A laser printing path generation method for a geometric texture fusion model

Abstract

The application discloses a laser printing path generation method for a geometric texture fusion model. The geometric texture is migrated to a curved surface model to obtain a geometric texture fusion model, and a laser printing curved surface path of the model is generated. First, a user inputs a curved surface model and a geometric texture; the SLIM method which can ensure that the triangular facets of the grid are low deformation and non-intersecting after parameterization is used to parameterize the user-input curved surface model; the geometric texture is migrated to the user-input curved surface model based on a height field migration method to obtain the geometric texture fusion model; the user-input geometric texture is sliced according to the z-axis to obtain a planar intersection line; a laser printing track of the layered geometric texture is planned; and the layered curved surface laser printing path is generated through inverse mapping. The method solves the current laser printing curved surface path generation problem.

Description

Technical Field

[0001] This invention relates to the field of 3D printing technology, and more specifically to a method for generating laser printing paths for geometric texture fusion models. Background Technology

[0002] 3D printing is a rapid prototyping technology, generally divided into additive manufacturing and subtractive manufacturing. This invention primarily addresses the latter, proposing a laser printing path generation method for geometric texture fusion models. Subtractive manufacturing fixes raw materials on a device and uses cutting tools to remove excess material layers from the blank or workpiece, creating chips to give the workpiece a specified geometric shape. 3D laser printing typically uses digital material printers and is used in mold making, industrial design, and other fields to manufacture models or parts. After years of development and innovation, from initial prototype manufacturing to today's widespread applications, 3D printing technology, represented by laser printing, is changing the way manufacturing and design are conducted and bringing enormous potential for innovation.

[0003] In recent years, geometric textures have not only been used to enhance the aesthetic value and expressiveness of model surfaces, but also to serve certain functional purposes. Therefore, efficiently and conveniently designing the desired geometric texture effects on product surfaces is of significant practical importance. Generally, models with geometric textures generated on curved surfaces often have curved slabs for printing. However, most current slab processing methods, such as the cross-sectional plane method and projection method, are often only suitable for planar slabs, or cannot be directly used for printing curved slabs, or are difficult to adapt to the characteristic variations of complex curved surfaces or complex curved surface textures. Summary of the Invention

[0004] To address the aforementioned problems, this invention employs a non-self-intersecting parametric technique to fuse geometric textures into a surface model. It then uses parametric mapping to generate layered trajectories for laser printing of the fused geometric texture model, avoiding the complex spatial intersection problems and excessive distortion of triangular facets inherent in existing algorithms when planning the surface printing path. This invention provides a method for generating laser printing paths for geometric texture fusion models. The purpose of this invention is to provide users with a high-fidelity method for generating laser printing surface paths for geometric texture models with minimal distortion.

[0005] The objective of this invention is achieved through the following technical solution: a laser printing path generation method for geometric texture fusion models, which is implemented through the following steps:

[0006] S1. Input the surface model and geometric texture, and use the SLIM method to parameterize the surface model to obtain the surface parametric model;

[0007] S2. Select the position of the geometric texture on the surface model, perform texture migration, and calculate the coordinates of each geometric texture vertex migrated to the surface model;

[0008] S3. Construct geometric texture slices, and find the intersection of geometric texture slices, parametric models and surface parametric models in the 2D coordinate system to obtain the planar layered printing trajectory;

[0009] S4. Map the planar layered printing trajectory to the surface. Obtain the spatial layered printing trajectory by using the mapping points of the planar layered trajectory and the unit normal vector of the surface model at the mapping points.

[0010] Furthermore, in S1, the SLIM method is used to parameterize the user-input surface model M onto a plane, and the surface parameter model M... uv ={V u F u}, where V u ={V u0 V u1 , ..., V uu} represents the UV coordinates of the parametric model, where u is the number of vertices and V is the number of vertices. ui =(x ui y ui ), i∈u, F u ={F u0 F u1 F uv} is a set of triangular facets, F ui =(V ui0 V ui1 Vu i2 ), i∈v, where v is the number of triangular facets.

