CN114942615B - Equal-bow-height error interpolation method, device and storage medium - Google Patents
Equal-bow-height error interpolation method, device and storage medium Download PDFInfo
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Abstract
The interpolation method of the invention needs to analyze the curvature change condition of the free curve in advance, divide the curve to be processed into sections according to the curvature change rate, and calculate interpolation points by adopting different strategies for each section. The section with stable curvature is calculated by adopting the traditional geometric method preferentially, the verification function is abandoned, and the calculation efficiency is improved as much as possible; the section with obvious curvature fluctuation needs to strictly monitor curvature change, automatically adjusts the step size according to errors, and ensures that the machining precision meets the requirements. The novel interpolation method constructed based on the curvature partition strategy solves the problems of overrun error and overserved step length existing in the traditional equal-bow-height error method on the basis of flexible parameter control, rapid, stable and reliable calculation.
Description
Technical Field
The invention relates to the technical field of numerical control machining motion control, in particular to an equal-bow-height error interpolation method, equipment, a device and a computer storage medium.
Background
The continuous forward progress of industrialization brings higher requirements to the design and manufacture of products, and free-form surfaces are also produced. Numerical control technology is also developing towards high speed, high precision and reliability as a main mode of free-form surface processing, and a free-form curve interpolation method is a key technology for influencing the free-form surface processing quality.
At present, the engineering uses a plurality of equidistant steps, equal parameter steps, parameter screening and equal bow height error methods. The equal distance method is adopted to interpolate the tool paths, so that approximation errors are met, values are conservative, and more redundant tool paths are generated. The equal parameter step-by-step method is to equally divide curve parameters to obtain a plurality of discrete parameter nodes, and the discrete parameter nodes are used as interpolation points in actual processing, so that the error fluctuation between the interpolation points is large due to the nonlinear relation between a parameter equation and a curve equation, the processing quality is uneven, and even a situation of large approximation error occurs locally. The parameter screening method requires that the initial discrete points are sufficiently dense, so that the calculated amount is large, the calculated speed is low, and the bow height error obtained by the method is uneven, so that the precision of a processing surface is affected. The equal bow height error method considers the change of curvature, and is better improved than the method, but the accuracy is still to calculate the step length by means of the circular arc, so that the error is required to be repeatedly checked, the calculation performance is reduced, and the checking result still possibly exceeds the error allowable range. While the existing improvement scheme still has certain defects: (1) The calculation of the bow-height error value between adjacent tangential points is improved by means of a space vector, and although the more accurate bow-height error value can be obtained, the precision of the free curve after interpolation can be improved to a certain extent, the problem of error overrun and the problem of step length overservice caused by curvature abrupt change are not solved; (2) The optimal step value meeting the requirement of the bow height error among all the contact points is found through iterative calculation, curve conditions are not considered, the bow height error meets the requirement through calculation, partial redundancy calculation exists, and the execution efficiency of an algorithm is reduced.
Disclosure of Invention
Therefore, the invention aims to solve the technical problems of low calculation efficiency and inaccurate calculation in the prior art.
In order to solve the technical problems, the invention provides a method, a device and a device for equal-bow-height error interpolation and a computer storage medium, comprising the following steps:
calculating to obtain a parameter expression of the Bezier curve according to control vertex data of the curve to be processed;
calculating the curvature of the Bezier curve to obtain the change rate of the curvature along with the change of curve parameters;
if the change rate of the current section is not greater than the reference value, calculating to obtain the minimum curvature radius in the current section by utilizing the geometric relationship, and calculating the interpolation step length by taking the minimum curvature radius as the arc radius;
if the change rate of the current section is larger than the reference value, calculating the curvature radius of the initial point of the current section by utilizing a geometric relation, and obtaining an initial step by approximate calculation with the curvature radius of the initial point as an arc radius, and iteratively updating the initial step until an optimal step meeting the requirement of the bow-height error is solved;
calculating a corresponding interpolation endpoint according to the optimal step length, judging whether the current section is calculated completely or not, if not, updating the initial point position to the interpolation endpoint, and returning to the step of solving the optimal step length;
and after all the sections are calculated, merging the discrete interpolation points to obtain a complete discrete point path.
