CN116551457B - Method and equipment for connecting and processing straight line segment and circular arc segment through spline curve - Google Patents
Method and equipment for connecting and processing straight line segment and circular arc segment through spline curve Download PDFInfo
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- G05B19/41—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path
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Abstract
The application discloses a method and equipment for connecting and processing a straight line segment and an arc segment through a spline curve, and belongs to the technical field of numerical control processing. The method comprises the following steps: determining a straight line segment and a circular arc segment to be connected; determining an intersection point of the straight line segment and the circular arc segment as a third control point, setting a first control point and a second control point on a corresponding straight line of the straight line segment, and setting a fourth control point, a fifth control point and a sixth control point near the circular arc segment; calculating the position of the first control point, the position of the second control point, the position of the fourth control point, the position of the fifth control point and the position of the sixth control point; determining an expression of a spline curve according to the position of the first control point, the position of the second control point, the position of the third control point, the position of the fourth control point, the position of the fifth control point and the position of the sixth control point, and inserting the spline curve into the straight line segment and the circular arc segment to be connected according to the expression of the spline curve.
Description
Technical Field
The application relates to the technical field of numerical control machining, in particular to a method and equipment for connecting and machining a straight line segment and an arc segment through a spline curve.
Background
For the numerical control machining at the present stage, the straight line section and the circular arc section are main components of the machining track section. Interpolation calculations within straight-line segments and circular segments are simpler, and how to better handle the connection between adjacent track segments is an important issue in interpolation algorithms. In the conventional method, deceleration processing is generally performed, and the instantaneous acceleration generated by abrupt change of the direction of the connecting point is controlled within the bearable range of the machine tool. Along with the proposal of high-speed and high-precision standards of numerical control technology, the traditional interpolation method is difficult to meet the requirements of high speed and high precision at the same time. To this end, bezier curves were introduced to address such issues.
The bezier curve fitting method at the present stage is a common method for processing the connection of the straight line segment and the circular arc segment, and the three-time bezier curve has the characteristic of continuous curvature, so that the continuity of the acceleration of the machine tool can be ensured, and the machining precision and stability are improved.
However, bezier curve fitting also suffers from the following problems: 1. in some special cases, such as when the direction vector of the straight line segment is collinear with the direction vector at the intersection point of the circular arc segment, the situation that the end point of the Bezier curve still cannot keep curvature continuity with the connected segment easily occurs, so that abrupt change of acceleration is generated; 2. the fitting algorithm needs to calculate errors and iteratively determine control points, so that the calculated amount is large; 3. the number of fitting points is inversely related to the error of fitting, and calculation is more complicated due to the increase of the number of fitting points in the machining process with high precision requirement.
Disclosure of Invention
In order to solve the technical problems, the embodiment of the application provides a method and equipment for connecting and processing a straight line segment and an arc segment through a spline curve.
The embodiment of the application adopts the following technical scheme:
in one aspect, an embodiment of the present application provides a method for connecting a straight line segment and an arc segment by spline curves, the method comprising: determining a straight line segment and a circular arc segment to be connected; the intersection point of the straight line segment and the circular arc segment is determined to be a third control point, a first control point and a second control point are arranged on the corresponding straight line of the straight line segment, and a fourth control point, a fifth control point and a sixth control point are arranged nearby the circular arc segment; determining an intermediate node of a spline curve through the second control point, the third control point and the fourth control point, and determining the position relationship between the intermediate node and the third control point; determining the position of the first control point and the position of the second control point according to the relation between the position relation and a preset curve error; calculating the position of the fourth control point according to the position of the second control point and the circle center and the radius corresponding to the circular arc section; determining the position of the fifth control point and the position of the sixth control point by using a vector rotation algorithm through the position of the fourth control point based on the processing principle of the connection point between the circular arc segment and the spline curve; calculating an expression of the spline curve according to the positions of the first control point, the second control point, the third control point, the fourth control point, the fifth control point and the sixth control point; and inserting the spline curve into the to-be-connected straight line segment and circular arc segment according to the expression of the spline curve.
In one or more embodiments of the present disclosure, determining the position of the first control point and the position of the second control point according to the relationship between the positional relationship and a preset curve error specifically includes: determining a tangent vector of the circular arc segment at the third control point, and determining a direction vector of the straight line segment at the third control point; calculating a vector included angle cosine value according to the tangent vector and the direction vector; representing the position relationship between the third control point and the intermediate node by using the cosine value of the vector included angle and the distance between the second control point and the third control point; determining the distance between the second control point and the third control point through the magnitude relation between the preset curve error and the position relation; and on the straight line segment, determining the position of the second control point according to the distance between the second control point and the third control point and the position of the third control point.
