External tangent transition curve generation method applied to laser cutting and related equipment

Abstract

The embodiment of the invention belongs to the technical field of automation, and relates to an externally tangent transition curve generation method applied to laser cutting and related equipment, and the method comprises the following steps: obtaining linear track data and arc track data of laser cutting; judging whether a circumscribed transition curve needs to be constructed at corners of the linear track data and the arc track data or not; if the externally tangent transition curve needs to be constructed at the corner, constructing a first transition curve C0 and a second transition curve C1 which are continuous in G2 and monotonous in curvature; and performing G2 continuous splicing operation on the first transition curve C0 and the second transition curve C1 to obtain a target circumscribed transition curve. According to the method, the two sections of G2 continuous Bezier curves are adopted for splicing, G2 continuity of the straight line and arc externally tangent corner can be achieved, the corner precision can be guaranteed, meanwhile, the curvature extreme point of a transition curve does not need to be calculated iteratively, the uncertainty of the curvature extreme point on speed constraint is reduced, and the actual application effect of the straight line and arc corner is further improved.

Description

Technical Field

[0001] The present application relates to the field of automation technology, and in particular to a method for generating an externally cut transition curve for laser cutting and related equipment. Background Art

[0002] In laser cutting systems, non-tangent corners between straight lines and circular arcs often require smooth transitions through circumscribed transition curves.

[0003] There is a method for generating a tangent transition curve, which is to add a G2 continuous Bezier curve to smooth the transition and improve the processing efficiency of non-tangent corners of straight lines and circular arcs.

[0004] However, the applicant discovered that while using a G2-continuous Bezier curve to smoothly transition between straight and circular corners ensures G2 continuity at the transition curve's intersection with the straight lines and circular arcs before and after the corner, the curvature of the transition curve is non-monotonic. The extreme curvature points require iterative calculation, which can easily lead to computational errors. This results in inaccurate corner connection speed constraints based on curvature extreme value constraints. Furthermore, the maximum corner error between the transition curve and the corner is also difficult to accurately calculate. This suggests that conventional methods for generating circumscribed transition curves suffer from inaccurate corner connection speed constraints and low corner accuracy. Summary of the Invention

[0005] The purpose of the embodiments of the present application is to propose a method and related equipment for generating an externally tangential transition curve for laser cutting, so as to solve the problems of inaccurate corner connection speed constraints and low corner accuracy in traditional methods of generating externally tangential transition curves.

[0006] In order to solve the above technical problems, the present application provides a method for generating a circumscribed transition curve for laser cutting, which adopts the following technical solution:

[0007] Obtain the linear trajectory data and arc trajectory data of laser cutting;

[0008] Determining whether corners of the straight line trajectory data and the arc trajectory data need to construct circumscribed transition curves;

[0009] If the corner needs to construct a circumscribed transition curve, a first transition curve C0 and a second transition curve C1 with continuous G2 and monotonic curvature are constructed;

[0010] Perform a G2 continuous splicing operation on the first transition curve C0 and the second transition curve C1 to obtain a target circumscribed transition curve.

[0011] In order to solve the above technical problems, the embodiment of the present application further provides a device for generating a circumscribed transition curve for laser cutting, which adopts the following technical solution:

[0012] Trajectory data acquisition module, used to obtain linear trajectory data and arc trajectory data of laser cutting;

[0013] A circumscribed transition curve judgment module, used to judge whether a circumscribed transition curve is required to be constructed at the corners of the straight line trajectory data and the circular arc trajectory data;

[0014] A transition curve construction module, configured to construct a first transition curve C0 and a second transition curve C1 with continuous G2 and monotonic curvature if the corner needs to construct a circumscribed transition curve;

[0015] The transition curve splicing module is used to perform a G2 continuous splicing operation on the first transition curve C0 and the second transition curve C1 to obtain a target circumscribed transition curve.

[0016] In order to solve the above technical problems, the embodiment of the present application further provides a computer device, which adopts the following technical solution:

[0017] The invention comprises a memory and a processor, wherein the memory stores computer-readable instructions, and when the processor executes the computer-readable instructions, the steps of the method for generating a circumscribed transition curve for laser cutting as described above are realized.

[0018] In order to solve the above technical problems, the embodiment of the present application further provides a computer-readable storage medium, which adopts the following technical solution:

[0019] The computer-readable storage medium stores computer-readable instructions, and when the computer-readable instructions are executed by a processor, the steps of the method for generating a circumscribed transition curve for laser cutting as described above are implemented.

[0020] The present application provides a method for generating an externally tangent transition curve for laser cutting, comprising: obtaining linear trajectory data and circular arc trajectory data for laser cutting; determining whether a corner of the linear trajectory data and the circular arc trajectory data requires the construction of an externally tangent transition curve; if the corner requires the construction of an externally tangent transition curve, constructing a first transition curve C0 and a second transition curve C1 that are G2 continuous and have a monotonic curvature; and performing a G2 continuous splicing operation on the first transition curve C0 and the second transition curve C1 to obtain a target externally tangent transition curve. Compared with the prior art, the present application proposes a G2 continuous splicing transition method for laser cutting, targeting externally tangent corners of a line connecting to an arc (LC) or an arc connecting to a line (CL). This method selects a transition curve with monotonic curvature and a transition curve with only one maximum curvature point at the midpoint of the curve for G2 continuous splicing. It can not only achieve G2 continuity of the circumscribed corners of straight lines and circular arcs, but also ensure the accuracy of the corners. At the same time, there is no need to iteratively calculate the extreme curvature points of the transition curve, which reduces the uncertainty of the curvature extreme points on the speed constraint and further improves the practical application effect of straight line and circular arc corners. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the solutions in this application, a brief introduction will be given below to the drawings required for use in the description of the embodiments of this application. Obviously, the drawings described below are some embodiments of this application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0022] Figure 1 This is a flowchart of a method for generating a circumscribed transition curve for laser cutting according to an embodiment of the present application;