[0011] Furthermore, the steps to obtain the surface parametric model are as follows:

[0012] Let M = (V, F) represent the input surface model, where V is the vertex set and F is the triangular facet set;

[0013] A common way to define the energy of a mapped deformation is as a function that constructs its Jacobian matrix, if J f Let F be the Jacobian matrix for elements f ∈ F. Then the energy we want to minimize is:

[0014]

[0015] Where D is the deformation measure, x∈R 2|v| A represents the parameterized coordinates of all vertices. f Let f be the area of ​​triangle f. The degree of deformation of the triangle is measured using the symmetric Dirichlet energy, which is expressed as:

[0016]

[0017] The energy transformation above can be achieved by using a surrogate function as follows:

[0018]

[0019] When the aforementioned energy is minimized, the deformation occurring when the spatial mesh is parameterized to a plane is minimized; where R(J) f (x) is the closest to J f The rotation matrix of (x) is given, and W is the weight that makes the ARAP energy gradient equal to the Dirichlet energy gradient; then the reweighted Local / Global algorithm is used to solve the optimization problem.

[0020] Further, the selection of the position of the geometric texture on the surface model in S2 specifically involves: the user can customize the position of the geometric texture on the surface model and can perform translation, rotation, and scaling operations on the geometric texture. All of the above operations are performed on the 2D plane. After determining the position of the geometric texture on the parametric model, texture transfer is then performed. The implementation method is as follows: First, the center of the geometric texture is represented by C. T , The center of the surface model is represented by C. M , To make the center of the geometric texture coincide with the center of the surface model, let

[0021] C′ T =C T +d=C M

[0022] Where d is the displacement of the center of the geometric texture, and the vertex values ​​are calculated after all geometric texture vertices have been displaced:

[0023] T i ′=T i +d

[0024] The translation method for geometric textures is as follows: for each vertex T of the geometric texture whose center coincides with the center of the surface model... i ′=(x′ i y′ i Add the translation distances along the x, y, and z axes respectively:

[0025] x′ i +d x y′ i +d y

[0026] Where d x d y These represent the translation distances along the x and y axes, respectively.

[0027] The translated geometric texture vertices are multiplied by rotation and scaling matrices to complete the user's rotation and scaling operations. Since the operation is performed on a 2D plane, the rotation axis is the z-axis, and the rotation matrix can be represented as follows: The scaling matrix is ​​represented as

[0028] Furthermore, the texture transfer in S2 specifically involves: based on the surface parameter model, calculating the geometric texture vertex T in the 2D coordinate system where the parameterized model resides for all geometric texture vertices. i The triangular facet numbers and barycentric coordinates on the parametric model, where T i The triangular facet containing this facet is represented as: F ui =(V ui0 V ui1 V ui2 ), i∈v∩i∈t, T i In the triangular facet F ui Position F on i Represented in centroid coordinates:

[0029] P i =α i V ui0 +β i V ui1 +γ i V ui2

[0030] Where α i ,β i γ i It is a triangular facet F ui The weights of the three vertices are also the centroid coordinates of Ti;

[0031] According to F ui The number can be used to find the corresponding triangular facet F on the surface model. i =(V i0 V i1 V i2 ), and triangular facet F i Substitute the three vertices into P i The expression yields T i Coordinates on the surface model:

[0032] P i ′=α i V i0 +β i V i1 +γ i V i2

[0033] Also represented as P i ′=(x′ iy′ i , z′ i ), through the formula:

[0034]

[0035] Perform a height field transfer operation, where z i Texture vertex T i z-coordinate, It is point P i The normal vector at point ′; The calculation is based on T i barycentric coordinates and F i F is obtained by interpolating the normal vectors of the three vertices. i The normal vectors of the three vertices are respectively but

[0036]

[0037] Calculate the new coordinates of each geometric texture vertex as it migrates to the surface model to obtain the geometric texture fusion model.

