Path planning method for lattice material 3D printing

Abstract

A path planning method for lattice three-dimensional (3D) printing includes generating a 3D model; slicing the 3D model to generate a 2D contour; determining a region of the 2D contour; and generating a path. The 3D model is represented by an explicit mesh or implicit function. Slicing the 3D model to generate the 2D contour includes generating the 2D contour of the 3D model defined by an explicit or implicit function. For a 3D model defined by an explicit function, a 2D contour is generated by calculating intersections between slice layers and triangular meshes. The determination of the region comprises dividing the lattice structure or the thin-wall structure into two regions including a thin wall and a wall connection. Geometric features of the two regions are defined by the tilt angle and the plate thickness.

Description

[0001] Cross-reference to related applications

[0002] This application claims priority to U.S. Provisional Application No. 63 / 632,077, filed April 10, 2024, which is incorporated herein by reference in its entirety (including any forms, figures, or drawings). Background Technology

[0003] While 3D-printed lattice structures exhibit remarkable mechanical and thermal properties, the scalability of micron- and nanometer-scale fabrication methods remains a significant limitation. Furthermore, methods such as selective laser melting (SLM), laser powder bed melting (LPBF), and selective laser sintering (SLS) struggle to fabricate structures with feature sizes smaller than 100 μm. Currently, R67 infill paths with or without contour scanning are the most common method for fabricating lattice structures using powder bed 3D printing. However, these methods suffer from low computational efficiency, low printing resolution, and long printing times. Bridging this gap holds immense potential for exploring the wide range of applications of lattice materials in electronic and photonic devices, energy absorption and storage, and chemical catalysis. Summary of the Invention

[0004] Embodiments of the present invention relate to methods and systems for 3D printing lattice structures.

[0005] According to an embodiment of the present invention, a path planning method for three-dimensional (3D) lattice printing includes generating a 3D model; slicing to generate a 2D contour of the 3D model; determining the region of the 2D contour; and generating a path. The 3D model is represented by an explicit mesh or implicit functions. Slicing to generate the 2D contour of the 3D model includes generating the 2D contour of the 3D model defined by explicit or implicit functions. For a 3D model defined by explicit functions, the 2D contour is generated by calculating the intersections between the slice layers and the triangular mesh. For a 3D model defined by implicit functions, the 2D contour is obtained by calculating the following function: Φ(x,y,zi)=0, where zi is the z-coordinate of the i-th slice layer. Determining the region includes dividing the lattice structure or thin-wall structure into two regions, including the thin wall and wall nodes. Furthermore, the geometric features of these two regions are defined by the tilt angle and the plate thickness. For a 3D model defined by explicit functions, the tilt angle is calculated based on the 3D mesh file. For a model defined by implicit functions, the tilt angle is calculated based on the normal vector obtained by the following formula:

[0006]

[0007] Where φ ISThis is the control function for the implicit surface. The path generation involves directly obtaining a single-track path from line segments. Furthermore, the path generation includes generating path offsets at consecutive layers to suppress path overlap, thereby mitigating thermal deformation and improving surface quality. For 3D models defined by implicit functions, the path generation involves obtaining intersection points by calculating the zeros of the implicit function in a given layer and scan direction. The method may also include adaptive toolpaths or toolpath trimming, or both. Adaptive toolpaths involve adjusting the scan length and gap length for different curvature regions. Toolpath trimming involves applying Boolean operations between the defined geometry and the toolpath to obtain various external shapes of the lattice structure.

[0008] In another embodiment of the invention, a computer program product includes a non-transitory computer-executable storage device storing computer-readable program instructions that, when executed by a computer, cause the computer to perform a path planning method for three-dimensional (3D) lattice printing. The method includes: generating a 3D model; slicing to generate a 2D contour of the 3D model; determining regions of the 2D contour; and generating a path. The 3D model is represented by an explicit mesh or implicit functions. Slicing to generate the 2D contour of the 3D model includes generating the 2D contour of the 3D model defined by explicit or implicit functions. For a 3D model defined by explicit functions, the 2D contour is generated by calculating the intersections between the slice layers and the triangular mesh. For a 3D model defined by implicit functions, the 2D contour is obtained by calculating the following functions:

[0009] Φ(x,y,zi)=0

[0010] Where zi is the z-coordinate of the i-th slice layer. Determining the region involves dividing the lattice structure or thin-walled structure into two regions: one containing the thin wall and the other containing the wall nodes. These two regions are then assigned two different types of toolpaths. Attached Figure Description

[0011] Figure 1 A-1E is a schematic diagram of a toolpath planning method for crystal lattice structures, where: Figure 1 A displays a 3D model; Figure 1 B shows the outline; Figure 1 C displays the outline after the c value has been modified; Figure 1 D shows the toolpath for a single rail only; Figure 1 E illustrates a toolpath with a hybrid trajectory, according to an embodiment of the invention.

