Continuous small straight line segment cutter path smooth compression method and system based on dominant points
Through the smooth compression method of the trajectory based on the continuous small straight lines based on the leading point, the problem of high -efficiency and accurate knife trajectory fitting and processing is achieved by solving the problem of large trajectory storage, low processing efficiency and poor accuracy.
Patent Information
- Application Number
- CN202411490810.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-24
- Publication Date
- 2025-01-28
AI Technical Summary
The existing tool trajectory consists of a large number of data points, has a large storage volume, and the processing mode has frequent acceleration and deceleration, which causes machine tool vibration, reduces machining efficiency, accelerates tool wear, and poor machining accuracy and surface quality.
Adopt the smooth compression method of the trajectory of the continuous small straight segment based on the leading point. By entering the original knife data, the bid array is established, the discrete curvature rate is calculated, the leading point is used, and the fitting formula B -shaped curve control point is used to generate the production point B -shaped curve control point to generate generate Fitting the B -sized bar curve.
Improve the fitting speed and accuracy of the tool trajectory, reduce the vibration of the machine tool, improve the processing efficiency, extend the life of the tool, and improve the processing accuracy and surface quality.
Smart Images

Figure CN119376336A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of numerical control machining, and in particular to a method and system for smoothing and compressing tool trajectories of continuous small straight line segments based on dominant points. Background Art
[0002] In the field of computer-aided manufacturing and CNC machining, the tool path is first calculated based on the surface to be machined through the CAD / CAM system, and then the tool path is converted into program code through post-processing, and finally the corresponding G code is transmitted to the CNC system. The existing tool path is usually expressed by small line segments. This processing mode has the following disadvantages:
[0003] 1. The tool path consists of a large number of data points and requires large storage capacity;
[0004] 2. The tool trajectory only has G0 continuity, and the system frequently accelerates and decelerates, which easily causes machine tool vibration, reduces processing efficiency, and accelerates tool wear;
[0005] 3. The tool path smoothness is poor, and the part contour processing accuracy and surface quality are poor. Summary of the invention
[0006] Based on the above-mentioned shortcomings of the prior art, the purpose of the present invention is to provide a method and system for smoothing and compressing tool trajectories of continuous small straight line segments based on dominant points, so as to solve the above-mentioned technical problems.
[0007] To achieve the above object, the present invention provides the following technical solution: a method for smoothing and compressing tool trajectories of continuous small straight line segments based on dominant points, comprising:
[0008] S1: Input the original tool position data and create the marking array m[n];
[0009] S2: Calculate the discrete curvature of the labeled array m[n] and input the curvature threshold;
[0010] S3: inputting the tool position points whose curvature exceeds the curvature threshold into the marking array, and also inputting the tool position points whose curvature is the maximum value into the marking array;
[0011] S4: defining the mark array and the points that the tool path must pass through as the dominant points;
[0012] S5: Calculate the control points of the fitted B-spline curve using a fitting formula based on the dominant point and generate the fitted B-spline curve.
[0013] The present invention is further configured to calculate the discrete curvature of the marker array m[n], and the calculation logic includes: in, Q is the midpoint of the labeled array m[n] i The curvature estimate, Q i-1 , Qi and Q i+1 To mark three close data points in the array m[n], area is the vector product.
[0014] The present invention is further configured to define the points that the marking array and the tool path must pass through as the dominant points. When the data point Q i Selected as discrete data [Q i-3 , Q i+3 ]’s dominant point.