[0038] Furthermore, the geometric texture vertex T i The triangular facet numbering and centroid coordinates on the parametric model are as follows: the triangular facets of the parametric model are constructed into an AABB tree, and the geometric texture vertex T is quickly found by searching the AABB tree. i The triangular facet F is located ui .

[0039] Furthermore, the construction of the geometric slices specifically involves:

[0040] The z-axis layered slice of the geometric texture is represented as N. z ={N z0 N z1 , ..., N zs}, where s is the number of layers required by the user, that is, to find the intersection points and lines between s planes perpendicular to the z-axis and the geometric texture between 0 and the geometric texture height h.

[0041] Furthermore, the specific method of finding the intersection of the geometric texture slices, parametric models, and surface parametric models in the 2D coordinate system involves: finding the intersection of each layered slice N of the geometric texture. zi The intersection points of i∈s, after removing the z-axis, are placed in the parameterized model M. uv In the middle; constructing a parameterized model M uv The axis-bounding box is divided into regions of equal width, which serve as the base plane for the reciprocating planar trajectory. Then, the geometric texture layer slice N is calculated. zi The reciprocating planar trajectory can be obtained by finding the intersection of the parametric model and the axis bounding box.

[0042] Furthermore, S4 specifically refers to: parameterized mapping performed using the SLIM method. It is a globally unflipped mapping, therefore for its inverse mapping In terms of the parameterized model M uv Each vertex V on ui All of them are mapped to a unique and definite point V on the original surface model through this inverse mapping. i :

[0043]

[0044] The reciprocating planar trajectory is mapped onto a surface M. Since each layer's reciprocating planar trajectory corresponds to a layered slice of geometric texture at different heights, this paper proposes a surface mapping method for the height field. For a layered slice of geometric texture, assuming the z-axis height of the layer is h, its point V on the spatial layered printing trajectory is... z Represented as:

[0045]

[0046] Where V i These are the points mapped from the planar layered printing trajectory to the curved surface model M. Represents the surface model M in V i The unit normal vector at that location.

[0047] Furthermore, the surface model M in V i Unit normal vector at the location There are two cases: if V i A triangular facet F on surface M i When it is inside and not on the edge, at this time Equal to triangular face F i The unit normal vector;

[0048] If V i On one edge of surface M, the unit normal vector at that point cannot be directly represented by the surface's normal vector; except for the boundary edges, all other edges are common edges of two triangular faces, so the vertex V on the non-boundary edges... i The normal vector of a triangle can be expressed as the average of the normal vectors of the two triangles adjacent to that edge, i.e.:

[0049]

[0050] in and This represents the normal vector of the two adjacent triangular faces of a non-boundary edge. This represents the normal vector of the triangular facet containing the edge when it is a boundary edge.

[0051] The main advantages of this invention include:

[0052] Compared to the limitations of traditional textures, this method endows geometric textures with functional roles and processes curved surface slices through height field transfer, breaking the limitations of laser printing in processing curved surface slices and further enriching product design methods. Compared with other methods, this method avoids complex spatial intersection problems and excessive distortion of triangular facets in the process of generating laser-printed curved surface layer trajectories for geometric texture fusion models, thus saving memory space and computation time. Attached Figure Description

[0053] Figure 1 This is a flowchart of a laser printing path generation method for a geometric texture fusion model, as shown in one embodiment of the present invention.

[0054] Figure 2 This is a stage diagram of a laser printing path generation method for a geometric texture fusion model according to one embodiment of the present invention.

[0055] Figure 3 This is a schematic diagram of the laser-printed surface path generated by this invention from a surface model input by the user. Detailed Implementation

[0056] The present invention will be further illustrated below with reference to specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0057] It should be noted that in the claims and specification of this patent, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one" does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0058] Example