Preferably, the calculating the parameter expression of the bezier curve according to the control vertex data of the curve to be processed includes:
calculating to obtain a Bezier curve L according to control vertex data P of the given curve to be processed;
calculating to obtain a base function expression of the Bezier curve according to the number n of control vertexes:
wherein i=0, 1,2, …, n, curve parameter u e [0,1], thereby calculating the parameter expression of the bezier curve L:
preferably, the calculating the curvature of the bezier curve, to obtain the rate of change of the curvature with the change of the curve parameter includes:
calculating the curvature of the Bezier curveWherein c (u) is a parametric expression of the Bezier curve, c '(u) is a first derivative of the curve, and c' (u) is a second derivative of the curve;
calculating the rate of change of curvature with the change of curve parameters
Preferably, the iteratively updating the initial step size until the optimal step size meeting the bow-height error requirement is solved includes:
step a: calculating to obtain the maximum arch height error value between adjacent interpolation points of the current step length value;
step b: calculating the absolute value of the difference between the maximum bow-height error value of the current step length and the maximum bow-height error value allowable for processing, and comparing the absolute value with the iteration error;
step c: if the absolute value is larger than the iteration error, jumping to the step d, and if the absolute value is not larger than the iteration error, jumping out of the iteration calculation, and taking the current step as the optimal step;
step d: if the maximum bow-height error value of the current step is not greater than the maximum bow-height error value allowed by processing, increasing the parameter increment of the free curve, updating the current step value, jumping to the step a, taking the current step as the optimal step, otherwise, reducing the parameter increment of the free curve, updating the current step value, jumping to the step a, and until the maximum bow-height error value of the current step is not greater than the maximum bow-height error value allowed by processing.
Preferably, the parameter increment Δu= (1±α) Δu of the free curve is increased or decreased, wherein α is a preset step automatic adjustment coefficient.
Preferably, the updating the current step value is s i ＝c′(u i )Δu i Wherein c (u) is a parametric expression of the bezier curve, i=0, 1,2, …, n, u e [0,1]]；
Calculating the corresponding interpolation segment end point as c (u) i+1 )＝c(u i +Δu i )。
Preferably, the calculation obtains the maximum arch height error value e between adjacent interpolation points of the current step value 0 ＝||T 2 ||sinθ；
Wherein the included angle between the two vectorsIs a vector of two adjacent interpolation points, a->Is a vector formed from the starting point of the interpolation segment to any point on the curve segment.
The invention also provides a device for interpolating the equal bow height error, which comprises:
the curve parameter expression calculation module is used for calculating and obtaining a parameter expression of the Bezier curve according to control vertex data of the curve to be processed;
the curve change rate calculation module is used for calculating the curvature of the Bezier curve to obtain the change rate of the curvature along with the change of curve parameters;
the stable section interpolation step length calculation module is used for calculating to obtain the minimum curvature radius in the current section by utilizing the geometric relationship, and calculating the interpolation step length by taking the minimum curvature radius as the arc radius;
the fluctuation section optimal step length calculation module is used for calculating the curvature radius of an initial point position of the current section by utilizing a geometric relation, obtaining an initial step length by approximate approximation calculation by taking the curvature radius of the initial point position as an arc radius, and iteratively updating the initial step length until the optimal step length meeting the requirement of bow height error is solved;
the fluctuation section calculation completion judging module is used for calculating a corresponding interpolation terminal according to the optimal step length so as to judge whether the current section is completely calculated, if not, updating the initial point position into the interpolation terminal, and returning to the step of solving the optimal step length;
and the discrete interpolation point merging module is used for merging the discrete interpolation points after all the sections are calculated to obtain a complete discrete point path.
The invention also provides equipment for interpolating the equal bow height errors, which comprises the following steps:
a memory for storing a computer program; and the processor is used for realizing the step of the equal-bow-height error interpolation method when executing the computer program.
The present invention also provides a computer readable storage medium having stored thereon a computer program which when executed by a processor implements the steps of the above-described equal bow error interpolation method.
