JPH10240329A - Curve fine-segmentation method and numerical controller provided with spline interpolation function - Google Patents

Abstract

PROBLEM TO BE SOLVED: To prevent a spline curve passing through the point sequence from generating a large error with an original curve at the time of finely segmenting the curve and generating the point sequence by evaluating the error of a cubic spline curve and reconstituting the point sequence by adding a passing point inside a section in the case that the error exceeds an allowable value. SOLUTION: The curve is approximated fine segment data by the allowable error ε (S101). Then, the spline curve is generated from the (n) pieces of the passing points P1 , P2 ,...Pn-1 (S102). Then, a specified point Pj is initialized (S103) and whether or not the inflection point of the curve is provided inside the section is evaluated in the respective sections of the spline (104). Then, in the case of judging that the inflection point is provided inside the section (S105), the error in the respective sections Pj -Pj+1 of the cubic spline curve is evaluated (S106). Further, whether or not the obtained error dj exceeds the allowable error ε is evaluated (S107). It is defined that the error is within the allowable value error and (S109) is advanced at the time of dj <=ε and it is defined that it exceeds the allowable error and (S108) is advanced at the time of dj >ε.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of segmenting a curve into minute lines and a numerical controller having a spline interpolation function, and more particularly to a CAD / CAM apparatus in which a machining path passes through a curve by a numerical controller. And a numerical controller having a spline interpolation function for performing smooth interpolation control through a point sequence given by a spline interpolation function. .

[0002]

2. Description of the Related Art Conventionally, in a numerical controller, when a free curve in space is controlled as a movement path, the free curve is divided into minute sections in advance, and the free curve is approximated as minute line segment data to perform numerical control. In general, a method has been adopted in which the motion path is given to an apparatus and linearly interpolated and controlled on the movement path using the minute line segment data.

As a typical method of approximating a free curve to a minute line segment, as shown in FIGS. 19A and 19B, an allowable error ε is set and designated on the curves Ps to Pe. Point P
_i to P i + distance between the line segment and the curve connecting ₁ (chord error d _i) tolerances specified points so as not to exceed the epsilon P _i, is generating a sequence of points by setting P i _{+ 1} Was.

Here, in order to control the tool trajectory to a smooth curved trajectory by linear interpolation, it is necessary to set a small allowable error ε. However, factors such as the machining command program length and the machining speed at the time of linear interpolation are required. , The allowable error ε cannot be reduced indefinitely. Actually, the allowable error ε is set to a certain value, and the designated points P ₁ , P ₂ ,.
・ ・ It was approximated by a broken line passing through.

[0005] Therefore, such designated points P ₁ , P ₂ , ...
When it is necessary to obtain a smooth machining trajectory from, the technique of performing trajectory control by spline interpolation instead of linear interpolation between designated points is adopted.

[0006]

The error ε from the curve
When spline interpolation is performed on the designated point sampled by the above, a curve locus very close to the original curve is usually obtained, but a large distortion may occur depending on the arrangement of the sampled designated point.

FIG. 20 shows such an example. Figure 20 when it is a case of performing minute line segments approximate the curve B (t) with a tolerance ε indicated by the solid line, the designated points P _1, P _2, took · · · P _9, designated point P ₅ and because there is an inflection point between the P _6, since the chord error within tolerance ε can be taken on either side of the line segment (dp, d
q), as a result, the line segments P _{5 to} P ₆ are much longer than the line segments on both sides.

When the thus obtained point sequence is spline-interpolated by the numerical controller, the resulting interpolation trajectory is indicated by a broken line in FIG. 20 (a section not indicated by a dashed line is indicated by a dashed line). deemed curve should exhibit overlaps the solid curve), between the designated points P ₅ and P _6, the good processing result becomes what have considerable errors relative to the original curve is not obtained The following problem arises.

The present invention has been made in view of such a problem. Even when a numerical control device side linearly interpolates a passing point sequence which is output data when a curve is approximated by a minute line segment, A minute line segment approximation method for a curve whose interpolation trajectory guarantees sufficient error accuracy with respect to the original curve even if spline interpolation is performed, and from a specified passing point of minute line segment data approximated with a conventional allowable error It is another object of the present invention to provide a numerical controller that performs spline interpolation to guarantee an allowable error with respect to the original curve data.

[0010]

In order to achieve the above-mentioned object, a method for segmenting a curve into minute lines according to the present invention generates point sequence data obtained by minutely segmenting a free curve used as input data of a numerical controller. At this time, a point sequence is generated by performing a polygonal line approximation so that the string error is within an allowable value,
Generate a cubic spline curve passing through the point sequence, evaluate whether the section between each passing point has an inflection point of the curve within the section, and evaluate the section determined to have an inflection point. It is evaluated whether the error between the original curve and the generated cubic spline curve is within an allowable value, and if the error exceeds the allowable value, a passing point is added in the section to reconstruct the point sequence. Is what you do.

In the method for differentiating a minute line into a curve according to the present invention, it is evaluated whether an error between an original curve and a generated cubic spline curve is within an allowable value in a section determined to have an inflection point, When the error exceeds the allowable value, a passing point is added in the section, and a point sequence is set at a higher density as needed near the inflection point with respect to the original curve. As a result, a spline curve having a shape close to the original curve is obtained.

[0012] A method for differentiating a curve into minute lines according to the next invention is the method for differentiating a curve into small lines according to the invention described above,
If a passing point is added, a cubic spline curve that passes through this point sequence again is generated from the reconstructed point sequence, and whether the section between each passing point has an inflection point of the curve in the section Evaluate whether or not the error between the original curve and the generated cubic spline curve is within the allowable value for the section determined to have the inflection point. If the error exceeds the allowable value, Is a process of adding a passing point in the section and reconstructing the point sequence,
The process is repeated until no new pass point is added.

