Complex outer contour curve discrete data point axial symmetry judgment method

Abstract

The invention aims to provide an axisymmetric judgment method for discrete data points of a complex outer contour curve. The axisymmetric judgment method comprises the following steps: A, measuring by using a three-coordinate measuring instrument to obtain the discrete data points of the outer contour of a stamping sample piece; b, all discrete data points on each section of curve are regarded as a set and recorded as PI, each data point is represented by pIi (xi, yi), I and i represent the I curve and the i discrete data point respectively, and the initial sequence number is 1; c, for the set PI of each curve discrete point, finding out the longest straight line segment, and calculating the slope of the longest straight line segment; d, for the set PI of each curve discrete point, calculating a symmetry axis equation: Ax + By + C = 0; and F, judging each discrete point in each curve based on a symmetry axis equation, and determining whether the curve is axisymmetric or non-axisymmetric. The method can quickly judge whether the discrete curve shows the axial symmetry characteristic or not so as to quickly complete the mold design of a complex profile curve.

Description

Technical Field

[0001] The invention relates to the technical field of mold design, and in particular to a method for determining the axisymmetry of discrete data points of a complex outer contour curve. Background Art

[0002] Reverse design is a common method for mold design. The three-coordinate measurement of the sample is performed to collect its discrete data points. Then, through 3D software and corresponding algorithm recognition and curve fitting, the sample contour can be quickly and accurately modeled, laying the foundation for subsequent three-dimensional mold design.

[0003] It is worth noting that the shape of the sample may present a complex curve contour. The data collected by the three-coordinate system is a discrete data point set. How to use the algorithm to quickly identify the discrete curve data points and model the curve is a key core issue. Among them, the axisymmetric judgment method for discrete curve data points is an important part. Summary of the invention

[0004] The present invention aims to provide a method for determining the axisymmetry of discrete data points of a complex outer contour curve. The method can quickly determine whether a discrete curve presents axisymmetric characteristics and calculate the axis of symmetry, thereby performing curve fitting of discrete data points, so as to quickly complete the mold design of the complex contour curve.

[0005] The technical solution of the present invention is as follows:

[0006] The method for determining the axisymmetry of discrete data points of a complex outer contour curve comprises the following steps:

[0007] A. Use a three-coordinate measuring machine to measure and obtain discrete data points of the outer contour of the stamping sample; when measuring the closed structure on the stamping sample, the starting point is selected arbitrarily, and when measuring the non-closed structure, the starting point is selected from the two endpoints; the measurement method is to measure each point in sequence from the starting point in the same clockwise direction;

[0008] B. Consider all discrete data points on each curve as a set, denoted as P I , where each data point is represented by p Ii (x i ,y i ) indicates that I and i represent the I-th curve and the i-th discrete data point respectively, and the starting sequence number is 1;

[0009] C. For each set of discrete points P of the curve I , find the longest straight line segment and calculate the slope of the longest straight line segment;

[0010] D. For each set of discrete points P of the curve I, calculate the mean of its x-axis and y-axis, and record it as the geometric center p I,0 (x0, y0);

[0011] E. Use A=K, B=-1.0 and C=y0-K*x0 to calculate the equation of the axis of symmetry: Ax+By+C=0;

[0012] F. Select any point from any curve set as an active detection point, counted as p I,a (x a ,y a ), the theoretically strict symmetric point of this point is denoted as p I,a’ (x a’ ,y a’ ); traverse the remaining points in the set, for each point p I,i , calculate its value to p I,a’ (x a’ ,y a’ ) of the Euclidean distance Distance, if there exists a value that satisfies Distance≤threshold δ R point, then it is considered that the active detection point p I,a If (x1, y1) has a symmetric point, go to step G; otherwise, stop the calculation of the set, consider the discrete points of the set as non-axisymmetric, and go to step H;

[0013] G. Select the next active detection point in the curve set and repeat step F until all active detection points are checked. If the number of active detection points that find symmetric points accounts for a ratio greater than or equal to M of all active detection points, the discrete data points of the curve are considered to be axisymmetric; otherwise, the discrete data points are considered not to be axisymmetric.