In one or more embodiments of the present description, after determining the location of the second control point, the method further comprises: determining the second control point as an end point of the spline curve; determining a distance between the second control point and the first control point, equal to a distance between the second control point and the third control point; and on the straight line segment, determining the position of the first control point according to the distance between the second control point and the first control point and the position of the second control point.
In one or more embodiments of the present disclosure, according to the position of the second control point, calculating, by using the center and the radius corresponding to the arc segment, the position of the fourth control point specifically includes: characterizing an angle using a ratio between a distance between the second control point and the third control point and a radius of the arc segmentThe method comprises the steps of carrying out a first treatment on the surface of the Wherein the angle->The third control point is taken as a vertex, the straight line segment is taken as one side, and a connecting line between the third control point and the fourth control point is taken as an angle determined by the other side; determining a distance between the third control point and the fourth control point equal to a distance between the third control point and the second control point; according to the angle->The distance between the third control point and the fourth control point is determined, and the distance between the fourth control point and the circle center of the circular arc section is determined; according to the distance between the fourth control point and the center of the circular arc section, the radius of the circular arc section and the angle +.>And calculating the position of the fourth control point through the vector rotation algorithm by using a vector formed between the circle center of the circular arc section and the third control point.
In one or more embodiments of the present disclosure, determining, by using a vector rotation algorithm, the position of the fifth control point and the position of the sixth control point based on a processing principle of a connection point between the arc segment and the spline curve, by the position of the fourth control point specifically includes: determining a starting point of the spline curve on the arc segment; determining the distance between the circle center of the circular arc section and the fourth control point according to the processing principle of the connection point between the circular arc section and the spline curve, wherein the distance is equal to the distance between the circle center of the circular arc section and the fifth control point and the distance between the circle center of the circular arc section and the sixth control point; determining the distance between the starting point and the fifth control point, and representing a first central angle by utilizing the distance between the starting point and the fifth control point and the radius of the arc segment; the first central angle is an angle determined by taking the center of the circular arc section as a vertex, taking a connecting line between the center and the fourth control point as one side and taking a connecting line between the center and the fifth control point as the other side; and calculating the position of the fifth control point through the vector rotation algorithm according to the vector formed between the circle center of the circular arc section and the fourth control point and the first central angle.
In one or more embodiments of the present description, after calculating the position of the fifth control point, the method further includes: determining that the first central angle is equal to the second central angle in a first right-angle triangle formed by the center of the circular arc section, the fourth control point and the right-angle point and a second right-angle triangle formed by the center of the circular arc section, the sixth control point and the right-angle point; the second central angle is an angle determined by taking the center of the circular arc section as a vertex, taking a connecting line between the center and the fifth control point as one side and taking a connecting line between the center and the sixth control point as the other side; the right angle point is a point at which a connecting line between the center of the circular arc section and the starting point intersects with a connecting line between the fourth control point and the sixth control point, and the connecting line between the center of the circular arc section and the starting point is determined according to the processing principle of the connecting point between the circular arc section and the spline curve and is perpendicular to the connecting line between the fourth control point and the sixth control point; according to the position of the fifth control point, determining a vector formed between the center of the circle of the circular arc section and the fifth control point; and calculating the position of the sixth control point through the vector rotation algorithm according to the vector formed between the circle center of the circular arc section and the fifth control point and the second central angle.
In one or more embodiments of the present description, the spline curve employs a cubic uniform B-spline curve; determining the expression of the spline curve, which specifically comprises the following steps: obtaining a definition formula of the cubic uniform B spline curve; determining an expression of the cubic uniform B-spline curve according to the positions of the first control point, the second control point, the third control point, the fourth control point, the fifth control point and the sixth control point by the definition formula of the cubic uniform B-spline curve; the expression of the cubic uniform B-spline curve is defined by the cubic uniform B-spline curve determined by parameter values.