In the method for differentiating a curve into minute lines according to the present invention, it is evaluated whether an error between an original curve and a generated cubic spline curve is within an allowable value for a section determined to have an inflection point, If the error exceeds the allowable value, the addition of a passing point in the section is repeatedly performed until no new passing point is added, and the vicinity of the inflection point with respect to the original curve is increased as necessary. Point arrays are set at high density. As a result, a spline curve having a shape very close to the original curve is obtained.

[0014] The method for differentiating a curve into fine lines according to the next invention is the method for differentiating a curve from fine lines according to the invention described above,
The evaluation of whether or not there is an inflection point of the curve in the section, whether the start point vector of the spline curve of the section, the direction vector of the line segment of the section, the end point vector of the spline curve are continuous in a zigzag manner, This is performed by determining whether or not the ratio of the two angles of the start point vector and the end point vector of the spline curve to the direction vector of the line segment is larger than a reference value.

According to the method for differentiating a curved line into small lines according to the present invention, it is possible to easily and reliably evaluate whether or not a section has an inflection point of a curved line.

In order to achieve the above-mentioned object, a numerical controller having a spline interpolation function according to the present invention provides a sequence of passing points discretely taken on a curved machining trajectory, the distance between each passing point. A spline curve determining means for determining a spline curve in each section to be connected smoothly; and determining whether or not an error between the spline curve determined in each section and a line segment in the section exceeds an allowable value. And a spline curve correcting means for correcting the spline curve in the section so as to approach the line segment when the allowable value is exceeded.

In the numerical controller having a spline interpolation function according to the present invention, the spline curve determining means determines the spline curve in each section which smoothly connects between the passing points, and the spline curve correcting means determines the spline curve in each section. It is determined whether or not the error between the spline curve and the line segment in the section exceeds an allowable value, and if the error exceeds the allowable value, the spline curve in the section is corrected so as to approach the line segment.

A numerical controller having a spline interpolation function according to the next invention is the numerical controller according to the above-mentioned invention, wherein the correction of the spline curve by the spline curve correction means comprises the steps of: This is performed by reducing the magnitude of the tangent vector of the spline curve at both end points of the section so that the error between the spline curve and the line segment in the section falls within an allowable value.

In the numerical control apparatus having a spline interpolation function according to the present invention, the spline curve correcting means sets the tangent vector of the spline curve at both ends of the section to an error between the spline curve and the line segment of the section within an allowable value. The spline curve is corrected by reducing the magnitude of the tangent vector of the spline curve at both end points of the section so that

A numerical controller having a spline interpolation function according to the next invention is the numerical controller according to the above-mentioned invention, wherein the correction of the spline curve by the spline curve correction means is performed by changing a tangent vector of the spline curve at both end points of the section. By making the inflection point between the spline curve and the line segment of the section closer to the direction of the vector parallel to the line segment, the direction of the tangent vector of the spline curve at both ends of the section so that the error is within an allowable value. Is what you do.

In the numerical control apparatus having a spline interpolation function according to the present invention, the spline curve correcting means calculates a tangent vector of the spline curve at both end points of the section and an inflection point between the spline curve and the line segment of the section. The spline curve is corrected by making the direction of the tangent vector of the spline curve at both end points of the section closer to the direction of the vector parallel to the line segment so that is within the allowable value.

[0022]

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram of a numerical control apparatus having a curve minute line segmenting method and a spline interpolation function according to the present invention.

(Embodiment 1) Referring to FIG. 1, the flow of processing in one embodiment of a method for differentiating a minute line into a curve according to the present invention will be described.

(1) Let B (t) be the mathematical expression of the curve inside the computer. From the curve B (t), a curve is formed with an allowable error ε, as in the conventional example shown in FIG. It approximates to minute data (step S101). In this example, as shown in FIG. 20, the curve B (t) is represented by P ₁ , P ₂ ,.
It is represented by n (n = 10 in this example) passing points composed of P _n-1 .

(2) Next, the above-mentioned n passing points P ₁ ,
A spline curve is generated from P ₂ ,..., P _n-1 (step S102).

[0026] known curve theory (for example, "shape processing engineering (1)", Fujio Yamaguchi al., Published by Nikkan Kogyo Shimbun, Ltd.) According to the, n-number of the designated point _{P 1, P 2, P 3} , smooth ... P _n P (t) on the cubic spline curve passing through
_In the section illustrated in FIG. 2 from _j-1 to the designated point P _j , it is expressed by Expression (1).

[0027]

(Equation 1)

Here, q _j is a unit tangent vector at the designated point P _j , and c _j is a distance from P _{j -1} to P _j . Further, t is a curve parameter, and 0 ≦ t ≦ 1.

Although the spline curve represented by the equation (1) always passes through the designated point P _j (j = 1, 2, 3,..., N), if the unit tangent vector q _j is not set properly, The second derivative is not continuous at the specified point. 2
The condition for the next derivative to be continuous at each designated point P _j (j = 2, 3,..., N−1) is represented by Expression (2).

[0030]

(Equation 2)

With respect to the end points q ₁ and q _n , the following conditions are added, with the curvature at the end points being 0.

[0032] _{2c 2 q 1 + c 2 q} 2 = 3 (P 2 -P 1) ··· (3a) c n q n-1 + 2c n q n = 3 (P n -P n-1) ··· (3b)

By solving n simultaneous equations of equations (2), (3a) and (3b) to obtain a tangent vector q _j , a cubic spline curve for all sections is obtained.

That is, in each section from P _{j to} P _{j + 1} , the start point is Ps = P _j , the end point is Pe = P _{j + 1} , the unit tangent vector at the start point is qs = q _j , and the tangent vector at the end point is qe = Q _{j + 1} , and the length of the line segment is c = c _{j + 1} , K ₀ = Ps (4a) K ₁ = cqs (4b) K ₂ = 3 (Pe−Ps) _{-2cqs -cqe ··· (4c) K 3} = 2 (Ps -Pe) + cqs + cqe putting the ··· (4d), P _j ~P each point on the spline curve at _{j + 1} interval P (t ) is given by _{P (t) = K 3 t} 3 + K 2 t 2 + K 1 t + K 0 ··· (5) ( where, 0 ≦ t ≦ 1).

