Slicing Method and System, Computer Device, Storage Medium and Product

Abstract

The present application discloses a slicing method and system, a computer device, a computer-readable storage medium, and a computer program product. Among them, the slicing method includes the following steps: creating a plurality of continuous layers that can completely wrap the implicit expression model; selecting any number of continuous layers from the plurality of layers to form a subspace for hierarchical meshing of the subspace, including: recursively executing to respectively determine the value range of the implicit expression of each sub-grid at the current level to perform the next-level meshing on the sub-grids whose value range contains a threshold range until each sub-grid at the current level is a single-layer grid that meets the corresponding layer resolution; selecting the sub-grids whose value range of the implicit expression contains the threshold range among the single-layer grids that meet the corresponding layer resolution as key grids and filling in the output value of the implicit expression of at least one representative point therein to determine the slice contour of each selected layer.

Description

Technical Field

[0001] The present application relates to the field of 3D printing technology, and specifically relates to a slicing method and system, a computer device, a computer-readable storage medium, and a computer program product. Background Art

[0002] In the field of 3D printing, the STL (Standard Triangulation Language) file required for 3D printing equipment to print is obtained by slicing a 3D model. Currently, most slicing methods slice a triangular mesh model. When the 3D model is an implicit model obtained by implicit modeling, it is usually necessary to convert the implicit model into a triangular mesh model before slicing. However, a large amount of time is consumed in the process of converting the implicit model into a triangular mesh model, which results in a low slicing efficiency for the implicit model.

[0003] In view of this, how to efficiently slice an implicit model is an urgent technical problem to be solved. Summary of the Invention

[0004] In view of the above-mentioned disadvantages of the related art, the purpose of the present application is to provide a slicing method and system, a computer device, a computer-readable storage medium, and a computer program product to overcome the technical problem of how to efficiently slice an implicit model existing in the above-mentioned related art.

[0005] To achieve the above purpose and other related purposes, a first aspect of the present application discloses a slicing method, which includes the following steps: creating a plurality of continuous layers that can completely wrap an implicitly expressed model; wherein, the plurality of layers are respectively configured with layer resolutions; selecting any number of continuous layers from the plurality of layers to form a subspace and performing hierarchical meshing on the subspace, including: recursively executing to respectively determine the value range of the implicit expression of each sub-grid at the current level to perform the next-level meshing on the sub-grid whose value range contains a threshold range until each sub-grid at the current level is a single-layer grid that meets the corresponding layer resolution; selecting the sub-grid whose value range of the implicit expression contains the threshold range as a key grid in the single-layer grid that meets the corresponding layer resolution and filling in the output value of the implicit expression of at least one representative point therein to determine the slice contour of each selected layer.

[0006] The second aspect of the present application discloses a slicing system, which includes: a layer creation module for creating a plurality of continuous layers that can completely wrap an implicit expression model; wherein, each of the plurality of layers is configured with a layer resolution; a subspace determination module for selecting any number of continuous layers from the plurality of layers to form a subspace; a subspace slicing module, including: a meshing and filling unit for performing step-by-step meshing on the subspace, including: recursively determining the value range of the implicit expression of each sub-grid at the current level to perform the next-level meshing on the sub-grid whose value range contains a threshold range until each sub-grid at the current level is a single-layer grid that meets the corresponding layer resolution; and selecting, from the single-layer grids that meet the corresponding layer resolution, the sub-grids whose value range of the implicit expression contains the threshold range as key grids and filling in the output value of the implicit expression of at least one representative point therein; a slice contour determination unit for determining the slice contour of each layer based on the key grids filled in each layer in the subspace.

[0007] The third aspect of the present application discloses a computer device, including: a storage device for storing at least one program; a processing device connected to the storage device for calling the at least one program from the storage device and implementing the slicing method as described in the first aspect of the present application when executed.

[0008] The fourth aspect of the present application discloses a computer-readable storage medium storing at least one program, and when the at least one program is called and executed by a processor of a computer, the slicing method as described in the first aspect of the present application is implemented.

[0009] The fifth aspect of the present application discloses a computer program product, which, when running on a computer, causes the computer to execute the slicing method as described in the first aspect of the present application.

[0010] In summary, the present application discloses a slicing method and system, a computer device, a computer-readable storage medium, and a computer program product. The present application selects any number of continuous layers from a plurality of continuous layers that can completely wrap an implicit expression model to form a subspace for step-by-step meshing until each sub-grid at the current level is a single-layer grid that meets the corresponding layer resolution, and selects, from the single-layer grids that meet the corresponding layer resolution, the sub-grids whose value range of the implicit expression contains the threshold range as key grids and fills in the output value of the implicit expression of at least one representative point therein to determine the slice contour of each selected layer. In this way, the present application does not need to first convert the implicit expression model into a triangular mesh model for slicing, and only fills in the output value of the implicit expression in the key grids during the slicing process to determine the slice contour, reducing the computational complexity during the slicing process and achieving efficient slicing of the implicit expression model. Description of the Drawings

[0011] The features and advantages of the invention involved in the present application can be better understood by referring to the exemplary embodiments and the accompanying drawings described in detail below. A brief description of the drawings is as follows:

[0012] Figure 1 It shows a schematic flow diagram of the slicing method in an embodiment of the present application.

[0013] Figure 2 It shows a schematic diagram of the parameter configuration window in an embodiment of the present application.

[0014] Figure 3 It shows a schematic diagram of the layer positions of multiple layers in an embodiment of the present application.

[0015] Figure 4 It shows a schematic diagram of a plurality of consecutive layers created in an embodiment of the present application.

[0016] Figure 5 It shows a schematic diagram of a subspace selected in an embodiment of the present application.

[0017] Figure 6 It shows a schematic diagram of a subspace selected in another embodiment of the present application.

[0018] Figure 7 It shows the present application for Figure 5 a schematic diagram after the first meshing of the subspace in the illustrated embodiment.

[0019] Figure 8 It shows the present application for Figure 6 a schematic diagram after the first meshing of the subspace in the illustrated embodiment.

[0020] Figure 9 It shows the present application for Figure 7 a schematic diagram after the next-level meshing of the sub-grid whose value range of the implicit expression in the illustrated embodiment includes the threshold range.

[0021] Figure 10 It shows a schematic diagram of two subspaces formed by a plurality of consecutive layers in an embodiment of the present application.

[0022] Figure 11 It shows a block diagram of the slicing system in an embodiment of the present application.

[0023] Figure 12 It shows a schematic structural diagram of a computer device in an embodiment of the present application. Detailed implementation manners

[0024] The following specific embodiments illustrate the implementation manners of the present application. Those skilled in the art can easily understand the advantages of the present application and the technical effects that can be achieved from the content disclosed in this specification. In the following description, some embodiments may refer to the accompanying drawings. It should be understood that other embodiments without the drawn figures may also be used, and specific steps, modules or units, electrical, and operational changes may be made without departing from the spirit and scope of the present application. The following detailed description should not be considered restrictive, and the scope of the embodiments of the present application is only defined by the claims published in the present application. The terms used herein are only for describing specific embodiments and are not intended to limit the present application.

[0025] Although in some instances the terms first, second, or third, etc. are used herein to describe various elements or parameters, these elements or parameters should not be limited by these terms. These terms are only used to distinguish one object or parameter from another object or parameter, and are not used to define the order, timing, priority, or importance of multiple objects. For example, the first threshold may be referred to as the second threshold, and similarly, the second threshold may be referred to as the first threshold, without departing from the scope of the various described embodiments. The first threshold and the second threshold are both describing a threshold, but unless the context clearly indicates otherwise, they are not the same threshold.

[0026] Furthermore, as used herein, the singular forms "a", "an", and "the" are intended to also include the plural forms, unless the context indicates otherwise. It should be further understood that the terms "comprising", "including" indicate the presence of the described features, steps, operations, elements, components, items, types, and / or groups, but do not exclude the presence, occurrence, or addition of one or more other features, steps, operations, elements, components, items, types, and / or groups. For example, a process, method, system, product, or device that includes a series of steps or units need not be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products, or devices. Additionally, the term "and / or" that may be used hereinafter describes the association relationship of associated objects and indicates that three relationships may exist. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. Additionally, the character " / ", unless otherwise specified, generally represents an "and / or" relationship between the associated objects before and after. Additionally, in the description of the embodiments of the present application, "a plurality" means two or more than two.

[0027] Some nouns or terms used in each embodiment of the present application are explained below, and these nouns or terms are also part of the invention content. Those skilled in the art of the present technology can understand that unless otherwise defined, all terms used herein, including technical terms and scientific terms, have the same meaning as the general understanding of those of ordinary skill in the art to which the present application belongs. It should also be understood that terms such as those defined in a general dictionary should be understood to have a meaning consistent with the meaning in the context of the prior art, and will not be interpreted with an idealized or overly formal meaning unless specifically defined as herein.