Compared with the prior art, the technical scheme of the invention has the following advantages:
the invention provides an equal-bow-height error interpolation method in curve processing based on curvature partition. The interpolation method needs to analyze curvature change conditions of the free curve in advance, divide the curve to be processed into sections according to curvature change rates, and calculate interpolation points by adopting different strategies in each section. The section with stable curvature is calculated by adopting the traditional geometric method preferentially, the verification function is abandoned, and the calculation efficiency is improved as much as possible; the section with obvious curvature fluctuation needs to strictly monitor curvature change, automatically adjusts the step size according to errors, and ensures that the machining precision meets the requirements.
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In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings, in which:
FIG. 1 is a flow chart of an implementation of the equal bow height error interpolation method of the present invention;
FIG. 2 is a schematic diagram of a geometric method for calculating interpolation steps;
FIG. 3 is a schematic diagram of an automatic step adjustment mechanism based on curvature changes;
FIG. 4 is a flowchart of a method for equal bow error interpolation in an embodiment of the present invention;
FIG. 5 is a schematic illustration of a free curve to be processed;
FIG. 6 is a schematic view of the curvature change of a selected free curve to be processed;
FIG. 7 (a) shows discrete blade contact points after interpolation calculation by the equal bow height error method;
fig. 7 (b) shows the error distribution after interpolation calculation by the equal bow height error method;
FIG. 8 (a) shows discrete blade contacts after interpolation calculation by an equal bow height error interpolation method based on curvature partitioning;
fig. 8 (b) shows the error distribution after interpolation calculation by the equal-bow-height error interpolation method based on curvature partitioning;
fig. 9 is a block diagram of a device for interpolating an equal-bow-height error according to an embodiment of the present invention.
Detailed Description
The core of the invention is to provide a method, a device, equipment and a computer storage medium for interpolation of equal-bow-height errors, wherein a curve to be processed is divided into sections according to curvature change rate, and interpolation points are calculated by adopting different strategies in each section, so that the calculation precision and efficiency are improved.
In order to better understand the aspects of the present invention, the present invention will be described in further detail with reference to the accompanying drawings and detailed description. It will be apparent that the described embodiments are only some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1, fig. 1 is a flowchart illustrating an implementation of the equal-bow-height error interpolation method provided by the present invention; the specific operation steps are as follows:
system-given parameters, including: the method comprises the following steps of controlling vertex data P of a curve to be processed, the cutter radius r of a ball head cutter used for processing, the maximum bow height error e allowed by processing, a curvature change rate reference value mu of a divided section and a step automatic adjustment coefficient alpha;
s101: calculating to obtain a parameter expression of the Bezier curve according to control vertex data of the curve to be processed;
calculating to obtain a Bezier curve L according to control vertex data P of the given curve to be processed;
calculating to obtain a base function expression of the Bezier curve according to the number n of control vertexes:
wherein i=0, 1,2, …, n, curve parameter u e [0,1], thereby calculating the parameter expression of the bezier curve L:
first and second derivatives of bezier curves:
s102: calculating the curvature of the Bezier curve to obtain the change rate of the curvature along with the change of curve parameters;
assuming a parametric expression for a curve of c (u), the curvature k at a point on the curve is only related to the curve parameter u, the first derivative c' (u) and the second derivative c "(u):
thereby obtaining the change rate of curvature along with the change of curve parameters
S103: if the change rate of the current section is not greater than the reference value, calculating to obtain the minimum curvature radius in the current section by utilizing the geometric relationship, and calculating the interpolation step length by taking the minimum curvature radius as the arc radius;
if the change rate of the current zone is not greater than the reference value mu 0 Mu is less than or equal to mu, which means that the curvature change of the current curve segment is tiny, and the disturbance to interpolation step calculation is negligible;
as shown in figure 2, the geometric relationship between the curvature radius and the reciprocal of the curvature is utilized to calculate the minimum curvature radius in the current interpolation segmentAnd calculating the interpolation step length by using the same as the radius of the circular arc>Further realizing the discrete approximation of the curve segment;
introducing a time variable parameter t, where t=t i The curve parameter u is subjected to second-order Taylor expansion:
substituting the first and second derivatives t ', t' of the curve parameter u and the time parameter t into the above formula, and obtaining the interpolation step s by expansion reduction i And parameter delta u i The relation between the two is as follows: s is(s) i ＝c′(u i )Δu i ；
After the step calculation is performed on the current interpolation point, the position of the next interpolation point, namely the intersection point of the interpolation line segment and the curve, needs to be found, but the way of directly solving the intersection point is quite complex, and the parameter increment between the two interpolation points is generally utilized to realize the recursive calculation of the interpolation point, namely c (u) i+1 )＝c(u i +Δu i ) Therefore, all interpolation points in the current interpolation section can be recursively calculated, and the interpolation calculation of the curvature stable section is completed.
