JP2638851B2 - Numerical control processing method - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a numerical control processing method, and more particularly to a method suitable for processing a contour of a workpiece along a three-dimensional curve passing through a given point group. The present invention relates to a numerical control processing method.

[Summary of the Invention]

A vector passing through the center passing point is determined in parallel with the straight line between the three end points of the given four passing points, and one of the control points is provided on the vector.
Control points are similarly defined for two passing points, and a cubic Bezier curve passing through four points is generated by two passing points and two control points, thereby enabling high-speed generation of machining information. This is a numerical processing method that facilitates local change of a passing point and improves design efficiency.

[Prior art] CAD that handles data of three-dimensional free-form surfaces inside a computer and generates NC data (tool path data) for automatically processing the final product or die with an NC machine tool from these data / CAM system is being put to practical use.

When dealing with a curved surface such as a product outer shape in a computer, the Bezier equation or B-spline (Bezier) which has favorable properties for design such as good controllability of the shape (easy to deform and correct) and easy calculation. Spline) is often used in parametric expressions. The three-dimensional model is represented as a set of pixels (patches) composed of line elements that can be calculated by these equations.

A line element is generally defined as a three-dimensional free curve composed of a Bezier curve generated by specifying a passing point. Conventionally, such a Bezier curve is represented by a B-point passing through a given point group.
A spline curve was first generated, and the control points of the Bezier curve were determined from the control points.

[Problems to be solved by the invention]

In a CAD system, performing local control of a model
It is extremely important in creating an interactive interface.
For example, when designing the cross-sectional shape of a workpiece as shown in FIG. 5, point groups P ₁ , P _2, ... Are given, and a Bezier curve passing through all of these point groups is generated. However, as a result of the primary calculation, the processing contour line may be dented as shown in the X part of the figure. Also, the vertical and horizontal dimensions, A and B, may deviate from the given design values. In such a case,
Re-set some of the point clouds and recalculate the outline to get the desired contour.

However, the above-described method of generating a Bezier curve via a B-spline curve requires a very large amount of calculation to locally change the curve, and has a drawback that it is substantially difficult to partially correct the curve.

In FIG. 6, when passing points P ₀ , P ₁ ... P ₆ (three-dimensional position vectors, respectively) are given, B passing through each point
The spline curve is defined by linear simultaneous equations by control points Q ₀ , Q ₁ ... Q ₆ (each a three-dimensional position vector).

Q ₀ + 4Q ₁ + Q ₂ = 6P ₁ Q ₁ + 4Q ₂ + Q ₃ = 6P ₂ Q ₂ + 4Q ₃ + Q ₄ = 6P ₃ Q ₃ + 4Q ₄ + Q ₅ = 6P ₄ Q ₄ + 4Q ₅ + Q ₆ = 6P ₅ Controlled by these equations point vector Q ₁ to Q ₅ sought (shown by white circles), then signed between control points by a straight line, calculates three divided and control points of the Bezier curve (indicated by black dots).

Therefore, when the passing point is locally changed as in P ₁ ′, Q _{1 to} Q ₅
Must be recalculated.

In addition, in order to generate a Bezier curve, the control point of the B-spline curve must be obtained in the middle, which is inefficient. Although the B-spline curve has a feature of curvature continuity, in the case of three-dimensional modeling, a condition of continuation of a tangent plane is given, so that there is little practical value in generating a B-spline curve.

In view of this problem, an object of the present invention is to provide a method for generating numerically processed data in which a Bezier curve passing through a given point group can be directly generated, and therefore, the local change of the contour of the workpiece is extremely easy. And

[Means for solving the problem]

First, a group of passing points is given to determine a machining curve to be numerically controlled.

First, four consecutive points P _{1 to} P ₄ are taken out and three points P ₁
Respect to P _3, added a vector of a fraction of the length in parallel and the same direction from the point P ₁ and towards line P ₃ is the line segment P ₂ P ₃ to the point P _2, the control point Q ₂ and the end point '.

Further relates to 3-point P ₂ to P ₄ of the next successive, point P ₂ from the length in parallel and opposite directions and toward line P ₄ line segment P ₂ P fraction of point vectors P ₃ of ₃ And its end point is set as a control point Q ₂ ″.