(3) Next, j = 1 is initialized (step S103), and it is evaluated whether or not each section of the spline has an inflection point of a curve inside the section (step S10).
4).

The method of determining the presence or absence of an inflection point is shown in FIGS.
(C) will be described with reference to FIG. 3 (a) to 3 (c)
Are unit vectors u of line segments in the sections P _{j to} P _{j + 1} , respectively.
And the start point vector qs and end point vector qe of the spline curve spanned by the section P _{j to} P _{j + 1} are projected onto a plane where the unit vector u and the start point vector qs exist.

FIG. 3A shows a case where it is determined that there is no inflection point, and the start point vector qs and the end point vector qe make substantially equal angles in the opposite direction with respect to the unit vector u.

FIG. 3 (b) shows one case in which it is determined to have an inflection point, in which the start point vector qs and the end point vector qe make an angle in the same direction with respect to the unit vector u. That is, this is a case where the start point vector qs, the vector indicating the direction of the section, and the end point vector qe are continuous in a zigzag manner.

FIG. 3C shows another case where it is determined to have an inflection point. The start point vector qs and the end point vector qe
Makes an angle in the opposite direction to the unit vector u, but the ratio of each angle becomes relatively large.

FIG. 4 is a flowchart for determining the presence / absence of an inflection point. First, it is determined whether the start point vector qs, the unit vector u, and the end point vector qe are continuous in a zigzag manner (step S1001).

In step S1001, the vector angle θs formed by the unit vector u and the starting point vector qs is determined by the following equation.

Cos (θs) = (qs, u) / | qs |

Using the vector angle θs, the starting point vector qs can be decomposed into the vectors qsh and qsv shown in FIG. Here, the decomposition vector qsh is a component parallel to the line segments Ps to Pe of the vector qs, and the decomposition vector qsv is a component perpendicular to the line segments Ps to Pe of the vector qs, and is obtained by the following equation.

Qsh = | qs | · cos (θs) · u =
(Qs, u) · uqs = qs-qsh

Next, this vertical component (decomposition vector) q
By taking the inner product of sv and the end point vector qe, the decomposition vector q
The angle θ between sv and the end point vector qe can be determined. When (qsv, qe) ≦ 0, 90 ° <θ ≦ 180 ° when 0 ° ≦ θ ≦ 90 ° (qsv, qe)> 0.

Therefore, when (qsv, qe) ≦ 0,
Since qe is considered to be in the same direction as qs with respect to u, it is determined that qs, u, and qe are continuous in a zigzag manner.

In step S1001, the starting point vector qs
, The unit vector u and the end point vector qe are determined to be continuous in a zigzag manner, the flow shifts to step S1004, where it is determined that there is an inflection point in the section, and the process ends.

On the other hand, if it is determined that the start point vector qs, the unit vector u, and the end point vector qe are not continuous in a zigzag manner, the flow shifts to step S1002, where the ratio of the start and end point vector angles θs, θe is set to an allowable value. It is determined whether or not this is the case.

In step S1002, the angle of the start / end point vector is determined by the following equation.

First, cos (θs) = (qs, u) / | qs | cos (θe) = (qe, u) / | qe |: sin (θs) = SQRT (1−cos ² (θs)) The sine of the angles θs and θe of the start and end point vectors are obtained by sin (θe) = SQRT (1−cos ² (θe)). Here, SQRT (__) is a function for obtaining a square root.

When θ is small, θsin ≒ (θ). Therefore, the ratio of the magnitudes of the angles is evaluated using these sine. That is, with respect to a predetermined threshold value th, when sin (θs) / sin (θe)> th or sin (θe) / sin (θs)> th, the start point vector qs and the end point vector qe respectively Is determined to have a large angle ratio with the vector u indicating the direction of the section.

In step S1002, the starting point vector qs
Is the set value (allowable value) of the ratio between the angle formed by the interval vector u and the angle formed by the interval vector u and the end point vector qe.
If it is determined that the value is greater than the value, the process proceeds to step S1003.
Then, it is determined that there is an inflection point in the section, and the process ends.

In other cases, the flow shifts to step S1003, where it is determined that there is no inflection point in the section, and the processing ends.

(4) Next, returning to the processing flow shown in FIG. 1, when it is determined that there is an inflection point in the section (Yes at step S105), each section P _j . Evaluate the error at P _{j + 1} (step S10
6).

As a method of calculating this error, P _{j to} P _{j + 1}
In the section of the above, the point P (t) on the spline curve represented by the above equation (5) is changed to a point B on the original curve corresponding to each point P (t) while moving the parameter t in increments of Δt. the maximum value of the distance between (t '), this is the error d _j (see FIG. 6).

The method of finding the point B (t ') on the original curve corresponding to the point P (t) on the spline curve may be as follows. The equation (5), P (t) = K 3 t 3 + K 2 t 2 + K 1 t + K 0 ( where,
Because it is 0 ≦ t ≦ 1), the tangent vector v at the point P (t) can be easily determined by dP (t) / dt = 3K 3 t 2 + 2K 2 t + K 1.

The starting point P (0) of the spline curve in this section,
If the parameters of each point B (t ') of the original curve giving the end point P (1) are ts and te, respectively, the point P (t) (where 0 ≦
As an initial point of a point on the original curve corresponding to t ≦ 1), B
(t ') (provided that t' = ts + t. (te-ts)) (see FIG. 7A).

Next, the vector r from the point P (t) to the point B (t0) is taken, and the inner product (r, v) of the vector r and the tangent vector v is obtained. Assuming that the angle formed by the vector r and the tangent vector v is θ, the sign of the inner product is examined. When (r, v)> 0, θ <90 ° When (r, v) = 0, θ = 90 ° ( r, v) <0, θ> 90 °.