[0015] The present invention is further configured to calculate the control points of the fitted B-spline curve using a fitting formula based on the dominant point and generate the target of the fitted B-spline curve, and define the target function: Among them, L is the objective function, α is the error factor, 0≤α≤1, the larger α is, the higher the compression accuracy is, ω k is the weight coefficient used to control the expected error of each approximation midpoint, ω k The larger the value, the smaller the error. is the curve equation, q k,a represents the approach point, is the curvature limiting factor, which is used to balance the compression accuracy and the smoothness of the compression curve. is the node vector of the B-spline, and the value is determined by: Where d is the length of the entire tool path, q k is the coordinate of the kth tool position point;
[0016] Where tr represents the trace of the matrix, P = [p0, ...p m ] T ,
[0017] Each item in the C matrix can be expressed as: Among them, μ i,j =μ i -μ j ;
[0018] By combining the above conditions with the constraint equations and using the definition of the Frobenius norm in linear algebra, the problem of finding the minimum value of an expression containing a matrix equation can be transformed into the problem of finding the minimum value of the trace of the matrix equation, that is: Among them, A, B, C, and D are four non-zero matrices of the same order, |X| F is the Frobenius norm of the matrix X, and D = A T A, The above three objectives are integrated into the following equation to find the minimum value: Among them, R a , R i are the approximation point matrix and the dominant point matrix, B a , B i is the corresponding B-spline basis function matrix, W is the weight matrix, P is the control point matrix to be determined, θ is the Lagrangian operator, Find the partial derivatives separately: The solution is: The weight matrix W is the inflection angle θ of the continuous small line segments in the original data obtained when calculating the discrete curvature. i The empirical formula for calculation is: Among them, θ i is the small line segment angle at the i-th point; the control point matrix P can be obtained by the above logic and substituted into the following formula: in, is the corresponding B-spline basis function, p j is the control point, μ is the node vector, s(μ) is the curve equation, and the fitted B-spline curve is obtained.
[0019] The present invention also provides a system for smoothing and compressing tool trajectories of continuous small straight line segments based on dominant points, the system comprising:
[0020] Create array module: input original tool position data and create mark array m[n];
[0021] Curvature calculation module: calculates the discrete curvature of the labeled array m[n] and inputs the curvature threshold;
[0022] Input module: input the tool position whose curvature exceeds the curvature threshold into the marking array, and also input the tool position with the maximum curvature into the marking array;
[0023] Definition module: defines the marking array and the points that the tool path must pass through as dominant points;
[0024] Fitting module: Based on the dominant points, the fitting formula is used to calculate the control points of the fitting B-spline curve and generate the fitting B-spline curve.
[0025] The present invention provides a method and system for smoothing and compressing a continuous small straight line segment tool trajectory based on a dominant point. The method establishes a marker array m[n] by inputting original tool position data; calculating the discrete curvature of the marker array m[n] and inputting a curvature threshold; inputting tool position points whose curvature exceeds the curvature threshold into the marker array, and also inputting tool position points with a maximum curvature into the marker array; defining the marker array and the points that the tool path must pass through as dominant points; and calculating the control points of a fitted B-spline curve based on the dominant point using a fitting formula and generating a fitted B-spline curve. The beneficial effects produced include:
[0026] 1. Fast fitting speed: The present invention adopts Frobenius norm to calculate the matrix equation during fitting, which has a faster calculation speed than solving the matrix equation;
[0027] 2. High fitting accuracy: The present invention fully considers the effect of the dominant point on the entire tool trajectory during fitting, thereby improving the compression ratio of the tool trajectory of continuous small straight line segments while ensuring a high fitting accuracy.
[0028] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are listed below. BRIEF DESCRIPTION OF THE DRAWINGS
[0029] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:
[0030] Figure 1 A flowchart of a method for smoothing and compressing tool trajectories of continuous small straight line segments based on dominant points according to an exemplary embodiment of the present invention;
[0031] Figure 2 A logic flow chart of a method for smoothing and compressing tool trajectories of continuous small straight line segments based on dominant points according to an exemplary embodiment of the present invention;
[0032] Figure 3 A tool path to be fitted of a tool trajectory smoothing compression method for continuous small straight line segments based on dominant points is shown as an exemplary embodiment of the present invention;
[0033] Figure 4 The discrete curvature of the tool path to be fitted of the method for smoothing and compressing the tool trajectory of continuous small straight line segments based on dominant points is shown as an exemplary embodiment of the present invention;
[0034] Figure 5 The curvature of the fitted B-spline curve after fitting of the smooth compression method of the tool trajectory of continuous small straight line segments based on the dominant point is shown as an exemplary embodiment of the present invention;
[0035] Figure 6 The result of fitting the B-spline curve of the tool trajectory smoothing compression method of continuous small straight line segments based on dominant points is shown as an exemplary embodiment of the present invention;
[0036] Figure 7 The first derivative of the fitted B-spline curve of the tool trajectory smoothing compression method of continuous small straight line segments based on dominant points is shown as an exemplary embodiment of the present invention;
[0037] Figure 8 The second derivative of the fitted B-spline curve of the tool trajectory smoothing compression method of continuous small straight line segments based on dominant points is shown as an exemplary embodiment of the present invention;
[0038] Fig. 9 It is a schematic structural diagram of a system for smoothing and compressing tool trajectories of continuous small straight line segments based on dominant points according to an exemplary embodiment of the present invention. DETAILED DESCRIPTION
[0039] The following will describe the embodiments of the present invention with reference to the accompanying drawings and preferred embodiments. Those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are only for illustrating the present invention, not for limiting the scope of protection of the present invention.