₃ with the above P ₂ and P ₃ as ends and Q ₂ ′ and Q ₂ ″ as control points
Generate a next-order Bezier curve.

Numerical control processing data is obtained in which the generated curve is used as the contour of the workpiece.

[Action]

The point Q ₂ ′ is determined by the information of the three points P _{1 to} P ₃ , and the point Q ₂ ″ is 3
Determined by the information of the point P ₂ ~P _4. Therefore Bezier curve based on consecutive four information P ₁ to P ₄ were passing through the points are generated directly.

〔Example〕

FIG. 1 shows a method of generating an embodiment of a Bezier curve passing through a given point group, and FIG. 2 shows a flowchart. This method is applied when the passing points are given in a zigzag manner.

In Figure 1, a given pass point is P ₁ to P _5,
Each is given by data of a three-dimensional position vector. First relates three points P ₁ to P ₃ consecutive in step S1, P ₃ from the point P ₁
Distance length in parallel and the same direction as the straight line P ₁ P ₃ is between the P ₂ P ₃ towards the
seeking a vector a ₁ 1/3 of l _1, to the end and q ₂ 'by adding a ₁ to the point P _2. Similarly, in step S2, the next consecutive 3
Relates point _{P 2, P 3, P 4} , obtains a vector b ₁ length in parallel and opposite direction to the straight line P ₂ P ₄ towards the point P ₂ to P ₄ is l _1/3, the point a b ₁ P ₃
In addition, the terminator is represented by Q ₂ ″. The divisor of l ₁ may be appropriately determined, and is preferably 3 to 5.

In step S3, and the end point _{P 2, P 3, Q 2} ', to obtain a cubic Bezier curve C ₂ for the control point Q ₂ ".

When the number of given passing points is n, in the description of FIG. 2, subscripts 1, 2, and 3 are set to _m-1 , _m , and _{m + 1,} and _m = ₂ to
_By repeatedly performing _{n + 2} , continuous Bezier curves C _{2 to} C _n−2 passing through each passing point are obtained.

Note that although the processing of the end point P _1, as shown in the flowchart of FIG. 3, in step S1, the point P _1, P _2, P _3, through the intermediate point P _2, the point of two neighboring P _1, P ₃ String vector P ₁
And a ₂ parallel to vector and P _3. Next, in step S2, P ₂
Taking an outer product of P _1, chord P ₃ vector P ₂ P ₁ and P ₂ P ₃ as viewed from a vector b ₂ in. This vector is a normal vector of the plane π ₁ passing through the three points P ₁ , P ₂ , and P ₃ .

Then take the cross product of the vectors a ₂ and b ₂ in the step S3, a vector n ₂ is normalized. Then through the P ₂ in step S4,
A plane having n ₂ as a normal vector is defined as π ₂ . This plane π
_2, through the P _2, is parallel to the chord P ₁ P _3, wherein the P _1, P _2,
It is orthogonal to the plane [pi ₁ through P _3. Next, an arbitrary tangent vector V ₁ is given to P _{1 at the start end} , and the intersection of the extension line of V ₁ and the plane π ₂ is defined as Q ₁ . Then the P _1, Q _1, P ₂ generates a quadratic Bezier curve and the control points at Step S6, 3 it in step S7
Next, conversion is performed to obtain control points Q ₁ ′, Q ₁ ″ of the Bezier curve C ₁ .

Similarly, a tangent vector V ₂ is given at the terminal end Pn, and the intersection of the extension line and the plane π _n-2 (π _{4 in} the example of FIG. 1) is set as a control point, whereby the Bezier curve C _{n at the} terminal end is obtained. _-1 can be obtained.

The shape of the Bezier curve does not change even if the Bezier curve is converted into a third order by an arithmetic operation. The proof is as follows.

As shown in FIG. 4, P ₀ given in a three-dimensional space,
A Bezier curve represented by three control point vectors consisting of P ₂ (end point) and P ₁ is represented by R (t) = (1−t + te) ² P ₀ (1). t is a parameter that takes a value between 0 and 1 between both end points. E is a shift operator indicating each control point, where P ₁ = EP ₀ and P ₂ = E ² P ₀ .