[0014] H. Select the next curve set in the set and repeat steps F and G to obtain the axisymmetry judgment results of the discrete points of all curves.

[0015] In step C, for each set of discrete points P of the curve I , the calculation method to find the longest straight line segment is:

[0016] Select a set P of discrete points of a curve I The first point on the I,i (x i ,y i ), set i = 1, from p I,i Starting from the next point, check the subsequent points one by one, and set the current checkpoint to p I,j (x j ,y j ), and p I,j The next point is p I,k (xk ,y k ); by calculating the vector p I,i p I,j With p I,j p I,k The cross product of , to make a cross product judgment:

[0017] a. If the cross product is not zero, let i = k and continue to judge the cross product until the cross product is zero, then p I,i , p I,j , p I,k The three points are on the same line. Continue to look for points backwards, set k = k + 1, update k, and repeat the cross product judgment until the cross product is not zero again. At this time, from p I,i to p I,k-1 All the points form a straight line segment, record the starting point p of this straight line segment I,i , end point p I,k-1 ;

[0018] b. Then the last updated p I,k Set it as the new starting point, that is, let i = k, repeat the above step a, and continue to find the next straight line segment until all points are traversed; thus, a series of straight line segments are obtained, which are determined by the starting point p of each straight line segment. 1,i and the end point p 1,k-1 , calculate the length of each straight line segment: L = ((x i -x k-1 ) 2 +(y i -y k-1 ) 2 ) 1 / 2 , find the longest straight line segment by comparison and calculate its slope K = (y i -y k-1 ) / (x i -x k-1 ).

[0019] In step F, the active checkpoint p is obtained. I,a (x a ,y a ) is a theoretically strictly symmetric point p I,a’ (x a’ ,y a’ ) is calculated as:

[0020] The normal vector of the axis of symmetry is n = (A, B), and the slope of its perpendicular line is K' = -A / B, then the line passing through point p I,a (x a ,y a ) is the perpendicular line equation of the axis of symmetry: B(xx a )-A(yy a)=0, and the two equations combined with the symmetry axis equation can calculate the intersection coordinates The theoretical symmetry point is: p I,a’ (x a’ ,y a’ )=(2x ac -x a ,2y ac -y a ).

[0021] In the step F, the calculation formula of the Euclidean distance is: Distance = ((x i -x 1' ) 2 +(y i -y 1' ) 2 ) 1 / 2 .

[0022] The threshold δ R It is a constant and is set according to the shape, specifications and other factors of the designed parts during the design process.

[0023] In the step G, M is a constant, which is set according to the situation during the design process based on factors such as the shape and specifications of the designed part.

[0024] The present invention can conveniently judge the axisymmetry of the discrete point graphics of the stamping parts, and quickly perform graphics fitting, thereby improving work efficiency, providing convenience for completing the inverse modeling of the discrete point graphics and the subsequent reverse design of the mold, and has high practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is the final result diagram of fitting the discrete points of the complex curved stamping part according to the axisymmetric figure according to the method of Example 1; DETAILED DESCRIPTION

[0026] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0027] Example 1

[0028] The method for determining the axisymmetry of discrete data points of a complex outer contour curve comprises the following steps:

[0029] A. Use a three-coordinate measuring machine to measure and obtain discrete data points of the outer contour of the stamping sample; when measuring the closed structure on the stamping sample, the starting point is selected arbitrarily, and when measuring the non-closed structure, the starting point is selected from the two endpoints; the measurement method is to measure each point in sequence from the starting point in the same clockwise direction;

[0030] B. Consider all discrete data points on each curve as a set, denoted as P I , where each data point is represented by p Ii (x i ,y i ) indicates that I and i represent the I-th curve and the i-th discrete data point respectively, and the starting sequence number is 1;

[0031] C. For each set of discrete points P of the curve I , find the longest straight line segment and calculate the slope of the longest straight line segment;

[0032] For each set of discrete points P of the curve I , the calculation method to find the longest straight line segment is:

[0033] Select a set P of discrete points of a curve I The first point on the I,i (x i ,y i ), set i = 1, from p I,i Starting from the next point, check the subsequent points one by one, and set the current checkpoint to p I,j (x j ,y j ), and p I,j The next point is p I,k (x k ,y k ); by calculating the vector p I,i p I,j With p I,j p I,k The cross product of , to make a cross product judgment:

[0034] a. If the cross product is not zero, let i = k and continue to judge the cross product until the cross product is zero, then p I,i , p I,j , p I,k The three points are on the same line. Continue to look for points backwards, set k = k + 1, update k, and repeat the cross product judgment until the cross product is not zero again. At this time, from p I,i to p I,k-1 All the points form a straight line segment, record the starting point p of this straight line segment I,i , end point p I,k-1 ;

[0035] b. Then the last updated p I,k Set it as the new starting point, that is, let i = k, repeat the above step a, and continue to find the next straight line segment until all points are traversed; thus, a series of straight line segments are obtained, which are determined by the starting point p of each straight line segment. 1,i and the end point p1,k-1 , calculate the length of each straight line segment: L = ((x i -x k-1 ) 2 +(y i -y k-1 ) 2 ) 1 / 2 , find the longest straight line segment by comparison and calculate its slope K = (y i -y k-1 ) / (x i -x k-1 ).

[0036] D. For each set of discrete points P of the curve I , calculate the mean of its x-axis and y-axis, and record it as the geometric center p I,0 (x0, y0);

[0037] E. Use A=K, B=-1.0 and C=y0-K*x0 to calculate the equation of the axis of symmetry: Ax+By+C=0;

[0038] F. Select any point from any curve set as an active detection point, counted as p I,a (x a ,y a ), the theoretically strict symmetric point of this point is denoted as p I,a’ (x a’ ,y a’ ); traverse the remaining points in the set, for each point p I,i , calculate its value to p I,a’ (x a’ ,y a’ ) of the Euclidean distance Distance, if there exists a value that satisfies Distance≤threshold δ R point, then it is considered that the active detection point p I,a If (x1, y1) has a symmetric point, go to step G; otherwise, stop the calculation of the set, consider the discrete points of the set as non-axisymmetric, and go to step H;

[0039] Get active checkpoint p I,a (x a ,y a ) is a theoretically strictly symmetric point p I,a’ (x a’ ,y a’ ) is calculated as:

[0040] The normal vector of the axis of symmetry is n = (A, B), and the slope of its perpendicular line is K' = -A / B, then the line passing through point p I,a (x a ,y a ) is the perpendicular line equation of the axis of symmetry: B(xxa )-A(yy a )=0, and the two equations combined with the symmetry axis equation can calculate the intersection coordinates The theoretical symmetry point is: p I,a’ (x a’ ,y a’ )=(2x ac -x a ,2y ac -y a ).

[0041] In the step F, the calculation formula of the Euclidean distance is: Distance = ((x i -x 1' ) 2 +(y i -y 1' ) 2 ) 1 / 2 .

[0042] G. Select the next active detection point in the curve set and repeat step F until all active detection points are checked. If the number of active detection points that find symmetric points accounts for a ratio greater than or equal to M of all active detection points, the discrete data points of the curve are considered to be axisymmetric; otherwise, the discrete data points are considered not to be axisymmetric.

[0043] H. Select the next curve set in the set and repeat steps F and G to obtain the axisymmetry judgment results of the discrete points of all curves.

[0044] Example 2

[0045] For a complex curved stamping part, a three-coordinate measuring instrument is used to measure the discrete points of the stamping part contour, and its plane coordinate values ​​are extracted (ignoring the height direction values). The axisymmetric judgment method of Example 1 of the present invention is used to automatically judge the symmetry of the collected data points and calculate the symmetry axis. Therefore, when fitting the contour of the mold reverse design, the discrete points are fitted according to the axisymmetric figure. The final result is shown in FIG. Figure 1 .