[0040] It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and thus the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.
[0041] In the following description, numerous details are discussed to provide a more thorough explanation of the embodiments of the present invention. However, it is obvious to those skilled in the art that the embodiments of the present invention can be implemented without these specific details. In other embodiments, well-known structures and devices are shown in the form of block diagrams rather than in detail to avoid making the embodiments of the present invention difficult to understand.
[0042] Embodiment 1
[0043] The tool trajectory smoothing compression method of continuous small straight line segments based on dominant points, such as Figure 1 As shown, including:
[0044] S1: Input the original tool position data and create the marking array m[n];
[0045] S2: Calculate the discrete curvature of the labeled array m[n] and input the curvature threshold;
[0046] S3: inputting the tool position points whose curvature exceeds the curvature threshold into the marking array, and also inputting the tool position points whose curvature is the maximum value into the marking array;
[0047] S4: defining the mark array and the points that the tool path must pass through as the dominant points;
[0048] S5: Calculate the control points of the fitted B-spline curve using a fitting formula based on the dominant point and generate the fitted B-spline curve.
[0049] Specifically, Figure 3 As shown, Figure 3 The tool path to be fitted is shown, Figure 2 As shown in the figure, the logical flow of the tool trajectory smoothing compression method based on the dominant point continuous small straight line segment is as follows: input data points Q0-Q n , establish a marker array m[n], with m[0]=0, m[n-1]=n-1, and set the curvature value Klim; calculate the discrete curvature and store the result in the array K[n-1]; if K[i]>Klim, store its subscript in the marker array, that is, m[i]=i, and obtain the maximum curvature, and also store its subscript in the marker array, that is, m[j]=j; correspond the value in the marker array with the input data point subscript to obtain the dominant point; import the coordinates of the dominant point into the array Ra, and the remaining coordinate points into the array Ri; use the derivation formula to calculate the coordinates of the control points of the fitted B-spline curve, and generate the fitted B-spline curve; perform error detection on the non-dominant point and the fitted B-spline curve. If the error of a point is greater than the set error threshold rmax, mark this point as the dominant point and recalculate; output the fitted B-spline curve and node vector.
[0050] When judging the smoothness of a curve, the curvature value of the curve is usually used as a parameter to evaluate the smoothness of the curve. However, for discrete data points, it is impossible to obtain the exact value of the curvature based on the derivative of the curve. According to the method obtained from the literature, the curvature of discrete data points can be estimated as follows: in, Q is the midpoint of the labeled array m[n] i The curvature estimate, Q i-1 , Q i and Q i+1To mark three close data points in the array m[n], area is the vector product, such as Figure 4 As shown, Figure 4 Yes Figure 3 The estimated results of the curvature of the 62 data points (excluding the first and last points, that is, 60 points) in the figure will inevitably cause fluctuations in the calculated value after discretizing the continuous curve and then performing the estimated curvature calculation, which is particularly obvious at the larger curvature value. In order to more accurately extract the curvature maximum point of the discrete data point, the current curvature value point is compared with the first and second consecutive adjacent curvature value points, and the local curvature maximum points of the discrete data are screened out by analogy, and the data points at the curvature maximum are marked as dominant points. In order to ensure that the fitting curve can better interpolate or approximate the data points at the larger curvature values, in addition to the curvature maximum point, this paper also defines a curvature threshold K m , if the curvature value of the discrete data point is greater than the given curvature threshold K m , then it is also marked as the dominant point in curve fitting. Through the above selection method, 12 B-spline curve control points are determined.
[0051] In order to verify the rationality of the discrete point curvature estimation method, this paper recalculates the curvature value of the fitted continuous curve. The curvature value of the continuous curve is calculated by the method of increasing the interpolation parameter μ at equal intervals. The increment Δμ = 0.001, that is, 1001 points are selected on the curve with equal parameter intervals. The calculation results are as follows: Figure 5 As shown. Figure 4 and Figure 5 It can be seen that the above formula can reasonably estimate the curvature value at discrete points.
[0052] The present invention is further configured to define the points that the marking array and the tool path must pass through as the dominant points. When the data point Q i Selected as discrete data [Q i-3 , Q i+3 ]’s dominant point.
