CN113687629A - Circular arc straight line fitting method, system, equipment and storage medium for laser CAM processing - Google Patents
Circular arc straight line fitting method, system, equipment and storage medium for laser CAM processing Download PDFInfo
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Abstract
The invention is suitable for the technical field of automatic control, and discloses a method, a system, equipment and a storage medium for fitting a circular arc straight line in laser CAM processing. The method comprises the following steps: acquiring a spline point sequence based on the original graph track; judging the track type formed by three adjacent spline points based on the spline point sequence; judging whether the next spline point is collinear or collinear with or is in a circle with the first graph track based on the first graph track formed by the three adjacent spline points; if the next spline point is collinear or collinear with the first graph track, updating the next spline point to be the terminal point of the first graph track, and continuously judging whether the adjacent spline point is collinear or collinear with the first graph track; and if the next spline point is not collinear or collinear with the first graph track, taking the last spline point in the three adjacent spline points as the terminal point of the first graph track, and taking the next spline point as the starting point of the next section of new graph track. The invention can reduce the number of processing tracks and improve the processing efficiency.
Description
Technical Field
The invention belongs to the technical field of automatic control, and particularly relates to a method, a system, equipment and a storage medium for fitting a circular arc straight line in laser CAM (computer-aided manufacturing) processing.
Background
In the process of CAM (computer Aided Manufacturing) generating an NC (Numerical Control) program, a broken line segment is mostly adopted for fitting simple graphs at present. However, for complex graphs, such as curves with circular arcs or non-circular arcs, fitting such curves directly with straight lines can only approximately describe the direction of the curve, and cannot objectively reflect the characteristics of the curve, and the fitting accuracy is not high.
In the CAM processing, the straight-line circular arc mixed approximation is carried out on the graph outline, the numerical control system processing points can be discretized, the processing track is reduced, and the processing efficiency is improved. The optimal circular arc curve approximating the original contour can be obtained by adopting a least square curve fitting algorithm, but the starting point and the ending point of the original contour are difficult to fall on the fitted circular arc curve. This phenomenon will cause the machine tool to recognize the first arc when processing a plurality of continuous curves with breakpoints, and then the starting point of the next section of track cannot be found, which affects the processing precision and stops processing, thereby affecting the processing efficiency of the machine tool.
Disclosure of Invention
The invention provides a method, a system, computer equipment and a readable storage medium for fitting an arc straight line processed by laser CAM, and aims to solve the problem of low processing efficiency in the prior art.
The invention is realized in this way, a method for fitting circular arc straight line of laser CAM processing, comprising the following steps:
acquiring an original graph track of a graph to be processed;
fitting based on the original graph track to obtain a k-order B-spline curve, and acquiring a spline point sequence based on the B-spline curve;
sequentially selecting three adjacent spline points based on the spline point sequence coordinates, and judging the track type formed by the three adjacent spline points;
judging whether the next spline point is collinear or collinear with or is in a circle with the first graph track based on the first graph track formed by the three adjacent spline points;
if the next spline point is collinear or collinear with the first graph track, updating the next spline point as the terminal point of the first graph track, and continuously judging whether the adjacent spline point is collinear or collinear with the first graph track or is collinear or collinear with the first graph track;
and if the next spline point is not collinear or collinear with the first graph track, taking the last spline point in the three adjacent spline points as the terminal point of the first graph track, and taking the next spline point as the starting point of the next section of new graph track.
Preferably, the fitting based on the original graph trajectory to obtain a k-th-order B-spline curve, and the step of obtaining a spline point sequence based on the B-spline curve specifically includes:
determining a node vector u of the B spline curve by a chord length parameterization method;
substituting the node vector u into the base function of the k-th-order B spline, and determining a B spline curve according to the control vertex of the original graph track and the base function of the k-th-order B spline;
and acquiring a spline point sequence on the spline curve according to the control point distance of the B spline curve.
Preferably, the step of judging the type of the track formed by the three adjacent spline points specifically includes:
and judging whether the three adjacent spline points form a straight line or a section of circular arc or not based on a vector product mode.
Preferably, the step of determining whether the three adjacent spline points form a straight line or a section of circular arc based on the vector product mode specifically includes:
taking one spline point in the three adjacent spline points as a vertex, and calculating the product of the spline point and vectors of other two adjacent spline points;
if the product is equal to zero, determining that the three adjacent spline points form a straight line;
and if the product is larger than zero, determining that the three adjacent spline points form a section of circular arc.
The process of determining whether the next spline point is collinear with the first graph trajectory comprises:
and judging whether the last two adjacent spline points of the first graph track and the next spline point form a straight line or not based on a vector product mode.
Preferably, the step of determining whether the next spline point is concentric with the first graph track includes:
judging whether the bow height error from the next spline point to the first graph track is within the precision constraint range or not based on preset precision constraint;
and if the first graph track is within the precision constraint range, the first graph track is in a circle with the first graph track.
