Method and device for machining path planning based on parametric surface

Abstract

This invention provides a machining path planning method and apparatus based on parametric surfaces. The machining path planning method includes: obtaining at least two adjacent parametric surfaces corresponding to a machining area in a workpiece, and using the combination of at least two adjacent parametric surfaces as a parametric surface group; constructing a guide surface about the parametric surface group based on the geometric features of the parametric surface group; generating at least one auxiliary machining path from the guide surface; and projecting each auxiliary machining path onto each parametric surface in the parametric surface group to obtain several machining paths for the machining area in the workpiece. This invention, by constructing a guide surface corresponding to the parametric surface group and then constructing auxiliary machining paths on the guide surface, ensures the continuity of the machining paths projected onto each parametric surface, thereby guaranteeing the continuity of the machining paths for the machining area in the workpiece.

Description

Technical Field

[0001] This invention relates to the field of CNC machine tools and industrial robot machining technology, and in particular to a machining path planning method and apparatus based on parametric surfaces. Background Technology

[0002] In the field of CNC machine tools and industrial robot machining, it is necessary to first generate a machining path based on the geometric digital model of the object being machined, in order to control the CNC machine tool or industrial robot to move along the machining path and complete the machining process, such as milling, grinding, cutting, etc.

[0003] In generating machining paths based on the geometric digital model of the workpiece, the common method is to first assume that the surface to be machined is a parametric surface. The machining path is then generated based on the isoparametric lines of the parametric surface. However, this method is unsuitable for situations where there are two surfaces within the machining area of ​​the workpiece. When processing a set of adjacent parametric surfaces, the isoparametric lines generated on these surfaces are discontinuous at the boundary due to the different parametric equations. This prevents the direct generation of a continuous machining path that traverses the entire machining area. If the workpiece is still machined using this discontinuous path, it may cause machine tool / robot movement to stall or even result in tool collisions, ultimately leading to tool marks, overcutting, undercutting, or even scrapping of the part, or severely substandard precision. Summary of the Invention

[0004] This invention provides a machining path planning method and apparatus based on parametric surfaces to solve the defect in the prior art that it is impossible to generate a continuous machining path for the machining area when there are at least two adjacent surfaces in the machining area. It realizes that by constructing a guide surface corresponding to the parametric surface group and constructing an auxiliary machining path on the guide surface, the machining path projected onto each parametric surface is continuous, thereby ensuring the continuity of the machining path in the machining area of ​​the workpiece.

[0005] This invention provides a machining path planning method based on parametric surfaces, comprising the following steps: Obtain at least two adjacent parametric surfaces corresponding to the processing area in the workpiece, and take the combination of the at least two adjacent parametric surfaces as a parametric surface group; Construct a guide surface about the parametric surface group based on the geometric features of the parametric surface group; Generate at least one auxiliary processing path for the guide surface; Each of the auxiliary machining paths is projected onto each of the parameter surfaces in the parameter surface group to obtain several machining paths for the machining area in the workpiece.

[0006] According to the present invention, a machining path planning method based on parametric surfaces is provided, wherein the geometric features include shape and size, and the step of constructing a guide surface about the parametric surface group based on the geometric features of the parametric surface group includes: The preset guide surface type that is associated with the shape of the parametric surface group among several preset guide surface types is taken as the target type of the guide surface. The parameters of the guide surface are determined based on the target type of the guide surface and the shape and size of the parametric surface group. The wizard surface is generated based on the parameters of the wizard surface.

[0007] According to a machining path planning method based on parametric surfaces provided by the present invention, determining the parameters of the guide surface according to the target type of the guide surface, the shape and size of the parametric surface group includes: When the target type is ruled surface, the geometric definition parameters of the first guide curve and the second guide curve of the guide surface are determined according to the shape and size of the first boundary curve and the second boundary curve arranged along the preset processing direction in the parameter surface group. Furthermore, based on the relative positional relationship between the first boundary curve and the second boundary curve, the relative positional relationship between the first guide curve and the second guide curve is determined.

[0008] According to the present invention, a machining path planning method based on parametric surfaces is provided, the method further includes: Obtain the curvature distribution of each of the parametric surfaces in the parametric surface group; Based on the curvature distribution, adjust the geometric definition parameters of the first guide curve, the geometric definition parameters of the second guide curve, and / or the relative positional relationship.

[0009] According to a machining path planning method based on parametric surfaces provided by the present invention, generating at least one auxiliary machining path for the guide surface includes: Several equally spaced isoparametric lines on the guide surface are respectively used as each of the auxiliary processing paths; Alternatively, several equidistant offset curves determined by the guide surface according to a preset offset distance can be used as each of the auxiliary processing paths.

[0010] According to a machining path planning method based on parametric surfaces provided by the present invention, the step of projecting each of the auxiliary machining paths onto each of the parametric surfaces in the parametric surface group to obtain a plurality of machining paths for the machining area in the workpiece includes: Each of the auxiliary processing paths is sampled to obtain several sampling points for each auxiliary processing path; Project each of the sampling points onto the parametric surface group to obtain the projection points on each of the parametric surfaces; Interpolation is performed on the projection points corresponding to each of the auxiliary processing paths to obtain several processing paths for the processing area in the workpiece to be processed.

[0011] According to the processing path planning method based on parametric surfaces provided by the present invention, after interpolating the projection points corresponding to each auxiliary processing path to obtain several processing paths for the processing area in the workpiece, the method further includes: According to the scope requirements of the processing area, each of the processing paths is trimmed; The processed path after trimming is smoothed to obtain the final processed path for the processed area.

[0012] The present invention also provides a machining path planning device based on parametric surfaces, comprising the following modules: The processing area determination module is used to obtain at least two adjacent parametric surfaces corresponding to the processing area in the workpiece to be processed, and to take the combination of the at least two adjacent parametric surfaces as a parametric surface group. A guide surface determination module is used to construct a guide surface about the parametric surface group based on the geometric features of the parametric surface group. An auxiliary machining path generation module is used to generate at least one auxiliary machining path for the guide surface; The machining path determination module is used to project each of the auxiliary machining paths onto each of the parameter surfaces in the parameter surface group to obtain several machining paths for the machining area in the workpiece.