[0053] See also Figure 6-8 In step S5, let q i .k(k=0,…n i ) is the dominant point that needs to be accurately passed, q a,k (k=0,…n a ) is a non-dominant point that does not need to be accurately passed through. The above equations can be combined with the above equations to form an equation system to define a p-order B-spline trajectory that meets the requirements:
[0054]
[0055] in,
[0056] There are three goals to balance when calculating the control points for a fitted curve:
[0057] (1) The fitting curve passes through the dominant point.
[0058] (2) The error of the non-dominant point from the fitting curve should be as small as possible.
[0059] (3) The obtained fitting curve is as smooth as possible.
[0060] Based on the above objectives, the following objective function can be defined: Among them, L is the objective function, α is the error factor, 0≤α≤1, the larger α is, the higher the compression accuracy is, ω k is the weight coefficient used to control the expected error of each approximation midpoint, ω k The larger the value, the smaller the error. is the curve equation, q k,a represents the approach point, is the curvature limiting factor, which is used to balance the compression accuracy and the smoothness of the compression curve. is the node vector of the B-spline, and the value is determined by: Where d is the length of the entire tool path, q k is the coordinate of the kth tool position point;
[0061] Where tr represents the trace of the matrix, P = [p0, ...p m ] T , Each item in the C matrix can be expressed as: Among them, μ i,j =μ i -μ j ;
[0062] By combining the above conditions with the constraint equations and using the definition of the Frobenius norm in linear algebra, the problem of finding the minimum value of an expression containing a matrix equation can be transformed into the problem of finding the minimum value of the trace of the matrix equation, that is: Among them, A, B, C, and D are four non-zero matrices of the same order, |X| F is the Frobenius norm of the matrix X, and D = A T A, The above three objectives are integrated into the following equation to find the minimum value: Among them, R a , R iare the approximation point matrix and the dominant point matrix, B a , B i is the corresponding B-spline basis function matrix, W is the weight matrix, P is the control point matrix to be determined, θ is the Lagrangian operator, Find the partial derivatives separately: The solution is: The weight matrix W is the inflection angle θ of the continuous small line segments in the original data obtained when calculating the discrete curvature. i The empirical formula for calculation is: Among them, θ i is the small line segment angle at the i-th point; the control point matrix P can be obtained by the above logic and substituted into the following formula: in, is the corresponding B-spline basis function, p j is the control point, μ is the node vector, s(μ) is the curve equation, and the fitted B-spline curve is obtained.
[0063] Embodiment 2
[0064] See also Fig. 9 The exemplary dominant point-based continuous small straight line segment tool trajectory smoothing compression system includes:
[0065] Create array module: input original tool position data and create mark array m[n];
[0066] Curvature calculation module: calculates the discrete curvature of the labeled array m[n] and inputs the curvature threshold;
[0067] Input module: input the tool position whose curvature exceeds the curvature threshold into the marking array, and also input the tool position with the maximum curvature into the marking array;
[0068] Definition module: defines the marking array and the points that the tool path must pass through as dominant points;
[0069] Fitting module: Based on the dominant points, the fitting formula is used to calculate the control points of the fitting B-spline curve and generate the fitting B-spline curve.
[0070] It should be noted that the continuous small straight line segment tool trajectory smoothing compression system based on dominant points provided in the above embodiment and the continuous small straight line segment tool trajectory smoothing compression method based on dominant points provided in the above embodiment belong to the same concept, wherein the specific manner in which each module and unit performs operations has been described in detail in the method embodiment, and will not be repeated here. In actual applications, the continuous small straight line segment tool trajectory smoothing compression system based on dominant points provided in the above embodiment can allocate the above functions to different functional modules as needed, that is, divide the internal structure of the system into different functional modules to complete all or part of the functions described above, and this is not limited here.
[0071] The above embodiments can be implemented in whole or in part by software, hardware, firmware or any other combination. When implemented by software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions can be transmitted from one website site, computer, server or data center to another website site, computer, server or data center by wired (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that contains one or more available media sets. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium. The semiconductor medium can be a solid-state hard disk.
[0072] It should be understood that the term "and / or" in this article is only a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. A and B can be singular or plural. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship, but it may also indicate an "and / or" relationship. Please refer to the context for specific understanding.
[0073] In this application, "at least one" means one or more, and "more than one" means two or more. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, or c can be represented by: a, b, c, ab, ac, bc, or abc, where a, b, c can be single or multiple.