Preferably, the step of determining whether the bow height error from the next spline point to the first graph track is within the accuracy constraint range based on a preset accuracy constraint specifically includes:
calculating the radius and the center coordinate of the first graph track by adopting a method of solving the intersection point by vertical bisection;
calculating the bow height error from the next spline point to the first graph track according to the radius and the circle center coordinate;
comparing the bow height error with a constraint range of preset precision;
and if the height error is smaller than or equal to a constraint range of preset precision, determining that the height error is within the precision constraint range.
The invention also provides a circular arc straight line fitting system for laser CAM processing, which comprises:
the original graph track acquisition module is used for acquiring an original graph track of a graph to be processed;
the spline point sequence acquisition module is used for fitting the original graph track to obtain a k-order B-spline curve and acquiring a spline point sequence based on the B-spline curve;
the track type judging module is used for sequentially selecting three adjacent spline points based on the spline point sequence coordinates and judging the track type formed by the three adjacent spline points;
the track continuous judging module is used for judging whether a next spline point is collinear or collinear with or is in a circle with a first graph track formed by the three adjacent spline points;
the track updating module is used for updating the next spline point to be the terminal point of the first graph track if the next spline point is collinear or collinear with or is collinear with the first graph track, and continuously judging whether the adjacent spline point is collinear or collinear with or is collinear with the first graph track; and if the next spline point is not collinear or collinear with the first graph track, taking the last spline point in the three adjacent spline points as the terminal point of the first graph track and taking the next spline point as the starting point of the next section of new graph track.
The invention also provides computer equipment which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps of the circular arc straight line fitting method for laser CAM processing when executing the computer program.
The invention also provides a computer readable storage medium, wherein a computer program is stored on the computer readable storage medium, and when the computer program is executed by a processor, the steps of the circular arc straight line fitting method for laser CAM processing are realized.
The invention has the advantages that whether the spline point sequences belong to the same graph track is sequentially judged, so that the starting point and the end point of each segment of the graph track are on the fitted graph track, the number of the processed tracks is reduced, and the processing efficiency is improved.
Drawings
FIG. 1 is a schematic flow chart of a method for fitting a circular arc straight line according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of S2 in FIG. 1;
FIG. 3 is a schematic flow chart of S3 in FIG. 1;
FIG. 4 is a schematic view of the process of determining the co-circle in S4 in FIG. 1;
FIG. 5 is a schematic flow chart of S41 in FIG. 4;
FIG. 6 is a block diagram of a circular arc straight line fitting system according to an embodiment of the present invention;
FIG. 7 is a schematic flowchart of an application implementation of the circular arc straight line fitting method according to the embodiment of the present invention;
FIG. 8 is a basic block diagram of a computer device provided by an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides an arc straight line fitting method for CAM processing, which is used for carrying out straight line arc fitting processing on graph track data in laser CAM processing, generating an NC program based on the straight line arc fitting processing, and delivering the NC program to a numerical control system for processing, thereby reducing the number of machine tool cutting tracks and improving the processing efficiency under the condition of controllable precision.
Referring to fig. 1, fig. 1 is a method for fitting a circular arc straight line in laser CAM processing according to an embodiment of the present invention, which specifically includes the following steps:
and S1, acquiring an original graph track of the graph to be processed.
Specifically, by acquiring an image or a picture of a to-be-processed figure, the to-be-processed figure can be obtained by shooting or model scanning through a camera, wherein the to-be-processed figure can be spherical, cylindrical, arc-shaped and the like, and the specific to-be-processed figure is selected according to the current requirement. And obtaining the track of the original graph according to the shape of the obtained graph to be processed, and processing through the track of the original graph. The acquisition of the original image form and track data is mainly to complete the collection of curve data, because the figure and track imported by a laser CAM (computer Aided manufacturing) system are spline curves, the narrow concept of CAM refers to all production preparation activities from product design to processing and manufacturing, and the narrow concept of CAM includes CAPP, NC programming, calculation of man-hour quota, preparation of production plan, preparation of resource demand plan and the like.
And S2, fitting based on the original graph track to obtain a k-order B-spline curve, and acquiring a spline point sequence based on the B-spline curve.
The k-th-order B-spline curve can be approximate fitting and interpolation fitting, the approximate fitting is the characteristic point, the interpolation fitting is the characteristic point, but the interpolation fitting needs to obtain a control point through inverse calculation and then fits a B-spline curve equation of the characteristic point. Approximate fitting for a closed contour, the last segment can take the first two points as assistance, the approximate fitting curve is smooth, but is not an excessive characteristic point, and the fitting is performed by solving a control point through a point reverse method. The interpolation fitting is complex, the B spline describes some details well, and many details are close to the original contour, but the B spline has some defects, and the effect of the straight line fitting is not good. For non-closed or only one-segment curve fitting, another curve is good, for example, cubic spline interpolation fitting, the fitting effect is very close to that of the original curve, but in the process, a catch-up method is needed, and the catch-up method needs to meet a condition, and the cubic spline interpolation fitting for the closed curve does not meet the condition.