[0012] Figure 2 A-2E is a schematic diagram of path generation, where: Figure 2 A displays the parameters of the single-track path; Figure 2 B shows the path offset of the continuous layers; Figure 2C demonstrates the calculation of the zero point for the R67 path (the zero point is the point where the value of the function φ(x,y,z) is equal to zero); Figure 2 D shows the continuous trajectory; Figure 2 E shows the dashed line trajectory; according to an embodiment of the present invention.

[0013] Figure 3 A-3C is a schematic diagram of the toolpath operation, in which: Figure 3 A demonstrates adaptive toolpath generation; Figure 3 B-3C demonstrates toolpath trimming through Boolean operations between defined regions and paths; according to an embodiment of the present invention.

[0014] Figure 4 A is a schematic diagram of an explicit model represented by a triangular mesh; Figure 4 B is a schematic diagram of the implicitly defined surface visualized using the moving cube algorithm; according to an embodiment of the present invention.

[0015] Figure 5 A-5C is a toolpath diagram, in which: Figure 5 A shows the toolpath for the flower; Figure 5 B showcases a single-level D-type three-period minimum surface (TPMS); Figure 5 C illustrates a two-tiered hierarchical TPMS; according to an embodiment of the present invention.

[0016] Figure 6 A-6E is an image of the printed crystal lattice structure, in which: Figure 6 A showcases various types and unit sizes of TPMS plates for catalytic applications; Figure 6 B demonstrates a TPMS structure with arbitrary external shape and gradient; Figure 6 C displays pure copper flowers; Figure 6 D shows a small crystal lattice structure; Figure 6 E illustrates other lattices including pure copper and high-entropy alloy lattices; according to embodiments of the invention. Detailed Implementation

[0017] Embodiments of the present invention relate to a path planning method for three-dimensional (3D) printed lattice structures.

[0018] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used herein, the term “and / or” includes any and all combinations of one or more of the associated listed items. As used herein, the singular forms “a,” “an,” and “described” are intended to include the plural forms unless the context clearly indicates otherwise. It will also be further understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of the described features, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0019] Unless otherwise defined, all terms used herein (including technical and scientific terms) shall have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It will also be further understood that terms such as those defined in common dictionaries shall be interpreted as having the same meaning as they have in the relevant field and in this disclosure, and shall not be interpreted in an idealized or overly formal sense unless expressly defined herein.

[0020] When the term “about” is used in conjunction with numerical values ​​in this document, it should be understood that the value may be in the range of 90% to 110% of that value, i.e., the value may be ±10% of the stated value. For example, “about 1 kg” means 0.90 kg to 1.1 kg.

[0021] Reference Figure 1 A-1D, a hybrid toolpath planning method, seamlessly integrates single-track scanning and R67 rotary scanning methods, thereby improving print resolution without sacrificing mechanical performance.

[0022] The printed honeycomb lattice achieves ultrathin wall thicknesses in the range of 55-70 μm, while also exhibiting improved mechanical properties and better printing accuracy. Currently, no reported LPBF (laser-based powder bed fusion) technology can achieve such small feature sizes without compromising other performance aspects.

[0023] Design Methodology

[0024] According to an embodiment of the present invention, a path planning method for 3D printing lattice structures is provided. Method. The lattice structure or lattice material is fabricated in layers in a row-by-row manner using 3D printing technology. For example, 3D printing technologies using a row-by-row manner include selective laser melting (SLM), selective laser sintering (SLS), powder bed melting (PBF-EB / M or PBF-LB / M according to ISO / ASTM standards), directional energy deposition (DED according to ASTM standards), or fused deposition modeling (FDM).

[0025] The method is described below.