S104: if the change rate of the current section is larger than the reference value, calculating the curvature radius of the initial point of the current section by utilizing a geometric relation, and obtaining an initial step by approximate calculation with the curvature radius of the initial point as an arc radius, and iteratively updating the initial step until an optimal step meeting the requirement of the bow-height error is solved;
s105: calculating a corresponding interpolation endpoint according to the optimal step length, judging whether the current section is calculated completely or not, if not, updating the initial point position to the interpolation endpoint, and returning to the step of solving the optimal step length;
s106: and after all the sections are calculated, merging the discrete interpolation points to obtain a complete discrete point path.
The equal-bow-height error interpolation method model constructed by the invention comprises two main steps: segmentation and interpolation calculations.
The section division refers to fitting a Bezier curve by using control vertex data P of the curve to be processed, calculating the curvature of the curve obtained after fitting, and comparing the change rate mu of the curve curvature along with the change of curve parameters 0 And a curvature change rate reference value mu for the section division, thereby realizing the section division of the free curve to be processed, and the curvature change characteristics in the obtained sections are kept basically consistent.
The interpolation calculation is to calculate interpolation points of the sections with different curvature change characteristics obtained by dividing the free curve into sections by different calculation strategies. The free curve can be generally divided into three types of sections of stable curvature, increased curvature and reduced curvature, and each type of section has a corresponding interpolation calculation strategy. The section with stable curvature utilizes the geometric relationship to calculate the minimum curvature radius in the interpolation section, and the minimum curvature radius is used as the circular arc radius to approach the curve section, because the curvature in the section is kept stable, the verification part can be omitted in order to improve the algorithm execution efficiency. The curvature increasing section and the curvature decreasing section can be combined into a section with obvious curvature change, the change condition of the curvature of the curve at each position in the section needs to be monitored in real time, step length adjustment is automatically carried out by comparing the magnitude relation between the actual value and the given value of the discrete back bow height error, and the maximum step length meeting the given bow height error is found through iterative calculation for a certain number of times. Therefore, even if the curve curvature changes severely, the processing precision can meet the requirement, the surface error after processing is kept uniform, the number of steps required by processing is small, and the processing efficiency is high.
After the interpolation model is determined, the free curve to be processed is divided into a plurality of sections, and the subsequent interpolation calculation is performed by adopting a proper calculation strategy according to the curvature change characteristics of each section.
Referring to fig. 3, based on the above embodiments, steps S104 to S105 are further described in detail in this embodiment, and specifically as follows:
step a: calculating to obtain the maximum bow height error value e between adjacent interpolation points of the current step length value 0 ＝||T 2 ||sinθ；
Wherein the included angle between the two vectorsIs a vector of two adjacent interpolation points, a->Is a vector formed from the starting point of the interpolation segment to any point on the curve segment.
Step b: calculating the absolute value of the difference between the maximum bow-height error value of the current step length and the maximum bow-height error value e of the processing tolerance, and comparing the absolute value with the iteration error delta;
step c: if the absolute value is greater than the iteration error |e 0 -e| > delta, meaning the maximum arch height error value e generated by the current step size 0 If the difference value of the allowable bow-height error e with the processing does not meet the iteration precision requirement, judging the magnitude relation between the maximum bow-height error value of the current step length and the allowable maximum bow-height error value with the processing, if the absolute value is not larger than the iteration error |e 0 E is less than or equal to delta, the iterative calculation is skipped, and the current step length is taken as the optimal step length;
step d: e if the maximum bow-height error value of the current step is not greater than the processing allowable maximum bow-height error value 0 If the maximum bow-height error value of the current step length is larger than the processing allowable maximum bow-height error value, e 0 And e, reducing the parameter increment of the free curve, updating the current step value, and jumping to the step a until the maximum bow-height error value of the current step is not greater than the maximum bow-height error value allowed by processing.