The spline point sequence is a sequence of points or positions on the curve in order of magnitude of angle, facilitating the acquisition of the positions of the points. For example, points at 0 °, 45 °, 90 °, and 270 ° may be selected on a circle to make a sequence table, so that the spline points can be obtained conveniently on the circle with high efficiency.
Optionally, the fitting of the original graph trajectory may also be a least-squares fitting, a double-circular-arc fitting, or the like under the constraint conditions of the starting point and the end point.
Specifically, fitting is performed based on the original graph track, k-order B-spline curves can be obtained through fitting, and a spline point sequence is obtained based on the B-spline curves, so that the spline point sequence can be accurately obtained, and the efficiency is high.
S3, sequentially selecting three adjacent spline points (p) based on the spline point sequencei，pi+1，pi+2) Judging the three adjacent spline points (p)i，pi+1，pi+2) The type of track formed.
Specifically, based on the spline sequence, three adjacent spline points (p) are selected in sequencei，pi+1，pi+2) And according to three adjacent spline points (p)i，pi+1，pi+2) And judging the type of the track formed by the track. The track type can be a straight line, a circular arc and the like, firstly, track points of a graph to be processed are obtained, namely each graph track corresponds to a track point set (which can be realized by a two-dimensional array, a structural body and the like), and the track points are connected into a line, so that the track curve can be drawn.
Then, we require the distance between each trajectory curve. We can find the distance between all curves and obtain a distance matrix. Then we need to analyze this distance matrix and add a predetermined threshold as the discrimination condition for curve classification.
For example, by the distances from the curve a to the remaining curves, then finding the minimum of these distances and comparing it with a threshold, if greater than the threshold, then the curve a itself is classified as a class alone; if smaller than the threshold, curve A is classified as one from the curve that is away. Therefore, the trajectory curves can be successfully classified, and different trajectory types can be obtained. Therefore, the acquisition of the spline points can be improved, and the processing efficiency is improved.
S4, based on the three adjacent spline points (p)i，pi+1，pi+2) And judging whether the next spline point is collinear or collinear with or is in a common circle with the first graph track or not according to the formed first graph track and the corresponding track type.
In particular, by basing on said three adjacent spline points (p)i，pi+1，pi+2) The first graphic track is formed by dividing the first graphic track into corresponding track types, such as a straight line track, and judging whether the next spline point is in the corresponding straight line trackCollinear or co-circular with the first graphical locus. Therefore, after the first graph track is judged to correspond to the straight line track or the circular arc track according to the track type, whether the next spline point is collinear or collinear with the first graph track or is collinear or collinear with the first graph track is judged, and the judgment efficiency is high.
And S5a, if the next spline point is collinear or collinear with or is in a circle with the first graph track, updating the next spline point to be the terminal point of the first graph track, and continuously judging whether the adjacent spline point is collinear or in a circle with the first graph track.
Specifically, if the next spline point is collinear or collinear with the first graph track, the next spline point is updated to be the end point of the first graph track, and whether the adjacent spline points are collinear or collinear with the first graph track is continuously judged until all coordinate points are considered.
And S5b, if the next spline point is not collinear or collinear with the first graph track, taking the last spline point in the three adjacent spline points as the terminal point of the first graph track, and taking the next spline point as the starting point of the next section of new graph track.
And if all the spline points in the spline point sequence are judged, writing track data into the numerical control system and performing laser cutting.
Specifically, the embodiment of the invention sequentially judges whether the spline point sequences belong to the same graph track, so that the starting point and the end point of each segment of the graph track are on the fitted graph track, the number of the processed tracks is reduced, and the processing efficiency is improved.
Referring to fig. 2, fig. 2 is a schematic flow chart of S2 in fig. 1, and specifically includes the following steps:
in this embodiment, in step S2, the fitting based on the original graph trajectory to obtain a k-th-order B-spline curve, and the step of obtaining a spline point sequence based on the B-spline curve specifically includes:
and S21, determining the node vector u of the B spline curve by a chord length parameterization method.
Specifically, the B-spline is a kind of free curve, and its expression is as follows:
in the above formula, diThe control vertex of the profile curve. N is a radical ofi，kAnd (u) is a basis function of a k-th order B-spline. In the invention, the determination of the node vector u value mainly adopts a chord length parameterization method, and the concrete formula is as follows:
by the above method, the B-spline curve p (u) can be determined. The control point spacing of the B-spline p (u) to obtain a sequence of splines on the spline.