[0074] It should be understood that in the various embodiments of the present application, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.
[0075] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.
[0076] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.
[0077] In the several embodiments provided in the present application, it should be understood that the disclosed system can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.
[0078] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
[0079] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.
[0080] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in the various embodiments of the present application. The aforementioned storage media include: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (ROM), random access memories (RAM), magnetic disks or optical disks.
[0081] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.
Claims
1. A smooth compression method for tool trajectory of continuous small straight line segments based on dominant points, characterized in that: include: S1: Input the original tool position data and create the marking array m[n]; S2: Calculate the discrete curvature of the labeled array m[n] and input the curvature threshold; S3: inputting the tool position points whose curvature exceeds the curvature threshold into the marking array, and also inputting the tool position points whose curvature is the maximum value into the marking array; S4: defining the mark array and the points that the tool path must pass through as the master point; S5: Calculate the control points of the fitted B-spline curve using a fitting formula based on the dominant point and generate the fitted B-spline curve.
2. The method for smoothing and compressing tool trajectories of continuous small straight line segments based on dominant points according to claim 1, characterized in that: Calculate the discrete curvature of the labeled array m[n]. The calculation logic includes: in, Q is the midpoint of the labeled array m[n] i The curvature estimate, Q i-1 , Q i and Q i+1 To mark three close data points in the array m[n], area is the vector product.
3. The method for smoothing and compressing tool trajectories of continuous small straight line segments based on dominant points according to claim 2, characterized in that: Define the points that the marker array and tool path must pass through as dominant points. When the data point Q i Selected as discrete data [Q i-3 ,Q i+3 ]’s dominant point.
4. The method for smoothing and compressing tool trajectories of continuous small straight line segments based on dominant points according to claim 1, characterized in that: Based on the dominant point, the fitting formula is used to calculate the control points of the fitted B-spline curve and generate the target of the fitted B-spline curve. The objective function is defined as: Among them, L is the objective function, α is the error factor, 0≤α≤1, the larger α is, the higher the compression accuracy is, ω k is the weight coefficient used to control the expected error of each approximation midpoint, ω k The larger the value, the smaller the error. is the curve equation, q k,a represents the approach point, is the curvature limiting factor, which is used to balance the compression accuracy and the smoothness of the compression curve. is the node vector of the B-spline, and the value is determined by: Where d is the length of the entire tool path, q k is the coordinate of the kth tool position point; Where tr represents the trace of the matrix, P = p0,…p m ] T , Each item in the C matrix can be expressed as: Among them, m i,j =μ i -m j ; By combining the above conditions with the constraint equations and using the definition of the Frobenius norm in linear algebra, the problem of finding the minimum value of an expression containing a matrix equation can be transformed into the problem of finding the minimum value of the trace of the matrix equation, that is: Among them, A, B, C, and D are four non-zero matrices of the same order, |X| F is the Frobenius norm of the matrix X, and D = A T A, The above three objectives are integrated into the minimum value of the following equation for solution: Among them, R a , R i are the approximation point matrix and the dominant point matrix, B a , B i is the corresponding B-spline basis function matrix, W is the weight matrix, P is the control point matrix to be determined, θ is the Lagrangian operator, Find the partial derivatives separately: The solution is: The weight matrix W is the inflection angle θ of the continuous small line segments in the original data obtained when calculating the discrete curvature. i The empirical formula for calculation is: Among them, θ i is the small line segment angle at the i-th point; the control point matrix P can be obtained by the above logic and substituted into the following formula: in, is the corresponding B-spline basis function, p j is the control point, μ is the node vector, sμ is the curve equation, and the fitted B-spline curve is obtained.
5. A continuous small straight line segment tool trajectory smoothing compression system based on dominant points, characterized in that: include: Create array module: input original tool position data and create marking array m[n]; Curvature calculation module: calculates the discrete curvature of the labeled array m[n] and inputs the curvature threshold; Input module: input the tool position whose curvature exceeds the curvature threshold into the marking array, and also input the tool position whose curvature is the maximum value into the marking array; Definition module: defines the marking array and the points that the tool path must pass through as dominant points; Fitting module: Based on the dominant points, the fitting formula is used to calculate the control points of the fitting B-spline curve and generate the fitting B-spline curve.
Citation Information
Cited By
Numerical control industrial machining method and device based on trajectory curve fitting
CN120010391A