Step d: if the maximum bow-height error value of the current step is not greater than the processing allowable maximum bow-height error value e 0 If the current step length value is less than or equal to e, the parameter increment delta u= (1+alpha) delta u of the free curve is increased, the current step length value is updated, the step a is skipped, the current step length is taken as the optimal step length, and if e 0 > e, indicating that the current step value is too large, reducing the parameter increment delta of the free curveu= (1-alpha) deltau, updating the current step value, jumping to the step a until the current step maximum bow height error value is not greater than the processing allowable maximum bow height error value.
The interpolation method provided by the invention can fit control vertex data into a free curve according to given parameters of the system, analyze curvature change conditions of the curve in advance, divide the curve to be processed into sections according to the magnitude relation between the curvature change rate and the reference value, and calculate interpolation points of the sections by adopting different strategies. The section with stable curvature is calculated by adopting the traditional geometric method preferentially, the verification function is abandoned, and the calculation efficiency is improved as much as possible; the section with obvious curvature fluctuation needs to strictly monitor curvature change, and the step size is automatically adjusted according to the error so as to find the optimal step size value meeting the high error requirement of the arch, thereby ensuring that the machining precision meets the requirement. The novel interpolation method constructed based on the curvature partition strategy solves the problems of error overrun and step length overserving existing in the equal-bow-height error method on the basis of flexible parameter control, rapid, stable and reliable calculation.
As shown in fig. 4, based on the above embodiments, one free curve (such as fig. 5) of the free curves is selected as the experimental object in this embodiment, specifically as follows:
the tool radius r of the ball-end cutter used for machining is set to be 5mm, the maximum allowable bow height error e of machining is set to be 0.01mm, the curvature change rate reference value mu of the divided sections is set to be 0.03, and the step automatic adjustment coefficient alpha is set to be 0.005.
Fitting given control vertex data to obtain a Bezier curve, wherein the curvature change condition of the selected path to be processed is shown in figure 6;
when the curvature change is not greater than the reference value, the geometric relationship that the curvature radius and the curvature are reciprocal is utilized to calculate the minimum curvature radius rho in the current interpolation section, and the minimum curvature radius rho is used as the circular arc radius to calculate the interpolation step s, so that the discrete approximation of the curve section is realized;
if the curvature change is smaller than the reference value, the change condition of the curvature of the curve at each position is monitored in real time, and step length adjustment is automatically carried out by comparing the magnitude relation between the actual value and the given value of the discrete post-arch height error.
According to the method, the curvature characteristics of the curve to be processed are analyzed in advance, and corresponding partitioning is carried out, so that discrete calculation of the cutter contact is carried out by using different calculation strategies, and the problems of error overrun and step length overserving of an equal-bow-height error method are effectively avoided. From fig. 7 (a), 7 (b), 8 (a) and 8 (b), it can be seen that the equal bow height error method discretizes 41 blade contacts in total, and 34 blade contacts in total. Compared with the equal bow height error method, the number of knife contacts is reduced by 17%, the machining efficiency is effectively improved, and the time consumption of program calculation is greatly reduced. In the aspect of the surface quality after processing, the method reasonably uses a step automatic adjustment mechanism by analyzing the condition of curvature change in advance, and ensures that an algorithm can effectively track the curvature change. Compared with an equal-bow-height error method, the method can effectively avoid the problem of overrun of the maximum bow-height error and the problem of over conservation of the step length caused by over-small bow-height error. Therefore, the surface residual errors obtained after the processing by adopting the method are constant and the allowable maximum value, so that the uniformity of the processed surface quality is ensured, the processing efficiency is greatly improved, and meanwhile, the interference of curvature factors on the processing precision is avoided.
The interpolation method can fit control vertex data into a free curve according to given parameters of the system, analyze curvature change conditions of the curve in advance, divide the curve to be processed into sections according to the magnitude relation between the curvature change rate and the reference value, and calculate interpolation points of the sections by adopting different strategies. The section with stable curvature is calculated by adopting the traditional geometric method preferentially, the verification function is abandoned, and the calculation efficiency is improved as much as possible; the section with obvious curvature fluctuation needs to strictly monitor curvature change, and the step size is automatically adjusted according to the error so as to find the optimal step size value meeting the high error requirement of the arch, thereby ensuring that the machining precision meets the requirement. The novel interpolation method constructed based on the curvature partition strategy solves the problems of error overrun and step length overserving existing in the equal-bow-height error method on the basis of flexible parameter control, rapid, stable and reliable calculation.