[0028] The 3D printing device described in the embodiments of the present application prints 3D objects by solidifying the printing material layer by layer and accumulating the solidified layers. Taking the 3D printing device including an energy radiation device as an example, the method of solidifying layer by layer and accumulating the solidified layers is described. Under the control of the control device, the energy radiation device prints layer by layer according to the slice contour of each layer (for example, layer by layer exposure or scanning). When a layer is solidified, the workbench moves a layer spacing (which can also be called the layer thickness) in the Z-axis direction, and a new layer of printing material is covered on the just solidified surface for printing. The newly solidified layer is firmly bonded to the previous layer. Repeating this process, layer by layer stacking, finally forming the entire 3D object. Among them, before the 3D printing device executes printing, slice data corresponding to the 3D object to be printed needs to be generated in the 3D printing pre-processing. The slice data includes the slice contours of each slice layer (simply referred to as layers) of the 3D model corresponding to the 3D object to be printed and the layer spacing corresponding to each layer. When the layer is thin enough, it can be considered that the slice contours of the upper and lower surfaces of the layer are the same. In other words, when the layer is thin enough, the slice contour of the layer can be considered as a two-dimensional contour in the length and width directions. The slice contour of the layer can be described by image or coordinate data.

[0029] The computer three-dimensional space described in the embodiments of the present application is a computer space with three dimensions (X-axis, Y-axis, and Z-axis) for constructing 3D models. In the following embodiments, the direction corresponding to the X-axis in the layer and the grid is called the length direction, the direction corresponding to the Y-axis in the layer and the grid is called the width direction, and the direction corresponding to the Z-axis in the layer and the grid is called the height direction. In one embodiment, the 3D model is a model constructed in the field of 3D printing technology. Furthermore, the 3D model constructed in the computer three-dimensional space can be printed into a 3D object in the actual physical space by a 3D printer. Among them, the 3D object can be any 3D object such as aerospace parts, automotive parts, industrial equipment parts, handicrafts, medical devices, etc.

[0030] In the embodiments of the present application, the implicit expression model (which can also be referred to as an implicit model or a model based on implicit expression) expresses the geometric shape of a 3D model implicitly. Among them, the input of the implicit is the three-dimensional coordinates of points in the computer three-dimensional space, and the output is a numerical value indicating the relative position relationship between the point and the surface of the 3D model, which is also referred to as the output value in some embodiments. Specifically, the three-dimensional coordinates of each point in the computer three-dimensional space are respectively input into the implicit. Among them, the set of points with an output value of 0 defines the outer contour shape of the 3D model. These points can be regarded as being on the 3D model. If the output value of the implicit corresponding to a point is less than 0, it indicates that the point is inside the 3D model, and if the output value of the implicit corresponding to a point is greater than 0, it indicates that the point is outside the 3D model. Of course, in other embodiments, depending on the difference of the implicit, if the output value of the implicit corresponding to a point is less than 0, it can also indicate that the point is outside the 3D model, and if the output value of the implicit corresponding to a point is greater than 0, it indicates that the point is inside the 3D model.

[0031] The implicit expression (or simply referred to as implicit) described in the embodiments of the present application can be of any type or any combination of types. For example, in one example, the implicit expression is configured as an equation, that is, the geometric shape of the 3D model is expressed by an equation. In this example, taking a 3D model of a sphere with a radius of 1 as an example, its corresponding implicit expression is the implicit equation: , where, the value of is the output value of the implicit equation, is the input of the implicit equation. In another example, the implicit expression is configured to express the geometric shape of the 3D model through a function or a combination of functions. Examples of functions include the maximum function max(), the minimum function min(), the length function length(), and their combinations, etc. In yet another example, the implicit expression is configured to express the geometric shape of the 3D model through a conversion relationship or a specified algorithm, etc. For example, the conversion relationship from a triangular mesh to an implicit. The above examples are only illustrative. In other examples, the implicit expression can also be configured as a combination of any of the above examples. The present application does not limit the type or manner of the implicit expression, as long as it can represent the geometric shape of the 3D model in the manner defined above.

[0032] In view of the technical problem of how to efficiently slice an implicit model described in the background art, the present application discloses a slicing method and system, a computer device, a computer-readable storage medium, and a computer program product. The present application can select any number of consecutive layers from a plurality of consecutive layers that can completely wrap the implicit expression model to form a subspace, and perform hierarchical meshing until each sub-grid at the current level is a single-layer grid that meets the corresponding layer resolution. And select sub-grids whose implicit expression value range contains the threshold range as key grids among the single-layer grids that meet the corresponding layer resolution, and fill in the output value of the implicit expression of at least one representative point therein to determine the slice contour of each selected layer. In this way, the present application does not need to first convert the implicit expression model into a triangular mesh model for slicing, and only fills in the output value of the implicit expression in the key grids during the slicing process to determine the slice contour, reducing the calculation amount during the slicing process and realizing efficient slicing of the implicit expression model.

[0033] The following further describes the present application in detail with reference to the drawings and specific embodiments. The technical solutions in the embodiments of the present application are clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments and the achieved technical effects obtained by those of ordinary skill in the art without creative efforts should belong to the scope of protection of the present application. The phrase "an embodiment" or similar phrases mentioned throughout this specification means that the specific features, structures, or characteristics described in conjunction with the embodiment are included in at least one embodiment of the present application. Therefore, the appearance of the phrases "in an embodiment" and "in an embodiment" and similar phrases throughout this specification may (but not necessarily) refer to the same embodiment.

[0034] In some embodiments of the present application, a slicing method is provided. The slicing method can be executed by a computer device configured with a slicing system. The slicing system is a software tool or software module that can process data, and executes the slicing method by means of the operating environment provided by the hardware device and / or operating system in the computer device.

[0035] In one embodiment, the computer device can be configured as an electronic device, that is, the slicing method is executed by the electronic device. For example, the electronic device includes devices such as a desktop computer, a laptop computer, a tablet computer, a smart TV, a smart phone, a tablet, and an industrial control computer. The electronic device can also be an electronic device composed of a host with multiple virtual machines and a human-computer interaction device (such as a touch display screen, a keyboard, and a mouse) corresponding to each virtual machine.

[0036] In one embodiment, the computer device can be configured as a server, that is, the slicing method is executed by the server. The server can be arranged on one or more physical servers according to various factors such as function and load. In some examples, the server can be a cloud architecture-based server, which refers to a cloud computing platform provided by a cloud computing provider. The cloud computing platform can provide services such as IaaS (Infrastructure-as-a-Service), PaaS (Platform-as-a-Service), and SaaS (Software-as-a-Service). Among them, the cloud computing platform includes a public cloud, a private cloud, and a hybrid cloud, etc. In some examples, the server can be composed of a distributed or centralized server cluster. For example, the server cluster is composed of at least one physical server. Multiple virtual servers are configured in each physical server, and each virtual server runs at least one functional module in the system, and the virtual servers communicate with each other through a network.

[0037] Please refer to Figure 1 , which shows a schematic flowchart of the slicing method in an embodiment of the present application. As shown in the figure, the slicing method includes step S110, step S120, and step S130. The following takes the slicing method being executed by a computer device as an example to illustrate each embodiment.

[0038] In step S110, the computer device creates a plurality of continuous layers that can completely wrap the implicit expression model; wherein, the plurality of layers are respectively configured with layer resolutions. It should be noted that the plurality of layers being respectively configured with layer resolutions can be understood as each layer having a layer resolution. In subsequent partitioning operations of the subspace formed by any number of continuous layers, the partitioning on the plane where the layer is located cannot be performed without limit (for example, if the layer is on the X-Y plane, that is, the partitioning of the subspace on the X-Y plane cannot be performed without limit), and it does not mean whether the plurality of layers in step S110 have been partitioned according to the layer resolution. In addition, the continuous plurality of layers created in the related embodiments of this step can be understood as predefining a continuous plurality of layers, and it is not necessarily required to be presented in a visual manner in the display interface of the computer device.

[0039] Among them, the continuous multiple layers that can completely enclose the implicit expression model mean that the overall space of the continuous multiple layers can completely enclose the implicit expression model. Among them, the dimensions of the overall space of the continuous multiple layers in the length direction, width direction, and height direction are not less than the dimensions of the bounding box of the implicit expression model in the length direction, width direction, and height direction. The bounding box will be described in detail later.

[0040] Among them, the layer resolution is used to represent the granularity at which a layer can be meshed. It can be predefined or pre-stored, or determined based on user input. In one embodiment, the layer resolution is configured as the size of the smallest unit into which a layer can be divided (or can be understood as the unit size). Taking the layer aligned with the X-Y plane in the computer three-dimensional space as an example, the layer resolution is the size of the smallest unit obtained by dividing the layer in the X-axis and Y-axis directions. In the example where the layer is aligned with the X-Y plane, the height direction of the layer corresponds to the Z-axis direction. In some subsequent embodiments, the grid division will be described with the layer aligned with the X-Y plane and the height direction corresponding to the Z-axis direction as an example, and it should not be construed as a limitation to this application. Those skilled in the art can also align the layer in other ways under the inventive concept of this application, and only need to make corresponding direction adjustments to the division method.

[0041] Furthermore, the layer resolution includes the resolution in the X-axis direction of the layer (which can also be called the resolution in the length direction of the layer or the X-axis resolution of the layer), and the resolution in the Y-axis direction of the layer (which can also be called the resolution in the width direction of the layer or the Y-axis resolution of the layer). Taking the layer resolution configured as the size of the smallest unit of the above layer as an example, the resolution in the X-axis direction of the layer refers to the size of the smallest unit of the layer in the X-axis direction, which can be understood as the length of the smallest unit of the layer, and the resolution in the Y-axis direction of the layer refers to the size of the smallest unit of the layer in the Y-axis direction, which can be understood as the width of the smallest unit of the layer. Among them, the layer resolutions of different layers can be the same or different, and the resolutions in the X-axis and Y-axis directions on the same layer can be the same or different. For the convenience of description, in the following embodiments, an example will be given where the layer resolutions of different layers are the same and the resolutions in the X-axis and Y-axis directions on the same layer are also the same.