[0059] All documents mentioned in this invention are incorporated herein by reference as if each document were individually incorporated by reference. Furthermore, it should be understood that after reading the foregoing teachings of this invention, those skilled in the art can make various alterations or modifications to this invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0060] This invention relates to a laser printing path generation method for geometric texture fusion models. The method employs subtractive manufacturing, utilizing laser cutting to remove excess material to obtain the target shape. Specifically, the method includes: user input of a surface model; obtaining a parametric model with minimal distortion using the SLIM method; and determining the path based on the centroid coordinates of the geometric texture vertices on the triangular facets of the parametric model and the triangular facet identifier id. F The coordinates of the geometric texture vertices on the surface model are calculated, and the height of the geometric texture vertices is added along the normal vector direction to obtain the geometric texture fusion model. The geometric texture is intersected with a plane perpendicular to the z-axis according to the user-defined number of layers to obtain geometric texture layer slices. The intersection points of the geometric texture layer slices with the parametric model and the axis bounding box are obtained to obtain the reciprocating planar trajectory. The planar layer printing trajectory is mapped to space through the inverse operation of parametric mapping to obtain the spatial layer printing trajectory.

[0061] Figure 1 This is a flowchart of a laser printing path generation method for a geometric texture fusion model according to an embodiment of the present invention. The method includes the following steps: Step 101, the user inputs a surface model and a geometric texture; Step 102, the surface model is parameterized to a plane using the SLIM method to obtain a parameterized model; Step 103, the geometric texture fusion model is obtained using centroid coordinates and height field migration; Step 104, the planar layered printing trajectory is obtained by intersecting the geometric texture layered slices with the parameterized model and the axis bounding box; Step 105, the planar layered printing trajectory is mapped to space based on the inverse operation of the parameterized mapping to obtain a spatial layered printing trajectory.

[0062] Specifically, in one Figure 2 The mouse example shown in the invention provides a method for generating laser printing paths for a mouse model with geometric texture fusion, comprising the following steps:

[0063] Step 1: User inputs mouse surface model and geometric texture: The user inputs a mouse surface model in OBJ format: M = (V, F), where V = {V0, V1, ..., V...} n} is the vertex set, representing the 3D coordinates of the mouse surface model, n is the number of vertices, and V i =(x i y i , z i), i∈n, F={F0, F1,...,F m} is a set of triangular facets, F i =(V i0 V i1 V i2 ), i∈m, where m is the number of triangular facets, and the coordinates of the geometric texture vertices are represented as T={T0,T1,...,T t}, where t is the number of vertices in the geometric texture, T i ={x i y i , z i}, i∈t

[0064] Step 2, Mouse Surface Model Parametricization: To obtain a low-deformation, non-self-intersecting parametric mouse surface model, we use the SLIM method to parametricize the user-input mouse surface model M onto a plane, resulting in the parametric mouse model M. uv ={V u F u}, where V u ={V u0 V u1 , ..., V uu} represents the UV coordinates of the parametric model, where u is the number of vertices and V is the number of vertices. ui =(x ui γ ui ), i∈u, F u ={F u0 F u1 F uv} is a set of triangular facets, F ui =(V ui0 V ui1 V ui2 ), i∈v, v is the number of triangular facets. This method greatly reduces the deformation of triangular facets and achieves local non-self-intersection parameterization. The specific steps are as follows: M=(V,F) represents the input surface model, where V is the vertex set and F is the triangular facet set.

[0065] A common way to define the energy of a mapped deformation is as a function of constructing its Jacobian matrix, if J f Let F be the Jacobian matrix for elements f ∈ F. Then the energy we want to minimize is:

[0066]

[0067] Where D is the deformation measure, x∈R 2|v| A represents the parameterized coordinates of all vertices. f Let f be the area of ​​triangle f. Here, the symmetric Dirichlet energy is used to measure the degree of deformation of the triangle, and its expression is:

[0068]

[0069] Since we want to use ARAP's Local / Global algorithm to solve this problem, we transform the above energy into the following form using a surrogate function:

[0070]

[0071] When the aforementioned energy is minimized, the deformation occurring when the spatial mesh is parameterized to a plane is minimized; where R(J) f (x) is the closest to J f The rotation matrix of (x) is given, and W is the weight that makes the ARAP energy gradient equal to the Dirichlet energy gradient. The optimization problem is then solved using the reweighted Local / Global algorithm.

