JPH0682289B2 - Curve interpolation method in numerical controller - Google Patents

Description

Description: TECHNICAL FIELD OF THE INVENTION The present invention relates to a curve interpolation method in a numerical control (NC) device, and particularly has a three-dimensional free-form surface shape (hereinafter, simply referred to as “three-dimensional curved surface shape”). The present invention relates to a curve interpolation method of digitized data on a curved surface of a model.

(Technical background of the invention and its problems) Conventionally, when machining using an NC device, after measuring the model shape with a digitizer, the "contour control" method is used based on the measured point group data. NC processing data is created. In this "contour control" method, NC machining can be performed along the command line by simply giving the measurement point data, that is, the tool can be moved along the line segment or arc that is inclined between the measurement points. Thus, functions such as "linear interpolation" or "circular interpolation" are used.

However, when NC machining a general model with a three-dimensional curved surface shape, the above-mentioned "linear interpolation" function has been used conventionally.
Since NC processing data is created, NC processing is performed along the line segment that interpolates between the above measurement points, and the processed surface becomes multiple planes divided by multiple line segments, resulting in model shape. However, there is a problem that a smooth curved surface cannot be processed.

FIGS. 4 (A) and 4 (B) are views showing an example of the above-mentioned "linear interpolation" function which is conventionally used when NC machining a model having a general three-dimensional curved surface shape as described above. , (A) shows an example in which the intervals between the measurement points are wide, that is, the digitization data is small and the measurement is rough, and (B) in the figure shows the intervals between the measurement points are fine, that is, the digitization data is large. An example when the measurement is fine is shown.

As shown in FIG. 4 (A), one section of the original model shape
When creating NC machining data based on the measurement points D1, D2, D3, D4, D5, ... Obtained by the digitizer for MO (dotted line in the figure), the measurement points D1, D2, D3, D4, D5, ... are interpolated by inclined line segments (solid line portion in the figure), so if NC machining is performed based on the NC machining data, so-called "bite" W1, W2, W3 and "Uncut" W4 will be generated greatly. Therefore, it is necessary to preliminarily set a limit value in a portion where the above "bite" W1, W2, W3 is likely to occur, and to prevent the "bite" from occurring by not processing more than a predetermined amount. In addition to the problem of processing accuracy, there is a problem that the number of man-hours for finishing the relevant part increases.

Therefore, as shown in FIG. 4 (B), one cross section MO of the model shape is finely divided and measured, and the measurement points D11 to D
By interpolating line segments inclined between 25, ..., the machining accuracy is greatly improved and it becomes possible to machine a curved surface that approximates the model shape. In this case, the measurement point, that is, digitized data, increases and There is a problem in that it takes a lot of time and labor for the processing because it needs to be measured each time.

(Object of the Invention) The present invention has been made under the circumstances described above, and an object of the present invention is to provide a model having a general three-dimensional curved surface shape.
When NC machining is performed, it is possible to reproduce a smooth curved surface that approximates the model shape based on the measured point cloud data, without having to divide the measurement into small pieces with a digitizer.
The present invention relates to a curve interpolation method in NC equipment.

(Summary of the Invention) The present invention relates to a curve interpolation method in an NC device, after measuring a model having a three-dimensional free-form surface shape using a digitizer, successively extracting four consecutive points from the measurement points, Of the four measurement points, a first free curve passing through the first, second and third measurement points and a second free curve passing through the second, third and fourth measurement points are generated. Then, the first free-form curve and the second free-form curve are mixed between the second and third measurement points, and the second and the second free-form curves are set according to preset division accuracy between the measurement points. The X, Y, and Z interpolation data are calculated and created between the third measurement points.

(Embodiment of the Invention) In the curve interpolation method of the present invention, a discrete measurement point group measured by a digitizer is approximated to a smooth curve by using a mixture of free curves such as a quadratic Bezier curve. The measurement point group is subjected to curve interpolation so that it can be performed. That is, the above-mentioned curve interpolation is realized by calculating and obtaining data for each division point divided with a predetermined division accuracy in the blending curve of the quadratic Bezier curve obtained by interpolating the measurement point group.