In one or more embodiments of the present disclosure, the cubic uniform B-spline curve is defined as follows:
wherein ,representing three curves of the cubic uniform B-spline curve, +.>The position of the ith control point is represented, and the value of i is 1,2 and 3; />。
In one or more embodiments of the present disclosure, according to the expression of the spline curve, the spline curve is inserted into the to-be-connected straight line segment and circular arc segment, which specifically includes: simulating the straight line segment and the circular arc segment to be connected by utilizing MATLAB; and inputting the expression of the cubic uniform B spline curve into MATLAB so as to insert the spline curve in the straight line segment and the circular arc segment to be connected.
On the other hand, the embodiment of the application also provides equipment for connecting and processing the straight line segment and the circular arc segment through the spline curve, which comprises the following steps: at least one processor; and a memory communicatively coupled to the at least one processor; wherein the memory stores instructions executable by the at least one processor to cause the at least one processor to perform a method of connecting a machined straight line segment with a circular arc segment by spline curves as described above.
The method and the equipment for connecting and processing the straight line segment and the circular arc segment through the spline curve provided by the embodiment of the application have the following beneficial effects: by inserting the three-time uniform B-spline curve into the processing section, the whole curvature continuity of the processing path can be satisfied for the position conditions of any straight line section and circular arc section, and the problem of discontinuity at the end point under specific conditions can be avoided. The position of the control point is determined by the geometric characteristics of the B-spline, and the calculated amount is much smaller than that of the whole fitting method. Meanwhile, only very small parts of the processing sections are processed through the positions of the control points, so that the tracks of the straight line sections and the circular arc sections are reserved as much as possible, the adjacent processing sections are not easy to influence, the calculated amount of the connecting sections and the calculated amount of the subsequent interpolation flow are much smaller than those of the whole processing section fitting method, and the calculated amount is effectively reduced.
Drawings
In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings that are required to be used in the embodiments or the description of the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present application, and other drawings may be obtained according to the drawings without inventive effort to those skilled in the art. In the drawings:
FIG. 1 is a flow chart of a method for connecting a straight line segment and an arc segment by spline curves according to an embodiment of the present application;
fig. 2 is a schematic diagram of a straight line segment and an arc segment to be connected in an application scenario provided in an embodiment of the present application;
fig. 3 is a schematic diagram of setting positions of six control points in an application scenario provided in an embodiment of the present application;
fig. 4 is a schematic processing diagram of a connection point between a B-spline curve and a circular arc segment in an application scenario provided by an embodiment of the present application;
FIG. 5 is a diagram of a simulation effect in a general case provided by an embodiment of the present application;
FIG. 6 is a graph of curvature/length in the general case provided by an embodiment of the present application;
FIG. 7 is a diagram of simulation results in a special case according to an embodiment of the present application;
FIG. 8 is a curvature/length diagram for a particular case provided by an embodiment of the present application;
FIG. 9 is a diagram of simulation results in another special case provided by an embodiment of the present application;
FIG. 10 is a graph of curvature/length for another particular case provided by an embodiment of the present application;
fig. 11 is a schematic structural diagram of an apparatus for connecting a straight line segment and an arc segment by spline curves according to an embodiment of the present application.
Detailed Description
In order to make the technical solution of the present application better understood by those skilled in the art, the technical solution of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are only some embodiments of the present application, not all embodiments. All other embodiments, which can be made by one of ordinary skill in the art based on the embodiments herein without making any inventive effort, shall fall within the scope of the present application.
The method in the embodiment of the present application will be described in detail with reference to the accompanying drawings.
Fig. 1 is a flowchart of a method for connecting a straight line segment and an arc segment by spline curves according to an embodiment of the present application, where, as shown in fig. 1, the method in the embodiment of the present application at least includes the following execution steps:
and 101, determining a straight line segment and a circular arc segment to be connected.
The method for connecting and processing the straight line segment and the circular arc segment provided by the embodiment of the application comprises the steps of firstly determining the straight line segment and the circular arc segment to be connected, wherein the determination can be realized by simulating the straight line segment and the circular arc segment of the processing segment by using simulation software.
Fig. 2 is a schematic diagram of a straight line segment and an arc segment to be connected in an application scenario provided in an embodiment of the present application. As shown in the figure 2 of the drawings,and->Respectively a straight line section and an arc section to be connected, and the machining direction is +.>The intersection point of the arc and the line segment is +>The tangent vector of the arc at the intersection point is +.>The circle center of the arc is O, and the radius is +.>。
In one example of the present application, the determining the straight line segment and the circular arc segment to be connected may simulate the straight line segment and the circular arc segment in the simulation software by coordinates of various points as in fig. 2.
