uniform voxel grid structure based on the printing direction tensor field to obtain a continuous spiral printing path, including: The layer-to-layer equidistant surface sequence is obtained by performing isosurface analysis on the printing direction tensor field, and the reference spiral direction field is obtained by performing spiral angle mapping on the layer-to-layer equidistant surface sequence; The planar spiral layout diagram is obtained by performing geometric unfolding on the reference spiral direction field, and the variable-density spiral network is obtained by performing path density regulation based on the planar spiral layout diagram; The path connected graph is obtained by performing topological connection analysis on the variable-density spiral network, and the transition area path set is obtained by performing transition bridging design based on the path connected graph; The smoothing transition curve group is obtained by performing curvature continuity processing on the transition area path set through geometric optimization, and the initial spiral trajectory is obtained by performing path reconstruction based on the smoothing transition curve group; The continuous spiral printing path is obtained by performing path constraint inspection on the non-uniform voxel grid structure based on the initial spiral trajectory.

7. The 3D printing path planning method of claim 6, wherein, The planar spiral layout diagram is obtained by performing geometric unfolding on the reference spiral direction field, including: The degenerate surface sequence is obtained by performing manifold degeneration calculation on the reference spiral direction field, and the simplified topological structure is obtained by performing topological compression on the degenerate surface sequence; The initial planar mapping is obtained by performing geometric flattening on the simplified topological structure through discrete differentiation, and the constrained planar domain is obtained by performing boundary constraint processing based on the initial planar mapping; The regular grid cell group is obtained by performing equidistant grid division on the constrained planar domain, and the spiral path network is obtained by performing spiral interpolation calculation based on the regular grid cell group; The planar spiral layout diagram is obtained by performing topological reconnection based on the spiral path network.

8. A 3D printing path planning system, characterized by: It includes: The feature extraction module is configured to perform multi-scale geometric feature extraction on the to-be-printed three-dimensional model to obtain a hierarchical feature mapping set; The decomposition module is configured to perform adaptive voxelization decomposition on the to-be-printed three-dimensional model based on the hierarchical feature mapping set to obtain a non-uniform voxel grid structure; The direction field calculation module is configured to perform direction field calculation on the non-uniform voxel grid structure to obtain a printing direction tensor field; The printing path generation module is configured to perform spiral trajectory generation on the non-uniform voxel grid structure based on the printing direction tensor field to obtain a continuous spiral printing path; A printing module configured to control a pre-set printing nozzle to perform material deposition printing based on the continuous spiral printing path.

9. A computer-readable storage medium having stored thereon a program, characterized in that, The program, when executed by a processor, implements the steps of the 3D printing path planning method of any one of claims 1-7.

10. An electronic device comprising a memory, a processor, and a program stored on the memory and executable on the processor, characterized in that, The program, when executed by a processor, implements the steps of the 3D printing path planning method of any one of claims 1-7.

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