[0026] Step S1: Modeling

[0027] To construct 3D models represented by explicit meshes or implicit functions, 3D models can be modeled using computer-aided design (CAD) software, such as Pro / E, SolidWorks, or other suitable CAD software. Implicit surfaces can be modeled using functions.

[0028] Step S2: Slice

[0029] Models defined by explicit or implicit functions can generate 2D contours, such as... Figure 1As shown in Figure A. For models defined by explicit functions, taking an STL file as an example, the 2D polygonal contours represented can be generated by calculating the intersections between slice layers and triangular meshes. For models defined by implicit functions, the 2D contours can be obtained by calculating the following functions:

[0030] Φ(x,y,zi)=0

[0031] Where zi is the z-coordinate of the i-th slice layer.

[0032] Step S3: Area Determination

[0033] Even for surfaces with constant thickness, shape, size, and cross-sectional area, the basis for the slice plane will differ. Therefore, the type of toolpath planning must first be determined. Here, lattice structures or thin-walled structures are divided into two regions: thin-walled and wall-connected. The geometric characteristics of these regions can be described by the tilt angle and plate thickness. For models defined by explicit functions, the tilt angle can be calculated based on the 3D mesh file. For models defined by implicit functions, the tilt angle can be calculated based on the normal vector obtained from the following equation:

[0034]

[0035] Where φ IS It is the control function of the implicit surface.

[0036] Given a critical tilt angle, continuous cross-sectional regions can be divided into two types: wall-connected regions and thin-walled regions, such as... Figure 1 As shown in B.

[0037]

[0038] Taking the implicitly defined thin plate model as an example, the thin plate is defined by the function φ(x,y,z)=0, and the mid-surface of the thin plate is defined by φ IS =0 is defined. A thin plate is formed by enclosing a structure with φ. IS =c(x,y,z) and φ IS It is constructed from two surfaces defined by =-c(x,y,z).

[0039] Figure 1 B shows the outline of the thin plate model. Here, the inclination angle of the mid-surface is used as a criterion to distinguish between the wall-connected regions and the thin-walled regions. Specifically, the inclination angle of the wall-connected regions is smaller, while the inclination angle of the thin-walled regions is larger. Then, when the inclination angle is greater than a threshold, c(x,y,z) is assigned to zero, causing the thin plate to transform into a mid-surface with no thickness, as shown below. Figure 1 As shown in Figure C. Therefore, by changing the threshold, the thin-walled and connected regions can be adjusted. Furthermore, Figure 1 D-1E shows the toolpath obtained from two thresholds.

[0040] Step S4: Path Generation

[0041] In this step, the scan path is calculated from the two defined regions. A single-track path can be obtained directly from line segments. It's important to note that a high-resolution mesh is used to obtain an accurate lattice profile. Converting the profile to a path requires changing the line segment length and specifying the distance. To mitigate thermal stress and improve mechanical properties, both the line segment length (LS) and line spacing (LHD) are included in the toolpath design parameters, such as... Figure 2 As shown in A-2B. By adjusting LS and LHD, a good combination of printing time, surface quality, and mechanical properties can be achieved.

[0042] Furthermore, offsetting the paths on continuous layers to avoid path overlap reduces thermal deformation and improves surface quality, such as... Figure 2 As shown in B.

[0043] Furthermore, for models defined by implicit functions, a method for directly generating scan paths is proposed. Unlike calculating the intersection points between lines and polygons after slicing, the intersection points can be obtained by calculating the zeros of the implicit function at a given layer and scan direction (zeros are the points where the function φ(x,y,z) equals zero), such as... Figure 2 As shown in C-2E.

[0044]

[0045] Where φ(x,y,z) is the implicit function of the model, f(x,y)=0 is the function used to define the scanning direction, and z i Definition layer.

[0046] Step S5: Optional adaptive toolpath and toolpath trimming

[0047] Optional adaptive toolpaths and toolpath trimming involve two steps.

[0048] First, adaptive toolpaths are introduced to further improve the printing quality of lattice structures with large curvature variations. For example... Figure 3 As shown in Figure A, for low curvature regions, large scan lengths and large gap lengths can be used to speed up the printing process, while for high curvature regions, smaller scan paths can be used to ensure high-fidelity geometric representation.

[0049] Secondly, by performing Boolean operations between the defined geometry and the toolpath, various external shapes of the lattice structure can be realized, such as... Figure 3 As shown in B-3C. Based on this method, various lattice-filled structures, including layered structures, can be constructed.