[0072] Step 3, Texture Transfer: Users can customize the position of geometric textures on the curved surface model and perform translation, rotation, and scaling operations on the geometric textures. After the position is determined, the texture transfer operation is performed; based on the mouse parameterized model M obtained in Step 2... uv ={V u F u For all geometric texture vertices, calculate the geometric texture vertex T in the 2D coordinate system where the mouse parameterized model resides. i The triangular facet numbers and centroid coordinates on the mouse parametric model, where T i The triangular facet containing this facet is denoted as: F ui =(V ui0 V ui1 V ui2 ), i∈v∩i∈t, T i In triangular facet F ui Position P on i Represented in centroid coordinates:

[0073] P i =α i V ui0 +β i V ui1 +γ i V ui2

[0074] Where α i ,β i γ i It is a triangular facet F ui The weights of the three vertices are also T. i The coordinates of the centroid;

[0075] According to F uiThe number can be used to find the corresponding triangle F on the mouse surface model. i =(V i0 V i1 V i2 ), and triangular facet F i Substitute the three vertices into P i The expression yields T i Coordinates on the mouse surface model:

[0076] P′ i =αV i0 +βV i1 +γV i2

[0077] It is also represented as P′ i =(x′) i y′ i , z′ i ), through the formula:

[0078]

[0079] Perform a height field transfer operation, where z i Texture vertex T i z-coordinate, It is point P′ i The normal vector at that location. The calculation is based on T obtained above. i barycentric coordinates and F i It is obtained by interpolating the normal vectors of the three vertices: Assume F i The normal vectors of the three vertices are respectively but

[0080]

[0081] By calculating the new coordinates of each geometric texture vertex as it migrates to the mouse surface model, we can obtain the geometric texture fused mouse model.

[0082] Users can customize the position of geometric textures on the mouse surface model and perform translation, rotation, and scaling operations on the geometric textures. All of these operations are performed on the 2D plane. Texture transfer is performed after the position of the geometric texture on the parametric mouse model is determined. The implementation method is as follows: First, the center of the geometric texture is represented by CT. The center of the mouse surface model is represented by C. M , To make the center of the geometric texture coincide with the center of the mouse surface model, let

[0083] C′ T =C T +d=C M

[0084] Where d is the displacement of the center of the geometric texture, and the vertex values ​​are calculated after all geometric texture vertices have been displaced:

[0085] T i ′=T i +d

[0086] The translation method for geometric textures is as follows: for each vertex T of the geometric texture whose center coincides with the center of the mouse surface model... i ′=(x′ i y′ i Add the translation distances along the x, y, and z axes respectively:

[0087] x′ i +d x y′ i +d y

[0088] Where d x d y These represent the translation distances along the x and y axes, respectively.

[0089] The translated geometric texture vertices are multiplied by rotation and scaling matrices to complete the user's rotation and scaling operations. Since the operation is performed on a 2D plane, the rotation axis is the z-axis, and the rotation matrix can be represented as follows: The scaling matrix is ​​represented as

[0090] Specifically, in step three, the geometric texture vertex T is located in the 2D coordinate system where the mouse parametric model is situated. i The triangular facet numbers and centroid coordinates on the mouse parametric model, where T i The triangular facet containing this facet is denoted as: F ui =(V ui0 V ui1 V ui2 For i∈v∩i∈t, the method used here is to construct an AABB tree from the triangular faces of the mouse parameterized model, and then search the AABB tree to quickly find the geometric texture vertex T. i The triangular facet F is located ui .