[0013] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the machining path planning method based on parametric surfaces as described above.

[0014] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the machining path planning method based on parametric surfaces as described above.

[0015] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the machining path planning method based on parametric surfaces as described above.

[0016] This invention provides a machining path planning method and apparatus based on parametric surfaces. Compared with the scheme of generating machining paths separately on each parametric surface, which leads to discontinuities in the machining area, this invention first obtains a set of parametric surfaces corresponding to the machining area in the workpiece, then constructs a guide surface about the parametric surface set based on the geometric features of the parametric surface set, first constructs an auxiliary machining path on the guide surface, and then projects the auxiliary machining path onto each parametric surface, so that the machining paths on each parametric surface are continuous, thereby ensuring the continuity of the machining path in the machining area of ​​the workpiece. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Figure 1 This is one of the flowcharts of the processing path planning method based on parametric surfaces provided by the present invention.

[0019] Figure 2 This is the second flowchart of the processing path planning method based on parametric surfaces provided by the present invention.

[0020] Figure 3 This is a schematic diagram of the processing path planned according to the existing method provided by the present invention.

[0021] Figure 4 This is a schematic diagram of the machining path planned by the machining path planning method based on parametric surfaces provided by the present invention.

[0022] Figure 5 This is a schematic diagram of the processing path planning device based on parametric surfaces provided by the present invention.

[0023] Figure 6 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0025] The following is combined Figures 1 to 4The present invention describes a machining path planning method based on parametric surfaces. Figure 1 This is one of the flowcharts illustrating the parametric surface-based machining path planning method provided by this invention, such as... Figure 1 As shown, the method includes the following steps: Step 101: Obtain at least two adjacent parametric surfaces corresponding to the processing area in the workpiece to be processed, and take the combination of at least two adjacent parametric surfaces as a parametric surface group.

[0026] The subject of this invention can be an electronic device.

[0027] The workpiece to be processed can be a workpiece that requires machining such as milling, grinding, and cutting using CNC machine tools or industrial robots. The processing area in the workpiece is the area on the workpiece where the above-mentioned machining operations need to be performed.

[0028] In some applications, a geometric mathematical model of the workpiece can be obtained. The machining surface of the machining area includes at least two adjacent surfaces, each of which corresponds to a parametric surface in the geometric mathematical model. A parametric surface refers to a surface in three-dimensional space defined by mathematical parametric equations. Specifically, a parametric surface is mapped by a function of two independent parameters (usually denoted as u and v), specifically expressed as: S(u,v)=[x(u,v),y(u,v),z(u,v)], where (u,v) is a pair of parameters defined in a two-dimensional region (e.g., [0,1]×[0,1]). For each determined pair of (u,v), the function S gives the coordinates of a unique point in three-dimensional space. x(u,v), y(u,v), z(u,v) are functions of parameters u and v with the required continuity and differentiability, uniquely mapping a point in the two-dimensional parameter domain to a point (x,y,z) in three-dimensional space.

[0029] Two adjacent parametric surfaces refer to parametric surfaces in the geometric digital model of the workpiece whose edges are connected, have a common boundary, or whose boundary spacing meets the requirements of the machining process. The number of adjacent surfaces can be two, three, or more.

[0030] The methods for obtaining at least two adjacent parametric surfaces corresponding to the processing area may include, but are not limited to: 1. Receiving the user's selection operation through the software graphical interface displayed on the electronic device screen, where the user selects or clicks the processing area on the geometric digital model of the workpiece to be processed, and the electronic device identifies all parametric surfaces in the area and filters out adjacent parametric surfaces; 2. Automatically identifying the preset processing area in the geometric digital model according to the processing requirements of the workpiece to be processed, and extracting the adjacent parametric surfaces in the area.

[0031] After acquiring at least two adjacent parametric surfaces, the electronic device can combine them into a parametric surface group. The adjacent parametric surfaces are arranged along a preset processing direction within the parametric surface group.

[0032] Step 102: Construct a guide surface about the parametric surface group based on the geometric features of the parametric surface group.

[0033] Geometric features can be the spatial geometric properties of the parametric surface group as a whole, including but not limited to at least one of the following: the overall shape, size, curvature distribution, boundary profile, spatial orientation, etc. of the parametric surface group.

[0034] The guide surface is a virtual parametric surface with a standardized parametric equation form. That is, a guide surface can be defined using a single parametric equation. Optionally, the type of guide surface can include, but is not limited to, planes, cylindrical surfaces, and ruled surfaces. After obtaining the geometric features of the parametric surface group, these features can be extracted and analyzed to obtain the overall shape type (e.g., gently sloping planar, cylindrical, irregular curved surface), overall size range (e.g., length, width, height, or radial and axial dimensions), and / or overall spatial orientation (e.g., normal direction of the machining area, main extension direction, etc.). Then, based on the analysis results, a guide surface matching the parametric surface group is constructed. The spatial range of the guide surface can completely cover the parametric surface group, or it can be slightly larger than the parametric surface group according to machining requirements, ensuring that subsequent projection operations can cover the entire parametric surface group.

[0035] Step 103: Generate at least one auxiliary processing path for the guide surface.

[0036] Auxiliary machining paths are virtual paths generated on the guide surface and used for projection onto the parametric surface group. The number of auxiliary machining paths can be determined based on the machining process requirements of the machining area in the workpiece, such as machining accuracy, machining allowance, and number of tool passes.

[0037] Because the guide surface has a standardized parametric equation form, the electronic device can generate regularly distributed auxiliary machining paths on the guide surface based on its parametric characteristics. For example, isoparametric lines can be directly generated as auxiliary machining paths based on the guide surface's parametric equations, or equidistant offset curves can be generated on the guide surface using an offset algorithm. The key is to ensure that the generated auxiliary machining paths are continuous curves and cover the entire range of the guide surface. Alternatively, in other application scenarios, if the processing area of ​​the workpiece needs to be machined into a specific shape, at least one auxiliary machining path can be generated on the guide surface based on that specific shape. This embodiment does not specifically limit the method of generating the auxiliary machining paths.