[0050] The embodiments of the present invention have the following advantages and improvements over existing methods, equipment or materials: 1. Machine versatility

[0051] The method of this invention is generally applicable to line-by-line 3D printing methods, such as laser powder bed melting / sintering (LPBF / LPBS), selective laser melting / sintering (SLM / SLS), directional energy deposition (DED), and fused deposition modeling (FDM). Furthermore, it can be adapted to various scanning sources other than lasers, such as electron beams. By using this method, printing resolution can be maximized.

[0052] 2. Material versatility

[0053] This planning method incorporates key parameters such as scan length, gap length, and threshold angle, providing significant flexibility for diverse printing challenges with a wide range of materials, including pure copper, stainless steel, and high-entropy alloys. In addition to metallic materials, the method is also applicable to various polymeric materials, such as polylactic acid (PLA), polycarbonate (PC), or acrylonitrile-butadiene-styrene (ABS).

[0054] 3. High computational efficiency and low storage requirements

[0055] Compared to the R67 toolpath planning method, the hybrid path method significantly reduces the number of scan paths, thereby lowering computational costs and printing time. Furthermore, this method offers two ways to generate toolpaths: explicit and implicit functions. For lattice structures defined by implicit functions, toolpaths can be generated directly from these functions without involving intermediate steps in STL files, further reducing computational costs and storage requirements.

[0056] 4. Compatibility

[0057] This method is flexible and can fill various components to form lattice structures or internal channels. It allows for seamless Boolean operations between generated toolpaths and arbitrary geometries.

[0058] 4. Ultralight weight, high surface area or microlattice

[0059] This method allows for the easy printing of lattice structures with small features. For example, lattice structures with large aspect ratios can achieve lightweight designs, while lattice structures with small unit cell sizes can achieve high surface area to volume ratios.

[0060] This method is helpful for printing lattice structures with small features. For example, structures with a large aspect ratio can achieve lightweight properties, while structures with small unit cell sizes can achieve a high surface area to volume ratio.

[0061] The following are example procedures illustrating the practice of this invention. These examples should not be construed as limiting. All percentages are by weight, and all solvent mixture proportions are by volume, unless otherwise stated.

[0062] Example—Printing TPMS lattice structures using a hybrid path planning method on an LPBF system 1. Modeling

[0063] Here, for explicit models, flowers are used to represent them. These models are constructed from triangular meshes and are typically saved as STL files, such as... Figure 4 As shown in A, the three-periodic minimal surface (TPMS) described by equations (1a)-(1c) is used to demonstrate the implicit model, as follows. Figure 4 As shown in B.

[0064] φ P (x,y,z)=cos(ωx)+cos(ωy)+cos(ωz)+c0 Eq.(1a)

[0065] φ D (x,y,z)=sin(ωx)sin(ωy)sin(ωz)+cos(ωx)sin(ωy)sin(ωz)+c0

[0066] (1b)

[0067] +sin(ωx)cos(ωy)sin(ωz)+sin(ωx)sin(ωy)cos(ωz)

[0068] φ G (x,y,z)=cos(ωx)sin(ωy)+cos(ωy)sin(ωz)+cos(ωz)sin(ωx)+c0(1c)

[0069] 2. Toolpath generation:

[0070] like Figure 5 As shown in A-5B, the flower shape represented by an explicit mesh is assigned a single-path toolpath, while the D-type TPMS (Triple-Period Minimal Surface) structure is assigned a hybrid toolpath to achieve ultra-low wall thickness and good mechanical properties. Furthermore, Figure 5 C demonstrates a hierarchical TPMS structure constructed by trimming toolpaths of a single-level structure.

[0071] 3. Print via LPBF

[0072] The experiment utilized a self-developed high-power LPBF system, Hans M100μ, equipped with a Yb (ytterbium) laser with a wavelength λ = 1.07 μm and a spot size of 25 μm. Based on a hybrid toolpath method, various lattice structures with different types, unit cell sizes, materials, and external geometries were fabricated, such as... Figure 6 As shown in A-6E, the fabricated lattice structure has potential applications in a variety of fields, including catalytic processes, mechanical shock energy absorption, lightweight engineering, thermal management devices, and bone implants.