Referring to fig. 9, fig. 9 is a block diagram of a device for interpolating an equal-bow-height error according to an embodiment of the present invention; the specific apparatus may include:
the curve parameter expression calculation module 100 is configured to calculate a parameter expression of the bezier curve according to control vertex data of the curve to be processed;
the curve change rate calculation module 200 is configured to calculate a curvature of the bezier curve, so as to obtain a change rate of the curvature along with a change of a curve parameter;
a stable section interpolation step calculation module 300, configured to calculate a minimum radius of curvature in the current section using a geometric relationship, and calculate an interpolation step with the minimum radius of curvature as a radius of an arc;
the wave section optimal step length calculation module 400 is configured to calculate a curvature radius of an initial point location of the current section by using a geometric relationship, and approximate approximation calculation is performed by using the curvature radius of the initial point location as an arc radius to obtain an initial step length, and the initial step length is iteratively updated until an optimal step length meeting the requirement of a bow height error is solved;
the judging module 500 is used for judging whether the calculation of the current section is finished according to the calculation of the interpolation end point of the optimal step length, if not, updating the initial point position to the interpolation end point, and returning to execute the step of solving the optimal step length;
the discrete interpolation point merging module 600 is configured to merge the discrete interpolation points after all the segments are calculated, so as to obtain a complete discrete point path.
The equal-bow-height error interpolation device of this embodiment is used to implement the equal-bow-height error interpolation method described above, and therefore, the specific implementation of the equal-bow-height error interpolation device can be seen in the foregoing example portions of the equal-bow-height error interpolation method, for example, the curve parameter expression calculation module 100, the curve change rate calculation module 200, the plateau interpolation step calculation module 300, the fluctuation zone optimal step calculation module 400, the fluctuation zone calculation completion determination module 500, and the discrete interpolation point combination module 600, which are respectively used to implement steps S101, S102, S103, S104, S105 and S106 in the equal-bow-height error interpolation method described above, so that the specific implementation thereof can refer to the description of the corresponding examples of each portion and will not be repeated herein.
The specific embodiment of the invention also provides equipment for interpolating the equal-bow-height errors, which comprises the following steps: a memory for storing a computer program; and the processor is used for realizing the step of the equal-bow-height error interpolation method when executing the computer program.
The specific embodiment of the invention also provides a computer readable storage medium, wherein the computer readable storage medium is stored with a computer program, and the computer program realizes the steps of the equal bow height error interpolation method when being executed by a processor.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. 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.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
It is apparent that the above examples are given by way of illustration only and are not limiting of the embodiments. Other variations and modifications of the present invention will be apparent to those of ordinary skill in the art in light of the foregoing description. It is not necessary here nor is it exhaustive of all embodiments. While still being apparent from variations or modifications that may be made by those skilled in the art are within the scope of the invention.
Claims (10)
1. An equal bow height error interpolation method, comprising:
calculating to obtain a parameter expression of the Bezier curve according to control vertex data of the curve to be processed;
calculating the curvature of the Bezier curve to obtain the change rate of the curvature along with the change of curve parameters;
if the change rate of the current section is not greater than the reference value, calculating to obtain the minimum curvature radius in the current section by utilizing the geometric relationship, and calculating the interpolation step length by taking the minimum curvature radius as the arc radius;
if the change rate of the current section is larger than the reference value, calculating the curvature radius of the initial point of the current section by utilizing a geometric relation, and obtaining an initial step by approximate calculation with the curvature radius of the initial point as an arc radius, and iteratively updating the initial step until an optimal step meeting the requirement of the bow-height error is solved;
calculating a corresponding interpolation endpoint according to the optimal step length, judging whether the current section is calculated completely or not, if not, updating the initial point position to the interpolation endpoint, and returning to the step of solving the optimal step length;
and after all the sections are calculated, merging the discrete interpolation points to obtain a complete discrete point path.