Therefore, when (r, v)> 0,
When t′−dt ′ → t ′, and (r, v) <0, t ′
+ Dt ′ → t ′ is updated, the process of obtaining the point B (t ′) on the curve and the vector r again and obtaining the inner product (r, v) is repeated.

Here, dt 'is a small increment value of the parameter of the curve by the point B (t).
Decreases, and if t ′ decreases, the angle θ increases.

As shown in FIG. 7B, every time the sign of the inner product (r, v) is inverted, the minute increment value dt 'is reduced by half, so that the vector r approaches perpendicular to the tangent vector v each time the repetition processing is performed. become.

Therefore, at the time of the repetition processing at which the desired accuracy is obtained, the repetition processing is interrupted to obtain a point B (t ') on the original curve corresponding to the point P (t) on the spline curve ( FIG. 7C).

[0063] (5) Next, the error d _j calculated as described above to evaluate whether or not exceed the allowable error epsilon (step S107). If d _j ≦ ε, it is determined that the error is within the allowable error, and the process proceeds to step S109.
_{If j} > ε, it is determined that the error has exceeded the allowable error, and the flow advances to step S108.

[0064] (6) error d _{if j} has exceeded the allowable error ε are the passing point on the curve to add a point in the interval the P _j to P _{j + 1} (step S108), after the step S109
Proceed to.

As a method of determining a new passing point, if parameters giving points P _j and P _{j + 1} on the original curve B (t ′) are t _j and t _{j + 1} , respectively, the parameter t ′ is , T ′ = t _j + (t _j−1 −t _j ) / 2, and a new passing point P _{j ′} = B (t ′).

Alternatively, if the distance of the line segment is P _j P _{j ′} = P _{j ′} P
_The parameter t ′ may be obtained by a convergence operation so as to be _{j + 1} .

In the example shown in FIG. 8, the sections P _{5 to} P
_{In FIG. 6} , since the spline curve draws a locus greatly deviating from the original curve B (t ′), the error increases, and d
_{Since 5} > ε, a new passing point P _{5 ′} is added.

(7) In step S109, it is checked whether the evaluation has been completed for all the sections. If j <(n-1) (No in step S109), j + 1 → j is updated (step S110). Step S104 to Step S
Repeat 108.

(8) If the evaluation has been completed for all sections (Yes at Step S109), it is checked whether or not a new passing point has been added (Step S111). Affirmative in S111), a new passing point sequence is generated by adding the passing points (step S112).

Here, the number n of passing points increases by the number of new passing points. In the present example, new point sequences P ₁ , P ₂ ,..., P ₁₀ are generated by adding the added passing points P _{5 ′} .

In FIG. 9, P _{5 ′} is updated to P ₆ , and P ₇ ,
P ₈ , P ₉ and P ₁₀ respectively correspond to the original P ₆ , P ₇ , P ₈ and P _{9 shown} in FIG.

Thereafter, the flow returns to step S102, where the spline curve is generated again by the updated passing point sequence, and the evaluation of the error of the newly generated spline curve is repeated.

In this way, if the error between the spline curve generated from the passing point sequence and the original curve becomes sufficiently small,
When no new passing point is added and no additional passing point is added (No at Step S111),
The process ends.

As described above, when the spline curve has a large error from the original curve in a certain section, a passing point is added to the original curve in the section to reconstruct a point sequence. When a spline curve is applied to the reconstructed point sequence, a spline curve very close to the original curve is obtained.When a point sequence as a final output is spline-interpolated by a numerical controller, a desired error accuracy is obtained. A simple machining trajectory can be obtained, and this point sequence can be used for both linear interpolation and spline interpolation.

Further, a spline curve is drawn again on the reconstructed point sequence, and when it is determined that an inflection point exists in each section in each section, the error between the spline curve, the original curve line segment, and the spline curve is determined. If the value exceeds the allowable value, the point sequence is reconstructed by adding a passing point to the section until the new passing point is no longer added. When the interpolation is executed, it is guaranteed that the error between the interpolation locus and the original curve is within an allowable value, and a good machining locus is obtained.

The determination of the presence or absence of an inflection point in the section is based on the determination that three consecutive vectors of the spline curve start point vector, the section line direction vector, and the spline curve end point vector are continuous in a zigzag manner. And whether the ratio of the two angles of the start point vector and the end point vector of the spline curve with respect to the direction vector of the line segment is larger than a reference value is determined. Can be easily evaluated.

(Embodiment 2) FIG. 10 shows a configuration of a main part of an embodiment of a numerical controller according to the present invention. This numerical control device has a command input unit 1, a spline curve calculation unit 2, a spline curve correction unit 3, an interpolation calculation unit 4, and a servo drive unit 5.

The command input unit 1 receives a sequence of passing points P on a curved path.
_j (where j = 1, 2,..., n) is input, and the data of the passing point sequence P _j , the section vector u _j between the passing point sequences, and the distance c _j are sent to the spline curve calculation unit 2. Output.

The spline curve calculation unit 2 is _supplied with data of the passing point sequence P _j , the section vector u _j between the passing point sequences, and the distance c _j from the command input unit 1, and determines a spline curve for each section.

The spline curve correction unit 3 evaluates whether the error between the spline curve calculated by the spline curve calculation unit 2 and the line segment in the section is within the allowable error ε, and the error exceeds the allowable error ε. If necessary, correct the spline curve.

The interpolation operation unit 4 includes a spline curve correction unit 3
Calculates the curve interpolation for each sampling time from the spline coefficient and interpolation speed of each axis calculated in the above.

The servo drive unit 5 is constituted by each axis servo system controlled by each axis coordinate value Px (t), Py (t) and Pz (t) calculated by the interpolation operation unit 4.