[0073] Example 1. A path planning method for three-dimensional (3D) printed lattices, comprising:

[0074] Generate 3D models;

[0075] Slice to generate a two-dimensional (2D) outline of the 3D model;

[0076] The region defining the 2D contour; and

[0077] Generate path.

[0078] Example 2. The method according to Example 1, wherein the 3D model is represented by an explicit mesh or an implicit function.

[0079] Example 3. The method of claim 1, wherein slicing to generate the 2D contour of the 3D model includes generating the 2D contour of the 3D model defined by an explicit or implicit function.

[0080] Example 4. According to the method described in Example 3, wherein for a 3D model defined by an explicit function, the 2D contour is generated by calculating the intersections between the slice layer and the triangular mesh.

[0081] Example 5. The method according to Example 3, wherein for a 3D model defined by an implicit function, the 2D contour is obtained by calculating the following function:

[0082] Φ(x,y,zi)=0

[0083] Where zi is the z-coordinate of the i-th slice layer.

[0084] Example 6. According to the method of Example 1, the determination of the region includes dividing the lattice structure or thin-wall structure into two regions, including the thin wall and the wall node, and the two regions are respectively assigned two types of tool paths.

[0085] Example 7. According to the method described in Example 6, the geometric features of the two regions are determined by tilting. Angle and plate thickness definitions.

[0086] Example 8. The method according to Example 7, wherein for a 3D model defined by an explicit function, the tilt angle is calculated based on a 3D mesh file.

[0087] Example 9. The method according to Example 7, wherein for a model defined by an implicit function, the tilt angle is calculated based on the normal vector obtained by the following formula:

[0088]

[0089] Where φ IS It is the control function of the implicit surface.

[0090] Example 10. The method according to Example 1, wherein generating the path includes obtaining a single-track path directly from the line segment.

[0091] Example 11. The method according to Example 1, wherein generating a path includes generating a path offset at consecutive layers to suppress path overlap, thereby mitigating thermal deformation and improving surface quality.

[0092] Example 12. According to the method of Example 1, wherein for a 3D model defined by implicit functions, the path generation includes obtaining the intersection point by calculating the zeros of the implicit functions in a given layer and scan direction.

[0093] Example 13. The method according to Example 1 further includes adaptive toolpath and / or toolpath trimming.

[0094] Example 14. The method according to Example 13, wherein the adaptive toolpath includes adjusting the scan length and gap length for different curvature regions, and the toolpath trimming includes applying Boolean operations between the defined geometry and the toolpath to obtain lattice structures of various external shapes.

[0095] Example 15. A computer program product, comprising:

[0096] A non-transitory computer-executable storage device storing computer-readable program instructions that, when executed by a computer, cause the computer to perform a path planning method for three-dimensional (3D) printed lattices, the method comprising:

[0097] Generate 3D models;

[0098] Slice to generate the 2D outline of the 3D model;

[0099] The region defining the 2D contour; and

[0100] Generate path.

[0101] Example 16. The computer program product according to Example 15, wherein the 3D model is represented by an explicit mesh or an implicit function.

[0102] Example 17. The computer program product according to Example 15, wherein slicing to generate the 2D contour of the 3D model includes generating the 2D contour of the 3D model defined by explicit or implicit functions.

[0103] Example 18. The computer program product according to Example 17, wherein for a 3D model defined by an explicit function, the 2D contour is generated by calculating the intersections between slice layers and triangular meshes.

[0104] Example 19. The computer program product according to Example 17, wherein for a 3D model defined by an implicit function, the 2D contour is obtained by calculating the following function:

[0105] Φ(x,y,zi)=0

[0106] Where zi is the z-coordinate of the i-th slice layer.

[0107] Example 20. The computer program product according to Example 15, wherein determining the region includes dividing the lattice structure or thin-wall structure into two regions, including the thin wall and the wall node, and the two regions are respectively assigned two types of toolpaths.

[0108] Example 21. A toolpath generation strategy for lattice structures and thin-walled structures.

[0109] Example 22. A single-track scanning method is used to explore the printing limits of a machine, wherein the minimum wall thickness is directly related to and close to the melt pool width.

[0110] Example 23. A dashed line scanning method is used to alleviate thermal stress and deformation, wherein the scan length and void length can be precisely controlled to adapt to different lattice structures and materials.