In the above formula, k is the degree of B-spline, which is equivalent to the order minus 1, diFor the control vertex of the profile curve, djS is the k +1 th order of the B-spline, which is the control endpoint of the contour curve.
And S22, substituting the node vector u into the base function of the B spline, and determining the B spline curve according to the control vertex of the original graph track and the base function of the k-th-order B spline.
And S23, acquiring a spline point sequence on the spline curve according to the control point spacing of the B spline curve.
Wherein, the solving process of the fitting point coordinate comprises the following steps: the control point coordinate of the spline is multiplied by p (u), and the control point coordinate is obtained by the following formula:
in the above formula, (fx)i，fyi) And (cx)i，cyi) (where i is 0, 1, 2, …, n) represents a fitting point coordinate and a control point coordinate, respectively, and the control point (cx) represents a virtual point coordinatei，cyi) Are input spline curve expression points. (fx)i，fyi) Are points on the spline curve, fitting points for fitting the straight line arc by the late spline, where p (u) is the calculation of sum u as in step S21, Ni，k(u) the de-boolean recursion formula is used, the concrete formula is as follows:
specifically, the fitting of the later-stage circular arc straight line is performed in order to obtain enough spline point sequences and increase the fitting precision devM. In the embodiment of the invention, the spline point sequence fitted by the circular arc straight line is obtained by substituting the node vector u value into the basic function N by using a Boolean recursion formula for p (u)i，k(u) obtained in (a). The value of the node vector u is obtained by equally spacing delta between 0 and 1lAnd calculated. Wherein, DeltalThe mathematical expression is as follows:
in the above formula,. DELTA.lThe laser CAM is generally set to have a value of α equal to 10, mainly to ensure that the distance between the spline coordinate points is within the range of precision control, so as to reduce the curve fitting error in the later period.
In this embodiment, in step S3, the three adjacent spline points p are determinedi，pi+1，pi+2The formed track type is based on a vector product mode to judge whether the three adjacent spline points form a straight line or a section of circular arc.
Referring to fig. 3, fig. 3 is a schematic flow chart of S3 in fig. 1; the method specifically comprises the following steps:
in this embodiment, the step of determining whether the three adjacent spline points form a straight line or a section of an arc based on a vector-vector product specifically includes:
and S31, taking one spline point in the three adjacent spline points as a vertex, and calculating the product of the spline point and vectors of other two adjacent spline points.
S32, if the product is equal to zero, determining that the three adjacent spline points form a straight line.
S33, if the product is larger than zero, determining that the three adjacent spline points form a section of circular arc.
Specifically, after the spline point sequence is obtained, in order to implement fitting of the straight-line circular arc, continuous spline points need to be searched, a point sequence meeting the circular arc fitting condition is judged, and corresponding fitting operation is performed on the point sequence. In the invention, a vector product mode is adopted to judge whether the continuous points can form a section of circular arc. For example, three successive spline points p are selectedi，pi+1，pi+2With pi+1Is a vertex, then a vector
And
the vector formula of (a) is:
if it is not
The three consecutive spline points are collinear, and it can be determined that the three spline points constitute a straight-line trajectory.
If it is not
The three continuous points can form a circular arc, and the radius R and the center coordinate (x) of the fitting circular arc are calculated by adopting a method of solving the intersection point by perpendicular bisection0，y0)。
Wherein, in the formula above,
is a function of the absolute value of the signal,
is a vector
Sum vector
Angle therebetween, so
Is greater than or equal to 0.
In this embodiment, the step S4 of determining whether the next spline point is collinear with the first graph track includes: and judging whether the last two adjacent spline points of the first graph track and the next spline point form a straight line or not based on a vector product mode.
In particular, with three spline points pi+1，pi+2，pi+3The straight line formed is the first graphic track and the next adjacent spline point is pi+3At this time, three continuous sample points p are judgedi+1，pi+2，pi+3Whether or not the collinearity is formed is determined by the same method as above for the three spline points pi，pi+1，pi+2The same way of judging, if, three spline points pi+1，pi+2，pi+3If the sample is determined to be collinear, the sample point p is determinedi+3Updating to the end point of the first graph track, repeating the steps, continuing to judge and comparing with the step pi+3Whether the next adjacent spline point is collinear with the first graph track or not, and if not, the spline point p is usedi+3As the starting point of the next new graphical track.
Referring to fig. 4, fig. 4 is a schematic diagram illustrating a flow of determining a common circle in S4 in fig. 1; the method specifically comprises the following steps:
in this embodiment, the step S4 of determining whether the next spline point is concentric with the first graph track includes:
and S41, judging whether the bow height error from the next spline point to the first graph track is in the preset precision constraint range or not based on preset precision constraint.
And S42, if the precision is within the preset precision constraint range, the first graph track is concentric with the first graph track.