[0023] Figure 2 This is an example diagram of the G2 continuous splicing of the CL corner where the clockwise arc G02 and the straight line L are connected, provided in an embodiment of the present application;

[0024] Figure 3 This is an example diagram of the control points of the transition curve C0 provided in an embodiment of the present application;

[0025] Figure 4 This is an example diagram of the control points of the transition curve C1 provided in an embodiment of the present application;

[0026] Figure 5 Schematic diagram of the structure of the device for generating a circumscribed transition curve for laser cutting provided in an embodiment of the present application;

[0027] Figure 6 It is a structural diagram of an embodiment of a computer device according to the present application. DETAILED DESCRIPTION

[0028] Unless otherwise defined, all technical and scientific terms used herein have the same meanings as commonly understood by those skilled in the art to which this application belongs. The terms used in the specification of the application are for the purpose of describing specific embodiments only and are not intended to limit this application. The terms "including" and "having" and any variations thereof in the specification and claims of this application and the above-mentioned drawings are intended to cover non-exclusive inclusions. The terms "first", "second", etc. in the specification and claims of this application or the above-mentioned drawings are used to distinguish different objects, not to describe a specific order.

[0029] References herein to "embodiments" mean that a particular feature, structure, or characteristic described in connection with the embodiments may be included in at least one embodiment of the present application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor does it constitute an independent or alternative embodiment that is mutually exclusive of other embodiments. It is understood, both explicitly and implicitly, by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0030] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings.

[0031] Continue to refer Figure 1 , shows a flow chart of an embodiment of a method for generating a circumscribed transition curve for laser cutting according to the present application. The method for generating a circumscribed transition curve for laser cutting includes: step S101, step S102, step S103 and step S104.

[0032] In step S101 , linear trajectory data and arc trajectory data of laser cutting are acquired.

[0033] In an embodiment of the present application, the linear trajectory data of laser cutting can be obtained by extracting geometric parameters (starting point and end point coordinates) from a three-dimensional CAD model.

[0034] In an embodiment of the present application, the arc trajectory data of laser cutting can be obtained by using the three-point method (starting point, end point, and middle point) or the method of defining the arc by center + radius + angle range.

[0035] In step S102 , it is determined whether the corners of the straight line trajectory data and the arc trajectory data need to construct circumscribed transition curves.

[0036] In the present application, a circumscribed transition curve refers to a curve constructed at the corner between two adjacent trajectories (e.g., a straight line, a straight line, an arc, or an arc) that is tangent to both trajectories. Its primary function is to ensure smoother and more continuous motion around corners, avoiding impact, vibration, and sudden changes in velocity and acceleration caused by sudden changes in trajectory direction.

[0037] In step S103 , if the corner needs to construct a circumscribed transition curve, a first transition curve C0 and a second transition curve C1 with continuous G2 and monotonic curvature are constructed.

[0038] In the embodiment of the present application, if the corner does not need to construct a circumscribed transition curve, the end operation is performed.

[0039] In step S104, a G2 continuous splicing operation is performed on the first transition curve C0 and the second transition curve C1 to obtain a target circumscribed transition curve.

[0040] Compared to the prior art, this application proposes a G2 continuous splicing transition method for laser cutting of circumscribed corners between a line and an arc (LC) or a circle and a line (CL). This method selects a transition curve with monotonic curvature and a transition curve with a single maximum curvature point at the midpoint of the curve for G2 continuous splicing. This method not only achieves G2 continuity for circumscribed corners of lines and arcs, but also ensures corner accuracy. Furthermore, it eliminates the need for iterative calculation of the curvature extreme points of the transition curve, reducing the uncertainty of the curvature extreme points on speed constraints and further improving the practical application of line and arc corners.

[0041] In some optional implementations of the embodiments of the present application, the step of determining whether the corners of the straight line trajectory data and the arc trajectory data need to construct a circumscribed transition curve specifically includes the following steps:

[0042] Select the external transition curve judgment point P in the linear trajectory data m ;

[0043] Calculate the judgment point P of the circumscribed transition curve m The distance d to the center C0 of the arc trajectory data;

[0044] Determine whether the distance d is less than or equal to the radius R of the arc trajectory data;

[0045] If it is less than or equal to, it is determined that the corner does not need to construct a circumscribed transition curve;

[0046] If it is greater than, it is determined that the corner needs to construct an external transition curve.

[0047] In the embodiment of this application, combined with Figure 2 The G2 continuous splicing example diagram of the clockwise arc G02 and the CL corner connected by the straight line L is shown. The diagram is formed by the clockwise arc (G02) C and the CL corner connected by the straight line L. Among them, the radius of the arc C is R, and the coordinates of the center of the circle are O(x o ,y o ), the starting point coordinates are P0(x0,y0), and the end point coordinates are P1(x1,y1); the starting point coordinates of the straight line L are P1(x1,y1), and the end point coordinates are P2(x2,y2). It should be noted that, Figure 2 Only the G2 continuous splicing of the CL corner connected by the straight line L is shown. The circumscribed transition curve generation method provided in this application is also applicable to the G2 continuous splicing of the LC corner.

[0048] In the embodiment of the present application, in order to determine whether the CL corner can construct a transition curve located outside the corner and tangent to the clockwise arc (G02) C and the straight line L, the design scheme is to first take a point P on the straight line L. m :

[0049] P m =P1-mT L

[0050] In the above formula, is the unit tangent vector of the straight line L. Post-calculation point P m The distance to the center of the arc d = || P m If d≤R, it means that the corner of CL does not meet the conditions for a circumscribed transition curve, and the next step is not processed. Otherwise, it means that the corner of CL meets the conditions for a circumscribed transition curve.