2. The equal-bow-height error interpolation method according to claim 1, wherein the calculating the parameter expression of the bezier curve according to the control vertex data of the curve to be processed comprises:
control vertex data according to given curve to be processedCalculating to obtain Bezier curve +.>；
According to the number of control vertexesCalculating to obtain a base function expression of the Bezier curve:
wherein,,curve parameters->From this, the Bezier curve is calculated>Is defined by the parameter expression:
。
3. the equal bow height error interpolation method according to claim 2, wherein the calculating the curvature of the bezier curve to obtain the rate of change of the curvature with the change of the curve parameter comprises:
calculating the curvature of the Bezier curveWherein->For the parametric expression of the bezier curve, and (2)>For the first derivative of the curve +.>Is the second derivative of the curve;
calculating the rate of change of curvature with the change of curve parameters。
4. The equal bow-height error interpolation method of claim 1, wherein iteratively updating the initial step size until an optimal step size meeting bow-height error requirements is solved comprises:
step a: calculating to obtain the maximum arch height error value between adjacent interpolation points of the current step length value;
step b: calculating the absolute value of the difference between the maximum bow-height error value of the current step length and the maximum bow-height error value allowable for processing, and comparing the absolute value with the iteration error;
step c: if the absolute value is larger than the iteration error, jumping to the step d, and if the absolute value is not larger than the iteration error, jumping out of the iteration calculation, and taking the current step as the optimal step;
step d: if the maximum bow-height error value of the current step is not greater than the maximum bow-height error value allowed by processing, increasing the parameter increment of the free curve, updating the current step value, jumping to the step a, taking the current step as the optimal step, otherwise, reducing the parameter increment of the free curve, updating the current step value, jumping to the step a, and until the maximum bow-height error value of the current step is not greater than the maximum bow-height error value allowed by processing.
5. A method of equal bow error interpolation according to claim 4, wherein the increasing or decreasing the parameter delta of the free curveWherein->And automatically adjusting the coefficient for a preset step length.
6. The equal bow-height error interpolation method according to claim 5, wherein the updating the current step value isWherein->For the parametric expression of the bezier curve, and (2)>，/>；
Calculating the corresponding interpolation segment end point as。
7. The equal-arch-height error interpolation method according to claim 1, wherein the calculation results in a maximum arch-height error value between adjacent interpolation points of the current step value；
Wherein the included angle between the two vectors，/>Is a vector of two adjacent interpolation points, a->Is a vector formed from the starting point of the interpolation segment to any point on the curve segment.
8. An apparatus for equal arch height error interpolation, comprising:
the curve parameter expression calculation module is used for calculating and obtaining a parameter expression of the Bezier curve according to control vertex data of the curve to be processed;
the curve change rate calculation module is used for calculating the curvature of the Bezier curve to obtain the change rate of the curvature along with the change of curve parameters;
the stable section interpolation step length calculation module is used for calculating the minimum curvature radius in the current section by utilizing the geometric relation and calculating the interpolation step length by taking the minimum curvature radius as the arc radius if the change rate of the current section is not greater than the reference value;
the fluctuation section optimal step length calculation module is used for calculating the curvature radius of an initial point position of the current section by utilizing a geometric relation if the change rate of the current section is larger than a reference value, and obtaining an initial step length by approximate calculation with the curvature radius of the initial point position as an arc radius, and iteratively updating the initial step length until the optimal step length meeting the bow height error requirement is solved;
the fluctuation section calculation completion judging module is used for calculating a corresponding interpolation terminal according to the optimal step length so as to judge whether the current section is completely calculated, if not, updating the initial point position into the interpolation terminal, and returning to the step of solving the optimal step length;
and the discrete interpolation point merging module is used for merging the discrete interpolation points after all the sections are calculated to obtain a complete discrete point path.
9. An apparatus for equal bow height error interpolation, comprising:
a memory for storing a computer program;
a processor for implementing the steps of a method of equal bow height error interpolation as claimed in any one of claims 1 to 7 when executing said computer program.
10. A computer readable storage medium, characterized in that the computer readable storage medium has stored thereon a computer program which, when executed by a processor, implements the steps of a method of equal bow error interpolation according to any one of claims 1 to 7.
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