In order to obtain a cubic spline curve in each section from the n number of point sequences (j = 1, 2,..., N), n of the above-mentioned equations (2), (3a) and (3b) It is necessary to solve several simultaneous equations. For this purpose, an enormous amount of calculation for obtaining an n × n inverse matrix is required. Therefore, it is generally difficult for a numerical controller requiring real-time properties to obtain a complete spline curve formula. . From this, in this example, an approximate spline curve is derived in order to secure the real-time property required in the numerical controller.

First, in order to explain the flow of data from the command input unit 1 to the spline curve calculation unit 2 and the content of the calculation in the spline curve calculation unit 2, the principle of the spline curve calculation in this embodiment will be described. Here, when Expression (2) is modified, Expression (6) is obtained.

[0085]

(Equation 3)

Here, u _j is a unit vector directed from the designated point P _j-1 to P _j , and is expressed by equation (7).

U _j = (P _j −P _j−1 ) / c _j (7) In the apparatus according to the present invention, an approximate tangent vector of each designated point satisfying the expression (6) is obtained, and it is repeated. The basic principle of calculating a spline curve is to gradually improve the accuracy by calculation.

Hereinafter, the unit tangent vector at the designated point P _{j at the} k-th repetition is represented by q _j ^[k] , and the calculation procedure is shown.

(Step 1) It is assumed that k = 0. Three designated points P
passes through the _j-1, P _j and P _{j + 1,} we obtain a spline curve, such as a unit vector in the specified point P _{j- 1} is u _j, the unit vector in the point P _{j + 1} becomes u _{j + 1.} In other words, the tangent vectors q _j at a designated point P _j from equation (6)
^[1] is calculated by the following equation (8).

[0090]

(Equation 4)

As for the start point (j = 1) and the end point (j = n), the curvature at the end point is set to 0, and the equations (4a) and (4
b) are determined by equations (9) and (10), respectively.

[0092]

(Equation 5)

(Step 2) Next, k ← k + 1 is set. 3
Pass through the two designated points P _j−1 , P _j and P _{j + 1} , the tangent vector at the designated point P _j−1 is q _j−1 ^[k] , and the designated point P
tangent vector at _{j + 1} seeks spline curve such that q _{j + 1} ^[k]. Here, Equation (11) is used based on Equation (6).

[0094]

(Equation 6)

The tangent vectors q _l ^{[k + 1]} and q _n ^{[k + 1]} are obtained from equations (9) and (10), respectively, as in the case of step 1.

(Step 3) Step 2 and subsequent steps are repeated an arbitrary number of times.

By appropriately setting the number of repetitions k according to the above process, an approximate spline curve close to a theoretical spline curve can be obtained. In practice, a practical spline curve can be obtained with about ^two repetitions (obtained up to q _j ^[2] ).

FIG. 11 conceptually shows the process of obtaining up to q _j ^[2] as j = 1, 2,..., 8 (P ₈ is the end point).

Based on the above spline curve calculation principle,
Calculation contents in the command input unit 1 and the spline curve determination unit 2 will be described. Hereinafter, j = 1, 2,..., 8 (n
= 8), and P ₈ is described as the end point.

FIG. 12 shows a schematic flow of processing in the command input unit 1.

When a spline interpolation command is input to the command input unit 1, the processing flow shown in FIG. 12 is started.

First, in step S201, the coordinate values of the _three designated points P ₁ , P ₂ , and P ₃ from the start point are input. In step S202, the distance c from the designated point P ₁ to the designated point P ₂ is input. ₂ and the distance c ₃ from the designated point P ₂ to the designated point P ₃ are obtained, and then the respective unit vectors u ₂ and u ₃ are obtained by Expression (7).

In step S203, j is initialized to j = 3. In step S204, j + 1 → j (j = 4).

Next, at step S205, the designated point P ₄
Is input, and in step S206, the designated point P ₃
Is calculated from the distance c ₄ to the designated point P ₄ and its unit vector u ₄ .

[0105] Then in step S207, the command input unit 1 designated point coordinates _{P 1, P 2, P 3} , P 4, between each designated point distance c _2, c _3, c ₄ and unit vector u _2, u ₃ , U
₄ is output to the spline curve determination unit 2. Step S2
At 07, after confirming that the data output by the spline curve determination unit 2 has been received, the next step S208
Proceed to. At this time, as described later, the spline curve determination unit 2
In determining the spline curve of designated points P ₁ to P ₂ interval.

In step S208, it is checked whether or not j = n, that is, whether or not P _j is the end point.
If ≠ n (j = 4, n = 8), the process loops to step S204, where j + 1 → j.

If j ≧ 5, the coordinate value of the designated point P _j is input in step S205, and the distance c _j from the designated point P _{j -1} to the designated point P _j and its unit vector u _j are entered in step S106. Is calculated.

In step S207, the command input unit 1 outputs the designated point coordinates P _j , the designated point distance c _j , and the unit vector u _j to the spline curve determination unit 2. In step S107, after confirming that the data output by the spline curve determination unit 2 has been received, the process proceeds to the next step. At this time, as described later, the spline curve determination unit 2 determines a spline curve in the section between the designated points P _{j-3 to} P _j-2 .

In step S208, it is checked whether or not j = n, that is, whether or not P _j is the end point.
If ≠ n, the process loops to step S204, and if j = n, the process ends.

Next, the processing of the spline curve determination unit 2 will be described with reference to FIG.

Data is input from the command input unit 1 to the spline curve determination unit 2 (step S207 in FIG. 12).
Then, the processing flow shown in FIG. 13 is started.

First, in step S301, j = 4.
If so, the designated point coordinates P₁, P_Two, P_Three, P_Four, Between each designated point
Distance c_Two, C_Three, C_Four, And the unit vector u_Two,
u_Three, U _FourEnter If j ≧ 5, the designated point
Coordinates P_j, Distance between designated points c_jAnd the unit vector u_jTo
input.

Next, in step S302, it is checked whether or not j = 4 (whether the processing includes the starting point?).
If so, in step S303, the tangent vector q ₂ ^[1] of the designated point P ₂ is obtained from equation (8) using the following equation (12).