[0051] In some optional implementations of the embodiments of the present application, the first transition curve C0 includes a first curve control point First curve control point 2 First curve control point three And the first curve control point four The second transition curve C1 includes a second curve control point Second curve control point 2 Second curve control point three And the second curve control point four Among them, the first curve control point four And the second curve control point 1 It is the splicing point of the first transition curve C0 and the second transition curve C1. If the corner needs to construct a circumscribed transition curve, the step of constructing the first transition curve C0 and the second transition curve C1 with continuous G2 and monotonic curvature specifically includes the following steps:

[0052] Determine the first curve control point 2 on the arc trajectory data Coordinate data of

[0053] According to the first curve control point The coordinate data of the first curve control point is determined on the arc trajectory data. Coordinate data of

[0054] According to the first curve control point And the first curve control point 2 The coordinate data of the first curve control point 3 is determined on the arc trajectory data C. And the first curve control point four Coordinate data of

[0055] According to the first curve control point The first curve control point three And the first curve control point four The coordinate data of the second curve control point 1 is determined The second curve control point 2 The second curve control point three And the second curve control point four coordinate data.

[0056] In the embodiment of the present application, for the CL corner with the circumscribed transition condition, a transition curve C0 with a monotonic curvature and a transition curve C1 with only one maximum curvature point at the midpoint of the curve are selected for G2 continuous splicing. Among them, the four control points of the transition curve C0 are and The four control points of the transition curve C1 are and and It is the joint point of curve C0 and curve C1. Transition curves C0 and C1 are not only at the joint point Satisfies G2 continuity and also corresponds to the original arc C and straight line L at point and point G2 continuity is also satisfied.

[0057] In the embodiment of this application, the focus of this application is how to select a transition curve C0 with monotonic curvature and a transition curve C1 with only one maximum curvature point, and the maximum curvature point is at the midpoint of the curve. In order to make the transition curve C0 meet the curvature monotonicity, one endpoint has a curvature of 0. Let In this design, the four control points of the constraint transition curve C0 satisfy the following relationship:

[0058]

[0059] λ≥0.58,β∈(0,π)

[0060] In the above formula, the transition curve C0 of this design is a line at the control point The curvature is At the control point The curvature is 0, and the control point constraint diagram of the transition curve C0 is as follows Figure 3 shown.

[0061] In the embodiment of the present application, in order to ensure that the transition curve C1 has only one maximum curvature point, and the maximum curvature point is at the midpoint of the curve, in this design, the four control points constraining the transition curve C1 satisfy the following relationship:

[0062]

[0063] In the above formula, the transition curve C1 of this design is a line at the control point and control points The curvature is 0, and at the control point The curvature is the largest in The control point constraint diagram of the transition curve C1 is as follows Figure 4 shown.

[0064] Compared with the prior art, the present application can effectively confirm the coordinate data of the control points of the first transition curve C0 and the second transition curve C1 with G2 continuity and monotonic curvature.

[0065] In some optional implementations of the embodiment of the present application, the first curve control point 2 is determined on the arc trajectory data. The steps of obtaining the coordinate data specifically include the following steps:

[0066] Select point P on the arc trajectory data C t (x ti ,y ti );

[0067] At the point P t (x ti ,y ti ) Select the circumscribed arc C O , wherein the circumscribed arc C O Tangent to the arc trajectory data C at the point P t (x ti ,y ti ), and the circumscribed arc C OTangent to the linear trajectory data, the circumscribed arc C O The center of the circle O O (x oi ,y oi ) is expressed as:

[0068] O O (x oi ,y oi )=P t +T t R O

[0069]

[0070] Among them, a1 and a1 respectively represent the coefficients of the parametric equation of the linear trajectory data, which are expressed as a1=y1-y2, b1=x2-x1, c1=y2x1-y1x2, R O Represents the circumscribed arc C O Radius, T t Indicates that the center of the arc trajectory data C points to the point P t (x ti ,y ti )'s unit vector;

[0071] According to the point P t (x ti ,y ti ) and the circumscribed arc C O The center of the circle O O (x oi ,y oi ) coordinate data to calculate the first curve control point 2 The coordinate data of the first curve control point 2 The coordinate data is expressed as:

[0072]

[0073] Wherein, Δ represents the circumscribed arc C O Radius R O Along the vector direction P t O O The amount of shrinkage.

[0074] In the embodiment of the present application, the control point of the transition curve C0 is determined The design scheme first takes a point P on the arc t (x ti ,y ti ), so that point P t (x ti ,y ti ) to the center angle of corner P1 is φt =0.3φ c Then click P t (x ti ,y ti ) to find a circumscribed arc C O , so that arc C O They are tangent to the arc C at point P t (x ti ,y ti ), which is also tangent to the line L. Assume that the circumscribed arc C O The radius is R O (R O >0), the center of the circle is O O (x oi ,y oi ), then it satisfies the following relationship:

[0075] O O (x oi ,y oi )=P t +T t R O

[0076]

[0077] In the above formula, A, B, and C are the coefficients of the parametric equation of the straight line L, which are a1=y1-y2, b1=x2-x1, and c1=y2x1-y1x2 respectively. For arc C at point P t Point from the center to P t The unit vector of . Combining the above formulas, we can know or Since R O >0, so R O Take a positive value.

[0078] In order to ensure that the transition curve C0 can be G2 continuously connects to arc C. For the case of CL corner tangent, the control point of transition curve C0 is It is best to be located outside the arc C. Therefore, this design will circumscribe the arc C O Radius R O (R O >0) along the vector direction P t O O In this design, Δ is 0.01 mm. O Inward radius R N =R O -Δ, a new circle C' separated from the arc C and the straight line L respectively O At this time, the control point of the transition curve C0 for:

[0079]

[0080] Compared with the prior art, this application can effectively determine the control point of the transition curve C0 's coordinates.