Specifically, the bow height error from the next spline point to the first graph track is obtained, and based on a preset precision constraint, whether the bow height error from the next spline point to the first graph track is within the preset precision constraint range is judged. And if the bow height error is within the preset precision constraint range, the bow height error is in a circle with the first graph track.
In this embodiment, if the position is not within the preset accuracy constraint range, S43 is not concentric with the first graphic track.
Referring to fig. 5, fig. 5 is a schematic flow chart of S41 in fig. 4, and specifically includes the following steps:
in this embodiment, the step of determining whether the bow height error from the next spline point to the first graph track is within the accuracy constraint range based on the preset accuracy constraint specifically includes:
s411, calculating the radius and the center coordinate of the first graph track by adopting a method of perpendicularly bisecting and solving the intersection point.
The method for solving the intersection point by vertically bisecting is a method for solving the intersection point by vertically bisecting, passes through the middle point of a certain line segment, and is a straight line which is perpendicular to the line segment and is the vertical bisector of the line segment.
Specifically, by adopting a method of solving the intersection point by perpendicular bisection, the radius and the center coordinate of the first graph track can be calculated. Therefore, the radius and the center coordinate of the first graph track are accurately and conveniently calculated.
And S412, calculating the bow height error from the next spline point to the first graph track according to the radius and the circle center coordinate.
Specifically, the bow height error from the next uniform point to the first graph track is obtained according to the radius and the circle center coordinate obtained in the step S411.
And S413, comparing the bow height error with a constraint range of preset precision.
And S414, if the bow height error is less than or equal to a constraint range of preset precision, determining that the bow height error is in the precision constraint range.
S415, if the bow height error is larger than a preset precision constraint range, determining that the bow height error exceeds the precision constraint range.
Specifically, whether the bow height error is within the precision constraint range is determined by comparing the bow height error with the constraint range of preset precision. And if the height error is smaller than or equal to a constraint range of preset precision, determining that the height error is within the precision constraint range, and enabling the spline point to be on the circular arc track.
Further, if the bow height error is larger than a constraint range of preset precision, determining that the bow height error is not in the precision constraint range. And obtaining the next spline point which is not positioned on the arc of the previous section, taking the next spline point as the terminal point of the arc track of the previous spline point, and taking the next spline point as the starting point of the next section of new graphic track.
In the specific embodiment, under the constraint of the precision devM, the point p of the spline is confirmedi，pi+1，pi+2When the first formed graph track is an arc track, whether the next spline point is in a known arc (a common circle) is considered, and the embodiment of the invention mainly considers Pi+3Bow height error from point to known arc
The mathematical model is as follows:
in the above formula, xi+3And yi+3Is Pi+3Coordinate of (a), x0And y0Is the center coordinate of the arc if
Indicating that the bow height error exceeds a defined accuracy, then Pi+3Is not on the previous arc track and is taken as Pi+2And taking the point as the end point of the previous arc track and the starting point of the next new track, and continuously inspecting the next coordinate point by adopting the method. If it is not
Indicates that the bow height error is within the precision control, Pi+3On the fitted first graphical trajectory (i.e. the circular arc trajectory). At this time, P is addedi+3Updating the curve to be the terminal point of the first graph track, and continuously inspecting the next spline point. If the next spline point is not on the same end arc track as the first graph track, P is determinedi+3As the starting point of the next new graphical track.
Further, firstly, three points determine a circle, judge whether the next point is on the circle, and take the next point to be considered as the end point of the circular arc, wherein the start point takes the start point of the previous circular arc as the start point, the second point of the three points as the known point, a new circular arc can be determined by taking the start point, the known point and the new end point, and the four points obtained by inspection can be calculated by calculating the distance from the new end point to the center of the circle, and if the difference between the distance from the new end point to the center of the circle and the radius from the three points to the center of the circle is within the above-mentioned arc height error, the four points can be determined to be on the same circular arc track, so the method can be used for inspecting the next point co-circle. And if the difference between the distance from the new terminal point to the center of the circle and the radius from the three points to the center of the circle is within the height error, the four points can be determined to be on the same circular arc track.
According to the embodiment of the invention, the starting point and the end point of the processing track can be ensured to fall on the fitting circular arc by the circular arc straight line fitting method with controllable precision, the number of the processing tracks is reduced, and the processing efficiency is improved.