And 102, setting control points according to the straight line segment and the circular arc segment to be connected.
After determining the straight line segment and the circular arc segment to be connected, control points of spline curves are arranged near the circular arc segment and the straight line segment, and in one example of the application, the straight line segment and the circular arc segment to be connected are smoothly transited through six control points and three B spline curves.
In one example of the present application, an intersection point of a straight line segment and an arc segment is determined as a third control point, and then, a first control point and a second control point are set on the straight line segment, and a fourth control point, a fifth control point and a sixth control point are set near the arc segment. The proximity may be defined by the distance of the control points from the arc segment not exceeding a preset value.
Fig. 3 is a schematic diagram of setting positions of six control points in an application scenario provided in an embodiment of the present application. As shown in the figure 3 of the drawings,for six control points of the spline curve, +.>Is the starting point and the end point of a spline curve, wherein +.>Is the intersection point of the straight line segment and the circular arc segment, < + >>On the straight line where the straight line segment is located, +.>Near the arc segment.
Step 103, calculating the position of each control point.
In the embodiment of the application, three sections of B spline curves are controlled by six control points, so that the positions of all the control points are determined firstly in order to determine the spline curves.
Taking the setting position of each control point in fig. 3 as a reference, at this time, the position of the third control point P3 is known as the position of the P point, and the position calculation process of each control point is as follows:
1) The position of the first control point P1 and the position of the second control point P2 are calculated:
first, the arc isTangent vector of the segment at intersection point P (i.e., third control point P3)Vector of direction with straight line segmentThe included angle of (2) is recorded as->Then:
next, the intermediate node C3 of the spline is determined from the second control point P2, the third control point P3 and the fourth control point P4, whereby the positional relationship between the intermediate node C3 and the third control point P3 can be determinedThe method meets the following conditions:
thereby, spline curveIs>The following are satisfied:
where u is a mathematical parameter in the spline definition.
Thereby, the distance between the second control point P2 and the third control point P3 is determined:
in one example of the application, to avoid vector anglesApproach->When (I)>Too long a situation occurs, so provision is made for:
finally, the position of the second control point P2 can be determined on the straight line segment according to the position of the third control point P3:
further, as can be seen from fig. 3, the terminal end C1 of the spline curve is the second control point P2, so that the length between the second control point P2 and the first control point P1 has no influence on the spline curve, so that the spline curve is definedThen, on the straight line segment, the position of the first control point P1 is determined according to the position of the second control point P2:
2) The position of the fourth control point P4 is calculated:
first, by determining the second control pointZoom at position, fourth control point +.>The following should be satisfied or approximately satisfied:
thereby utilizing the distance between the second control point and the third control pointAnd the radius r of the arc segment, characterizing the angle +.>The method comprises the following steps:
and provides for:
；
finally, a fourth control point is obtained by using a vector rotation transformation algorithmIs defined by the position of:
3) The position of the fifth control point P5 and the position of the sixth control point P6 are calculated:
first, in calculating the fifth control point and the sixth control point, a processing principle of connecting the spline curve with the arc segment is used, and a determination process of the principle is described in the following related description, and this part is only to apply the principle to perform the position calculation of the fifth control point P5 and the sixth control point P6.
Briefly, the foregoing principle mainly includes the following two points: firstly, the first step of the method is that,the method comprises the steps of carrying out a first treatment on the surface of the And secondly, the second step is that,. Wherein C1 is the starting point of the spline curve, and C1 is on the arc segment.
After that, recordThen
Obtaining a fifth control point by using a vector rotation transformation algorithmPosition:
obtaining a sixth control point by using a vector rotation transformation algorithmPosition:
thus, the position determination process of the six control points is completed.
In one or more possible implementation manners of the embodiment of the present application, the processing principle of the connection point between the spline curve and the arc segment is determined as follows:
fig. 4 is a schematic processing diagram of a connection point between a B-spline curve and a circular arc segment in an application scenario provided by an embodiment of the present application. As shown in FIG. 4, the arc in the figure is the arc segment PC to be connected, the pointIs the end point of the intersection of the B-spline and the arc segment,is three control points of the B-spline.