[0081] In some optional implementations of the present application, the point P is selected on the arc trajectory data C. t (x ti ,y ti ) step, further comprising the following steps:

[0082] Let the point P t (x ti ,y ti ) to the center angle of the corner point P1 is

[0083] Let the point P t (x ti ,y ti ) to the center angle of the corner point P1 is for Wherein, n represents the central angle of the circle The adjustment factor, The center angle of the arc corresponding to the arc trajectory data C;

[0084] According to the first curve control point 2 The coordinate data of the first curve control point is determined on the arc trajectory data. The steps of obtaining the coordinate data specifically include the following steps:

[0085] Let the circumscribed arc C O The center of the circle is respectively to the first curve control point And the first curve control point 2 Corner

[0086] Select point P1 on the arc trajectory data C, and let the circumscribed arc C O The center of the circle is respectively to the first curve control point And the angle of the point P1

[0087] If the If the coordinate data of the point P1 is established, the coordinate data of the point P1 is determined as the first curve control point 1. Coordinate data of

[0088] If the If not, increase the central angle The value of the adjustment coefficient n is used to recalculate Until Established.

[0089] In the embodiment of the present application, the control point of the transition curve C0 is determined The coordinates of this design are determined. The method is as follows:

[0090] First calculate

[0091] Then calculate

[0092] In order to ensure a smooth transition of continuous CL corners or LC corners, it is necessary to judge If the conditions are met, take The point is the control point Otherwise, increase the central angle The value of the adjustment coefficient n is set, and a new first curve control point 2 is determined on the arc trajectory data. and the first curve control point Coordinate data to recalculate Until Established.

[0093] Compared with the prior art, this application can effectively determine the control point of the transition curve C0 's coordinates.

[0094] In some optional implementations of the embodiments of the present application, the above-mentioned first curve control point is And the first curve control point 2 The coordinate data of the first curve control point C is determined on the arc trajectory data And the first curve control point four The steps of obtaining the coordinate data specifically include the following steps:

[0095] According to the first curve control point And the first curve control point 2 Calculate the unit vector from the coordinate data

[0096] The unit vector T0 is rotated by β according to the direction of the arc trajectory data C to obtain a vector The unit vector T1, where:

[0097]

[0098] According to the unit vector T1, the first curve control point 2 The coordinate data of the first curve control point three is determined And the first curve control point four The coordinate data is expressed as:

[0099]

[0100] in,

[0101] If λ≥0.58 is true, then the value of λ is determined to be 0.58, and the current The coordinate data of the first curve control point three And the first curve control point four Coordinate data of

[0102] If λ≥0.58 does not hold, increase the central angle The value of the adjustment coefficient n is used to recalculate λ until λ ≥ 0.58 is established.

[0103] In the embodiment of the present application, the control point of the transition curve C0 is determined and control points First, the control points are determined by the above schemes (a) and (b). and control points After that, you can calculate and the unit vector According to the control point Curvature

[0104] for Then we have:

[0105]

[0106] According to the geometric relationship of the arc Therefore

[0107] Then, the unit vector T0 is rotated by β in the direction of arc C to obtain the vector The unit vector T1:

[0108]

[0109] Finally, the control point of the transition curve C0 and control points The coordinates can be expressed as follows:

[0110]

[0111] In the above formula If λ≥0.58, then take λ=0.58. Otherwise, increase the central angle The value of the adjustment coefficient n is used to recalculate λ and re-determine the new first curve control point 2 on the arc trajectory data. and the first curve control point The coordinate data of the transition curve C0 is determined until the new λ≥0.58 is established. and

[0112] Compared with the prior art, this application can effectively determine the control point of the transition curve C0 and control points 's coordinates.

[0113] In some optional implementations of the present application, when determining the control point of the transition curve C0 and After the coordinates of the transition curve C0, it is necessary to determine the control point and rationality, such as Figure 2 As shown, it is necessary to ensure that the four control points of the transition curve C0 are located on the same side of the straight line L.

[0114] In the embodiment of the present application, the present application can determine the control point of the transition curve C0 by the following method: and Rationality:

[0115] (1) Use inverse trigonometric functions to calculate and

[0116] (2) If If it holds, it means that the four control points of the transition curve C0 constructed by the above method are located on the same side of the straight line L, which is reasonable;

[0117] (3) If If it is not true, you need to increase the central angle The value of the adjustment coefficient n is Established, then determine the control point of the transition curve C0 and

[0118] In some optional implementations of the embodiments of the present application, the above-mentioned first curve control point 2 The first curve control point three And the first curve control point four The coordinate data of the second curve control point 1 is determined The second curve control point 2 The second curve control point three And the second curve control point four The steps of obtaining the coordinate data specifically include the following steps:

[0119] According to the first curve control point The first curve control point three And the first curve control point four The coordinate data of the control points of the second transition curve C1 are respectively expressed as:

[0120]

[0121] in, is the unit tangent vector of the straight line L, and P2 represents the starting point coordinates P1 (x1, y1) and the end point coordinates P2 (x2, y2) of the straight line trajectory data respectively;

[0122] Calculating Line Segments The intersection point of the straight line and the linear trajectory data L

[0123]

[0124] in, and They are The horizontal and vertical coordinates of the line L; a1, b1, c1 are the coefficients of the parametric equation of the straight line L, a2, b2, c2 are the line segments The coefficients of the parametric equation of the straight line, assuming that the point and point The coordinates of and Then a2, b2, c2 are expressed as

[0125] Calculate the control points of the second transition curve C1 Distance to corner point P1

[0126] like If the control point of the second transition curve C1 is Satisfy the smooth transition of the continuous trajectory and obtain the second curve control point The second curve control point 2 The second curve control point three And the second curve control point four Coordinate data of

[0127] like If not, increase the central angle The value of the adjustment coefficient n is used to recalculate Until Established.

[0128] In the embodiment of the present application, the control point of the transition curve C1 is determined and In order to ensure that the connection G2 between the transition curve C0 and the transition curve C1 is continuous, and the constructed transition curve C1 has only one maximum curvature point, and the curvature maximum point is at the midpoint of the curve, then the control points of the transition curve C1 are:

[0129]

[0130] In the above formula, You can calculate the line segment first The intersection of the line and line L

[0131]

[0132] In the above formula, and They are The horizontal and vertical coordinates of the line. a1, b1, c1 are the coefficients of the parametric equation of the straight line L, and a2, b2, c2 are the line segments. The coefficients of the parametric equation of the straight line, assuming that the point and point The coordinates of and Then a2, b2, c2 are

[0133] In order to ensure the control point of transition curve C1 In order to smoothly transition between corners of a continuous trajectory, it is necessary to detect control points The distance to the corner point P1, if Describe the control point you are looking for Satisfy the smooth transition of the continuous trajectory, otherwise increase the central angle The value of the adjustment coefficient n is used to recalculate Until is established to reconstruct the transition curves C0 and C1.