As shown in fig. 6, an embodiment of the present invention also provides a circular arc straight line fitting system for laser CAM processing, including:
an original graph track obtaining module M1, configured to obtain an original graph track of a graph to be processed;
a spline point sequence obtaining module M2, configured to fit the original graph trajectory to obtain a k-th-order B-spline curve, and obtain a spline point sequence based on the B-spline curve;
the track type judging module M3 is used for sequentially selecting three adjacent spline points based on the spline point sequence coordinates and judging the track type formed by the three adjacent spline points;
a track continuity judging module M4, configured to judge, based on a first graph track formed by the three adjacent spline points, whether a next spline point is collinear or collinear with the first graph track;
a trajectory updating module M5, configured to update the next spline point to the end point of the first graph trajectory if the next spline point is collinear or collinear with the first graph trajectory, and continue to determine whether the subsequent adjacent spline point is collinear or collinear with the first graph trajectory; and if the next spline point is not collinear or collinear with the first graph track, taking the last spline point in the three adjacent spline points as the terminal point of the first graph track, and taking the next spline point as the starting point of the next section of new graph track.
The system sequentially judges whether the spline point sequences belong to the same graph track, so that the initial point and the terminal point of each segment of the graph track are on the fitted graph track, the number of processed tracks is reduced, and the processing efficiency is improved. Meanwhile, straight line circular arc fitting processing is carried out on the graph track data in laser CAM processing, an NC program is generated based on the straight line circular arc fitting processing, and the NC program is sent to a numerical control system for processing, so that the processing precision can be controlled, and the safety is high.
In this embodiment, the spline point sequence obtaining module includes:
the chord length parameterization unit is used for determining a node vector u of the B spline curve through a chord length parameterization method;
the first determining unit is used for substituting the node vector u into the base function of the B spline and determining the B spline curve according to the control vertex of the contour curve and the base function of the B spline;
and the acquisition unit is used for acquiring the spline point sequence on the spline curve according to the control point distance of the B spline curve.
In this embodiment, the track type determining module includes:
and the first vector product unit is used for judging whether the three adjacent spline points form a straight line or a section of circular arc.
In this embodiment, the first vector product unit includes:
and the first vector product subunit is used for taking one spline point in the three adjacent spline points as a vertex and calculating the product of the spline point and vectors of other two adjacent spline points.
A second determining unit, configured to determine that the three adjacent spline points form a straight line if the product is equal to zero.
And the third determining unit is used for determining that the three adjacent spline points form a section of circular arc if the product is larger than zero.
In this embodiment, the trajectory continuation judging module includes:
and the second vector product unit is used for judging whether the last two adjacent spline points of the first graph track and the next spline point form a straight line or not.
In this embodiment, the trajectory continuation judging module includes:
and the bow height error judging unit is used for judging whether the bow height error from the next spline point to the first graph track is within the preset precision constraint range or not based on preset precision constraint.
And the bow height error determining unit is used for making a circle with the first graph track if the bow height error is within the preset precision constraint range.
In this embodiment, the bow height error determination unit includes:
and the first calculation unit is used for calculating the radius and the center coordinate of the first graph track by adopting a method of dividing the intersection point by a vertical bisector.
And the second calculation unit is used for calculating the bow height error from the next spline point to the first graph track according to the radius and the circle center coordinate.
And the comparison unit is used for comparing the bow height error with a constraint range of preset precision.
And the height error judgment subunit is used for determining that the height error is within the precision constraint range if the height error is smaller than or equal to the constraint range of the preset precision.
As shown in fig. 7, based on the foregoing embodiment, a specific application embodiment is further provided in the embodiment of the present invention, which includes the following steps:
t1, acquiring trajectory data (original graph trajectory data);
t2, determining the node vector of the spline curve by using a chord length parameterization method;
t3, obtaining coordinate points (spline points) on the spline curve according to the control point spacing;
t4, traverse the coordinate points, select 3 adjacent coordinate points in turn,
t5, judging whether the 3 adjacent coordinate points are collinear;
t6a, if collinear, updating the end point of the linear track; after the spline point sequence is obtained, in order to realize the fitting of the straight circular arc, continuous spline points need to be searched, the point sequence which meets the circular arc fitting condition is judged, and corresponding fitting operation is carried out on the point sequence. In the invention, a vector product mode is adopted to judge whether the continuous points can form a section of circular arc. For example, three successive spline points p are selectedi，pi+1，pi+2With pi+1Is a vertex, then a vector
To know
The vector formula of (a) is:
if it is not
The three consecutive spline points are collinear, and it can be determined that the three spline points constitute a straight-line trajectory. And updating the linear end point track according to a linear arc fitting method. For example, since the three spline points are already collinear to form a straight line trajectory, the start point and the end point are connected to form a straight line, when updating whether the next spline point is collinear with the straight line, a preset distance from one point to the straight line is given, and by calculating whether the distance between the spline point and the straight line is within the preset distance, if so, the spline point is updated as the straight line end point trajectory.
Wherein, in the formula above,
is a function of the absolute value of the signal,
is a vector
Sum vector
Angle therebetween, so
Is greater than or equal to 0.