[0042] In one embodiment, the step of creating continuous multiple layers that can completely enclose the implicit expression model includes creating the multiple layers based on the length, width, and height information of the bounding box of the implicit expression model, the grid parameters of the layer plane, and the layer spacing of the multiple layers.

[0043] Among them, the bounding box of the implicit expression model can be defined as the smallest space that encloses the implicit expression model, which can be, for example, a bounding box in the form of an AABB (Axis Aligned Bounding Box), or can also be, for example, a bounding box in the form of an OBB (Oriented Bounding Box). The length, width, and height information of the bounding box includes the length information of the bounding box, the width information of the bounding box, and the height information of the bounding box. Among them, the length information of the bounding box is the size occupied by the bounding box on the X-axis (i.e., the length of the bounding box). Correspondingly, the width information of the bounding box is the size occupied by the bounding box on the Y-axis (i.e., the width of the bounding box). The height information of the bounding box includes the Z-axis coordinates of the lowest point and the highest point of the bounding box. The height information of the bounding box can also include the size occupied by the bounding box on the Z-axis (i.e., the height of the bounding box).

[0044] Among them, the grid parameters of the layer plane (which can also be called the grid parameters of the layer) can be, for example, predefined or pre-stored, or can also be determined based on the user's input. In some examples, the grid parameters of the layer plane include the minimum cell size of the grid for each layer. The minimum cell size can further include the size (length) occupied by the minimum cell on the X-axis and the size (width) occupied by the minimum cell on the Y-axis. In another example, the grid parameters of the layer plane (which can also be called the grid parameters of the layer) include the number of minimum cells in the length and width directions for each layer. It should be noted that the grid parameters of the layer planes of different layers can be the same or different. For the convenience of description, in the following embodiments, the case where the grid parameters of the layer planes of different layers are the same is taken as an example for description.

[0045] Among them, the layer spacing is the size of the layer in the height direction (i.e., the Z-axis direction). The layer spacings of different layers can be the same or different.

[0046] In one embodiment, creating a continuous plurality of layers that can completely wrap the implicit expression model further includes the step of providing a parameter configuration window for the user to input the layer spacing and / or the grid parameters of the layer plane. Among them, the parameter configuration window can be used only for the user to input the layer spacing or the grid parameters of the layer plane, or can be used for the user to input both the layer spacing and the grid parameters of the layer plane. Taking the case where a parameter configuration window can be used for the user to input both the layer spacing and the grid parameters of the layer plane as an example, please refer to Figure 2, which shows a schematic diagram of the parameter configuration window in an embodiment of the present application. It is shown by taking the grid parameters of the layer plane including the minimum unit size of the grid for each layer and the minimum unit size of the grid for each layer being the same, and the layer spacing for each layer being the same as an example. Input boxes for the layer spacing, the size of the minimum unit of the grid in the X-axis direction, and the size of the minimum unit of the grid in the Y-axis direction are provided in the parameter configuration window. The user can input data in the corresponding input boxes to complete the input of the layer spacing and the grid parameters of the layer plane. It should be understood that Figure 2 is only an example. In examples where, for example, the layer spacing for each layer is different or the minimum unit size of the grid for each layer is different, input windows for configuring different layer spacings or the minimum unit size of the grid for each layer can be correspondingly provided in the parameter configuration window. Additionally, in examples where the grid parameters of the layer plane are configured with other parameters, those skilled in the art can also make adaptive adjustments to the content and interface layout that can be displayed in the parameter configuration window under the guidance of the present application. The present application places no restrictions on this.

[0047] In an embodiment, the step of creating the multiple layers based on the length, width, and height information of the bounding box of the implicit expression model, the grid parameters of the layer plane, and the layer spacing of the multiple layers includes: determining the layer positions of the multiple layers based on the height information of the bounding box of the implicit expression model and the layer spacing of the multiple layers, and determining the length and width dimensions of the multiple layers based on the length and width information of the bounding box and the grid parameters of the layer plane to create the continuous multiple layers.

[0048] Among them, the layer positions of the multiple layers are used to indicate the height positions of the multiple layers. For example, the layer positions of the multiple layers can be represented by the Z-axis coordinates of the upper surfaces of the multiple layers and / or the Z-axis coordinates of the lower surfaces of the multiple layers.

[0049] In an embodiment, the computer device determines the layer positions of the multiple layers based on the height information of the bounding box of the implicit expression model and the layer spacing. In this embodiment, the height information of the bounding box includes the Z-axis coordinates of the lowest point and the highest point of the bounding box. Specifically, based on the Z-axis coordinate of the lowest point of the bounding box, the layer spacing corresponding to each layer is stacked layer by layer until the stacked value is greater than the Z-axis coordinate of the highest point of the bounding box, and then the stacking stops to obtain the layer positions of the multiple layers. For example, please refer to Figure 3, which shows a schematic diagram of the layer positions of multiple layers in an embodiment of the present application. As shown in the figure, the Z-axis coordinates of the lowest point and the highest point of the bounding box B are Min_z and Max_z respectively. The Z-axis coordinate Min_z of the lowest point of the bounding box B is used as the Z-axis coordinate of the lower surface of the first layer. The layer spacing d1 of the first layer c1 is added to obtain the Z-axis coordinate of the upper surface of the first layer Min_z + d1, which is the Z-axis coordinate of the lower surface of the second layer c2. After adding the layer spacing d2 of the second layer c2 to the layer position Min_z + d1 of the first layer c1, the Z-axis coordinate of the upper surface of the second layer c2, Min_z + d1 + d2, can be determined, which is the Z-axis coordinate of the lower surface of the third layer c3. Continuing in this way for subsequent layers until, as Figure 3 shown, the Z-axis coordinate of the upper surface of the (n - 1)th layer cn - 1 determined, Min_z + d1 + d2 + … + dn - 1, is less than or equal to the highest point Max_z of the bounding box, while the Z-axis coordinate of the upper surface of the nth layer cn, Min_z + d1 + d2 + … + dn - 1 + dn, is greater than the highest point of the bounding box. Then, the calculation of determining the layer positions of multiple layers is stopped, as shown in Figure 3 shown, and finally the layer positions of n layers are determined. These n layers can completely wrap the implicit expression model in the height direction. It should be understood that Figure 3 only shows the determination of the layer positions of each layer, and does not include the planar size of the layer (it can also be understood as not showing the format size or length and width of the layer). In addition, the calculation method for determining the layer positions of the multiple layers in the above embodiment is only for example. Those skilled in the art can make adaptive changes to the determination method under the guidance of the present application to obtain the layer positions of multiple layers. The present application does not limit this, as long as the total height of the multiple layers is not less than the height of the bounding box of the implicit expression model.

[0050] In an embodiment, for example, in the embodiment where the grid parameters of the layer plane include the minimum unit size of the grid of each layer, the computer device further determines the length and width dimensions of the multiple layers based on the length and width information of the bounding box and the grid parameters of the layer plane. Specifically, the computer device can determine the dimension of each layer in the length direction according to the length of the minimum unit of the grid of each layer and the length of the bounding box, and can determine the dimension of each layer in the width direction according to the width of the minimum unit of the grid of each layer and the width of the bounding box. It should be understood that in the embodiment where the grid parameters of the layer plane of each layer are the same, the length and width dimensions of the multiple layers are the same, and the overall space of the multiple layers is a regular three-dimensional space (such as a cube space or a cuboid space). In other embodiments where the grid parameters of the layer plane of each layer are different, the length and width dimensions of the multiple layers are also different, and the overall space of the multiple layers can be an irregular three-dimensional space.

[0051] Taking the example that the grid parameters of the layer plane of each layer are the same, this paper illustrates how a computer device determines the length and width dimensions of multiple layers. Specifically, the computer device can round up the value obtained by dividing the length of the bounding box by the length of the smallest unit to get the number of the smallest units in the length direction. The product of this number and the length of the smallest unit can be used as the length of multiple layers. The width of multiple layers can be determined in the same way. Of course, other methods can also be adopted. For example, the value obtained by adding a preset number to the value obtained by rounding up the value of dividing the length of the bounding box by the length of the smallest unit is used as the number of the smallest units in the length direction. The product of this number and the length of the smallest unit can be used as the length of multiple layers. The preset number is, for example, any integer from 1 to 10. The width of the corresponding multiple layers can be determined in the same way. This application does not limit the method of determining the length and width of multiple layers, as long as the length and width of multiple layers are not less than those of the bounding box, so as to ensure that the multiple consecutive layers created can completely enclose the implicit expression model in the length and width directions.

[0052] It should be noted that in embodiments where the grid parameters of the layer plane of each layer are different, the calculation of determining the length and width can be performed once for the grid parameters of each different layer plane according to the description of the above embodiments to determine the length and width dimensions of multiple layers.

[0053] In another embodiment, for example, in an embodiment where the grid parameters of the layer plane include the number of the smallest units in the length and width directions of each layer, the computer device can directly determine the length and width of multiple layers according to the length and width of the bounding box of the implicit expression model. Among them, the method of determining the length and width of multiple layers, for example, can be to increase a certain size on the basis of the length and width of the bounding box to determine the length and width of multiple layers, or directly use the length and width of the bounding box as the length and width of multiple layers.