[0134] Compared with the prior art, this application can effectively determine the control point of the transition curve C1 and 's coordinates.

[0135] In some optional implementations of the present application, the splicing segment C of the transition curve C0 and the transition curve C1 can also be accurately detected. p The method used in this application is to directly calculate the corner point P1 of CL circumscribed to the line segment The distance ε of the straight line, such as Figure 2 As shown:

[0136]

[0137] Among them, ε max is the maximum allowable error of corner fitting, if ε≤ε max Explain the splicing section C of the above CL tangent corner p Satisfy the machining accuracy, otherwise the center angle can be readjusted The value of the adjustment coefficient n is set until ε≤ε max .

[0138] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing related hardware via computer-readable instructions. The computer-readable instructions can be stored in a computer-readable storage medium, and when the program is executed, it can include the processes in the above-described method embodiments. The aforementioned storage medium can be a non-volatile storage medium such as a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0139] It should be understood that although the steps in the flowcharts of the accompanying drawings are shown in sequence as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some of the steps in the flowcharts of the accompanying drawings may include multiple sub-steps or multiple stages, and these sub-steps or stages are not necessarily executed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be executed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.

[0140] Further references Figure 5 , as a response to the above Figure 2 In order to realize the method shown in FIG, the present application provides an embodiment of a device for generating a circumscribed transition curve for laser cutting. Figure 2 Corresponding to the method embodiment shown, the device can be specifically applied to various electronic devices.

[0141] like Figure 5As shown, the circumscribed transition curve generating device 200 for laser cutting according to the embodiment of the present application includes:

[0142] Trajectory data acquisition module, used to obtain linear trajectory data and arc trajectory data of laser cutting;

[0143] A circumscribed transition curve judgment module, used to judge whether a circumscribed transition curve is required to be constructed at the corners of the straight line trajectory data and the circular arc trajectory data;

[0144] A transition curve construction module, configured to construct a first transition curve C0 and a second transition curve C1 with continuous G2 and monotonic curvature if the corner needs to construct a circumscribed transition curve;

[0145] The transition curve splicing module is used to perform a G2 continuous splicing operation on the first transition curve C0 and the second transition curve C1 to obtain a target circumscribed transition curve.

[0146] Compared to the prior art, this application proposes a G2 continuous splicing transition method for laser cutting of circumscribed corners between a line and an arc (LC) or a circle and a line (CL). This method selects a transition curve with monotonic curvature and a transition curve with a single maximum curvature point at the midpoint of the curve for G2 continuous splicing. This method not only achieves G2 continuity for circumscribed corners of lines and arcs, but also ensures corner accuracy. Furthermore, it eliminates the need for iterative calculation of the curvature extreme points of the transition curve, reducing the uncertainty of the curvature extreme points on speed constraints and further improving the practical application of line and arc corners.

[0147] In some optional implementations of the embodiments of the present application, the circumscribed transition curve judgment module includes: a circumscribed transition curve judgment point selection submodule, a judgment point-circumference center distance calculation submodule, a judgment point-circumference center distance judgment submodule, a confirmation-not-required submodule, and a confirmation-required submodule, wherein:

[0148] The circumscribed transition curve judgment point selection submodule is used to select the circumscribed transition curve judgment point P in the linear trajectory data. m ;

[0149] The judgment point-circle center distance calculation submodule is used to calculate the judgment point P of the circumscribed transition curve. m The distance d to the center C0 of the arc trajectory data;

[0150] A point-center distance determination submodule is used to determine whether the distance d is less than or equal to the radius R of the arc trajectory data;

[0151] No confirmation submodule is required, for determining that the corner does not need to construct a circumscribed transition curve if it is less than or equal to;

[0152] A confirmation submodule is required to determine that if it is greater than, the corner needs to construct an external transition curve.

[0153] In some optional implementations of the embodiments of the present application, the first transition curve C0 includes a first curve control point First curve control point 2 First curve control point three And the first curve control point four The second transition curve C1 includes a second curve control point Second curve control point 2 Second curve control point three And the second curve control point four Among them, the first curve control point four And the second curve control point 1 It is the splicing point of the first transition curve C0 and the second transition curve C1. The above-mentioned transition curve construction module includes: a first curve control point second coordinate determination submodule, a first curve control point first coordinate determination submodule, a first curve control point third and fourth coordinate determination submodule, and a second curve control point coordinate determination submodule, wherein:

[0154] The first curve control point second coordinate determination submodule is used to determine the first curve control point second on the arc trajectory data. Coordinate data of

[0155] The first curve control point 1 coordinate determination submodule is used to determine the coordinates of the first curve control point 2 The coordinate data of the first curve control point is determined on the arc trajectory data. Coordinate data of

[0156] The first curve control point three and four coordinates determination submodule is used to determine the first curve control point three and four coordinates according to the first curve control point one And the first curve control point 2 The coordinate data of the first curve control point 3 is determined on the arc trajectory data C. And the first curve control point four Coordinate data of

[0157] The second curve control point coordinate determination submodule is used to determine the coordinates of the first curve control point according to the second The first curve control point three And the first curve control point four The coordinate data of the second curve control point 1 is determined The second curve control point 2 The second curve control point three And the second curve control point four coordinate data.