FIG. 1 is a block configuration diagram showing an outline of an NC device that realizes the method of the present invention. Reference numeral 1 is an input device composed of a keyboard or the like for inputting various data and commands, and 2 is an interpolation device.
In order to obtain the division data between the measurement points, the curve interpolation condition setting unit that defines the division accuracy for obtaining each division point obtained by dividing the two measurement points by a predetermined number of divisions, 3 is the curve interpolation condition It is a curve interpolation setting data memory that stores the division accuracy and the like set by the setting unit 2. Here, the division accuracy and the like set by the curve interpolation condition setting unit 2 are also displayed on the CRT display screen 9 so as to be visually confirmed. On the other hand, 4 is an NC data memory that stores various measurement data (digitizing data, etc.) of a model measured by a digitizer (not shown),
Reference numeral 5 is a curve interpolation point sequence data memory for extracting and storing only the measurement point sequence data from the measurement data stored in the NC data memory 4, and 6 is stored in the curve interpolation point sequence data memory 5. From the stored measurement point sequence data,
Four consecutive measurement points are extracted, and three adjacent points (first, second and third points, and second, third and fourth points among the four measurement points are extracted.
Is a free curve generation unit that generates two free curves. And, as will be described later, 7 is an intermediate point between four consecutive points (first, second, third and fourth points) where the two free curves generated by the free curve generating section 6 exist. At two points (second and third points), the two free curves are mixed according to the division accuracy stored in the curve interpolation setting data memory 3 to calculate X, Y, Z interpolation data. A curve interpolation calculation processing unit, 8 is the curve interpolation calculation processing unit 7
In the X, Y, Z function generator that generates the X, Y, Z axis control command values, taking into account the X, Y, Z interpolation data calculated in step 1 and the origin offset value, tool offset value, etc. is there. Further, 10 is an X that drives the X, Y, Z control axes 11 according to the X, Y, Z axis control command values generated by the X, Y, Z function generating section 8 to execute predetermined NC machining. , Y, Z control axis drive unit.

A method of calculating the X, Y, Z interpolation data in the curve interpolation calculation processing section 7 in the NC device having the above-described configuration will be described below.

FIG. 3 (A) shows four consecutive points P _i , P _{i + 1 of} the measurement point group {P _i } (i = 1, N) measured by the digitizer.
It is a figure which shows an example of P _{i + 2} , P _{i + 3.} First, the four points P _i ,
Of P _{i + 1} , P _{i + 2} , P _{i + 3} , the first three points P _i , P _{i + 1} , P
_{The first} quadratic Bezier obtained by approximating _{i + 2} and the last three points P _{i + 1} , P _{i + 2} , and P _{i + 3} to the quadratic Bezier curve indicated by the dotted lines in the figure, respectively.
A curve R _i (u) and a second quadratic Bezier curve P _{i + 1} (v) are obtained.

Here, the first quadratic Bezier curve R _i (u) is R _i (0) = P _i , R _i (0.5) = P _{i + 1} , R _i (1) = P _{i + 2} , The second quadratic Bezier curve R _{i + 1} (v) is R _{i + 1} (0) = P _{i + 1} , R _{i + 1} (0.5) = P _{i + 2} , R _{i + 1} (1) = Let P _{i + 3} .

Such first quadratic Bezier curve R _i (u) and second quadratic
When the Bezier curve R _{i + 1} (v) is mixed, a mixed curve C (t) represented by the following equation is obtained between the points P _{i + 1} and P _{i + 2} where the two curves overlap. It can be obtained (solid line in the figure).

C (t) = (1- t) · R 1 (u) + t · R i + 1 (v) ......
(1) Here, t is a divided numerical value between 0 and 1 according to the number of divisions according to the division accuracy, and the mixed curve C (t) is C (0) = R _i (0.5) = R _{i + 1} (0) = P _{i + 1} C (1) = R _i (1) = R _{i + 1} (0.5) = P _{i + 2} . Therefore, assuming that t, u, and v are linear, the following equation holds.

On the other hand, the first quadratic Bezier curve R _i (u) and the second
Since the quadratic Bezier curve R _{i + 1} (v) of is a quadratic Bezier curve, it can be expressed by the following equation using the control point ▲ Q ⁱ _j ▼.

R _i (u) = (1-u) ²・ ▲ Q ⁱ ₀ ▼ + 2 (1-u) ・ u ・ ▲ Q
ⁱ ₁ ▼ + u ²・ ▲ Q ¹ ₂ ▼ R _{i + 1} (v) = (1-v) ²・ ▲ Q ^{i + 1} ₀ ▼ + 2 (1-v) ・ v ・
▲ Q ^{i + 1} ₁ ▼ + v ²・ ▲ Q ^{i + 1} ₂ ▼ (3) Therefore, the above-mentioned mixed curve C (t) is a control point ▲ from the above equations (1), (2) and (3). It can be expressed as follows using Q ⁱ _j ▼.

On the other hand, in the equation (3), the first quadratic Bezier curve R _i (u) is And the second quadratic Bezier curve R _{i + 1} (v) is Becomes Therefore, as shown in FIG. 3B, the relationship between the four measurement points P _i , P _{i + 1} , P _{i + 2} , P _{i + 3} and the control point ▲ Q ⁱ _j ▼ is as follows. Is asked.

Therefore, from the expressions (4) and (5), the mixed curve C (t) can be expressed as the following expression.

Here, the blended curve C (t) has a continuous first derivative at its internal point. Therefore, the following equation is obtained from the above equations (1) and (2).

Here, since v = 0 and u = 0.5 at t = 0, R
_{i + 1} (0) = R _i (0.5) = P _{i + 1} , and at t = 1 v =
Since 0.5, u = 1, R _{i + 1} (0.5) = R _i (1) = P _{i + 2} . Therefore, Therefore, the point P among the above four measurement points P _i , P _{i + 1} , P _{i + 2} , P _{i + 3}
The curve interpolation can be continuously performed up to the first derivative between _{i + 1} and P _{i + 2} . Then, such curve interpolation is performed on the following four measurement points P _{i + 1} , P _{i + 2} , P _{i + 3} , and P _{i + 4} by curve interpolation of the points P _{i + 2} and P _{i + 3.} By repeating the above operation, the curve interpolation is completed for all the measurement points.