[0054] According to the description of any of the above embodiments, the computer device can determine the layer positions of the multiple layers and the length and width dimensions of the multiple layers. Furthermore, the computer device can create the multiple consecutive layers according to the determined layer positions of the multiple layers and the length and width dimensions of each layer. For example, please refer to Figure 4 , which shows a schematic diagram of multiple consecutive layers created in an embodiment of this application. As shown in the figure, the number of the multiple consecutive layers is 7, that is, the multiple consecutive layers include the first layer c1, the second layer c2, the third layer c3, the fourth layer c4, the fifth layer c5, the sixth layer c6, and the seventh layer c7. The length and width dimensions of each layer are the same.

[0055] In one embodiment, the slicing method further includes a step of determining the layer resolution based on the grid parameters of the layer plane. In one example, the grid parameters of the layer plane include the minimum cell size of the grid for each layer, and the minimum cell size of the grid for each layer can be directly used as the layer resolution for each layer. In another example, the grid parameters of the layer plane include the minimum number of cells in the length and width directions for each layer, and then the computer device determines the layer resolution for each layer according to the minimum number of cells in the length direction and the width direction for each layer and the length and width of each layer. Specifically, the X-axis resolution of each layer is configured as the ratio of the length of each layer to the minimum number of cells in the length direction of each layer, and the Y-axis resolution of each layer is configured as the ratio of the width of each layer to the minimum number of cells in the width direction of each layer.

[0056] In step S120, the computer device selects any number of consecutive layers from the multiple layers to form a subspace and performs hierarchical meshing on the subspace, including: recursively executing to determine the value range of the implicit expression of each sub-grid at the current level to perform the next-level meshing on the sub-grid whose value range includes a threshold range until each sub-grid at the current level is a single-layer grid that meets the corresponding layer resolution; where the any number of consecutive layers includes a single layer or multiple layers (such as two or more consecutive layers), and the implicit expression is the implicit expression of the implicit expression model, which will not be elaborated in subsequent embodiments.

[0057] In one embodiment, the computer device selects any number of consecutive layers from the multiple layers to form a subspace. In the embodiment where the any number of consecutive layers is multiple layers, the computer device can select multiple consecutive layers from the multiple layers to form the subspace. Specifically, the overall space corresponding to the selected multiple consecutive layers is used as the subspace. For example, please refer to Figure 5 , which shows a schematic diagram of a subspace selected in one embodiment of the present application. As shown in the figure, the computer device selects the consecutive first layer c1, second layer c2, third layer c3, and fourth layer c4 from the multiple layers (the first layer c1, second layer c2, third layer c3, fourth layer c4, fifth layer c5, sixth layer c6, seventh layer c7) to form a subspace V1. In the embodiment where the any number of consecutive layers is a single layer, the computer device can select one layer from the multiple layers to form a subspace. For example, please refer to Figure 6 , which shows a schematic diagram of a subspace selected in another embodiment of the present application. As shown in the figure, the computer device selects the first layer c1 from the multiple layers (the first layer c1, second layer c2, third layer c3, fourth layer c4, fifth layer c5, sixth layer c6, seventh layer c7) to form a subspace V2.

[0058] In one embodiment, when selecting multiple layers to constitute the subspace layer, in order to enable the subspace to be divided in the length and width directions when performing step-by-step gridding, continuous layers with the same layer resolution need to be divided into one subspace, that is, the layer resolution of each layer in the subspace is the same.

[0059] In one embodiment, the computer device also provides a layer number configuration window for the user to configure the number of layers constituting the subspace. Specifically, the user can enter the number of layers constituting the subspace in the configuration window, and then the computer device can select a number of continuous layers corresponding to the number of layers input from the multiple layers based on the number of layers input by the user to constitute a subspace. For example, if the number of layers constituting the subspace input by the user is 1, the computer device selects a layer from the multiple layers to constitute a subspace. It should be noted that when the number of layers constituting the subspace input by the user is more than 2, the computer device can constitute a subspace with continuous layers not exceeding the number of layers input. In this way, the user can enter different numbers of layers according to the memory of the computer device. For example, when the computer memory is low, 1 layer or a smaller number of layers can be entered to avoid the problem of slicing failure due to memory limitations.

[0060] In one embodiment, the step of meshing the subspaces step by step by the computer device further includes meshing the subspaces for the first time to obtain a plurality of initially meshed subgrids.

[0061] In the embodiment where the subspace includes multiple layers, the computer device evenly divides the subspace in the length direction, width direction, and height direction to obtain multiple subgrids after the first gridding. Figure 7 , showing that this application is Figure 5 The schematic diagram of the subspace after the first meshing in the embodiment shown in the figure is as shown in the figure. Figure 5 The length, width, and height directions of the subspace V1 are divided into two equal parts to obtain eight subgrids (subgrid v11, subgrid v12, subgrid v13, subgrid v14, subgrid v15, subgrid v16, subgrid v17, and subgrid v18). In the embodiment where the subspace includes a single layer, the computer device divides the subspace equally in the length and width directions to obtain multiple subgrids after the first gridding. In this embodiment, the subspace can be regarded as a two-dimensional plane in the length and width directions for two-dimensional division. Please refer to Figure 8 , showing that this application is Figure 6 The schematic diagram of the subspace after the first meshing in the embodiment shown in the figure is as shown in the figure. Figure 6 The subspace V2 is divided into two equal parts in the length and width directions to obtain four subgrids (subgrid v21, subgrid v22, subgrid v23, and subgrid v24).

[0062] For the convenience of illustration, Figure 7 and Figure 8 the divided sub-grids are illustrated in a separated and listed manner in [reference], which does not mean that the sub-grids will be separated or arranged in the way shown in the figure.

[0063] It should be noted that although in the Figure 7 and 8 illustrated embodiments, the equal division in the length direction, width direction, and height direction is a binary division, in other embodiments, it can also be a ternary division, a quaternary division or other equal divisions of other quantities, and different quantities of equal divisions can also be performed in different directions, and it can also be an approximate equal division. The approximate equal division means that the difference between the sub-grids after approximate equal division in the corresponding direction is not significant (for example, the difference in the number of the smallest units included in the sub-grids after approximate equal division in the corresponding direction is within 50%). For example, when the number of the smallest units included in the sub-space in the length, width, and / or height direction is odd, the corresponding direction can be approximately equally divided. For example, when the sub-space is composed of an odd number of layers, the computer device can approximately equally divide the height direction of the sub-space V1. Taking the approximate equal division of a sub-space composed of 7 layers into an approximate binary division as an example, after the approximate binary division, the sizes of the 8 sub-grids in the height direction can include the height corresponding to 3 layers and the height corresponding to 4 layers. In the following embodiments, for the convenience of description, the equal division in different directions is taken as an example of binary division for description.

[0064] The computer device can regard the first meshing as the first-level meshing, and take the multiple sub-grids after the first-level meshing as the multiple sub-grids of the first level, and recursively execute to respectively determine the value range of the implicit expression of each sub-grid of the current level to perform the next-level meshing on the sub-grids whose value range contains a threshold range until each sub-grid of the current level is a single-layer grid that meets the layer resolution of the corresponding layer. The recursive execution means selecting sub-grids with the same selected conditions to continue the next-level subdivision until the termination condition is reached. In this embodiment, the selected condition for each level is that the value range of the implicit expression of the sub-grids of this level contains the threshold range, and the termination condition is that each sub-grid of this level is a single-layer grid that meets the corresponding layer resolution, that is, the termination condition is that each sub-grid of this level is a single-layer grid and meets the corresponding layer resolution. Among them, the single-layer grid means that the sub-grid only contains one layer in the height direction, and the sub-grid meets the corresponding layer resolution means that the sub-grid meets the resolution of the layer that constitutes the sub-space. Specifically, the sub-grid needs to reach the corresponding resolution in both the length and width directions to meet the corresponding layer resolution.

[0065] Specifically, the recursive execution process described in this embodiment can be expanded as follows. When the sub-grids at the first level do not reach the corresponding layer resolution and are not single-layer grids, the computer device will respectively determine the value ranges of the implicit expressions of the sub-grids at the first level, and perform second-level grid division on the sub-grids whose value ranges contain the threshold range, and the sub-grids at the second level can be obtained. Then, when the sub-grids at the second level do not reach the corresponding layer resolution and are not single-layer grids, the computer device will continue to determine the value ranges of the implicit expressions of the sub-grids at the second level, and continue to perform third-level grid division on the sub-grids whose value ranges contain the threshold range, and the sub-grids at the third level can be obtained. This process of continuously performing the next-level grid division is repeated until the sub-grids at the current level are single-layer grids that meet the corresponding layer resolution, and then the grid division will no longer continue.

[0066] In one embodiment, the step of respectively determining the value ranges of the implicit expressions of the sub-grids at the current level to perform the next-level grid division on the sub-grids whose value ranges contain a threshold range includes respectively determining the value ranges of the implicit expressions of the sub-grids at the current level, comparing the threshold range with the value ranges of the sub-grids respectively, and performing the next-level grid division on the corresponding sub-grids under the condition that it is determined that the value range contains the threshold range.