[0158] In some optional implementations of the embodiment of the present application, the above-mentioned first curve control point second coordinate determination submodule includes: t (x ti ,y ti ) Select unit, circumscribed arc C O A selection unit and a first curve control point second coordinate determination unit, wherein:

[0159] P t (x ti ,y ti ) selection unit, used to select point P on the arc trajectory data C t (x ti ,y ti );

[0160] Circumscribed arc c O Select the unit for the point P t (x ti ,y ti ) Select the circumscribed arc C O , wherein the circumscribed arc C O Tangent to the arc trajectory data C at the point P t (x ti ,y ti ), and the circumscribed arc C O Tangent to the linear trajectory data, the circumscribed arc C O The center of the circle O O (x oi ,y oi ) is expressed as:

[0161] O O (x oi ,y oi )=P t +T t R O

[0162]

[0163] Among them, a1 and a1 respectively represent the coefficients of the parametric equation of the linear trajectory data, which are expressed as a1=y1-y2, b1=x2-x1, c1=y2x1-y1x2, R O Represents the circumscribed arc C O Radius, T t Indicates that the center of the arc trajectory data C points to the point P t (xti ,y ti )'s unit vector;

[0164] The first curve control point second coordinate determination unit is used to determine the coordinates of the first curve control point according to the point P r (x ti ,y ti ) and the circumscribed arc C O The center of the circle O O (x oi ,y oi ) coordinate data to calculate the first curve control point 2 The coordinate data of the first curve control point 2 The coordinate data is expressed as:

[0165]

[0166] Wherein, Δ represents the circumscribed arc C O Radius R O Along the vector direction P t O O The amount of shrinkage.

[0167] In some optional implementations of the embodiment of the present application, the first curve control point coordinate determination submodule further includes: t (x ti ,y ti ) Central angle determination unit and P t (x ti ,y ti ) The center angle adjustment unit, the first curve control point coordinate determination submodule includes: Determine unit and angle an adjustment unit, a first curve control point coordinate determination unit, and a first curve control point coordinate re-determination unit, wherein:

[0168] P t (x ti ,y ti ) a center angle determination unit for determining the point P t (x ti ,y ti ) to the center angle of the corner point P1 is

[0169] P t (x ti ,y ti ) a center angle adjustment unit for adjusting the point P r (x ti ,y ti ) to the center angle of the corner point P1 is for Wherein, n represents the central angle of the circle The adjustment factor, The center angle of the arc corresponding to the arc trajectory data C;

[0170] Corner Determining unit, used to make the circumscribed arc C O The center of the circle is respectively to the first curve control point And the first curve control point 2 Corner

[0171] horn The adjustment unit is used to select a point P1 on the arc trajectory data C and make the circumscribed arc C O The center of the circle is respectively to the first curve control point And the angle of the point P1

[0172] The first curve control point coordinate determination unit is used for determining the coordinates of the first curve control point. If the coordinate data of the point P1 is established, the coordinate data of the point P1 is determined as the first curve control point 1. Coordinate data of

[0173] The first curve control point coordinate re-determining unit is used for If not, increase the central angle The value of the adjustment coefficient n is used to recalculate Until Established.

[0174] In some optional implementations of the embodiments of the present application, the first curve control point three- and four-coordinate determination submodule includes: a unit vector T0 determination unit, a unit vector T1 determination unit, a first curve control point three- and four-coordinate representation unit, a first curve control point three- and four-coordinate determination unit, and a first curve control point three- and four-coordinate re-determination unit, wherein:

[0175] The unit vector T0 determining unit is configured to determine the first curve control point according to the first curve control point. And the first curve control point 2 Calculate the unit vector from the coordinate data

[0176] The unit vector T1 determining unit is used to rotate the unit vector T0 by β according to the direction of the arc trajectory data C to obtain a vector The unit vector T1, where:

[0177]

[0178] The first curve control point three or four coordinate representation unit is used to represent the first curve control point according to the unit vector T1, the first curve control point two The coordinate data of the first curve control point three is determined And the first curve control point four The coordinate data is expressed as:

[0179]

[0180] in,

[0181] The first curve control point three and four coordinate determination unit is used to determine the value of λ as 0.58 if λ≥0.58 is established, and determine the current The coordinate data of the first curve control point three And the first curve control point four Coordinate data of

[0182] The third and fourth coordinates redetermining unit of the first curve control point is used to increase the central angle if λ≥0.58 does not hold. The value of the adjustment coefficient n is used to recalculate λ until λ ≥ 0.58 is established.

[0183] In some optional implementations of the embodiment of the present application, the above-mentioned second curve control point coordinate determination submodule includes: a second curve control point coordinate representation unit, an intersection point Calculation unit, distance a calculation unit, a second curve control point coordinate determination unit, and a second curve control point coordinate re-determination unit, wherein:

[0184] The second curve control point coordinate representation unit is used to represent the coordinates of the first curve control point according to the second The first curve control point three And the first curve control point four The coordinate data of the control points of the second transition curve C1 are respectively expressed as:

[0185]

[0186] in, is the unit tangent vector of the straight line L, and P2 represents the starting point coordinates P1 (x1, y1) and the end point coordinates P2 (x2, y2) of the straight line trajectory data respectively;

[0187] Intersection Point Calculation unit, used to calculate line segments The intersection point of the straight line and the linear trajectory data L

[0188]

[0189] in, and They are The horizontal and vertical coordinates of the line L; a1, b1, c1 are the coefficients of the parametric equation of the straight line L, a2, b2, c2 are the line segments The coefficients of the parametric equation of the straight line, assuming that the point and point The coordinates of and Then a2, b2, c2 are expressed as

[0190] distance A calculation unit, configured to calculate the control points of the second transition curve C1 Distance to corner point P1

[0191] The second curve control point coordinate determination unit is used to determine if If the control point of the second transition curve C1 is Satisfy the smooth transition of the continuous trajectory and obtain the second curve control point The second curve control point 2 The second curve control point three And the second curve control point four Coordinate data of

[0192] The second curve control point coordinate redefinition unit is used if If not, increase the central angle The value of the adjustment coefficient n is used to recalculate Until Established.

[0193] To solve the above technical problems, the present application also provides a computer device. Figure 6 , Figure 6 This is a basic structural block diagram of the computer device according to an embodiment of the present application.