Demand pointIs continued twice, i.e. the curvature of the processing path is at the point +.>3, then dot->The following should be satisfied:
(1) The first-order vector and the second-order vector of the circular arc section and the B spline have the same direction;
(2) The curvature of the arc section is equal to that of the B spline;
according to the geometrical characteristics of B spline nodes, pointsIs defined by three adjacent control points +.>Decision, thereby->The following geometrical properties should be satisfied:
(1) The first order director direction is the same:therefore->；
(2) The second order director direction is the same:at->Is arranged on the extension line of the (c);
(3)；
(4) The curvatures are equal:；
from these geometries the following deductions can be made:
(1)the positions are not unique, and the positions of three points can be determined by determining the positions of any point;
(2) Recording deviceThen at +.>In (a)
The processing principle of the connection point of the spline curve and the arc section is the above.
And 104, determining an expression of the spline curve according to the positions of the control points.
After determining the above six controlled positions, the spline expression can be calculated according to the positions of the six points, and it should be noted that the parameter values in the expression are determined.
Specifically, the position data of the six control points are substituted into the following three-degree uniform B-spline defining expression:
wherein ,
it should be noted that the number of the substrates,three curves representing three-degree uniform B-spline curves,>indicating the position of the i-th control point.
And 105, inserting spline curves into the to-be-connected straight line segments and circular arc segments according to the expression of the spline curves.
After determining the expression of the spline curve, inputting the straight line segment, the circular arc segment and the spline curve to be connected into MATLAB for simulation so as to realize the insertion of the cubic uniform B spline curve in the straight line segment and the circular arc segment to be connected.
In order to verify the connection method in the embodiment of the present application, the following simulation process is performed in the embodiment of the present application:
1) General cases
Inputting a predetermined curve error, i.e. error limitInputting a given straight line segment and a given circular arc segment +.>，；
Calculating six control points by the methodIs a position of (2);
finally, the expression of the cubic uniform B-spline curve is calculated from the six control points, and is simulated and plotted by matlab, fig. 5 is a simulation effect diagram, and fig. 6 is a curvature/length diagram.
2) Special cases: the straight line segment and the circular arc segment are tangent at the intersection point and have the same direction.
Input error limitingStraight line segment and circular arc segment->The calculation process is the same as above, and omitted.
Simulation by matlab and drawing, the simulation effect diagram of fig. 7 and the curvature/length diagram of fig. 8 are obtained.
3) Special cases: the straight line segment and the circular arc segment are tangent at the intersection point and have opposite directions.
Input error limitingStraight line segment and circular arc segment->The calculation process is the same as above, and omitted.
Simulation by matlab and drawing, the simulation effect diagram of fig. 9, the curvature/length diagram of fig. 10, was obtained.
As shown in fig. 5, 7 and 9, the broken line is an input machining path, the marked point is a control point, and the solid line is a connecting segment B-spline curve. The starting point and the ending point of the B spline meet the condition that the directions of the straight line and the circular arc Duan Yi order vector and the second order vector are the same, and the curvatures are the same.
As shown in fig. 6, 8 and 10, the curvature is shown on the ordinate, the length is shown on the abscissa, the starting point is a point on a straight line segment, and the ending point is a point on a circular arc segment, and it can be seen that the curvature of the connecting portion is continuous.
From the simulation graph, it can be seen that the curvature continuity of the whole processing path, namely the continuity of the speed direction and the acceleration direction, can be ensured by cutting off a part of the head and the tail of the original processing section and connecting the head and the tail with the B-spline section.
Based on the same inventive concept, the embodiment of the application also provides a device for connecting and processing the straight line segment and the circular arc segment through the spline curve, and the structure of the device is shown in fig. 11.
Fig. 11 is a schematic structural diagram of an apparatus for connecting a straight line segment and an arc segment by spline curves according to an embodiment of the present application. As shown in fig. 11, the apparatus 1100 in the embodiment of the present application specifically includes: at least one processor 1101; and a memory 1103 communicatively coupled (via bus 1102) to the at least one processor 1101; the memory 1103 stores instructions executable by the at least one processor 1101 to enable the at least one processor 1101 to perform a method of connecting a machined straight line segment with a circular arc segment by spline curves as described in the above embodiments.