[0067] Among them, the value range of the implicit expression of the sub-grid represents the estimated range of the numerical intervals where all the output values obtained by respectively inputting the implicit expressions of all points in the sub-grid into the implicit expression model are located. Among them, the estimated range is wider than (or greater than) the numerical interval formed by the smallest and largest of all the output values. For example, after all the points in a sub-grid are input into the implicit expression, the numerical interval formed by the smallest and largest of the output values is [i, j], then the lower limit i1 of the value range [i1, j1] of the implicit expression of the sub-grid is less than or equal to the lower limit i of the numerical interval, and the upper limit j1 is greater than or equal to the upper limit j of the numerical interval.

[0068] In one embodiment, the computer device determines the value range of the sub-grid based on the diagonal vertices of the sub-grid. The diagonal vertices of the sub-grid are the two endpoints of the body diagonal of the sub-grid. For example, the diagonal vertices of the sub-grid are configured to correspond to the points closest to the coordinate origin (the minimum position points) and the points farthest from the coordinate origin (the maximum position points), respectively. In one example, for instance, the implicit expression is configured as an equation, a function, a combination of functions, or a combination of functional equations. The computer device may pre-store a corresponding range calculation algorithm. The computer device can call the range calculation algorithm based on the determined diagonal vertices of the sub-grid to output the value range. In another example, the computer device determines the length of the body diagonal of the sub-grid based on the diagonal vertices of the sub-grid, and determines the value range of the sub-grid based on the length of the body diagonal and the output value of the implicit expression of the center point of the sub-grid. Specifically, the computer device determines the length r of the body diagonal of the sub-grid based on the coordinates of any pair of diagonal vertices of the sub-grid, and the output value p obtained by inputting the coordinates of the center point of the sub-grid into the implicit expression. The difference between the output value p and half of the length r of the body diagonal is used as the lower limit of the value range, and the sum of the output value p and half of the length r of the body diagonal is used as the upper limit of the value range. Thus, the value range of the sub-grid can be obtained as [p - 0.5r, p + 0.5r]. In this embodiment, the value range of the sub-grid can be quickly obtained while ensuring that the value range must include the actual output value range, improving the calculation speed of the gridification of the implicit expression model.

[0069] In another embodiment, the computer device determines the value range of the sub-grid based on the key points of the sub-grid. Specifically, the key points of the sub-grid are respectively substituted into the implicit expression to obtain multiple output values, and the range formed by the minimum value and the maximum value among the obtained multiple output values is determined as the value range of the sub-grid. In one example, the key points include the vertices of the sub-grid, the center point of the sub-grid, the midpoints of the edges of the sub-grid, the center points of the faces of the sub-grid, or the corner vertices of the sub-grid, but are not limited thereto. In other examples, those skilled in the art can add other points (such as points on the body diagonal) in the sub-grid as key points according to the accuracy requirements under the inspiration of this application.

[0070] It should be noted that this application does not limit the method for determining the value range of the implicit expression of the sub-grid, as long as an estimated value of the output value range can be quickly obtained.

[0071] According to the method for determining the value range of sub - grids described in any of the above - mentioned embodiments, the value ranges of the implicit expressions of each sub - grid at the current level can be determined, so as to compare the threshold range with the value ranges of each sub - grid respectively, and then determine whether the value range of each sub - grid contains the threshold range. In the following embodiments, it is exemplified that the output value of the implicit corresponding to a point being less than 0 indicates that the point is inside the 3D model, and the output value of the implicit corresponding to a point being greater than 0 indicates that the point is outside the 3D model.

[0072] In one embodiment, the threshold range is configured as the boundary value of the implicit expression. The boundary value of the implicit expression represents the output value of the implicit expression of the points on the outer contour of the implicit expression model. Taking the output value of 0 representing the points on the outer contour as an example, the boundary value is 0. That is, in this embodiment, the threshold range is configured as the single - point range [0, 0]. In this embodiment, comparing the threshold range with the value ranges of each sub - grid respectively can be, for example, comparing the lower limit value and / or the upper limit value of the value range of the sub - grid with the boundary value. Further, in one example, when the lower limit value of the value range of the sub - grid is greater than the boundary value, it is determined that the value range is greater than the threshold range. At this time, the sub - grid is completely located outside the implicit expression model. For example, if the value range of a sub - grid is [1, 2] and the boundary value is 0, then it is determined that the value range of this sub - grid is greater than the threshold range. In another example, when the upper limit value of the value range of the sub - grid is less than the boundary value, it is determined that the value range is less than the threshold range. At this time, the sub - grid is completely located inside the implicit expression model. For example, if the value range of a sub - grid is [-2, -1] and the boundary value is 0, then it is determined that the value range of this sub - grid is less than the threshold range. In yet another example, when the lower limit value of the value range of the sub - grid is less than or equal to the boundary value and the upper limit value of the value range is greater than or equal to the boundary value, it is determined that the value range of the corresponding sub - grid contains the threshold range. At this time, the sub - grid may be completely located inside the implicit expression model, may be completely located outside the implicit expression model, or may be partially located inside the implicit expression model and partially located outside the implicit expression model. For example, if the value range of a sub - grid is [-1, 1] and the boundary value is 0, then it is determined that the value range of this sub - grid contains the threshold range.

[0073] In another embodiment, the threshold interval is configured as an interval with the first threshold as the upper limit and the second threshold as the lower limit, which includes the boundary value of the implicit expression. In other words, the boundary value of the implicit expression is included in the threshold interval with the first threshold as the upper limit and the second threshold as the lower limit. In an example, the first threshold is a positive number close to 0, and the second threshold is a negative number close to 0. For example, the first threshold can be any positive number between [0 - 0.5], and the second threshold can be any negative number between [-0.5 - 0]. In this embodiment, comparing the threshold interval with the value range of each sub-grid can be, for example, comparing the lower limit value of the value range of the sub-grid with the upper limit value of the threshold interval and / or comparing the upper limit value of the value range of the sub-grid with the lower limit value of the threshold interval. Further, in an example, when the lower limit value of the value range of the sub-grid is greater than the first threshold, it is determined that the value range is greater than the threshold interval. At this time, the sub-grid is completely outside the implicit expression model. For example, the threshold interval is configured as [-0.1, 0.1], and the value range of a sub-grid is [0.2, 0.4], then it is determined that the value range is greater than the threshold interval. In another example, when the upper limit value of the value range of the sub-grid is less than the second threshold, it is determined that the value range is less than the threshold interval. At this time, the sub-grid is completely inside the implicit expression model. For example, the threshold interval is configured as [-0.1, 0.1], and the value range of a sub-grid is [-1, -0.3], then it is determined that the value range is less than the threshold interval. In yet another example, when the lower limit value of the value range of the sub-grid is less than or equal to the first threshold and the upper limit value of the value range is greater than or equal to the second threshold, it is determined that the value range of the corresponding sub-grid includes the threshold interval. At this time, the sub-grid may be completely inside the implicit expression model, may be completely outside the model, or may be partially inside and partially outside the model. For example, the value range of a sub-grid is [-1, 0.05], and the threshold interval is [-0.1, 0.1], then it is determined that the value range of the sub-grid includes the threshold interval.

[0074] In other embodiments, when the output value of the implicit corresponding to a point is less than 0, it indicates that the point is outside the 3D model, and when the output value of the implicit corresponding to a point is greater than 0, it indicates that the point is inside the 3D model. Then, under the condition that the value range is greater than the threshold interval, it is determined that the sub-grid is completely inside the implicit expression model, and under the condition that the value range is less than the threshold interval, it is determined that the sub-grid is completely outside the implicit expression model.

[0075] The computer device performs the next-level meshing on the corresponding sub-grid under the condition that the value range includes the threshold range. In one embodiment, the next-level meshing is configured to traverse the length, width, and height directions of the current-level sub-grid and perform meshing in a way of equally dividing the directions that can be equally divided. Specifically, when performing the next-level meshing on the current-level sub-grid, traverse the length, width, and height directions of the current-level sub-grid, regard the direction that does not reach the layer resolution in the length and width directions as the direction that can be equally divided, and regard the height direction as the direction that can be equally divided when the height direction is not a single-layer grid. After equally dividing the directions that can be equally divided of the current-level sub-grid, the next-level meshing of the sub-grid is realized. Among them, the way of equally dividing the directions that can be equally divided of the current-level sub-grid is the same as or similar to the way of equally dividing the length direction, width direction, and height direction during the first meshing described above, and will not be elaborated here.

[0076] Taking the way of equally dividing in the direction that can be equally divided as an example of binary division for detailed description, if the length, width, and height directions are all directions that can be equally divided, then after performing the next-level meshing on a sub-grid, the sub-grid can be divided into 8 sub-grids. In this embodiment, the way of dividing the sub-grid is the same as Figure 7 the division way of the first meshing shown; if only two of the length, width, and height directions are directions that can be equally divided, then after performing the next-level meshing on a sub-grid, the sub-grid can be divided into 4 sub-grids. In this embodiment, the way of dividing the sub-grid is the same as Figure 8 the division way of the first meshing shown; if only one of the length, width, and height directions is a direction that can be equally divided, then after performing the next-level meshing on a sub-grid, the sub-grid can be divided into 2 sub-grids.