[0194] The computer device 300 includes a memory 310, a processor 320, and a network interface 330 that are interconnected through a system bus. It should be noted that the figure only shows a computer device 300 having components 310-330, but it should be understood that it is not required to implement all the components shown, and more or fewer components can be implemented instead. Among them, those skilled in the art can understand that the computer device here is a device that can automatically perform numerical calculations and / or information processing according to pre-set or stored instructions, and its hardware includes but is not limited to microprocessors, application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), embedded devices, etc.

[0195] The computer device may be a desktop computer, notebook computer, PDA, cloud server, etc. The computer device may interact with the user via a keyboard, mouse, remote control, touchpad, or voice control device.

[0196] The memory 310 includes at least one type of readable storage medium, including flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, magnetic disk, optical disk, etc. In some embodiments, the memory 310 may be an internal storage unit of the computer device 300, such as a hard disk or memory of the computer device 300. In other embodiments, the memory 310 may also be an external storage device of the computer device 300, such as a plug-in hard disk equipped on the computer device 300, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. Of course, the memory 310 may also include both the internal storage unit of the computer device 300 and its external storage device. In the embodiment of the present application, the memory 310 is generally used to store an operating system and various application software installed on the computer device 300, such as computer-readable instructions for a method for generating a circumscribed transition curve for laser cutting. Furthermore, the memory 310 can also be used to temporarily store various data that has been output or is about to be output.

[0197] In some embodiments, the processor 320 may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip. The processor 320 is generally used to control the overall operation of the computer device 300. In the embodiment of the present application, the processor 320 is used to execute computer-readable instructions or process data stored in the memory 310, such as executing computer-readable instructions for the method for generating a circumscribed transition curve for laser cutting.

[0198] The network interface 330 may include a wireless network interface or a wired network interface. The network interface 330 is generally used to establish a communication connection between the computer device 300 and other electronic devices.

[0199] The computer device provided in this application proposes a G2 continuous splicing transition method for laser cutting of circumscribed corners between a line and an arc (LC) or a circle and a line (CL). This method selects a transition curve with monotonic curvature and a transition curve with a single maximum curvature point at the midpoint of the curve for G2 continuous splicing. This method not only achieves G2 continuity for circumscribed corners of lines and arcs, but also ensures corner accuracy. Furthermore, it eliminates the need for iterative calculation of the curvature extreme points of the transition curve, reducing the uncertainty of the curvature extreme points on speed constraints and further improving the practical application of line and arc corners.

[0200] The present application also provides another embodiment, namely, providing a computer-readable storage medium, which stores computer-readable instructions, and the computer-readable instructions can be executed by at least one processor to enable the at least one processor to perform the steps of the method for generating an external transition curve for laser cutting as described above.

[0201] The computer-readable storage medium provided in this application proposes a G2 continuous splicing transition method for laser cutting of circumscribed corners between a line and an arc (LC) or a circle and a line (CL). This method selects a transition curve with monotonic curvature and a transition curve with a single maximum curvature point at the midpoint of the curve for G2 continuous splicing. This method not only achieves G2 continuity for circumscribed corners of lines and arcs, but also ensures corner accuracy. Furthermore, it eliminates the need for iterative calculation of the curvature extreme points of the transition curve, reducing the uncertainty of the curvature extreme points on speed constraints and further improving the practical application of line and arc corners.

[0202] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus the necessary general hardware platform, and of course can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), and includes a number of instructions for enabling a terminal device (which can be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in each embodiment of the present application.

[0203] Obviously, the embodiments described above are only some of the embodiments of the present application, rather than all of the embodiments. The preferred embodiments of the present application are given in the accompanying drawings, but they do not limit the patent scope of the present application. The present application can be implemented in many different forms. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosure of the present application more thorough and comprehensive. Although the present application has been described in detail with reference to the aforementioned embodiments, for those skilled in the art, it is still possible to modify the technical solutions described in the aforementioned specific embodiments, or to make equivalent replacements for some of the technical features therein. Any equivalent structure made using the contents of the present application specification and the accompanying drawings, directly or indirectly used in other related technical fields, is also within the scope of patent protection of the present application.

Claims

1. A method for generating a circumscribed transition curve for laser cutting, characterized in that: The steps include: Obtain the linear trajectory data and arc trajectory data of laser cutting; Determining whether corners of the straight line trajectory data and the arc trajectory data need to construct circumscribed transition curves; If the corner needs to construct a circumscribed transition curve, a first transition curve C0 and a second transition curve C1 with continuous G2 and monotonic curvature are constructed; Perform a G2 continuous splicing operation on the first transition curve C0 and the second transition curve C1 to obtain a target circumscribed transition curve.

2. The method for generating a circumscribed transition curve for laser cutting according to claim 1, characterized in that: The step of determining whether the corners of the straight line trajectory data and the circular arc trajectory data need to construct a circumscribed transition curve specifically includes the following steps: Select the external transition curve judgment point P in the linear trajectory data m ; Calculate the judgment point P of the circumscribed transition curve m The distance d to the center C0 of the arc trajectory data; Determine whether the distance d is less than or equal to the radius R of the arc trajectory data; If it is less than or equal to, it is determined that the corner does not need to construct a circumscribed transition curve; If it is greater than, it is determined that the corner needs to construct an external transition curve.

3. The method for generating a circumscribed transition curve for laser cutting according to claim 1, wherein: First curve control point three And the first curve control point four The second transition curve C1 includes a second curve control point Second curve control point 2 Second curve control point three And the second curve control point four Among them, the first curve control point four And the second curve control point 1 It is the splicing point of the first transition curve C0 and the second transition curve C1. If the corner needs to construct a circumscribed transition curve, the step of constructing the first transition curve C0 and the second transition curve C1 with continuous G2 and monotonic curvature specifically includes the following steps: Determine the first curve control point 2 on the arc trajectory data Coordinate data of According to the first curve control point The coordinate data of the first curve control point is determined on the arc trajectory data. Coordinate data of According to the first curve control point And the first curve control point 2 The coordinate data of the first curve control point 3 is determined on the arc trajectory data C. And the first curve control point four Coordinate data of According to the first curve control point The first curve control point three And the first curve control point four The coordinate data of the second curve control point 1 is determined The second curve control point 2 The second curve control point three And the second curve control point four coordinate data.