In one or more possible implementations of the embodiments of the present application, the foregoing processor is configured to perform, determine a straight line segment and a circular arc segment to be connected; the intersection point of the straight line segment and the circular arc segment is determined to be a third control point, a first control point and a second control point are arranged on the corresponding straight line of the straight line segment, and a fourth control point, a fifth control point and a sixth control point are arranged nearby the circular arc segment; determining an intermediate node of a spline curve through the second control point, the third control point and the fourth control point, and determining the position relationship between the intermediate node and the third control point; determining the position of the first control point and the position of the second control point according to the relation between the position relation and a preset curve error; calculating the position of the fourth control point according to the position of the second control point and the circle center and the radius corresponding to the circular arc section; determining the position of the fifth control point and the position of the sixth control point by using a vector rotation algorithm through the position of the fourth control point based on the processing principle of the connection point between the circular arc segment and the spline curve; calculating an expression of the spline curve according to the positions of the first control point, the second control point, the third control point, the fourth control point, the fifth control point and the sixth control point; and inserting the spline curve into the to-be-connected straight line segment and circular arc segment according to the expression of the spline curve.
In general, the connecting method in the embodiment of the application only processes the local part of the connecting part of the original processing section, so the calculated amount of the connecting section and the calculated amount of the subsequent interpolation flow are much smaller than those of the integral fitting method of the processing section, and the control point determining method is simpler than the local fitting method because the control point determining method is determined by the geometric characteristics of the B spline end points. The connecting method in the embodiment of the application has the same good treatment effect on special conditions such as tangent of the straight line segment and the circular arc segment, and the description method has generality.
It will be appreciated by those skilled in the art that the present description may be provided as a method, system, or computer program product. Accordingly, the present specification embodiments may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present description embodiments may take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.
The present description is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the specification. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article or apparatus that comprises the element.
The description may be described in the general context of computer-executable instructions, such as program modules, being executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The specification may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote computer storage media including memory storage devices.
In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for apparatus, devices, non-volatile computer storage medium embodiments, the description is relatively simple, as it is substantially similar to method embodiments, with reference to the section of the method embodiments being relevant.
The foregoing describes specific embodiments of the present disclosure. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims can be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.
The foregoing is merely one or more embodiments of the present description and is not intended to limit the present description. Various modifications and alterations to one or more embodiments of this description will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, or the like, which is within the spirit and principles of one or more embodiments of the present description, is intended to be included within the scope of the claims of the present description.
Claims (8)
1. A method of connecting a straight line segment to a circular arc segment by spline curves, the method comprising:
determining a straight line segment and a circular arc segment to be connected;
determining an intersection point of the straight line segment and the circular arc segment as a third control point, setting a first control point and a second control point on a corresponding straight line of the straight line segment, and setting a fourth control point, a fifth control point and a sixth control point near the circular arc segment;
determining an intermediate node of a spline curve through the second control point, the third control point and the fourth control point, and determining the position relationship between the intermediate node and the third control point;
determining the position of the first control point and the position of the second control point according to the relation between the position relation and a preset curve error;
calculating the position of the fourth control point according to the position of the second control point and the circle center and the radius corresponding to the circular arc section;
determining the position of the fifth control point and the position of the sixth control point by using a vector rotation algorithm through the position of the fourth control point based on the processing principle of the connection point between the circular arc segment and the spline curve;
calculating an expression of the spline curve according to the positions of the first control point, the second control point, the third control point, the fourth control point, the fifth control point and the sixth control point;
inserting the spline curve into the to-be-connected straight line segment and circular arc segment according to the expression of the spline curve, wherein the spline curve adopts a cubic uniform B spline curve;
wherein, confirm the expression of the said spline, include specifically: obtaining a definition formula of the cubic uniform B spline curve; determining an expression of the cubic uniform B-spline curve according to the positions of the first control point, the second control point, the third control point, the fourth control point, the fifth control point and the sixth control point by the definition formula of the cubic uniform B-spline curve; the expression of the cubic uniform B spline curve is defined by the cubic uniform B spline curve determined by parameter values;
the cubic uniform B-spline curve is defined as follows:
wherein ,representing three curves of the cubic uniform B-spline curve, +.>The position of the ith control point is represented, and the value of i is 1,2 and 3; />。
2. The method for connecting a straight line segment and a circular arc segment by spline curve according to claim 1, wherein determining the position of the first control point and the position of the second control point according to the relationship between the position relationship and a preset curve error specifically comprises:
determining a tangent vector of the circular arc segment at the third control point, and determining a direction vector of the straight line segment at the third control point;
calculating a vector included angle cosine value according to the tangent vector and the direction vector;
representing the position relationship between the third control point and the intermediate node by using the cosine value of the vector included angle and the distance between the second control point and the third control point;
determining the distance between the second control point and the third control point through the magnitude relation between the preset curve error and the position relation;
and on the straight line segment, determining the position of the second control point according to the distance between the second control point and the third control point and the position of the third control point.