[0038] Step 104: Project each auxiliary machining path onto each parametric surface in the parametric surface group to obtain several machining paths for the machining area in the workpiece.

[0039] "Several" refers to at least one. For example, each auxiliary machining path, after projection, can correspond to a machining path for the machining area in the workpiece.

[0040] Projection refers to the operation of mapping the auxiliary machining path on the guide surface to each parametric surface of the parametric surface group. The projection direction can be determined according to the geometric characteristics of the parametric surface group and the type of the guide surface. For example, when the guide surface is a plane, it can be projected along the normal direction of the guide surface, or along the direction of the spatial coordinate axis (such as the X-axis, Y-axis, Z-axis), or along the axis of the machining tool. This embodiment does not specifically limit the specific projection direction.

[0041] Since the guide surface is a parametric surface constructed for the entire parametric surface group, and the auxiliary machining path is a continuous path on the guide surface, continuous curves will be formed on each adjacent parametric surface of the parametric surface group after projection. The electronic device integrates these continuous curves to obtain several machining paths for the machining area in the workpiece. These machining paths are continuous paths that run through the entire machining area and can be directly imported into the control system of CNC machine tools or industrial robots to control them to move along the path to complete the machining.

[0042] In the above scheme, compared with the scheme that generates machining paths separately on each parametric surface, resulting in discontinuous paths in the machining area, the present invention first obtains the parametric surface group corresponding to the machining area in the workpiece, and then constructs a guide surface about the parametric surface group based on the geometric features of the parametric surface group. Auxiliary machining paths are first constructed on the guide surface, and then the auxiliary machining paths are projected onto each parametric surface, so that the machining paths on each parametric surface are continuous, thereby ensuring the continuity of the machining path in the machining area of ​​the workpiece.

[0043] In one possible embodiment, geometric features include shape and size. Shape may include data characterizing the contour of the parametric surface group as a whole in three-dimensional space. For example, the contour of the parametric surface group may be a gently curvatured surface, a cylindrical surface, a partially cylindrical surface, or an irregular surface. Size refers to the three-dimensional spatial dimensional parameters of the parametric surface group, which may include, but is not limited to, one or more of the following: the length, width, height, and dimensional parameters of each boundary curve of the parametric surface group along a preset processing direction, etc., and specific values ​​can be obtained by coordinate extraction and dimensional calculation from the geometric digital model of the workpiece.

[0044] The above-mentioned methods for constructing a guide surface about a set of parametric surfaces based on its geometric features can include, for example: Figure 2 The following steps are shown: Step 201: Select the preset guide surface type that is associated with the shape of the parametric surface group from among several preset guide surface types as the target type of the guide surface.

[0045] The number can be greater than or equal to 1. A preset guide surface type is a guide surface type configured in advance in the computer-aided manufacturing software, possessing a standardized parametric equation form. The preset guide surface type can include at least one of the following: plane, cylindrical surface, ruled surface. Of course, other curved surface types with standardized parametric forms can be added according to actual processing requirements. This embodiment does not limit the specific number of preset guide surface types.

[0046] The association between the shape of each parametric surface group and each preset guide surface type is established in advance. Considering that for each parametric surface group's shape, the associated guide surface target type needs to match the shape features of the parametric surface group to the greatest extent possible, ensuring that the subsequently generated guide surface can completely cover and conform to the processing area, the method for establishing the association between the shape of each parametric surface group and each preset guide surface type in this invention can be: comparing the shape of the parametric surface group with the morphological features of each preset guide surface type, and selecting the preset guide surface type with the highest morphological matching degree as the guide surface type associated with the shape of the parametric surface group. Different shapes can correspond to different preset guide surface types.

[0047] For example, if the shape of the parametric surface group is a gently curvatured surface with low curvature variation, the type of its associated guide surface can be a plane; if the shape of the parametric surface group is a cylindrical or semi-cylindrical surface that extends in an arc along the circumference and in a straight line along the axial direction, the type of its associated guide surface can be a cylindrical surface; if the overall shape of the parametric surface group is an irregular surface with large curvature variation and no fixed regular shape, the type of its associated guide surface can be a ruled surface.

[0048] Step 202: Determine the parameters of the guide surface based on the target type of the guide surface, the shape and size of the parametric surface group.

[0049] The parameters of the guide surface are mathematical parameters used to define the specific shape and size of the guide surface. Different guide surface target types correspond to different parameter systems. These parameters can be determined by combining the target type of the guide surface, the shape characteristics and size parameters of the parametric surface group, so as to ensure that the final generated guide surface not only conforms to the parameter form specification of the target type, but also covers the parametric surface group.

[0050] Step 202 can be implemented as follows: First, based on the target type of the guide surface, obtain the standard parametric equations and parameter system corresponding to the target type; then, combined with the shape characteristics of the parametric surface group, determine the parameters used to characterize the shape of the guide surface. Finally, based on the specific dimensional parameters of the parametric surface group, determine the dimensional parameters of the guide surface. This method ensures that the contour shape of the guide surface is as consistent as possible with the shape of the parametric surface group, and that the spatial dimensions of the guide surface match the processing area dimensions of the parametric surface group, ensuring that the guide surface completely covers the processing area. Alternatively, depending on the processing requirements, the size of the guide surface can be slightly larger than the size of the processing area to allow for subsequent projection operations.