T7a, judging whether the limit of the coordinate points is exceeded; the limitation of the number of the coordinate points refers to that a curve is only provided outside, a plurality of points can be provided on the curve, then the curve is deduced according to the algorithm to obtain a plurality of points, when the last point of the spline point sequence is deduced, after the point sequence is finished, the previous points are indicated to be on the curve, the point is judged to reach the end point, at the moment, the next spline point investigation is not needed, and the determined points are led into the numerical control system for processing.
T8a, if yes, writing track data into the numerical control system and performing laser cutting, otherwise, returning to the step T4;
t6b, if not collinear, storing the previous section of straight line track, and calculating the radius and the center coordinate of the circular arc by adopting a perpendicular bisector method; since numerical control systems mainly machine straight lines and circular arcs, the function
Is a function of absolute value and, therefore, if not collinear, of
And calculating the radius R and the center coordinate (x) of the fitting circular arc by adopting a method of dividing the intersection point vertically and equally by taking the last spline point of the three adjacent spline points as the end point of the first graph track and the next spline point as the starting point of the next section of new graph track, and calculating the radius R and the center coordinate (x) of the fitting circular arc by adopting a method of dividing the intersection point vertically and equally by taking the three continuous points obtained after the new starting point as the starting point of the next section of new graph track0，y0). Then the plurality of spline points are co-circular.
T7b, judging whether the limit of the coordinate points is exceeded;
and T8b, if the number of the tracks exceeds the preset number, writing track data into the numerical control system and performing laser cutting, otherwise, entering the step T9, wherein the numerical control system mainly processes straight lines and circular arcs, so that the track data mainly comprise straight line track data and circular arc track data, the straight line track can be given a starting point and an end point, and the straight line track is formed by connecting the starting point and the end point. The circular arc trajectory may be given a start point, an end point, and a deviation point therebetween, by connecting the start point, the end point, and the deviation point using a curve. The linear trajectory data and the circular arc trajectory data are expressed as data (programming data) that can be processed by the numerical control system, and the data are processed.
T9, selecting the next adjacent coordinate point, and calculating the distance (arch height) from the point to the center of the known circular arc;
t10, judging whether the height of the bow exceeds the control precision;
t11c, if the distance exceeds the preset distance, storing the arc track and inspecting the next track;
t11d, if not, the end point of the arc trajectory is updated and the next coordinate point is examined.
In order to solve the technical problem, an embodiment of the present application further provides a computer device. Referring to fig. 8, fig. 8 is a block diagram of a basic structure of a computer device according to the present embodiment.
The computer device 100 includes a memory 101, a processor 102, and a network interface 103 communicatively coupled to each other via a system bus. It is noted that only computer device 100 having components 101 and 103 is shown, but it is understood that not all of the illustrated components are required and that more or fewer components may alternatively be implemented. As will be understood by those skilled in the art, the computer device is a device capable of automatically performing numerical calculation and/or information processing according to a preset or stored instruction, and the hardware includes, but is not limited to, a microprocessor, an Application Specific Integrated Circuit (ASIC), a Programmable Gate Array (FPGA), a Digital Signal Processor (DSP), an embedded device, and the like.
The computer device can be a desktop computer, a notebook, a palm computer, a cloud server and other computing devices. The computer equipment can carry out man-machine interaction with a user through a keyboard, a mouse, a remote controller, a touch panel or voice control equipment and the like.
The memory 101 includes at least one type of readable storage medium including a flash memory, a hard disk, a multimedia card, a card type memory (e.g., SD or DX memory, etc.), a Random Access Memory (RAM), a Static Random Access Memory (SRAM), a Read Only Memory (ROM), an Electrically Erasable Programmable Read Only Memory (EEPROM), a Programmable Read Only Memory (PROM), a magnetic memory, a magnetic disk, an optical disk, etc. In some embodiments, the storage 101 may be an internal storage unit of the computer device 100, such as a hard disk or a memory of the computer device 100. In other embodiments, the memory 101 may also be an external storage device of the computer device 100, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), or the like, provided on the computer device 100. Of course, the memory 101 may also include both internal and external storage devices of the computer device 100. In this embodiment, the memory 101 is generally used for storing an operating system installed in the computer device 100 and various types of application software, such as program codes of a circular arc and straight line fitting method of laser CAM processing. Further, the memory 101 may also be used to temporarily store various types of data that have been output or are to be output.
The processor 102 may be a Central Processing Unit (CPU), controller, microcontroller, microprocessor, or other data Processing chip in some embodiments. The processor 102 is generally operative to control overall operation of the computer device 100. In this embodiment, the processor 102 is configured to execute the program code stored in the memory 101 or process data, for example, execute the program code of the circular arc and straight line fitting method for laser CAM processing.
The network interface 103 may comprise a wireless network interface or a wired network interface, and the network interface 103 is generally used for establishing communication connection between the computer device 100 and other electronic devices.