4. The method for generating a circumscribed transition curve for laser cutting according to claim 3, characterized in that: Determining the first curve control point 2 on the arc trajectory data The steps of obtaining the coordinate data specifically include the following steps: Select point P on the arc trajectory data C t (x ti ,y ti ); At the point P t (x ti ,y ti ) Select the circumscribed arc C O , wherein the circumscribed arc C O Tangent to the arc trajectory data C at the point P t (x ti ,y ti ), and the circumscribed arc C O Tangent to the linear trajectory data, the circumscribed arc C O The center of the circle O O (x oi ,y oi ) is expressed as: O O (x oi ,y oi )=P t +T t R O Among them, a1 and a1 respectively represent the coefficients of the parametric equation of the linear trajectory data, which are expressed as a1=y1-y2, b1=x2-x1, c1=y2x1-y1x2, R O Represents the circumscribed arc C O Radius, T t Indicates that the center of the arc trajectory data C points to the point P t (x ti ,y ti )'s unit vector; According to the point P t (x ti ,y ti ) and the circumscribed arc C O The center of the circle O O (x oi ,y oi ) coordinate data to calculate the first curve control point 2 The coordinate data of the first curve control point 2 The coordinate data is expressed as: Wherein, Δ represents the circumscribed arc C O Radius R O Along the vector direction P t O O The amount of shrinkage.

5. The method for generating a circumscribed transition curve for laser cutting according to claim 4, characterized in that: Select point P on the arc trajectory data C t (x ti ,y ti ) step, further comprising the following steps: Let the point P t (x ti ,y ti ) to the center angle of the corner point P1 is Let the point P t (x ti ,y ti ) to the center angle of the corner point P1 is for Wherein, n represents the central angle of the circle The adjustment factor, The center angle of the arc corresponding to the arc trajectory data C; According to the first curve control point 2 The coordinate data of the first curve control point is determined on the arc trajectory data. The steps of obtaining the coordinate data specifically include the following steps: Let the circumscribed arc C O The center of the circle is respectively to the first curve control point And the first curve control point 2 Corner Select point P1 on the arc trajectory data C, and let the circumscribed arc C O The center of the circle is respectively to the first curve control point And the angle of the point P1 If the If the coordinate data of the point P1 is established, the coordinate data of the point P1 is determined as the first curve control point 1. Coordinate data of If the If not, increase the central angle The value of the adjustment coefficient n is used to recalculate Until Established.

6. The method for generating a circumscribed transition curve for laser cutting according to claim 5, characterized in that: The first curve control point And the first curve control point 2 The coordinate data of the first curve control point C is determined on the arc trajectory data And the first curve control point four The steps of obtaining the coordinate data specifically include the following steps: According to the first curve control point And the first curve control point 2 Calculate the unit vector from the coordinate data The unit vector T0 is rotated by β according to the direction of the arc trajectory data C to obtain a vector The unit vector T1, where: According to the unit vector T1, the first curve control point 2 The coordinate data of the first curve control point three is determined And the first curve control point four The coordinate data is expressed as: in, If λ≥0.58 is true, then the value of λ is determined to be 0.58, and the current The coordinate data of the first curve control point three And the first curve control point four Coordinate data of If λ≥0.58 does not hold, increase the central angle The value of the adjustment coefficient n is used to recalculate λ until λ ≥ 0.58 is established.

7. The method for generating a circumscribed transition curve for laser cutting according to claim 5, characterized in that: According to the first curve control point 2 The first curve control point three And the first curve control point four The coordinate data of the second curve control point 1 is determined The second curve control point 2 The second curve control point three And the second curve control point four The steps of obtaining the coordinate data specifically include the following steps: According to the first curve control point The first curve control point three And the first curve control point four The coordinate data of the control points of the second transition curve C1 are respectively expressed as: in, is the unit tangent vector of the straight line L, and P2 represents the starting point coordinates P1 (x1, y1) and the end point coordinates P2 (x2, y2) of the straight line trajectory data respectively; Calculating Line Segments The intersection point of the straight line and the linear trajectory data L in, and They are The horizontal and vertical coordinates of the line L; a1, b1, c1 are the coefficients of the parametric equation of the straight line L, a2, b2, c2 are the line segments The coefficients of the parametric equation of the straight line, assuming that the point and point The coordinates of and Then a2, b2, c2 are expressed as Calculate the control points of the second transition curve C1 Distance to corner point P1 like If the control point of the second transition curve C1 is Satisfy the smooth transition of the continuous trajectory and obtain the second curve control point The second curve control point 2 The second curve control point three And the second curve control point four Coordinate data of like If not, increase the central angle The value of the adjustment coefficient n is used to recalculate Until Established.

8. A device for generating a circumscribed transition curve for laser cutting, characterized in that: include: Trajectory data acquisition module, used to obtain linear trajectory data and arc trajectory data of laser cutting; A circumscribed transition curve judgment module, used to judge whether a circumscribed transition curve is required to be constructed at the corners of the straight line trajectory data and the circular arc trajectory data; A transition curve construction module, configured to construct a first transition curve C0 and a second transition curve C1 with continuous G2 and monotonic curvature if the corner needs to construct a circumscribed transition curve; The transition curve splicing module is used to perform a G2 continuous splicing operation on the first transition curve C0 and the second transition curve C1 to obtain a target circumscribed transition curve.

9. A computer device comprising a memory and a processor, characterized in that: The memory stores computer-readable instructions, and when the processor executes the computer-readable instructions, the steps of the method for generating a circumscribed transition curve for laser cutting according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer-readable instructions, which, when executed by a processor, implement the steps of the method for generating a circumscribed transition curve for laser cutting according to any one of claims 1 to 7.

Images