[0091] Specifically, in step three, the geometric texture vertex T is calculated based on the centroid coordinates. i The specific method for determining coordinates on the mouse surface model is as follows:

[0092] First, the definition of barycentric coordinates is: given the coordinates of three points A, B, and C of a triangle, any point (x, y) in the plane can be written as a linear combination of these three coordinates, i.e., (x, y) = αA + βB + γC, satisfying α + β + γ = 1. Then, the weights α and βγ of the three coordinates A, B, and C are called the barycentric coordinates of the point (x, y). The method for solving α and βγ is as follows: directly connect the point (x, y) in the plane to the three points A, B, and C, forming three triangles with areas A, B, and C respectively. A B B C C The centroid coordinates can then be defined as:

[0093]

[0094] The method for calculating the area of ​​the triangle is as follows: Since the geometric meaning of the dot product of two vectors is the area of ​​the parallelogram enclosed by these two vectors, we use the dot product of vectors to calculate the area of ​​the triangle, and name the point (x, y) P:

[0095]

[0096] Specifically, in step three, since each triangular facet of the mouse surface model has a unique number, and the number still exists on the parameterized mouse surface model after parameterization, the mouse surface model triangular facet corresponding to the texture vertex T can be obtained by the number. At the same time, the three vertices of the triangular facet are also obtained, and then the coordinates of the texture vertex T on the mouse surface model can be calculated based on the centroid coordinates.

[0097] Step 4, Construct geometric texture slices: Based on user requirements, the number of layers is set to 6, so the z-axis layered slices of the geometric texture are represented as N. z ={N z0 N z1 , ..., N z6 That is, to find the intersection points and lines between the geometric texture and the six planes perpendicular to the z-axis between 0 and the geometric texture height h;

[0098] Step 5, Generate Planar Layered Printing Trajectory: The user-input mouse surface model M and the geometric texture N share a common world coordinate system. Therefore, the planar layered printing trajectory can be obtained by intersecting the layered slices of the geometric texture with the parametric mouse model: Each layered slice N of the geometric texture... zi The intersection points of i∈s, after removing the z-axis, are placed in the mouse parameterization model M. uv In the middle; constructing a mouse parameterized model M uv The axis-bounding box is divided into regions of equal width, which serve as the base plane for the reciprocating planar trajectory. Then, the geometric texture layer slice N is calculated. ziThe reciprocating planar trajectory can be obtained by finding the intersection points of the mouse parametric model and the axis bounding box. Calculate the geometric texture layer slice N. zi The specific method for determining the intersection of the mouse parametric model and the axis bounding box is as follows:

[0099] Taking a reciprocating printing trajectory parallel to the x-axis as an example, first construct a mouse parameterized model M. uv The bounding box of the axis. Assuming the spacing of the planar layered printing trajectory is Δl, the y-axis length of the bounding box is l, and the coordinates of the lower left corner of the bounding box are (0, 0), then there are a total of There are 3 parallel straight lines, and their y-axis coordinates are represented as... in Represents the largest integer not greater than a. Interconnect these lines with the parameterized grid M. uv After finding the intersection with the layered intersection lines of the geometric texture, a series of sequential intersection points are obtained. These intersection points constitute the trajectory. Finally, the intersection points and line segments inside the geometric texture intersection lines are removed, and the beginning and end endpoints of the parallel straight lines are connected to form a reciprocating planar trajectory.

[0100] Step 6: Generate spatially layered printing tracks. Figure 3 This example demonstrates a partial spatial layered printing trajectory. Users can specify the number of layers in the spatial layered printing trajectory. Figure 3 The three images in the diagram represent three layers of the spatially layered printing trajectory. This is due to the parametric mapping used in step two. It is a globally unflipped mapping, therefore for its inverse mapping In terms of mouse parameterization model M uv Each vertex V on ui All of these can be mapped to a unique and definite point V on the original mouse surface model through this inverse mapping. i :

[0101]

[0102] Specifically, based on the parametric mapping of the triangular mesh The piecewise linear and bijective characteristics of the mouse parameterization model M uv A triangular facet F ui =(V ui0 V ui1 V ui2 A point V on ) ui Both can be represented as F on the mouse surface model M. i =(V i0 V i1 V i2 The unique and definite point V i The details are as follows:

[0103]

[0104] in yes The inverse operation, m and n are respectively (V ui1 -V ui0 ) and (V ui2 -V ui0 The weight of ).