3. A method of connecting a machined straight line segment with a circular arc segment through a spline according to claim 2, wherein after determining the location of the second control point, the method further comprises:
determining the second control point as an end point of the spline curve;
determining a distance between the second control point and the first control point, equal to a distance between the second control point and the third control point;
and on the straight line segment, determining the position of the first control point according to the distance between the second control point and the first control point and the position of the second control point.
4. The method for connecting a straight line segment and an arc segment through spline curves according to claim 1, wherein calculating the position of the fourth control point through the circle center and the radius corresponding to the arc segment according to the position of the second control point specifically comprises:
characterizing an angle using a ratio between a distance between the second control point and the third control point and a radius of the arc segmentThe method comprises the steps of carrying out a first treatment on the surface of the Wherein the angle->The third control point is taken as a vertex, the straight line segment is taken as one side, and a connecting line between the third control point and the fourth control point is taken as an angle determined by the other side;
determining a distance between the third control point and the fourth control point equal to a distance between the third control point and the second control point;
according to the angleThe distance between the third control point and the fourth control point is determined, and the distance between the fourth control point and the circle center of the circular arc section is determined;
according to the distance between the fourth control point and the center of the circular arc section, the radius of the circular arc section and the angleAnd calculating the position of the fourth control point through the vector rotation algorithm by using a vector formed between the circle center of the circular arc section and the third control point.
5. The method for connecting a straight line segment and a circular arc segment through a spline curve according to claim 1, wherein determining the position of the fifth control point and the position of the sixth control point by using a vector rotation algorithm based on the processing principle of the connection point between the circular arc segment and the spline curve includes:
determining a starting point of the spline curve on the arc segment;
determining the distance between the circle center of the circular arc section and the fourth control point according to the processing principle of the connection point between the circular arc section and the spline curve, wherein the distance is equal to the distance between the circle center of the circular arc section and the fifth control point and the distance between the circle center of the circular arc section and the sixth control point;
determining the distance between the starting point and the fifth control point, and representing a first central angle by utilizing the distance between the starting point and the fifth control point and the radius of the arc segment; the first central angle is an angle determined by taking the center of the circular arc section as a vertex, taking a connecting line between the center and the fourth control point as one side and taking a connecting line between the center and the fifth control point as the other side;
and calculating the position of the fifth control point through the vector rotation algorithm according to the vector formed between the circle center of the circular arc section and the fourth control point and the first central angle.
6. The method of connecting a machined straight line segment and a circular arc segment by spline curve according to claim 5, wherein after calculating the position of the fifth control point, the method further comprises:
determining that the first central angle is equal to the second central angle in a first right-angle triangle formed by the center of the circular arc section, the fourth control point and the right-angle point and a second right-angle triangle formed by the center of the circular arc section, the sixth control point and the right-angle point; the second central angle is an angle determined by taking the center of the circular arc section as a vertex, taking a connecting line between the center and the fifth control point as one side and taking a connecting line between the center and the sixth control point as the other side; the right angle point is a point at which a connecting line between the center of the circular arc section and the starting point intersects with a connecting line between the fourth control point and the sixth control point, and the connecting line between the center of the circular arc section and the starting point is determined according to the processing principle of the connecting point between the circular arc section and the spline curve and is perpendicular to the connecting line between the fourth control point and the sixth control point;
according to the position of the fifth control point, determining a vector formed between the center of the circle of the circular arc section and the fifth control point;
and calculating the position of the sixth control point through the vector rotation algorithm according to the vector formed between the circle center of the circular arc section and the fifth control point and the second central angle.
7. The method for connecting and processing a straight line segment and a circular arc segment through a spline according to claim 1, wherein the spline is inserted into the straight line segment and the circular arc segment to be connected according to an expression of the spline, specifically comprising:
simulating the straight line segment and the circular arc segment to be connected by utilizing MATLAB;
and inputting the expression of the cubic uniform B spline curve into MATLAB so as to insert the spline curve in the straight line segment and the circular arc segment to be connected.
8. An apparatus for connecting a straight line segment to a circular arc segment by spline curves, the apparatus comprising:
at least one processor; and a memory communicatively coupled to the at least one processor; wherein the memory stores instructions executable by the at least one processor to cause the at least one processor to perform a method of connecting a machined straight line segment with a circular arc segment by spline curves according to any one of claims 1-7.
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