Similarly cubic Bezier curve, R (t) = (1 -t + E) 3 P 0 = (1-t) 3 P 0 +3 (1-t) 2 EP 0 +3 (1-t) t 2 E 2 P ₀ + t ³ E ³ P ₀ ... (2) In FIG. 4, P ₀ , EP ₀ , E ² P ₀ , and E ³ P _{0 respectively} correspond to the four control points P ₀ , Q ₁ , Q ₂ , and P ₂ of the cubic Bezier curve (EP ₀ = Q ^{_{1, E 2 P 0 = Q}} 2, E 3 P 0 = P 2).

By multiplying both sides of the first equation by (1−t) + t = 1, Becomes Therefore, if the second and third equations are equal, then It is. That is, the fourth line segment as shown in FIG P ₀ P ₁ 2: 1 to Motomari control points Q ₁ if proportional division, the line segment P ₂ P ₁ 2: control points if proportional divided into 1 Q ₂ Is found. The cubic Bezier curve determined by the four control points P ₀ , Q ₁ , Q ₂ , and P ₂ obtained in this manner is the same as the quadratic Bezier curve defined by the three control points P ₀ , P ₂ , and P ₁ It is.

Using the above method, a boundary curve network such as a quadrilateral or a triangle is formed by a cubic Bezier curve while giving passing points,
Bezier curve models can be created. The local change of the passing point is easy, and it is only necessary to recalculate before and after the change point. In addition, since the B-spline curve is not intermediately generated, a tangent discontinuous curve can also be generated.

When a boundary network is formed by a cubic Bezier curve using the method of the present invention and a free-form surface model is formed, even if each boundary line does not satisfy the condition of tangent continuity, the condition of tangent plane continuity is satisfied. In order to satisfy one of the above, there is a key to smoothly connect all the curved surfaces. One of the conditions of the tangent plane continuity is that a normal vector between a vector along a boundary of an adjacent plane element and a vector in a direction crossing the boundary is in the same direction with respect to both plane elements. A method of generating a curved surface with tangent plane continuation is disclosed in, for example, Japanese Patent Application No. 61-69385 by the present applicant.

The generated geometric model data of the three-dimensional free-form surface is then input to a free-form surface cutting tool path generation system, and is converted into machining data for an NC milling machine (NC milling machine).

In the above description, the passing point group is given in the three-dimensional space. However, a plane curve in Bezier expression can be generated by specifying the passing point group on a plane. in this case,
Since the control points of the second-order and third-order Bezier curves can be plotted and obtained, the curves can be intuitively predicted.

[Effects of the Invention] According to the numerical processing method of the present invention, a cubic Bezier curve passing a given point group can be directly generated without using a B-spline curve as a medium. Since information can be generated and local changes are extremely easy, a high-level interactive interface with a computer can be constructed, and shape modeling as intended by the designer can be performed.

[Brief description of the drawings]

FIG. 1 is a diagram showing a method of generating a Bezier curve with a designated passing point according to an embodiment of the present invention, FIG. 2 is a flowchart showing a procedure of the first method, and FIG. FIG. 4 is a diagram showing a Bezier curve and control points, FIG. 5 is a diagram of a sectional model of a workpiece, and FIG. 6 shows a conventional Bezier curve generation method for intermediately generating a B-spline curve. FIG. In still code used in the drawings, P ₁ ~P ₅ ...... passing point Q ₂ ', Q ₂ "...... a control point C ₁ ~C _n-1 ...... Bezier curve.

Claims (1)

(57) [Claims] 1. A method for performing numerical control machining along a curve passing through a given point group, wherein four consecutive points P _{1 to} P ₄ are taken out, and three points P _{1 to} P _{3 are set to} a point P ₁ length in parallel and the same direction and towards line P ₃ is added a vector of a fraction of a line segment P ₂ P ₃ to the point P ₂ from the first step of a control point Q ₂ 'the end point relates three points P ₂ to P ₄ of the next successive, the vector of the fraction of the length in the parallel and opposite direction from the point P ₂ and towards line P ₄ line segment P ₂ P ₃ to the point P ₃ In addition, a second step in which the end point is a control point Q ₂ ″, and a third step in which a cubic Bezier curve having the above-mentioned P ₂ and P ₃ as ends and Q ₂ ′ and Q ₂ ″ as control points are generated. A numerically controlled machining method comprising: generating numerically controlled machining data using a generated curve as a contour of a workpiece.