[0105] Utilizing this property, the reciprocating planar trajectory generated in step five can be mapped onto the surface M. Since each layer of the reciprocating planar trajectory corresponds to a layered slice of geometric texture at different heights, this paper proposes a surface mapping method based on the height field. For a layered slice of geometric texture, assuming the z-axis height of this layer is h, its point V on the spatial layered printing trajectory is... z Represented as:

[0106]

[0107] Where V i These are the points mapped from the planar layered printing trajectory to the mouse surface model M. Represents the mouse surface model M in V i The unit normal vector at V. There are two cases here: (1) If V i A triangular facet F on surface M i When it is inside and not on the edge, at this time Equal to triangular face F i The unit normal vector, (2) if V i On an edge of surface M, the unit normal vector at that point cannot be directly represented using the surface's normal vector. We propose a method based on the direction of the common edge of the face to represent the unit normal vector at that point. Specifically, except for boundary edges, all other edges are common edges of two triangular faces. Therefore, the vertex V on a non-boundary edge... i The normal vector of a triangle can be expressed as the average of the normal vectors of the two triangles adjacent to that edge, i.e.:

[0108]

[0109] in and This represents the normal vector of the two adjacent triangular faces of a non-boundary edge. This represents the normal vector of the triangular facet containing the edge when it is a boundary edge.

[0110] It should be noted that in the claims and specification of this patent, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one" does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0111] The above embodiments are used to explain and illustrate the present invention, but not to limit the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A method for generating laser printing paths for geometric texture fusion models, characterized in that, This method is implemented through the following steps: S1. Input the surface model and geometric texture, and use the SLIM method to parameterize the surface model to obtain the parametric surface model. The steps to obtain the parametric surface model are as follows: use Represents the input surface model, where It is a vertex set. It is a set of triangular facets; A common way to define the energy of a mapped deformation is as a function that constructs its Jacobian matrix, if using Represents element Given a Jacobian matrix, the energy we want to minimize is: Where D is the deformation measure. These are the parameterized coordinates of all vertices. It is a triangle The area of ​​the triangle is measured using the symmetric Dirichlet energy, which is expressed as: The energy transformation above can be achieved by using a surrogate function as follows: When the aforementioned energy is minimized, the deformation occurring when the spatial mesh is parameterized to a plane is minimized; where The closest The rotation matrix, The weights that make the ARAP energy gradient equal to the Dirichlet energy gradient are used; then the reweighted Local / Global algorithm is used to solve the optimization. S2. Select the position of the geometric texture on the surface model, perform texture migration, and calculate the coordinates of each geometric texture vertex migrated to the surface model; S3. Construct geometric texture slices, and find the intersection of the geometric texture slices and the surface parametric model in the 2D coordinate system to obtain the planar layered printing trajectory; S4. Map the planar layered printing trajectory to the surface model, and obtain the spatial layered printing trajectory through the mapping points of the planar layered trajectory and the unit normal vector of the surface model at the mapping points.

2. The laser printing path generation method for a geometric texture fusion model according to claim 1, characterized in that, In S1, the SLIM method is used to process the surface model input by the user. Parametric modeling of planes and surfaces ,in This represents the UV coordinates of the parametric model, where u is the number of vertices. , It is a set of triangular facets. , It represents the number of triangular facets.

3. The laser printing path generation method for a geometric texture fusion model according to claim 1, characterized in that, The selection of the position of the geometric texture on the surface model in S2 specifically involves: the user can customize the position of the geometric texture on the surface model and perform translation, rotation, and scaling operations on the geometric texture. All of these operations are performed on a 2D plane. Texture migration is performed after determining the position of the geometric texture on the parametric model. The implementation method is as follows: First, the center of the geometric texture is represented as... , The center of the surface model is represented as , To make the center of the geometric texture coincide with the center of the curved surface model, let in This is the displacement of the center of the geometric texture, calculated after displacing all geometric texture vertices: The translation method for geometric textures involves translating each vertex of the geometric texture whose center coincides with the center of the surface model. Add the translation distances along the x, y, and z axes respectively: in These represent the translation distances along the x and y axes, respectively. The translated geometric texture vertices are multiplied by rotation and scaling matrices to complete the user's rotation and scaling operations. Since the operation is performed on a 2D plane, the rotation axis is the z-axis, and the rotation matrix can be represented as follows: The scaling matrix is ​​represented as .