Claims

1. A method for determining the axisymmetry of discrete data points of a complex outer contour curve, characterized in that: The following steps are involved: A. Use a three-coordinate measuring machine to measure and obtain discrete data points of the outer contour of the stamping sample; when measuring the closed structure on the stamping sample, the starting point is selected arbitrarily, and when measuring the non-closed structure, the starting point is selected from the two endpoints; the measurement method is to measure each point in sequence from the starting point in the same clockwise direction; B. Consider all discrete data points on each curve as a set, denoted as P I , where each data point is represented by p Ii (x i ,y i ) indicates that I and i represent the I-th curve and the i-th discrete data point respectively, and the starting sequence number is 1; C. For each set of discrete points P of the curve I , find the longest straight line segment and calculate the slope of the longest straight line segment; D. For each set of discrete points P of the curve I , calculate the mean of its x-axis and y-axis, and record it as the geometric center p I,0 (x0, y0); E. Use A=K, B=-1.0 and C=y0-K*x0 to calculate the equation of the axis of symmetry: Ax+By+C=0; F. Select any point from any curve set as an active detection point, counted as p I,a (x a ,y a ), the theoretically strict symmetric point of this point is denoted as p I,a’ (x a’ ,y a’ ); traverse the remaining points in the set, for each point p I,i , calculate its value to p I,a’ (x a’ ,y a’ ) of the Euclidean distance Distance, if there exists a value that satisfies Distance≤threshold δ R point, then it is considered that the active detection point p I,a If (x1, y1) has a symmetric point, go to step G; otherwise, stop the calculation of the set, consider the discrete points of the set as non-axisymmetric, and go to step H; G. Select the next active detection point in the curve set and repeat step F until all active detection points are checked. If the number of active detection points that find symmetric points accounts for a ratio greater than or equal to M of all active detection points, the discrete data points of the curve are considered to be axisymmetric; otherwise, the discrete data points are considered not to be axisymmetric. H. Select the next curve set in the set and repeat steps F and G to obtain the axisymmetry judgment results of the discrete points of all curves.

2. The method for determining the axisymmetry of discrete data points of a complex outer contour curve according to claim 1, characterized in that: In step C, for each set of discrete points P of the curve I , the calculation method to find the longest straight line segment is: Select a set P of discrete points of a curve I The first point on the I,i (x i ,y i ), set i = 1, from p I,i Starting from the next point, check the subsequent points one by one, and set the current checkpoint to p I,j (x j ,y j ), and p I,j The next point is p I,k (x k ,y k ); by calculating the vector p I,i p I,j With p I,j p I,k The cross product of , to make a cross product judgment: a. If the cross product is not zero, let i = k and continue to judge the cross product until the cross product is zero, then p I,i , p I,j , p I,k The three points are on the same line. Continue to look for points backwards, set k = k + 1, update k, and repeat the cross product judgment until the cross product is not zero again. At this time, from p I,i to p I,k-1 All the points form a straight line segment, record the starting point p of this straight line segment I,i , end point p I,k-1 ; b. Then the last updated p I,k Set it as the new starting point, that is, let i = k, repeat the above step a, and continue to find the next straight line segment until all points are traversed; thus, a series of straight line segments are obtained, which are determined by the starting point p of each straight line segment. 1,i and the end point p 1,k-1 , calculate the length of each straight line segment: L = ((x i -x k-1 ) 2 +(y i -y k-1 ) 2 ) 1 / 2 , find the longest straight line segment by comparison and calculate its slope K = (y i -y k-1 ) / (x i -x k-1 ).

3. The method for determining the axisymmetry of discrete data points of a complex outer contour curve according to claim 2, characterized in that: In step F, the active checkpoint p is obtained. I,a (x a ,y a ) is a theoretically strictly symmetric point p I,a’ (x a’ ,y a’ ) is calculated as: The normal vector of the axis of symmetry is n = (A, B), and the slope of its perpendicular line is K' = -A / B, then the line passing through point p I,a (x a ,y a ) is the perpendicular line equation of the axis of symmetry: B(xx a )-A(yy a )=0, and the two equations combined with the symmetry axis equation can calculate the intersection coordinates The theoretical symmetry point is: p I,a’ (x a’ ,y a’ )=(2x ac -x a ,2y ac -y a ).

4. The method for determining the axisymmetry of discrete data points of a complex outer contour curve according to claim 1, characterized in that: In the step F, the calculation formula of the Euclidean distance is: Distance = ((x i -x 1' ) 2 +(y i -y 1' ) 2 ) 1 / 2 .

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