[0051] For example, if the target type is a plane, the parameters used to characterize its shape include normal parameters, and the dimensional parameters include boundary coordinate parameters. The standard parametric equation for a plane is: ax + by + cz + d = 0. Combining the planar shape characteristics of the parametric surface group, the normal parameters (a, b, c) of the plane are determined to maintain consistency with the normals of the parametric surface group. Then, based on the length, width, and other dimensional parameters of the parametric surface group, the boundary coordinate parameters of the plane are determined, thus completing the parameter determination of the planar guide surface. If the target type is a cylindrical surface, its standard parametric equation is (xa). 2 +(yb) 2 =R 2 The electronic device combines the shape characteristics of the parametric surface group to determine the center coordinates (a, b) and axial direction of the cylindrical surface to maintain consistency with the parametric surface group. Then, the radius R of the cylindrical surface is determined according to the radial dimension of the parametric surface group, and the axial extension range of the cylindrical surface is determined according to the axial dimension of the parametric surface group, thereby completing the parameter determination of the guide surface of the cylindrical surface type.

[0052] Step 203: Generate the wizard face based on the parameters of the wizard face.

[0053] After determining all the parameters of the guide surface, each parameter can be substituted into the standard parametric equation corresponding to the target type. A preset surface generation algorithm then generates a guide surface that meets the parameter requirements. This generation process is based on standardized parametric equations and quantified parameter values. The generated guide surface has a unified and standardized parameter form and is highly compatible with the shape and size of the parametric surface group, completely covering the processing area of ​​the workpiece.

[0054] In the above scheme, the preset guide surface type associated with the shape of the parametric surface group among several preset guide surface types is used as the target type of the guide surface. The parameters of the guide surface are determined by combining the target type of the guide surface, the shape and size of the parametric surface group. This makes the generated guide surface highly compatible with the processing area of ​​the parametric surface group, can completely cover the processing area and has a standardized parameter form, so that the auxiliary processing path generated on the guide surface can be better projected onto each parametric surface.

[0055] In one possible embodiment, the method of determining the parameters of the guide surface based on the target type of the guide surface, the shape and size of the parametric surface group may include the following steps: When the target type is ruled surface, the geometric definition parameters of the first guide curve and the second guide curve of the guide surface are determined according to the shape and size of the first boundary curve and the second boundary curve arranged along the preset processing direction within the parametric surface group. Furthermore, the relative positional relationship between the first guide curve and the second guide curve is determined based on the relative positional relationship between the first boundary curve and the second boundary curve.

[0056] A ruled surface is a surface formed by sweeping across two arbitrary smooth curves at both ends and a straight line connecting corresponding points on the two curves. Ruled surfaces have a standardized parametric form and can adapt to groups of parametric surfaces with large curvature variations and irregular shapes by adjusting the guide curves. When the shape of the parametric surface group is an irregular surface with no fixed rules and a large variation in curvature distribution, a ruled surface can be selected as the type of guide surface.

[0057] The preset machining direction refers to the preset tool path of the CNC machine tool or industrial robot during the machining process of the machining area of ​​the workpiece. It is also the preset extension direction of the machining path on the parametric surface group. It can be preset by the user according to the machining process requirements and the structural characteristics of the workpiece. The electronic equipment can also determine it by itself according to the shape of the parametric surface group. It can be any spatial direction such as the length direction, width direction, curvature extension direction of the parametric surface group.

[0058] For example, the electronic device can filter all boundary curves of the parametric surface group according to a preset processing direction, extract two boundary curves arranged at both ends along that direction, and define them as the first boundary curve and the second boundary curve according to the start and end ends of the preset processing direction, respectively. If the preset processing direction changes, the selection results of the first boundary curve and the second boundary curve will also be adjusted accordingly. That is, the first boundary curve can be considered as the boundary curve of the parametric surface group at the start end of the preset processing direction, and the second boundary curve can be considered as the boundary curve of the parametric surface group at the end end of the preset processing direction.

[0059] The first guide curve and the second guide curve are the two core baselines for constructing the ruled surface. The overall contour of the ruled surface is determined by these two guide curves and the generatrix connecting them. The first guide curve and the second guide curve correspond to the first boundary curve and the second boundary curve of the parametric surface group, respectively.

[0060] Geometric definition parameters include parameters used to define the spatial shape, size, and contour direction of a curve. Different types of curves correspond to different geometric definition parameters, such as the coefficient parameters of a polynomial curve, the coordinate parameters of the control points of a spline curve, and the center, radius, and radian parameters of a circular arc curve. Geometric definition parameters are the core parameters that determine the spatial form of a curve, and their values ​​directly determine the shape and size of the curve.

[0061] Optionally, the method of determining the geometric definition parameters of the first guide curve and the second guide curve of the guide surface based on the shape and size of the first boundary curve and the second boundary curve arranged along the preset processing direction within the parameter surface group can be as follows: determine the geometric definition parameters of the first guide curve based on the shape and size of the first boundary curve; determine the geometric definition parameters of the second guide curve based on the shape and size of the second boundary curve. For example, the geometric definition parameters of the first boundary curve can be determined based on the shape and size of the first boundary curve, and these geometric definition parameters can be used as the geometric definition parameters of the first guide curve. Similarly, the geometric definition parameters of the second boundary curve can be determined based on the shape and size of the second boundary curve, and these geometric definition parameters can be used as the geometric definition parameters of the second guide curve.

[0062] For example, if the first boundary curve is a cubic spline curve, and its geometric definition parameters are the three-dimensional coordinates of several control points, the electronic device directly uses the coordinates of these control points as the geometric definition parameters of the first guide curve. Alternatively, if the first boundary curve is an irregular free curve, the electronic device extracts its core shape and size parameters as the geometric definition parameters of the first guide curve through a curve fitting algorithm.

[0063] The relative positional relationship between two curves includes, but is not limited to, at least one of the following: the positional arrangement of the two curves in three-dimensional space, including spatial positional attributes such as spatial distance, parallelism, included angle, projection offset, and relative position of axes.

[0064] In other words, when the target type is a ruled surface, the parameters of the guide surface include the geometric definition parameters of the first guide curve and the second guide curve, and the relative positional relationship between the first guide curve and the second guide curve.