4. The laser printing path generation method for a geometric texture fusion model according to claim 1, characterized in that, The texture transfer in S2 specifically involves: calculating the geometric texture vertices in the 2D coordinate system where the surface parameter model resides, based on the surface parameter model. The triangular facet numbers and centroid coordinates on the surface parametric model, where... The triangular facet containing the triangle is represented as: , In the triangular facet The position above Represented in centroid coordinates: in It is a triangular facet The weights of the three vertices are also The coordinates of the centroid; according to Find the corresponding triangular facet on the surface model by its number. triangular pieces Substitute the three vertices The expression is obtained Coordinates on the surface model: It is also expressed as Through the formula: Perform height field migration operation, where Texture vertices z-coordinate, It is a point The normal vector at that location; The calculation is based on centroid coordinates and It is obtained by interpolating the normal vectors of the three vertices: The normal vectors of the three vertices are respectively ,but Calculate the new coordinates of each geometric texture vertex as it migrates to the surface model to obtain the geometric texture fusion model.

5. The laser printing path generation method for a geometric texture fusion model according to claim 4, characterized in that, The geometric texture vertex The triangular facet numbering and centroid coordinates on the parametric surface model are as follows: the triangular facets of the parametric model are constructed into an AABB tree, and the geometric texture vertices are quickly found by searching the AABB tree. The triangular facet .

6. The laser printing path generation method for a geometric texture fusion model according to claim 1, characterized in that, The specific steps for constructing geometric texture slices are as follows: The z-axis layered slice of the geometric texture is represented as ,in This is the number of layers required by the user, which means finding the intersection points and lines between the geometric texture and the s planes perpendicular to the z-axis between 0 and the geometric texture height h.

7. The laser printing path generation method for a geometric texture fusion model according to claim 1, characterized in that, The specific method of finding the intersection of the geometric texture slices and the surface parametric model in the 2D coordinate system is as follows: for each layer of the geometric texture slices... The intersection points, after removing the z-axis, are placed on the parametric model. In China; constructing a parameterized model The axis-bounding box is divided into regions of equal width, serving as the base plane for the reciprocating planar trajectory. Then, geometric texture layering and slicing are calculated. The reciprocating planar trajectory can be obtained by finding the intersection of the parametric model and the axis bounding box.

8. The laser printing path generation method for a geometric texture fusion model according to claim 1, characterized in that, Specifically, S4 refers to: parameter mapping performed using the SLIM method. It is a globally unflipped mapping, therefore for its inverse mapping In terms of parameterized models Each vertex on All of them are mapped to a unique and definite point on the original surface model through this inverse mapping. : Mapping planar layered printing trajectories to a curved surface model Since the reciprocating planar trajectory of each layer corresponds to a layered slice of geometric texture at different heights, a surface mapping method for the height field is proposed. For a layered slice of geometric texture, it is assumed that the layer... Shaft height is At this point, its point on the spatial layered printing trajectory Represented as: in It is a planar layered printing trajectory mapped to a curved surface model. point, Representation of surface model exist The unit normal vector at that location.

9. A laser printing path generation method for a geometric texture fusion model according to claim 8, characterized in that, Surface model exist Unit normal vector at the location There are two possibilities: if In curved surface model A triangular facet When it is inside and not on the edge, at this time Equal to triangular face The unit normal vector; like In curved surface model On one edge, the unit normal vector of that point cannot be directly represented by the normal vector of the face; except for the boundary edges, all other edges are common edges of two triangular faces, so the vertices on the non-boundary edges... The normal vector is expressed as the average of the normal vectors of the two triangular faces adjacent to that edge, that is: in and This represents the normal vector of the two adjacent triangular faces of a non-boundary edge. This represents the normal vector of the triangular facet containing the edge when it is a boundary edge.

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