[0114]

(Equation 7)

Further, in step S304, the tangent vector q ₁ of the start point P ₁ is obtained by the following equation (13) from the equation (9).
^{Find [1]} .

[0116]

(Equation 8)

Next, in step S305, the following equation (1) is obtained.
The tangent vector q _j-1 ^[1] of the designated point P _j-1 is obtained by 4).

[0118]

(Equation 9)

Next, in step S306, the following equation (1) is obtained.
The tangent vector q _j-2 ^[1] of the designated point P _j-2 is obtained by 5).

[0120]

(Equation 10)

Next, in step S307, j = 4.
Is checked (is processing including the starting point?), J = 4
Then, the starting point P is calculated by the following equation (16).₁Tangent vector of
Le q ^[2]Ask for.

[0122]

[Equation 11]

[0123] In the above processing, the pass point P _j-3, P tangent vector of ^{_{j-2 q j-3 [}} 2], since q ^{_{j-2 [2]}} is determined, in step S309, P _j-3 The spline curve in the section from ~ P _j-2 is determined. That is, from equation (1), K ₀ = P _j−3 (17a) K ₁ = c _j−2 q _j−3 ^[2] (17b) K ₂ = 3 (P _j−2 − P _j-3 ) -2c _j-2 q _j-3 ^[2] -c _j-2 q _j-2 ^[2] (17c) K ₃ = 3 (P _j-3 −P _j-2 ) + C _j−2 q _j−3 ^[2] + c _j−2 q _j−2 ^[2] (17d) In this case, the spline curve P (t) in the section from P _{j−3 to} P _j−2 It is given by _{P (t) = K 3 t} 3 + K 2 t 2 + K 1 t + K 0 (0 ≦ t ≦ 1) ··· (18).

[0124] In step S310, whether or not (or P _j is an end point?) Is a j = n check, if j ≠ n, but the process is terminated, the case of j = n (P _j is an end point) Performs the following end point processing.

First, in step S311, the expression (1)
0), a tangent vector q _n ^[1] at the end point P _n is obtained by the following equation (19).

[0126]

(Equation 12)

Next, in step S312, the tangent vector q _n-1 ^[2] of the designated point P _n-1 is obtained by the following equation (20) ^.
Ask for.

[0128]

(Equation 13)

Next, in step S313, P _j-3
ＰP _{j−2 in} the section from Pj to
By setting j = n + 1 in 7a) to (17d),
It is determined by equation (18).

Finally, spline curves in the last sections P _{n-1 to} P _n are obtained. In step S314, the tangent vector q _n ^[2] at the end point P _n is calculated from the equation (10) by the following equation (2).
Determined by 1).

[0131]

[Equation 14]

Next, at step S313, P _j-3
ＰP _{j−2 in} the section from Pj to
By setting j = n + 2 in 7a) to (17d),
It is determined by equation (18).

The processing shown in FIG. 12 and FIG.
As is clear from the flow, the command input unit 1
4 points including P₁, P_Two, P_Three, P_FourWhen you enter
The first curve P₁~ P_TwoSupra
An in-curve is determined (A in FIG. 14). Then a new finger
Fixed point P_jEach time (j> 4) is input, the interval P_j-3~ P
_j-2Is determined (B in FIG. 14). Soshi
And the end point P_nAt the stage of inputting three sections P_n-3~ P
_n-2, P_n-2~ P_n-1, P_n-1~ P_nSupra corresponding to
The in-curve is determined (C in FIG. 14 (example of n = 8)).

As described above, assuming that the tangent vector of the passing point is approximately calculated and the number of repetitions of the calculation is k, the passing point after the k-th point is read without reading all the passing points up to the end point. Then, a tangent vector is obtained by a simple calculation, and a spline curve between the tangent vector and the passing point is sequentially generated, so that a spline curve can be generated in real time.

The spline curve calculation section 2 outputs the calculation result to the spline curve correction section 3 every time the spline curve of each section is determined. FIG. 15 is a processing flowchart of the spline curve correction unit 3. Hereinafter, the contents of the processing will be described with reference to this flowchart.

In step S401, the spline curve correction unit 3 first determines various data for determining a spline curve from the spline curve calculation unit, that is, the spline curve equation P (t) and the two ends used to derive the respective coefficients. The position vectors Ps and Pe at the point and the unit tangent vector q
s, qe and the length c of the line segment Ps-Pe are input.
(See FIG. 16).

Next, in step S402, the error in each section of the spline is evaluated. As an error calculation method, for example, a curve P (t) expressed by the equation (5) in the section from Ps to Pe is moved to each point P (t) and a line segment Ps to Pe while moving the parameter t in steps of Δt. Is determined as the error dmax.

Next, in step S403, it is evaluated whether the obtained error dmax does not exceed the allowable error ε. If dmax ≦ ε, it is determined that the error is within the allowable error.
05, if dmax> ε, it is determined that the error has exceeded the allowable error and the process proceeds to step S404.

If the error exceeds the allowable error, in step S404, the spline curve equation is corrected in the following manner.

Although the spline curve equation is determined by the position vector and the tangent vector at both end points, the tangent vector represents the momentum (speed) of the curve at both end points. In general, the smaller the magnitude of the tangent vector is, the closer the curve becomes to the line segment. Note that, depending on the shape of the curve, the smaller the tangent vector over the entire range of the parameter t (0 ≦ t ≦ 1), the smaller the tangent vector may not be. .

Here, the tangent vectors to the parameter t at both end points are cqs and cqe, and c represents the magnitude of the tangent vector.

In step S404, the size of the tangent vector is reduced by updating c to a smaller value, and the shape of the spline curve is corrected to a shape closer to a line segment. Specifically, for the calculated maximum error dmax and allowable error ε, c is updated by c · ε / dmax → c, and the spline curve equation (5) is recalculated from equations (4a) to (4b). .