[0065] The above-mentioned method of determining the relative positional relationship between the first guide curve and the second guide curve based on the relative positional relationship between the first boundary curve and the second boundary curve can be: directly taking the relative positional relationship between the first boundary curve and the second boundary curve as the relative positional relationship between the first guide curve and the second guide curve, or increasing the spatial distance between the first guide curve and the second guide curve to ensure that the ruled surface defined by the first guide curve and the second guide curve can cover the parametric surface group.

[0066] In the above scheme, for the ruled surface type guide surface, the first boundary curve and the second boundary curve of the parametric surface group along the preset processing direction are used as the core reference. The geometric definition parameters and relative position parameters of the two guide curves of the ruled surface are determined respectively, so that the parameter setting of the ruled surface guide surface is adapted to the inherent shape and size of the parametric surface group, ensuring that the generated ruled surface guide surface can accurately fit the parametric surface group with large curvature changes and irregular shape.

[0067] In one possible embodiment, the method further includes: Obtain the curvature distribution of each parametric surface in the parametric surface group; based on the curvature distribution, adjust the geometric definition parameters of the first guide curve, the geometric definition parameters of the second guide curve, and / or their relative positional relationships.

[0068] The curvature distribution may include, but is not limited to, at least one of the following: the curvature values ​​of each parametric surface in the parametric surface group at different positions in three-dimensional space, the curvature variation trend, and the distribution of curvature extrema. Curvature is a geometric index that characterizes the degree of curvature of a surface; a larger curvature value indicates a higher degree of curvature, and the curvature distribution can reflect the complexity of the surface morphology of the parametric surface group.

[0069] Optionally, the curvature distribution of each parametric surface in the parametric surface group can be obtained in ways including but not limited to: 1. Directly extracting the curvature distribution of each parametric surface from the geometric digital model of the workpiece to be processed, where the curvature distribution can be the inherent geometric data when the drawing software constructs the surface; 2. Solving the parametric equations of each parametric surface using a geometric algorithm to calculate the curvature values ​​of the surface at different coordinate positions, thereby obtaining the curvature distribution; 3. Performing spatial mesh sampling on each parametric surface, measuring the curvature value of each sampling point, and then obtaining the curvature distribution of the entire parametric surface group through interpolation fitting.

[0070] In some application scenarios, the geometric definition parameters of the first guide curve or the second guide curve can be adjusted according to the curvature distribution. For example, if the curvature variation of the parametric surface group is concentrated in the surface region corresponding to the first boundary curve, the geometric definition parameters of the first guide curve are adjusted according to the curvature distribution of that region. For example, the coordinates of the control points of the spline curve are adjusted, or the radius of curvature of the arc curve is modified, so that the curvature of the first guide curve matches the curvature characteristics of the corresponding region. Alternatively, if the curvature variation of the parametric surface group is concentrated in the surface region corresponding to the second boundary curve, the geometric definition parameters of the second guide curve are adjusted to adapt to the curvature characteristics of that region.

[0071] In some application scenarios, if the overall curvature of the parametric surface group changes significantly, or if the curvature of the surface in the preset processing direction exhibits a gradual characteristic, the relative positional relationship between the first guide curve and the second guide curve can be adjusted according to the overall curvature distribution. For example, the normal distance, spatial angle, and projection offset between the two can be adjusted so that the generatrix connecting the two guide curves can adaptively tilt with the curvature of the surface, ensuring the fit between the overall surface shape of the ruled surface and the parametric surface group.

[0072] In some application scenarios, if the curvature distribution of the parametric surface group is complex, with both local high curvature regions and overall curvature gradient characteristics, the geometric definition parameters of the first guide curve and the second guide curve and their relative positional relationship can be adjusted simultaneously to achieve comprehensive adaptation to complex curvature characteristics.

[0073] For example, if the parametric surface group has a high curvature protrusion in the region corresponding to the first boundary curve, and the curvature value is much higher than that of other regions, the geometric definition parameters of the first guide curve are adjusted to increase the curvature at the corresponding position, so that the first guide curve fits the high curvature region better; if the parametric surface group presents a gradual change from flat to high curvature in the preset processing direction, the electronic device finely adjusts the relative positional relationship between the first guide curve and the second guide curve, so that the normal distance between them gradually increases along the preset processing direction, so that the generatrix of the ruled surface guide surface can adapt to the gradual curvature feature.

[0074] In the above scheme, by adjusting the geometric definition parameters of the first guide curve, the geometric definition parameters of the second guide curve, and / or their relative positional relationships according to the curvature distribution, the guide surface can better characterize the geometric features of the parametric surface group, making the determined auxiliary machining path more accurate.

[0075] In one possible embodiment, the method of generating at least one auxiliary machining path of the guide surface may include the following steps: using several equally spaced isoparametric lines on the guide surface as each auxiliary machining path; or using several equidistant offset curves determined by the guide surface according to a preset offset distance as each auxiliary machining path.

[0076] In this context, an isoparametric line refers to a spatial curve on a parametric surface generated by the variation of one of two parameters (u, v) when one of them remains constant. Specifically, isoparametric lines can include U-axis isoparametric lines and V-axis isoparametric lines. U-axis isoparametric line: When parameter v is fixed at a constant value v_c, the curve S(u,v_c) formed by the variation of parameter u within its domain; V-axis isoparametric line: When parameter u is fixed at a constant value u_c, the curve S(u_c,v) formed by the variation of parameter v within its domain.

[0077] An equidistant offset curve is a curve generated by offsetting a base curve on the guide surface along the normal direction or a preset offset direction, according to a preset offset distance. Each subsequent curve is generated by offsetting the previous offset curve as a reference. The reference curve can be arbitrarily selected by the user on the guide surface (such as the boundary curve of the guide surface or any isoparametric line), or the electronic device can select the reference curve from several curves on the guide surface, such as using the center curve of the guide surface as the reference curve.

[0078] The preset offset distance can be preset according to the processing requirements of the workpiece (such as the diameter of the machining tool, the machining allowance, the tool feed step distance, etc.).