[0111] Example 24. A sub-region threshold is used to control the number of paths / scan time and the mechanical properties of the lattice structure.

[0112] Example 25. A region determination method, applied to divide the entire scanning region into sub-regions, including a single-track scanning region and an R67 scanning region.

[0113] Example 26. A method for generating toolpaths directly from implicit functions and explicit surfaces.

[0114] All patents, patent applications, provisional applications, and publications mentioned or cited herein are incorporated herein by reference in their entirety (including all figures and tables) without conflict with the express teachings of this specification.

[0115] It should be understood that the examples and embodiments described herein are for illustrative purposes only, and those skilled in the art will make various modifications or alterations based thereon, which should be included within the spirit and scope of this application and the appended claims. Furthermore, any element or limitation of any invention or embodiment disclosed herein may be combined with any and / or all other elements or limitations disclosed herein (alone or in any combination) or any other invention or embodiment, and all such combinations are within the scope of this invention and are not limited thereto.

Claims

1. A path planning method for three-dimensional (3D) printed lattice structures, comprising: Generate 3D models; Slice to generate a two-dimensional (2D) outline of the 3D model; The region of the 2D contour is defined; as well as Generate path.

2. The method according to claim 1, wherein the 3D model is represented by an explicit mesh or an implicit function.

3. The method of claim 1, wherein slicing to generate the 2D contour of the 3D model includes generating the 2D contour of the 3D model defined by an explicit or implicit function.

4. The method of claim 3, wherein for a 3D model defined by an explicit function, the 2D contour is generated by calculating the intersections between the slice layer and the triangular mesh.

5. The method of claim 3, wherein for a 3D model defined by an implicit function, the 2D contour is obtained by calculating the following function: Φ(x,y,zi)=0 Where zi is the z-coordinate of the i-th slice layer.

6. The method of claim 1, wherein determining the region includes dividing the lattice structure or thin-wall structure into two regions, including the thin wall and the wall node, and wherein the two regions are respectively assigned two types of toolpaths.

7. The method of claim 6, wherein the geometric features of the two regions are defined by the tilt angle and the plate thickness.

8. The method of claim 7, wherein for a 3D model defined by an explicit function, the tilt angle is calculated based on a 3D mesh file.

9. The method of claim 7, wherein for a model defined by an implicit function, the tilt angle is calculated based on the normal vector obtained by the following formula: Where φ IS It is the control function of the implicit surface.

10. The method of claim 1, wherein generating the path comprises obtaining a single-track path directly from the line segment.

11. The method of claim 1, wherein generating the path includes generating path offsets at consecutive layers to suppress path overlap, thereby mitigating thermal deformation and improving surface quality.

12. The method of claim 1, wherein for a 3D model defined by implicit functions, generating a path includes obtaining the intersection point by calculating the zeros of the implicit functions in a given layer and scan direction.

13. The method of claim 1, further comprising adaptive toolpath and / or toolpath trimming.

14. The method of claim 13, wherein the adaptive toolpath includes adjusting the scan length and gap length for different curvature regions, and the toolpath trimming includes applying Boolean operations between the defined geometry and the toolpath to obtain lattice structures of various external shapes.

15. A computer program product comprising: A non-transitory computer-executable storage device having stored computer-readable program instructions thereon, which, when executed by a computer, cause the computer to perform a path planning method for three-dimensional (3D) printed lattices, the method comprising: Generate 3D models; Slice to generate the 2D outline of the 3D model; The region defining the 2D contour; and Generate path.

16. The computer program product of claim 15, wherein the 3D model is represented by an explicit mesh or an implicit function.

17. The computer program product of claim 15, wherein slicing to generate a 2D outline of the 3D model comprises generating a 2D outline of the 3D model defined by an explicit or implicit function.

18. The computer program product of claim 17, wherein for a 3D model defined by an explicit function, the 2D contour is generated by calculating the intersections between slice layers and triangular meshes.

19. The computer program product of claim 17, wherein for a 3D model defined by an implicit function, the 2D contour is obtained by calculating the following function: Φ(x,y,zi)=0 Where zi is the z-coordinate of the i-th slice layer.

20. The computer program product of claim 15, wherein defining the region includes dividing the lattice structure or thin-wall structure into two regions, including the thin wall and the wall node, and wherein the two regions are respectively assigned two types of toolpaths.

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