In FIG. 16, the updated c and the curve equation P (t) are represented by c ′ and P ′ (t), respectively, to show the difference from the curve before the update.

Next, the maximum error between the corrected spline curve P (t) and the line segments Ps to Pe is obtained by looping back to step S403, and the same processing is repeated thereafter.

If it is determined in step S403 that the maximum error is within the allowable error, the flow shifts to step S405, in which the spline curve equation at that time is output to the interpolation calculation unit 4, and the processing is terminated. The spline curve equation output here is such that, at both end points, the sections on both sides thereof and the first derivative are continuous, and the maximum error of the curve and the line segment is within the allowable error.

With respect to the spline curve determined in this way, the interpolation calculating section 4 displays the spline curve on the curve at every interpolation cycle ΔT.
A point (interpolation point) whose length from the current point is the specified interpolation length (= target interpolation length) according to the speed command value F
And outputs the coordinate value to the servo drive unit 5.

As described above, when the generated spline curve has an error exceeding the allowable value with the line segment of the section, the magnitude of the tangent vector of the spline curve at both end points of the section is reduced. Since the spline curve is corrected so that the error with the line segment is within the allowable value, the smooth spline in which the error with the line segment is within the allowable value in each section and the direction of the tangent vector is continuous at the joint of each section An interpolation trajectory is obtained.

In the spline curve correction processing by the spline curve correction unit 3, as shown in FIG. 17, the spline curve equation can be corrected in the following manner. In FIG. 17, steps having the same contents as those in FIG. 15 are denoted by the same step numbers, and description thereof is omitted.

If the maximum error dmax exceeds the allowable error ε (No at Step S403), at Step S404 ′, the spline curve equation is modified in the following manner.

First, the unit vector u of the line segments Ps to Pe is determined, and the angle θs formed by the unit vector u and the starting point vector qs is determined by the following equation.

Cos (θs) = (qs, u) / | qs |

Again, using this angle θs, the vector qs can be decomposed into the vectors qsh and qsv shown in FIG. Here, qsh is a line segment Ps to Ps of vector qs.
The component parallel to e, qsv is the line segment Ps to Pe of the vector qs.
Qsh = | qs | · cos (θs) · u = (qs, u) ·
u qsv = qs-qsh.

Next, assuming that g is a constant and qs' = qsh + gqsv (where 0 <g <1) as shown in FIG. It will be. As a method of determining the constant g, g = ε / dmax may be set using the maximum error dmax and the allowable error ε obtained in step S502.

Next, by the same method, the vector qe
Is calculated in the direction of the line segment Ps-Pe, qs, qe are updated to qs '→ qs, qe' → qe, and the spline curve equation (5) is obtained from the equations (4a)-(4b). Ask again.

[0155] Since the spline curve corrected in this manner corrects the inclination of the tangent line at both end points so as to approach the line segments Ps to Pe, the resulting curve is smaller than the previous curve by the line segment Ps to Ps. The maximum error with respect to Pe is small. FIG. 18 shows the updated tangent vectors qs, qe, and curve equation P (t) as qs', qe ', and curve equation P' (t), respectively.
And how the curve changes before and after updating.

As described above, in this embodiment, if the generated spline curve has an error exceeding the allowable value with the line segment of the section, the slope of the tangent vector of the spline curve at both end points of the section is expressed by a line. Since the spline curve is corrected so that the error with the line segment is within the allowable value by approaching the vector direction of the minute, a spline interpolation trajectory in which the error with the line segment is within the allowable value is obtained in each section.

[0157]

As is apparent from the above description, according to the method for dividing a free curve into minute lines according to the present invention, a sequence of points is generated by dividing a free curve into minute lines such that a chord error is within an allowable value. After that, a spline curve is drawn so as to pass through this point sequence, and it is determined that there is an inflection point in the section in each section.If the error between the spline curve and the original curve exceeds an allowable value, Since the point sequence was reconstructed by adding a passing point to that section,
In the initial point sequence, if the spline curve has a large error from the original curve in a certain section depending on the original curve shape, the passing point on the original curve is added to that section and the point sequence is reconstructed When a spline curve is applied to the reconstructed point sequence as a result, a spline curve very close to the original curve is obtained.When a point sequence as a final output is spline-interpolated by a numerical controller, a desired error accuracy is obtained. There is an effect that a good machining locus can be obtained. Further, there is an effect that this point sequence can be used for both linear interpolation and spline interpolation.

According to the method for differentiating a curved line into small lines according to the next invention, a spline curve is formed again on a reconstructed point sequence, and when it is determined that there is an inflection point in each section in each section, the spline curve and the When the error between the original curve line segment and the spline curve exceeds the allowable value, the point sequence is reconstructed by adding a passing point to that section until no new passing point is added. If you perform spline interpolation on the resulting point sequence,
It is ensured that the error between the interpolation trajectory and the original curve is within an allowable value, and there is an effect that a good machining trajectory can be obtained.

According to the curve minute line differentiation method according to the next invention, it is determined whether or not the section has an inflection point of the curve in the section.
Whether the start point vector of the spline curve of the section, the direction vector of the line segment of the section, the end point vector of the spline curve are continuous in a zigzag manner, and two angles of the start point vector and the end point vector of the spline curve with respect to the direction vector of the line segment Is evaluated by determining whether or not the ratio is larger than the reference value. Therefore, there is an effect that this evaluation can be easily and reliably performed.

According to the numerical control apparatus having a spline interpolation function according to the next invention, the spline curve determining means determines the spline curve in each section connecting the passing points smoothly, and the spline curve correcting means determines the spline curve in each section. It is determined whether or not the error between the determined spline curve and the line segment in the section exceeds an allowable value, and if the error exceeds the allowable value, the spline curve in the section is corrected so as to approach the line segment. Therefore, there is an effect that a spline curve that guarantees an allowable error can be generated in real time.