[0079] In one possible embodiment, the method of projecting each auxiliary machining path onto each parametric surface in the parametric surface group to obtain several machining paths for the machining area in the workpiece may include: First, each auxiliary machining path is sampled to obtain several sampling points for each path. Sampling methods can include, but are not limited to, equal-interval sampling, isoparametric sampling, or adaptive sampling. Adaptive sampling can involve selecting fewer sampling points in smooth sections of the auxiliary machining path and more sampling points in sections with abrupt curvature changes and high curvature. This method reduces the number of sampling points while maintaining projection accuracy, balancing accuracy and efficiency, and adapting to irregular auxiliary machining paths with large curvature variations. Each sampling point is a discrete point selected on the auxiliary machining path, and each sampling point has unique three-dimensional spatial coordinates.

[0080] Then, each sampling point is projected onto the parametric surface group to obtain the projection points on each parametric surface. Optionally, different projection methods can be set for different wizard types. For example, the parametric surface group of the workpiece to be processed and the constructed wizard surface are first arranged in space in the same three-dimensional coordinate system. For planar and ruled surface wizard surfaces, the spatial coordinate axis pointing to the spatial arrangement direction in the three-dimensional coordinate system is selected as the projection reference axis, and each sampling point is projected onto the parametric surface group along the axial direction of the projection reference axis to obtain the corresponding projection point; for cylindrical surface wizard surfaces, each sampling point is projected onto the parametric surface group along the radial direction of its corresponding position on the wizard surface (the normal direction of the tangent plane of the cylindrical surface at the sampling point) to obtain the corresponding projection point.

[0081] Next, interpolation is performed on the projection points corresponding to each auxiliary machining path to obtain several machining paths for the machining area in the workpiece. The interpolation can be performed by fitting the discrete projection points corresponding to each auxiliary machining path in their original order to a machining path for the machining area in the workpiece using a mathematical interpolation algorithm. Each resulting machining path passes through all adjacent parametric surfaces in the parametric surface group and can be directly used to control CNC machine tools or industrial robots for machining.

[0082] In the above scheme, discrete sampling reduces the complexity of projection calculation and improves the efficiency of path generation. Furthermore, the interpolation algorithm ensures the accuracy of the projection points and the continuity of the processing path.

[0083] In one possible embodiment, after interpolating the projection points corresponding to each auxiliary processing path to obtain several processing paths for the processing area in the workpiece, the method further includes: trimming each processing path according to the range requirements of the processing area; and smoothing the trimmed processing paths to obtain the final processing path for the processing area.

[0084] The processing area can be defined by a closed curve on a set of parametric surfaces, indicating the specific spatial range where machining operations need to be performed. This requirement is determined by the design drawings of the workpiece, the machining process documents, or by the user manually selecting a group of parametric curves on the display interface of the electronic device.

[0085] Trimming refers to the operation of removing the portion of the interpolated machining path that exceeds the required machining area, retaining only the machining path segments within the machining area. For example, if the machining area of ​​the workpiece is a rectangular region bounded by a closed boundary curve on a parametric surface group, and one end of an interpolated machining path extends beyond the boundary of this rectangle, the electronic device uses a geometric algorithm to calculate the intersection point A between the machining path and the rectangular boundary curve. Then, it cuts off the invalid path segments outside point A, retaining only the valid path segments within the rectangular region inside point A, thus completing the trimming of the machining path.

[0086] Smoothing refers to the local optimization of the trimmed processing path using mathematical algorithms to eliminate problems such as boundary burrs, sharp inflection points, and local path distortion that may occur during the trimming operation. Optionally, smoothing methods may include, but are not limited to, Gaussian smoothing algorithms and least squares fitting smoothing algorithms.

[0087] For example, the specific method for smoothing the trimmed processing path to obtain the final processing path for the processing area can be as follows: First, identify sharp inflection points, boundary burrs, and other local locations in the path that need optimization due to trimming. Based on the processing technology's requirements for path smoothness, set relevant smoothing parameters, such as the kernel radius of Gaussian smoothing and the number of smoothing iterations. Substitute the processing path containing the local locations requiring optimization into the selected smoothing algorithm, adjust the paths containing these locations, eliminate sharp inflection points and boundary burrs, and make the curvature change of the processing path smoother and more continuous. Determine the smoothed processing path as the final processing path for the processing area of ​​the workpiece. After completing the smoothing of all processing paths according to the above rules, obtain the final processing path set covering the entire processing area.

[0088] In the above scheme, each processing path is trimmed according to the range requirements of the processing area, so that the determined processing path does not exceed the area to be processed. Then, considering that the trimming of the processing path may cause sharp turning points, boundary burrs and other problems, the present invention further smooths the trimmed processing path, which can improve the smoothness and continuity of the processing path.

[0089] In some applications, a guide surface is constructed based on the shapes of at least two adjacent parametric surfaces corresponding to the machining area. A set of regularly distributed auxiliary machining paths is generated on the guide surface. Projecting these auxiliary machining paths onto the parametric surfaces yields the final required machining curves. In other words, only a set of adjacent parametric surfaces is needed to determine a series of equally spaced machining curves for a set of parametric surfaces.

[0090] In some application scenarios, the machining path planning method based on parametric surfaces may include the following steps: First, users can select a group of adjacent parametric surfaces to be processed in the graphical interface of computer-aided manufacturing software to obtain a parametric surface group.

[0091] Next, guide surfaces are constructed. Guide surfaces can be planes, cylinders, or ruled surfaces. For example, a plane of roughly parallel size to the parametric surface group can be created, based on the size and direction of the parametric surface group. Planes are characterized by their simple parametric form and ease of creation. Alternatively, if the parametric surface group is roughly cylindrical or partially cylindrical, a cylindrical or partially cylindrical surface can be created to enclose the parametric surface group. The parametric form of cylindrical surfaces is also standardized. Optionally, for complex machining areas, multiple parametric surface groups can be constructed, and corresponding guide surfaces (which can be combined from planes, cylinders, and ruled surfaces) can be built for each group. For example, different guide surfaces can be matched to different areas within the machining area (such as gently sloping areas or high-curvature areas) to achieve zoned guidance.