[0077] In a specific embodiment, please refer to Figure 9 and combine with Figure 7 , Figure 9 which shows a schematic diagram after performing the next-level meshing on the sub-grid whose implicit expression value range in the embodiment shown in this application includes the threshold range. For example, determine according to any of the above-described embodiments Figure 7 and Figure 7Among the multiple sub - grids (sub - grid v11, sub - grid v12, sub - grid v13, sub - grid v14, sub - grid v15, sub - grid v16, sub - grid v17, sub - grid v18) after the first - level gridification, the sub - grids whose implicitly expressed value ranges contain the threshold range include sub - grid v11, sub - grid v12, sub - grid v15, and sub - grid v16. Then, only sub - grid v11, sub - grid v12, sub - grid v15, and sub - grid v16 need to be further subdivided at the next level, while the remaining sub - grids (i.e., sub - grid v13, sub - grid v14, sub - grid v17, and sub - grid v18) do not need to be further subdivided subsequently. Taking the next - level gridification of sub - grid v16 as an example, the length, width, and height directions of sub - grid v16 will be traversed respectively. For example, if the length and width directions of sub - grid v16 do not reach the corresponding resolution, the length and width directions of sub - grid v16 will be used as the directions where equal division can be performed. For example, if the height direction of sub - grid v16 is not a single - layer grid, the height direction of sub - grid v16 will also be used as the direction where equal division can be performed. After equal division of the three directions, the second - level gridification of sub - grid v16 is achieved, that is Figure 9 in which sub - grid v16 is divided into 8 sub - grids. The next - level gridification of sub - grid v11, sub - grid v12, and sub - grid v15 is similar to that of sub - grid v16. The length, width, and height directions of sub - grid v11, sub - grid v12, and sub - grid v15 will be traversed respectively. For example, if the length, width, and height directions of sub - grid v11, sub - grid v12, and sub - grid v15 are all directions where equal division can be performed, after equal division of the three directions, the second - level gridification of sub - grid v11, sub - grid v12, and sub - grid v15 is achieved, Figure 9 in which sub - grid v11, sub - grid v12, and sub - grid v15 can also be divided into 8 sub - grids. Due to perspective problems, not all the divided sub - grids are shown.

[0078] In one embodiment, the step of respectively determining the value range of the implicit expression of each sub - grid at the current level to perform the next - level gridification on the sub - grids whose value ranges contain a threshold range further includes step S1200.

[0079] In step S1200, the computer device fills the corresponding sub - grid with a value indicating outside the implicit expression model under the condition that the value range is greater than the threshold range, and fills the corresponding sub - grid with a value indicating inside the implicit expression model under the condition that the value range is less than the threshold range. In this embodiment, the implicit is configured such that the output value of the implicit corresponding to a point less than 0 indicates that the point is inside the 3D model, and the output value of the implicit corresponding to a point greater than 0 indicates that the point is outside the 3D model.

[0080] In one embodiment, according to the comparison description of the value range and the threshold range in the foregoing embodiments, when the value range of a sub-grid is greater than the threshold range, it indicates that the sub-grid is completely outside the implicit expression model, and then the sub-grid can be filled with a value indicating outside the implicit expression model. When the value range of a sub-grid is less than the threshold range, it indicates that the sub-grid is completely inside the implicit expression model, and then the sub-grid can be filled with a value indicating inside the implicit expression model. Among them, the value indicating outside the implicit expression model and the value indicating inside the implicit expression model can be configured as any different values. For example, the value indicating outside the implicit expression model is configured as 0, and the value indicating inside the implicit expression model is configured as 2.

[0081] Please continue to refer to Figure 9 and in combination with Figure 7 , after comparing, the comparison results of sub-grid v13, sub-grid v14, sub-grid v17, and sub-grid v18 are all that the value range is greater than the threshold range. Then, the sub-grid v13, sub-grid v14, sub-grid v17, and sub-grid v18 are all filled with a value indicating outside the implicit expression model, for example, all filled with 0. It should be noted that when the threshold range is configured as the boundary value of the implicit expression, or the threshold range is configured as an interval including the boundary value of the implicit expression with the first threshold as the upper limit and the second threshold as the lower limit, the method of determining that the value range is greater than the threshold range and the method of determining that the value range is less than the threshold range are the same as or similar to those in the foregoing embodiments, and will not be elaborated here.

[0082] In other embodiments, when the implicit is configured such that the output value of the implicit corresponding to a point less than 0 indicates that the point is outside the 3D model, and the output value of the implicit corresponding to a point greater than 0 indicates that the point is inside the 3D model, the corresponding sub-grid can be filled with a value indicating inside the implicit expression model under the condition that the value range is greater than the threshold range, and the corresponding sub-grid can be filled with a value indicating outside the implicit expression model under the condition that the value range is less than the threshold range.

[0083] In one embodiment, when filling a value indicating outside the implicit expression model or a value indicating inside the implicit expression model in a sub-grid, the value indicating outside the implicit expression model or the value indicating inside the implicit expression model can be filled at the position of the center point in the sub-grid.

[0084] In one embodiment, in order to reduce the amount of data for subsequent calculations, the sub-grids with a value range greater than the threshold range and the sub-grids with a value range less than the threshold range may also not be filled with values.

[0085] It should be noted that when comparing the threshold interval with the value ranges of each sub-grid, the comparison can be made after the value ranges of all sub-grids are completely calculated, or the value range of each sub-grid can be compared with the threshold interval immediately after the calculation of the value range of each sub-grid is completed. Similar situations also include the step of further dividing the corresponding sub-grid. When performing this step, all sub-grids that meet the condition that the value range contains the threshold interval can be further divided together, or each sub-grid that meets the condition that the value range contains the threshold interval can be further divided one by one. Similar situations also include step S1200.

[0086] Further, according to step S120, when each sub-grid at the current level is a single-layer grid that meets the corresponding layer resolution, the further division to the next level will stop; otherwise, the selected sub-grid will continue to be divided to the next level according to the embodiments of step S120 provided above. Please continue to refer to Figure 9 , if all the sub-grids (i.e., 32 sub-grids) obtained after dividing sub-grids v11, v12, v15, and v16 reach the resolution in the length direction, reach the resolution in the width direction, and are single-layer grids in the height direction, it means that all 32 sub-grids after the second-level division are single-layer grids that meet the corresponding layer resolution. Then, the further division of sub-grids v11, v12, v15, and v16 will stop; otherwise, the value ranges of the 32 sub-grids will be determined respectively, and the sub-grids that meet the condition that the value range contains a threshold interval will continue to be divided to the next level.

[0087] After step S120 reaches the termination condition, that is, until the divided sub-grids are single-layer grids that meet the layer resolution of the corresponding layer, the further division will stop, and step S130 will be executed. In step S130, the computer device selects the sub-grids whose implicitly expressed value ranges in the single-layer grids that meet the corresponding layer resolution contain the threshold interval as key grids and fills in the output values of at least one representative point implicitly expressed therein to determine the slice contours of each selected layer. It should be understood that in step S130, the implicitly expressed value ranges of the single-layer grids that meet the corresponding layer resolution will be determined according to the embodiments provided in step S120, so as to make a judgment to select key grids. Of course, the process of determining the implicitly expressed value ranges of the single-layer grids that meet the corresponding layer resolution can also be executed in step S120, that is, when the sub-grid meets the corresponding layer resolution and is a single-layer grid, step S120 will further determine the implicitly expressed value ranges of these sub-grids respectively for use in step S130.

[0088] Given the estimation range of the output value of the implicit expression with the value range being the sub-grid, which includes the threshold range and may not necessarily be accurately determined that the sub-grid must be on the model (such as the case very close to the outer contour of the model), or even if it is indeed on the model, it may cross the outer contour of the model. Therefore, in step S130, the computer device selects, from the single-layer grids that meet the corresponding layer resolution, the sub-grids whose value ranges of the implicit expression include the threshold range as the key grids and fills in the output values of the implicit expression of at least one representative point thereof, and then uses them to determine the slice contours of each selected layer, that is, the slice contours of each layer of a subspace. Please continue to refer to Figure 9 , such as Figure 9 In the 32 sub-grids after the second-level grid division in, they are all single-layer grids that meet the corresponding layer resolution (that is, the resolution of the layer that constitutes subspace V1), and among the 32 sub-grids, only the value ranges of sub-grid v111, sub-grid v112, sub-grid v115, sub-grid v116, sub-grid v121, sub-grid v125, sub-grid v151, sub-grid v152, sub-grid v161, and sub-grid v166 include the threshold range. Then the computer device will use sub-grid v111, sub-grid v112, sub-grid v115, sub-grid v116, sub-grid v121, sub-grid v125, sub-grid v151, sub-grid v152, sub-grid v161, and sub-grid v166 as the key grids.