The above curve interpolation operation will be described in detail below with reference to the flowchart of FIG.

First, when the accuracy (the number of divisions, etc.) of the curve interpolation to be obtained by operating the input device 1 is input, the curve interpolation condition setting unit 2
The division accuracy set in step 3 is stored in the curve interpolation setting data memory 3 (step S1). On the other hand, among the measurement point group data stored in the NC data memory 4, four consecutive points to be interpolated first as shown in FIG. 3 (A).
The point sequence data of P _i , P _{i + 1} , P _{i + 2} , P _{i + 3} are extracted and stored in the curve interpolation point sequence data memory 5 (step S2). Therefore, in the free curve generation unit 6, as described above,
Using the following Bezier curve, the above four points P _i , P _{i + 1} , P _{i + 2} , P _{i + 3}
Of the first three free-form curves passing through the first three points P _i , P _{i + 1} , P _{i + 2} and the _second three free-passing points through the last three points P _{i + 1} , P _{i + 2} , P _{i + 3} And a free curve (step S3), and the curve interpolation calculation processing unit 7
In the above, using the mixture of the quadratic Bezier curves as described above, the two free-form curves passing through the intermediate two points P _{i + 1} and P _{i + 2} among the above four points are mixed, and the above curve interpolation is performed. Between the two points P _{i + 1} and P _{i + 2} according to the division accuracy set in the data memory 3.
X, Y, Z interpolation data is calculated (step S4). And
The X, Y, Z function generator 8 calculates the X, Y, Z axis control command values by adding the origin offset value, the tool offset value, etc. to the X, Y, Z interpolation data (step S5), The X, Y, Z control axes 11 are driven via the X, Y, Z control axis drive section 10 (step S6). Then, if there are remaining measurement points to be interpolated (step S7), the process returns to step S2 and the next four consecutive measurement points (in this case, points P _{i + 1} , P _{i + 2} , P _{i + 3} , _{Pi + 4} )
Is extracted, interpolation processing is performed, and the above steps S2 to S7 are repeated, whereby all the measurement points measured by the digitizer are curvedly interpolated and the processing is completed.

FIG. 5 is a diagram showing an example of a locus in which all measurement points DD1 to DD10 (examples of coordinate values thereof) measured by the digitizer in this way are curve-interpolated, and as described above. , First free curve B obtained from measurement points DD1, DD2, DD3
1 (= A0) and the second free curve B2 (C1) obtained from the measurement points DD2, DD3, DD4 are mixed to generate a locus B0 shown by a solid line between the measurement points DD2, DD3. Next, the second free curve C1 (= B2) and the third free curve C2 obtained from the measurement points DD3, DD4, DD5 are mixed, and the locus C0 shown by a solid line between the measurement points DD3, DD4 is shown. To generate. Then, by repeating these operations for all the measurement points in the same manner, it is possible to perform curve interpolation between all the measurement points with a locus shown by a solid line in the figure as shown in FIG. .

(Effect of the Invention) As described above, according to the method of the present invention, when NC machining of a model having a general three-dimensional curved surface shape, four consecutive points are sequentially extracted from the measurement point group data measured by the digitizer. Then, by calculating and interpolating each curve, it is possible to reproduce a smooth curved surface that approximates the model shape by NC processing in a short time with simple operations as before without finely dividing and measuring with a digitizer. Become.

[Brief description of drawings]

FIG. 1 is a block configuration diagram showing an outline of an embodiment of an NC device for realizing the method of the present invention, FIG. 2 is a flow chart for explaining an operation example of the method of the present invention, and FIGS. 3 (A) and 3 (B). )
5 and 5 are diagrams for explaining the method of the present invention, and FIGS. 4 (A) and 4 (B) are diagrams for explaining an example of a conventional interpolation method. 1 ... Input device, 2 ... Curve interpolation condition setting unit, 3 ... Curve interpolation setting data memory, 4 ... NC data memory, 5 ... Curve interpolation point sequence data memory, 6 ... Free curve generation unit, 7 ... Curve interpolation calculation processing unit , 8 ... X, Y, Z function generator, 9 ... CRT, 10 ... X, Y,
Z control axis drive, 11 ... X, Y, Z control axes.

Claims (1)

[Claims] 1. A model having a three-dimensional free-form surface is measured by using a digitizer, and then four consecutive points of the measurement points are sequentially extracted, and the first and second points of the four measurement points are extracted.
And a third free-form curve passing through the third measurement point and a second free-form curve passing through the second, third and fourth measurement points to generate the second and third measurement points. The first free-form curve and the second free-form curve are mixed between points, and X, Y between the second and third measurement points is set according to the preset division accuracy between the measurement points. , Z is used to calculate and create interpolation data, and a curve interpolation method in a numerical controller is provided.