[0092] A ruled surface is formed by sweeping across two arbitrary smooth curves at its two ends and a straight line connecting corresponding points on the two curves. Its precise mathematical definition is as follows: A ruled surface can be defined by linear interpolation between points on two spatial curves (called guide curves or baselines). For example, given two spatial curves corresponding to the parameter t in their domain: C1(t) (first guide curve) and C2(t) (second guide curve), the parametric equation of the ruled surface can be expressed as: S(t,u)=(1-u)×C1(t)+u×C2(t). Here, t is the ruling parameter, which determines which specific line in the family of lines. u is the linear interpolation parameter (usually u∈[0,1]), which, when t is fixed, varies from 0 to 1, describing the trajectory of a straight line from a point on curve C1(t) to a point on curve C2(t). The characteristics of a ruled surface are its standardized parameter form and the ability to use the boundary curves of the processing area at both ends, resulting in a ruled surface that fits the processing area well.

[0093] Then, after constructing the guide surface, the auxiliary machining paths are planned. For example, the constructed guide surface has a relatively standardized parameter form, so uniformly distributed isoparametric lines or equidistant offset curves can be directly used as guide paths or as auxiliary machining paths, respectively.

[0094] Next, the auxiliary machining path is projected onto each parametric surface. For example, the projection method could be to uniformly sample points on the guide curve, and then project these sampling points along the guide surface normal or spatial coordinate axis direction onto the machining surface to obtain a projection point, or no projection point may be generated. Interpolation is performed on the projection points obtained from a guide curve to obtain a smooth, continuous machining curve on the machining area, thus each guide curve can project a machining curve.

[0095] In some application scenarios, discontinuous machining paths generated by conventional path planning on parametric surfaces, such as... Figure 3 As shown, the parametric surface group 100 includes a first parametric surface 110 and a second parametric surface 120. The three machining paths planned in the first parametric surface 110 are machining path a, machining path b, and machining path c. The three machining paths planned in the second parametric surface 120 are machining path d, machining path e, and machining path f. Figure 3 It can be seen that the machining paths directly planned from the first parameter surface 110 and the second parameter surface 120 are all discontinuous. For example... Figure 4As shown, the machining path planned using the parametric surface-based machining path planning method provided by the present invention includes machining path g, machining path h, and machining path i that pass through the first parametric surface 110 and the second parametric surface 120 in the parametric surface group 100. Since machining path g, machining path h, and machining path i are continuous on the first parametric surface 110 and the second parametric surface 120, machining according to machining path g, machining path h, and machining path i can ensure the accuracy of machining the workpiece.

[0096] The following describes the machining path planning device based on parametric surfaces provided by this invention. The machining path planning device based on parametric surfaces described below can be referred to in correspondence with the machining path planning method based on parametric surfaces described above. For example... Figure 5 As shown, the machining path planning device 400 based on parametric surfaces may include the following modules: The processing area determination module 401 is used to obtain at least two adjacent parametric surfaces corresponding to the processing area in the workpiece to be processed, and to take the combination of the at least two adjacent parametric surfaces as a parametric surface group. Guide surface determination module 402 is used to construct a guide surface about the parametric surface group based on the geometric features of the parametric surface group; The auxiliary machining path generation module 403 is used to generate at least one auxiliary machining path for the guide surface; The machining path determination module 404 is used to project each of the auxiliary machining paths onto each of the parameter surfaces in the parameter surface group to obtain several machining paths for the machining area in the workpiece to be machined.

[0097] According to the present invention, a machining path planning device 400 based on parametric surfaces includes geometric features including shape and size. A guide surface determination module 402 constructs a guide surface about the parametric surface group based on the geometric features of the parametric surface group, including: The preset guide surface type that is associated with the shape of the parametric surface group among several preset guide surface types is taken as the target type of the guide surface. The parameters of the guide surface are determined based on the target type of the guide surface and the shape and size of the parametric surface group. The wizard surface is generated based on the parameters of the wizard surface.

[0098] According to a parametric surface-based machining path planning device 400 provided by the present invention, a guide surface determination module 402 determines the parameters of the guide surface according to the target type of the guide surface, the shape and size of the parametric surface group, including: When the target type is ruled surface, the geometric definition parameters of the first guide curve and the second guide curve of the guide surface are determined according to the shape and size of the first boundary curve and the second boundary curve arranged along the preset processing direction in the parameter surface group. Furthermore, based on the relative positional relationship between the first boundary curve and the second boundary curve, the relative positional relationship between the first guide curve and the second guide curve is determined.

[0099] According to the processing path planning device 400 based on parametric surfaces provided by the present invention, the guide surface determination module 402 is further used for: Obtain the curvature distribution of each of the parametric surfaces in the parametric surface group; Based on the curvature distribution, adjust the geometric definition parameters of the first guide curve, the geometric definition parameters of the second guide curve, and / or the relative positional relationship.

[0100] According to the present invention, a machining path planning device 400 based on parametric surfaces includes an auxiliary machining path generation module 403 that generates at least one auxiliary machining path for the guide surface, comprising: Several equally spaced isoparametric lines on the guide surface are respectively used as each of the auxiliary processing paths; Alternatively, several equidistant offset curves determined by the guide surface according to a preset offset distance can be used as each of the auxiliary processing paths.

[0101] According to a parametric surface-based machining path planning device 400 provided by the present invention, a machining path determination module 404 projects each of the auxiliary machining paths onto each of the parametric surfaces in the parametric surface group to obtain a plurality of machining paths for the machining area in the workpiece to be machined, including: Each of the auxiliary processing paths is sampled to obtain several sampling points for each auxiliary processing path; Project each of the sampling points onto the parametric surface group to obtain the projection points on each of the parametric surfaces; Interpolation is performed on the projection points corresponding to each of the auxiliary processing paths to obtain several processing paths for the processing area in the workpiece to be processed.