[0089] In an embodiment, the step of filling in the output value of the implicit expression of at least one representative point in the key grid includes selecting at least one representative point in the key grid to obtain the output value of the implicit expression of the at least one representative point, and filling the output value into the corresponding position in the key grid. Among them, the representative point can be configured as the center point of the key grid or other position points in the key grid such as the corner points of the key grid. In an example, the step of filling in the output value of the implicit expression of at least one representative point in the key grid includes selecting a representative point in the key grid to obtain the output value of the implicit expression of the representative point, and filling the output value into the position where the representative point is located in the key grid. Taking the representative point being configured as the center point of the key grid as an example, inputting the coordinates of the center point of the key grid into the implicit expression can obtain the output value of the implicit expression of the center point, and filling this output value into the corresponding key grid. Please continue to refer to Figure 9, after the coordinates of the center points of sub-grids v111, v112, v115, v116, v121, v125, v151, v152, v161, and v166 are respectively input into the implicit expression, the output values of the implicit expressions of the center points of sub-grids v111, v112, v115, v116, v121, v125, v151, v152, v161, and v166 can be obtained, and the output values are respectively filled into sub-grids v111, v112, v115, v116, v121, v125, v151, v152, v161, and v166. In this example, the computer device can fill the output value of the implicit expression of the center point of the key grid into the position where the center point is located in the key grid. Although in the above example, a representative point is selected in the key grid to obtain the output value of the implicit expression of the representative point, and the output value is filled into the key grid as an example for detailed description, it is not limited thereto. In other examples, multiple representative points (two or more) can also be selected in the key grid to obtain the output values of the implicit expressions of the multiple representative points, and then the output values of the implicit expressions of the multiple representative points are filled into the positions where the multiple representative points are located in the key grid. For example, the 4 corner points on the upper surface of the key grid are used as representative points, and the output values of the implicit expressions of the 4 corner points are respectively filled into the positions where the 4 corner points are located in the key grid.

[0090] It should be noted that the value filled in the key grid can also be any value with the same positive or negative sign as the output value of the implicit expression. For example, if the output value of the implicit expression of the center point of the key grid is -8, any negative number can be directly filled in this key grid. For example, if the output value of the implicit expression of the center point of the key grid is 8, any positive number can be directly filled in this key grid.

[0091] In one embodiment, the computer device can further use a preset algorithm to perform contour calculation on the key grid filled in each layer to generate the slice contours of each layer. Among them, the preset algorithm can be the Marching Squares algorithm, the two-dimensional Dual Contouring algorithm, etc. It should be noted that this application does not limit the preset algorithm, and those skilled in the art can select other linear interpolation algorithms that can convert the meshed data into slice contours based on the above examples of the preset algorithm.

[0092] Since this application only targets the output values implicitly expressed by critical grid calculations, the computational load is reduced. Further, this application can achieve the parallel execution described later under the condition of limited configuration of computer devices.

[0093] By performing step S120 and step S130, the step-by-step meshing of a subspace and the determination of the slice contours of each layer in the subspace can be achieved. In other words, by performing step S120 and step S130, the slice contours of multiple layers included in a subspace can be obtained. When the continuous multiple layers can form multiple subspaces, steps S120 and S130 need to be executed for each of the multiple subspaces to calculate the slice contours of the continuous multiple layers. Please refer to Figure 10 and combine with Figure 5 , Figure 10 which shows a schematic diagram of two subspaces formed by continuous multiple layers in an embodiment of this application. As shown in the figure, the continuous multiple layers are 7 layers. Subspace V1 is composed of 4 continuous layers, and subspace V3 is composed of 3 continuous layers.

[0094] In an embodiment, when performing the step-by-step meshing and determining the slice contours of each layer in the subspace for multiple subspaces, the computer device allocates threads to each of the multiple subspaces to perform the step-by-step meshing and determine the slice contours of each layer in the subspace in parallel. Among them, each thread can perform the step-by-step meshing of a subspace and calculate the slice contours of each layer in the subspace, thereby achieving the simultaneous calculation of multiple subspaces and obtaining the slice contours of each layer in multiple subspaces at one time, which speeds up the calculation speed. For example, please continue to refer to Figure 10 , the computer device allocates one thread to each of subspace V1 and subspace V3 to simultaneously perform the step-by-step meshing of subspace V1 and subspace V3 and determine the slice contours of each layer in the subspace. In one implementation, the parallel calculation is executed by the CUDA (Compute Unified Device Architecture) software package configured on the computer device. CUDA is a programming model of the GPU (Graphic Processing Unit). Its programming mode is single program multiple data, that is, multiple concurrent threads execute a single program to process multiple data, which greatly improves the data processing speed.

[0095] In another embodiment, the computer device can also perform the step-by-step meshing and determining the slice contours of each layer in the subspace for multiple subspaces serially.

[0096] In some embodiments, the present application further provides a slicing system, which can be deployed, for example, in a computer device as a software tool or software module capable of processing data, and executes data processing by virtue of the operating environment provided by the hardware device and / or operating system in the computer device.

[0097] Please refer to Figure 11 , which shows a module block diagram of the slicing system in an embodiment of the present application. As shown in the figure, the slicing system 1 includes a layer creation module 10, a subspace determination module 11, and a subspace slicing module 12. The layer creation module 10 is used to create a plurality of continuous layers that can completely wrap the implicit expression model. Among them, the plurality of layers are respectively configured with layer resolutions, and the layer creation module 10 is further used to determine the layer resolutions of the plurality of layers based on the grid parameters of the layer plane; the subspace determination module 11 selects any number of continuous layers from the plurality of layers to form a subspace; the subspace slicing module 12 includes: a meshing and filling unit, which is used to perform hierarchical meshing on the subspace, including: recursively executing to respectively determine the value range of the implicit expression of each sub-grid at the current level to perform the next-level meshing on the sub-grid whose value range contains a threshold range until each sub-grid at the current level is a single-layer grid that meets the corresponding layer resolution; and selecting the sub-grid whose value range of the implicit expression contains the threshold range as the key grid in the single-layer grid that meets the layer resolution of the corresponding layer and filling in the output value of the implicit expression of at least one representative point therein; a slice contour determination unit, which is used to determine the slice contour of each layer based on the key grids filled in each layer in the subspace. The subspace slicing module 12 is further used to allocate threads to a plurality of subspaces respectively to perform the hierarchical meshing and determine the slice contours of each layer in the subspaces in parallel.

[0098] In an embodiment, the layer creation module 10, the subspace determination module 11, and the subspace slicing module 12 included in the slicing system 1 respectively coordinate and execute the slicing method disclosed in any of the foregoing embodiments of the present application according to the functions described above. Please refer to any embodiment of Figures 1 to 10 and its related descriptions, which will not be elaborated here.

[0099] The layer creation module 10, the subspace determination module 11, and the subspace slicing module 12 can also be implemented in software run by different types of processors. For example, the module of executable code can include one or more physical or logical blocks of computer instructions, and the computer instructions are organized as objects, programs, or functions. However, the executable files of the module do not have to be physically located together, but can include different commands stored in different locations. When these commands are logically connected together, the commands include the module and achieve the specified goal of the module.

[0100] Of course, the module of executable code may be one or many instructions and may even be distributed in several different code segments, in different programs, and may be distributed in multiple storage devices. Similarly, the arithmetic data can be identified and shown within the module here, and the arithmetic data can be embodied in any suitable form and organized in any suitable type of data structure. The arithmetic data can be collected as a single data set or can be distributed in different locations (including different storage devices) and can exist at least partially only as electrical signals in the system or network. When a module or a part of a module is implemented in software, the software part is stored on one or more computer-readable media.

[0101] This application also provides a computer device, including a bus, a processor, a memory, and a communication interface. The processor, the memory, and the communication interface communicate with each other through the bus. The computing device can be a server, a laptop computer, a desktop computer, an edge device, etc., which are not specifically limited in the embodiments of this application. The embodiments of this application also do not limit the number of processors and memories in the computing device.

[0102] The bus can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc. For the sake of convenience in representation, only one line is shown in the figure, but it does not mean that there is only one bus or one type of bus. The bus can include a path for transmitting information between various components of the computing device (for example, the memory, the processor, the communication interface).

[0103] In one embodiment, the computer device is used to implement the slicing method described in any of the above embodiments. In one embodiment, the computer device is a device capable of performing digital calculations, logical processing, and information processing on data, including but not limited to: personal computers, industrial control computers, tablets, smart phones, servers, server clusters, intelligent terminals, server systems based on cloud architecture, etc.

[0104] Please refer to Figure 12 , which shows a schematic structural diagram of the computer device in one embodiment of this application. The computer device 2 includes a storage device 20 and a processing device 21 connected to the storage device 20. Further, the computer device also includes a communication interface 22.

[0105] In some embodiments, the storage device 20 is used to store at least one program, and the at least one program is executable by the processing device 21 to coordinate the storage device 20 to implement the slicing method described in any of the above embodiments. Herein, the storage device 20 includes but is not limited to: Read-Only Memory (ROM), Random Access Memory (RAM), Nonvolatile RAM (NVRAM). For example, the storage device 20 includes a flash device or other non-volatile solid-state storage devices. In certain embodiments, the storage device 20 may further include a memory remote from one or more processing devices 21, such as a network-attached memory accessed via an RF circuit or an external port and a communication network, where the communication network may be the Internet, one or more intranets, local area networks, wide area networks, storage area networks, etc., or a suitable combination thereof. The memory controller can control the access of other components of the device, such as the CPU and the peripheral interface, to the memory.

[0106] In some embodiments, the processing device 21 includes one or more processors. The processing device 21 operably performs data read and write operations with the storage device 20. The processing device 21 includes one or more general-purpose microprocessors, one or more application-specific integrated circuits (ASICs), one or more digital signal processors (DSPs), one or more field programmable gate arrays (FPGAs), or any combination thereof.

[0107] In some embodiments, the communication interface 22 includes at least one interface unit, and each interface unit is respectively used to output a visualization interface, receive human-computer interaction events generated according to the operations of technicians, etc. For example, the communication interface 22 includes but is not limited to: serial interfaces such as HDMI interfaces or USB interfaces, or parallel interfaces, etc. In one embodiment, the communication interface 22 further includes a network communication unit, which is a device for data transmission using a wired or wireless network, and examples thereof include but are not limited to: integrated circuits including network cards, local area network modules such as WiFi modules or Bluetooth modules, wide area network modules such as mobile networks, etc.