According to the numerical controller having a spline interpolation function according to the next invention, the spline curve correcting means determines the tangent vector of the spline curve at both end points of the section and the error between the spline curve and the line segment of the section. Since the spline curve is corrected by reducing the magnitude of the tangent vector of the spline curve at both ends of the section so as to be within the allowable value, the error from the line segment in each section is within the allowable value. There is an effect that a smooth spline interpolation trajectory in which the direction of the tangent vector is continuous at the joint of the sections is obtained.

According to the numerical controller having the spline interpolation function according to the next invention, the spline curve correcting means converts the tangent vector of the spline curve at both ends of the section into an inflection between the spline curve and the line segment in the section. By setting the point so that the error is within the allowable value, the direction of the tangent vector of the spline curve at both ends of the section is closer to the direction of the vector parallel to the line segment, so that the error with the line segment is within the allowable value. Since the correction of the spline curve is performed, there is an effect that in each section, a spline interpolation trajectory having an error from a line segment within an allowable value can be obtained.

[Brief description of the drawings]

FIG. 1 is a process flow chart showing the procedure of implementing a method for differentiating a curve into minute lines according to the present invention.

FIG. 2 is an explanatory diagram showing a spline curve represented by two points and a tangent vector thereof.

3 (a) to 3 (c) are starting points depending on the presence or absence of an inflection point,
FIG. 9 is an explanatory diagram showing characteristics of an end point vector.

FIG. 4 is a processing flowchart of an inflection point presence / absence determination routine.

FIG. 5 is an explanatory diagram showing an example of correcting a tangent vector.

FIG. 6 is an explanatory diagram showing a method for obtaining a maximum error between a spline curve and an original curve.

FIGS. 7A to 7C are explanatory diagrams showing how to find an original curved point corresponding to one point on a spline curve.

FIG. 8 is an explanatory diagram showing that a passing point is added to an original curve.

FIG. 9 is a diagram showing a reconstructed curved passage point sequence;

FIG. 10 is a block diagram showing a main configuration of a numerical control device according to the present invention.

FIG. 11 is a conceptual diagram showing a calculation procedure when a tangent vector of each passing point is obtained by repeated vector calculation.

FIG. 12 is a schematic flowchart of processing of a command input unit.

FIG. 13 is a schematic flowchart of a spline curve calculation process by a spline curve calculation unit.

FIG. 14 is a conceptual diagram showing that a spline curve of each section is sequentially obtained.

FIG. 15 is a schematic flowchart of a spline curve correction process by a spline curve correction unit.

FIG. 16 is an explanatory diagram showing a change in a curve shape due to correction of the magnitude of a tangent vector.

FIG. 17 is a schematic flowchart of another spline curve correction process by a spline curve correction unit.

FIG. 18 is an explanatory diagram illustrating a change in a curve shape due to correction of the inclination of a tangent vector.

FIG. 19 is an explanatory view showing a method of minutely segmenting a curve with a constant chord error.

FIG. 20 is an explanatory diagram showing a case where a large error occurs with respect to an original curve when spline interpolation is performed on a sequence of points generated by conventional fine line differentiation.

[Explanation of symbols]

1 command input section, 2 spline curve calculation section, 3 spline curve correction section, 4 interpolation calculation section, 5 servo drive section, passing point sequence on P _j curve path, section vector between u _j passing point sequence, c _j passing the distance between the point sequence, q _j units tangent vector.

Claims (6)

[Claims] In generating point sequence data obtained by subdividing a free curve serving as input data of a numerical controller into minute lines,
A point sequence is generated by performing a polygonal line approximation so that the chord error is within an allowable value, a cubic spline curve passing through the point sequence is generated, and a section between each passing point is an inflection of the curve within the section. It evaluates whether or not the section has an inflection point, and evaluates whether or not the error between the original curve and the generated cubic spline curve is within an allowable value. If the value exceeds the value, a passing point is added in the section to reconstruct the point sequence, and the method for differentiating a minute line into a curve is provided. 2. When a passing point is added, a cubic spline curve passing through the reconstructed point sequence is generated again from the reconstructed point sequence, and a section between each passing point is transformed into a curve within the section. Evaluate whether or not there is a curve point, and evaluate whether the error between the original curve and the generated cubic spline curve is within the allowable value for the section determined to have the inflection point, 2. The method according to claim 1, wherein when the value exceeds the value, a process of adding a passing point in the section and reconstructing the point sequence is repeated until no new passing point is added. Line differentiation method. 3. An evaluation as to whether or not the section has an inflection point of a curve in the section is performed by:
Whether the direction vector of the line segment of the section and the end point vector of the spline curve are continuous in a zigzag manner, and whether the ratio of the two angles of the start point vector and the end point vector of the spline curve to the line segment direction vector is larger than a reference value The method according to claim 1, wherein the method is performed by determining whether or not the curve is a fine line. 4. A spline curve determining means for determining a spline curve in each section that smoothly connects between the passing points, for a series of passing points discretely taken on the curve processing trajectory, and determining in each section. It is determined whether or not the error between the set spline curve and the line segment of the section exceeds an allowable value, and if the error exceeds the allowable value, the spline curve in the section is corrected so as to approach the line segment. A numerical controller having a spline interpolation function, comprising: a spline curve correcting unit. 5. A method for correcting a spline curve by the spline curve correcting means, wherein a tangent vector of the spline curve at both end points of the section is set so that an error between the spline curve and a line segment of the section is within an allowable value. 5. The numerical control device having a spline interpolation function according to claim 4, wherein the control is performed by reducing the magnitude of a tangent vector of a spline curve at both end points of the numerical value. 6. The spline curve is corrected by the spline curve correcting means by changing a tangent vector of the spline curve at both end points of the section to an inflection point between the spline curve and the line segment of the section within an allowable value. 5. The numerical control device having a spline interpolation function according to claim 4, wherein the control is performed by bringing a direction of a tangent vector of a spline curve at both end points of the section closer to a direction of a vector parallel to the line segment.