[0102] According to the parametric surface-based machining path planning device 400 provided by the present invention, after interpolating the projection points corresponding to each of the auxiliary machining paths to obtain several machining paths for the machining area in the workpiece to be machined, the machining path determination module 404 is further configured to: According to the scope requirements of the processing area, each of the processing paths is trimmed; The processed path after trimming is smoothed to obtain the final processed path for the processed area.

[0103] Figure 6 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 6 As shown, the electronic device may include a processor 510, a communications interface 520, a memory 530, and a communication bus 540, wherein the processor 510, communications interface 520, and memory 530 communicate with each other via the communication bus 540. The processor 510 can call logical instructions in the memory 530 to execute a parametric surface-based machining path planning method. This method includes: obtaining at least two adjacent parametric surfaces corresponding to a machining area in the workpiece, and using the combination of the at least two adjacent parametric surfaces as a parametric surface group; constructing a guide surface about the parametric surface group based on the geometric features of the parametric surface group; generating at least one auxiliary machining path from the guide surface; and projecting each of the auxiliary machining paths onto each of the parametric surfaces in the parametric surface group to obtain several machining paths for the machining area in the workpiece.

[0104] Furthermore, the logical instructions in the aforementioned memory 530 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, 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. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0105] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer is able to execute the machining path planning method based on parametric surfaces provided by the above methods. The method includes: obtaining at least two adjacent parametric surfaces corresponding to the machining area in the workpiece to be machined, and taking the combination of the at least two adjacent parametric surfaces as a parametric surface group; constructing a guide surface about the parametric surface group according to the geometric features of the parametric surface group; generating at least one auxiliary machining path of the guide surface; and projecting each of the auxiliary machining paths onto each of the parametric surfaces in the parametric surface group to obtain a plurality of machining paths for the machining area in the workpiece to be machined.

[0106] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a machining path planning method based on parametric surfaces provided by the above methods. The method includes: obtaining at least two adjacent parametric surfaces corresponding to a machining area in a workpiece, and taking the combination of the at least two adjacent parametric surfaces as a parametric surface group; constructing a guide surface about the parametric surface group based on the geometric features of the parametric surface group; generating at least one auxiliary machining path from the guide surface; and projecting each of the auxiliary machining paths onto each of the parametric surfaces in the parametric surface group to obtain a plurality of machining paths for the machining area in the workpiece.

[0107] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0108] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A machining path planning method based on parametric surfaces, characterized in that, include: Obtain at least two adjacent parametric surfaces corresponding to the processing area in the workpiece, and take the combination of the at least two adjacent parametric surfaces as a parametric surface group; Construct a guide surface about the parametric surface group based on the geometric features of the parametric surface group; Generate at least one auxiliary processing path for the guide surface; Each of the auxiliary machining paths is projected onto each of the parameter surfaces in the parameter surface group to obtain several machining paths for the machining area in the workpiece.

2. The method according to claim 1, characterized in that, The geometric features include shape and size, and the construction of a guide surface about the parametric surface group based on the geometric features of the parametric surface group includes: The preset guide surface type that is associated with the shape of the parametric surface group among several preset guide surface types is taken as the target type of the guide surface. The parameters of the guide surface are determined based on the target type of the guide surface and the shape and size of the parametric surface group. The wizard surface is generated based on the parameters of the wizard surface.

3. The method according to claim 2, characterized in that, The step of determining the parameters of the guide surface based on the target type of the guide surface and the shape and size of the parametric surface group includes: When the target type is ruled surface, the geometric definition parameters of the first guide curve and the second guide curve of the guide surface are determined according to the shape and size of the first boundary curve and the second boundary curve arranged along the preset processing direction in the parameter surface group. Furthermore, based on the relative positional relationship between the first boundary curve and the second boundary curve, the relative positional relationship between the first guide curve and the second guide curve is determined.

4. The method according to claim 3, characterized in that, The method further includes: Obtain the curvature distribution of each of the parametric surfaces in the parametric surface group; Based on the curvature distribution, adjust the geometric definition parameters of the first guide curve, the geometric definition parameters of the second guide curve, and / or the relative positional relationship.

5. The method according to any one of claims 1 to 4, characterized in that, The at least one auxiliary processing path for generating the guide surface includes: Several equally spaced isoparametric lines on the guide surface are respectively used as each of the auxiliary processing paths; Alternatively, several equidistant offset curves determined by the guide surface according to a preset offset distance can be used as each of the auxiliary processing paths.

6. The method according to any one of claims 1 to 4, characterized in that, The step of projecting each of the auxiliary machining paths onto each of the parametric surfaces in the parametric surface group to obtain several machining paths for the machining area in the workpiece includes: Each of the auxiliary processing paths is sampled to obtain several sampling points for each auxiliary processing path; Project each of the sampling points onto the parametric surface group to obtain the projection points on each of the parametric surfaces; Interpolation is performed on the projection points corresponding to each of the auxiliary processing paths to obtain several processing paths for the processing area in the workpiece to be processed.

7. The method according to claim 6, characterized in that, After interpolating the projection points corresponding to each of the auxiliary machining paths to obtain several machining paths for the machining area in the workpiece, the method further includes: According to the scope requirements of the processing area, each of the processing paths is trimmed; The processed path after trimming is smoothed to obtain the final processed path for the processed area.

8. A machining path planning device based on parametric surfaces, characterized in that, include: The processing area determination module is used to obtain at least two adjacent parametric surfaces corresponding to the processing area in the workpiece to be processed, and to take the combination of the at least two adjacent parametric surfaces as a parametric surface group. A guide surface determination module is used to construct a guide surface about the parametric surface group based on the geometric features of the parametric surface group. An auxiliary machining path generation module is used to generate at least one auxiliary machining path for the guide surface; The machining path determination module is used to project each of the auxiliary machining paths onto each of the parameter surfaces in the parameter surface group to obtain several machining paths for the machining area in the workpiece.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the machining path planning method based on parametric surfaces as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the machining path planning method based on parametric surfaces as described in any one of claims 1 to 7.

Images