[0108] The present application also provides a computer-readable storage medium storing at least one program, and the at least one program, when called and executed by a processor of a computer, implements the slicing method in any of the above embodiments.

[0109] The present application also provides a computer program product. When the computer program product runs on a computer, it causes the computer to execute the above-related steps to implement the slicing method in any of the above embodiments.

[0110] If the method is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions to enable a computer device installed with the storage medium to execute all or part of the steps of the methods described in various embodiments of the present application.

[0111] In the embodiments provided by the present application, the provided computer storage medium may include a read-only memory, a random access memory, an EEPROM, a CD-ROM, or other optical disc storage devices, a magnetic disk storage device, or other magnetic storage devices, a flash memory, a USB flash drive, a mobile hard disk, or any other medium that can be used to store the desired program code in the form of instructions or data structures and can be accessed by a computer. Additionally, any connection can be appropriately referred to as a computer-readable medium. For example, if the instructions are sent from a website, a server, or other remote sources using coaxial cables, fiber optic cables, twisted pairs, digital subscriber lines (DSL), or wireless technologies such as infrared, radio, and microwave, then the coaxial cables, fiber optic cables, twisted pairs, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of the medium. However, it should be understood that computer storage media and data storage media do not include connections, carrier waves, signals, or other transient media, but are intended for non-transient, tangible storage media. As used in the application, magnetic disks and optical discs include compact discs (CDs), laser discs, optical discs, digital versatile discs (DVDs), floppy disks, and Blu-ray discs, where magnetic disks typically reproduce data magnetically, while optical discs reproduce data optically using lasers.

[0112] In summary, for a slicing method, system, computer device, computer-readable storage medium, and computer program product disclosed in the present application, the present application can select any number of consecutive layers from multiple consecutive layers that can completely wrap the implicit expression model to form a subspace, and perform hierarchical meshing until each sub-grid at the current level is a single-layer grid that meets the corresponding layer resolution. Then, among the single-layer grids that meet the corresponding layer resolution, select the sub-grids whose implicit expression value ranges contain the threshold range as key grids, and fill in the output values of the implicit expressions of at least one representative point in them to determine the slice contours of the selected layers. In this way, the present application does not need to first convert the implicit expression model into a triangular mesh model for slicing, and only fills in the output values of the implicit expressions in the key grids during the slicing process to determine the slice contours, reducing the computational amount during the slicing process and achieving efficient slicing of the implicit expression model. Further, the present application can adapt to the memory configurations of different computer devices through single-layer or multi-layer switching to avoid problems such as slicing failure caused by memory limitations. Furthermore, through parallel computing of multiple subspaces, it is possible to simultaneously calculate multiple subspaces and obtain the slice contours of each layer in multiple subspaces at one time, improving the calculation speed.

[0113] The above embodiments only illustratively explain the inventive essence of the present application and the beneficial effects obtained therefrom, rather than limiting the present application. Any person familiar with this technology can modify or change the above embodiments without departing from the principles and scopes of the present application. Therefore, all equivalent modifications or changes made by those with ordinary knowledge in the technical field without departing from the spirit and technical ideas disclosed in the present application should still be covered by the claims of the present application.

Claims

1. A slicing method, characterized in that: The slicing method comprises the following steps: Creating a plurality of continuous layers that can completely wrap the implicit expression model; wherein the plurality of layers are respectively configured with layer resolutions; Selecting any number of continuous layers from the multiple layers to form a subspace to grid the subspace step by step, including: recursively executing the steps of respectively determining the value interval of the implicit expression of each subgrid of the current level to grid the subgrids whose value interval includes a threshold value interval to the next level, until each subgrid of the current level is a single-layer grid that meets the corresponding layer resolution; wherein, respectively determining the value interval of the implicit expression of each subgrid of the current level to grid the subgrids whose value interval includes a threshold value interval to the next level includes the following steps: respectively determining the value interval of the implicit expression of each subgrid of the current level to compare the threshold value interval with the value interval of each subgrid, and gridding the corresponding subgrid to the next level under the condition that the value interval includes the threshold value interval; In a single-layer grid that meets the corresponding layer resolution, a sub-grid whose implicit expression value range includes the threshold range is selected as a key grid and the output value of the implicit expression of at least one representative point is filled in it to determine the slice contours of the selected layers.

2. The slicing method according to claim 1, characterized in that: The step of creating multiple continuous layers that can completely wrap the implicit expression model includes: creating the multiple layers based on the length, width and height information of the bounding box of the implicit expression model, the grid parameters of the layer plane, and the layer spacing of the multiple layers.

3. The slicing method according to claim 2, characterized in that: Also included is the step of determining a layer resolution of the plurality of layers based on the grid parameters of the layer plane.

4. The slicing method according to claim 2, characterized in that: Creating a plurality of continuous layers that can completely wrap the implicit expression model also includes: providing a parameter configuration window for a user to input the grid parameters of the layer spacing and / or the layer plane.

5. The slicing method according to claim 4, characterized in that: The grid parameters of the layer plane include the minimum unit size of the grid of each layer or the minimum number of units of each layer in the length and width directions.

6. The slicing method according to claim 1, characterized in that: The next level of gridding is configured to traverse the length, width, and height directions of the current level of sub-grids to perform gridding in a manner of averaging the directions in which averaging can be performed.

7. The slicing method according to claim 1, characterized in that: The step of respectively determining the value range of the implicit expression of each sub-grid of the current level includes: determining the value range of the sub-grid based on the diagonal vertices of the sub-grid.

8. The slicing method according to claim 7, characterized in that: The step of determining the value range of the sub-grid based on the diagonal points of the sub-grid includes: determining the body diagonal length of the sub-grid based on the diagonal vertices of the sub-grid, and determining the value range of the sub-grid based on the output value of the implicit expression of the body diagonal length and the center point of the sub-grid.

9. The slicing method according to claim 1, characterized in that: The step of respectively determining the value range of the implicit expression of each sub-grid of the current level to grid the sub-grids whose value range contains a threshold range to the next level also includes: filling the corresponding sub-grid with a numerical value outside the implicit expression model under the condition that the value range is greater than the threshold range, and filling the corresponding sub-grid with a numerical value within the implicit expression model under the condition that the value range is less than the threshold range.

10. The slicing method according to claim 9, characterized in that: The threshold interval is configured as an interval containing implicitly expressed boundary values ​​with a first threshold as an upper limit and a second threshold as a lower limit. When the lower limit value of the value interval is greater than the first threshold, it is determined that the value interval is greater than the threshold interval; when the upper limit value of the value interval is less than the second threshold, it is determined that the value interval is less than the threshold interval.

11. The slicing method according to claim 1, characterized in that: The step of gridding the subspace step by step also includes gridding the subspace for the first time to obtain a plurality of subgrids of the first gridding.

12. The slicing method according to claim 1, characterized in that: The representative point is configured as a center point of the key grid.

13. The slicing method according to claim 1, characterized in that: The step of determining the slice contours of each layer includes using a preset algorithm to perform contour calculation on the key grid after each layer is filled to generate the slice contours of each layer.

14. The slicing method according to claim 1, characterized in that: The method also includes assigning threads to the plurality of subspaces respectively to perform the step-by-step gridding in parallel and determining the slice contours of each layer in the subspace.

15. The slicing method according to claim 1, characterized in that: The arbitrary number of continuous layers includes a single layer or multiple layers.

16. A slicing system, characterized in that: The slicing system comprises: A layer creation module, used to create a plurality of continuous layers that can completely wrap the implicit expression model; wherein the plurality of layers are respectively configured with layer resolutions; A subspace determination module, used for selecting any number of continuous layers from the multiple layers to form a subspace; Subspace slicing module, including: A gridding and filling unit, for gridding the subspace step by step, comprising: recursively determining the value interval of the implicit expression of each subgrid of the current level to grid the subgrids whose value interval includes a threshold interval to the next level, until each subgrid of the current level is a single-layer grid that meets the corresponding layer resolution; and selecting a subgrid whose value interval of the implicit expression includes the threshold interval as a key grid in the single-layer grid that meets the layer resolution of the corresponding layer and filling the output value of the implicit expression of at least one representative point thereof; wherein, respectively determining the value interval of the implicit expression of each subgrid of the current level to grid the subgrid whose value interval includes a threshold interval to the next level comprises: respectively determining the value interval of the implicit expression of each subgrid of the current level to compare the threshold interval with the value interval of each subgrid, and gridding the corresponding subgrid to the next level under the condition that the value interval includes the threshold interval; The slice contour determining unit is used to determine the slice contour of each layer based on the key grids after each layer is filled in the subspace.

17. A computer device, characterized in that: include: A storage device for storing at least one program; A processing device, connected to the storage device, is used to call the at least one program from the storage device and implement the slicing method as described in any one of claims 1 to 15 when executing it.

18. A computer-readable storage medium, characterized in that: At least one program is stored, and when the at least one program is called and executed by a processor of a computer, the slicing method as described in any one of claims 1 to 15 is implemented.

19. A computer program product, characterized in that When the computer program product is run on a computer, the computer is enabled to execute the slicing method according to any one of claims 1 to 15.

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