The present application further provides another embodiment, which is to provide a computer readable storage medium storing a laser CAM processed circular arc straight line fitting program, which is executable by at least one processor to cause the at least one processor to execute the steps of a laser CAM processed circular arc straight line fitting method as described above.
Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better implementation manner. Based on such understanding, the technical solutions of the present application may 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 instructions for enabling a terminal device (such as a mobile phone, a computer, a server, an air conditioner, or a network device) to execute the method according to the embodiments of the present application.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (10)
1. A circular arc straight line fitting method for laser CAM processing is characterized by comprising the following steps:
acquiring an original graph track of a graph to be processed;
fitting based on the original graph track to obtain a k-order B-spline curve, and acquiring a spline point sequence based on the B-spline curve;
sequentially selecting three adjacent spline points based on the spline point sequence, and judging the track type formed by the three adjacent spline points;
judging whether the next spline point is collinear or collinear with or is in a circle with the first graph track or not based on the first graph track formed by the three adjacent spline points and the corresponding track type;
if the next spline point is collinear or collinear with the first graph track, updating the next spline point as the terminal point of the first graph track, and continuously judging whether the adjacent spline point is collinear or collinear with the first graph track or is collinear or collinear with the first graph track;
and if the next spline point is not collinear or collinear with the first graph track, taking the last spline point in the three adjacent spline points as the terminal point of the first graph track, and taking the next spline point as the starting point of the next section of new graph track.
2. The method of claim 1, wherein the step of obtaining a spline point sequence based on the B-spline curve comprises:
determining a node vector u of the B spline curve by a chord length parameterization method;
substituting the node vector u into the base function of the k-th-order B spline, and determining a B spline curve according to the control vertex of the original graph track and the base function of the k-th-order B spline;
and acquiring a spline point sequence on the spline curve according to the control point distance of the B spline curve.
3. The method of claim 1, wherein the step of determining the type of the trajectory formed by the three adjacent spline points comprises:
and judging whether the three adjacent spline points form a straight line or a section of circular arc or not based on a vector product mode.
4. The method of claim 3, wherein the step of determining whether the three adjacent spline points form a straight line or a segment of a circular arc based on the vector product comprises:
taking one spline point in the three adjacent spline points as a vertex, and calculating the product of the spline point and vectors of other two adjacent spline points;
if the product is equal to zero, determining that the three adjacent spline points form a straight line;
and if the product is larger than zero, determining that the three adjacent spline points form a section of circular arc.
5. The method of claim 1, wherein said determining whether the next spline point is collinear with the first pattern trace comprises:
and judging whether the last two adjacent spline points of the first graph track and the next spline point form a straight line or not based on a vector product mode.
6. The method of claim 1, wherein said determining whether the next spline point is co-circular with the first pattern trace comprises:
judging whether the bow height error from the next spline point to the first graph track is within the preset precision constraint range or not based on preset precision constraint;
and if the first graph track is within the preset precision constraint range, the first graph track is in a common circle with the first graph track.
7. The method of claim 6, wherein the step of determining whether the pitch error of the next spline point to the first pattern trace is within the accuracy constraint based on a predetermined accuracy constraint comprises:
calculating the radius and the center coordinate of the first graph track by adopting a method of solving the intersection point by vertical bisection;
calculating the bow height error from the next spline point to the first graph track according to the radius and the circle center coordinate;
comparing the bow height error with a constraint range of preset precision;
and if the height error is smaller than or equal to a constraint range of preset precision, determining that the height error is within the precision constraint range.
8. A circular arc straight line fitting system for laser CAM processing is characterized by comprising:
the original graph track acquisition module is used for acquiring an original graph track of a graph to be processed;
the spline point sequence acquisition module is used for fitting the original graph track to obtain a k-order B-spline curve and acquiring a spline point sequence based on the B-spline curve;
the track type judging module is used for sequentially selecting three adjacent spline points based on the spline point sequence and judging the track type formed by the three adjacent spline points;
the track continuous judging module is used for judging whether a next spline point is collinear or collinear with or is in a circle with a first graph track formed by the three adjacent spline points;
the track updating module is used for updating the next spline point to be the terminal point of the first graph track if the next spline point is collinear or collinear with or is collinear with the first graph track, and continuously judging whether the adjacent spline point is collinear or collinear with or is collinear with the first graph track; and if the next spline point is not collinear or collinear with the first graph track, taking the last spline point in the three adjacent spline points as the terminal point of the first graph track and taking the next spline point as the starting point of the next section of new graph track.
9. A computer device comprising a memory having stored therein a computer program and a processor which when executed implements the steps of the circular arc straight line fitting method of laser CAM machining according to any one of claims 1 to 7.
10. A computer-readable storage medium, having stored thereon a computer program which, when being executed by a processor, carries out the steps of the circular arc straight line fitting method of laser CAM processing according to any one of claims 1 to 7.
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