JPH03135672A - Production of shape data - Google Patents

Abstract

PURPOSE:To easily and surely obtain the shortest distance by calculating a data group on the distance between a sampling point on a free curve and an intersecting point between an orthogonal plane and a straight line. CONSTITUTION:A plane Wi passes through a sampling point Ki set on a free curve R(t) and is orthogonal to the curve R(t), and a data group is obtained to show the distance di between the point Ki and an intersecting point Qi between the plane Wi and a set straight line L. Then the least value is detected out of the distance data group and therefore the shortest distance dmin is detected between the curve R(t) and the line L. Thus it is possible to quickly and surely obtain the distance dmin at all times. Then a free curve is designed with high efficiency.

Description

[Detailed description of the invention] The present invention will be explained in the following order.

A: Industrial field of application B: Outline of the invention C: Prior art (Figs. 6 and 7) D: Problem to be solved by the invention (Fig. 8) E: Means for solving the problem (Fig. 1) - Fig. 5) F Effect (Fig. 1 - Fig. 5) G Example (Fig. 1 - Fig. 5) H Effect of the invention
(computer aided design)
or CA M (computer aided
The present invention is suitable for application when deforming the shape of a generated free curve or free-form surface in manufacturing (manufacturing).

B. Summary of the Invention The present invention, in a shape data creation method, simply and reliably determines the shortest distance by calculating a distance data group representing the distance between a sampling point on a free curve and its orthogonal plane and the intersection point on a straight line. be able to.

C Conventional technology For example, when designing the shape of an object with a free curve (a curve that cannot be defined by a quadratic function) or a free-form surface (a curved surface that cannot be defined by a quadratic function) using a CAD method ( (geometric modeling), a designer generally specifies multiple points (these are called nodes) in a three-dimensional space through which a curved surface should pass, and uses a computer to create a boundary curve network connecting the specified multiple nodes using a desired vector function. A curved surface expressed in a so-called wire frame is created by calculating the .

As shown in FIG. 6, the free curves forming the boundary curve network are defined by two nodes P0 and Ps set at arbitrary intervals.
(Pt.2. and P(3+I, P,., and Pt3+X
,P. 3. It has a configuration in which a plurality of curve segments Ks6 (Kscl, Ksct, Ks.) separated by and P (313) are connected.

This curve segment) KSG uses a cubic Bezier equation,
It is expressed by a parametric space vector R(t) expressed by the following formula (1).

Here E is a shift operator and the curve segment KsG
Upper control point P! , and the parameter t is expressed by the following equation 0≦[≦1 . . . (3).

A large number of framework spaces surrounded by boundary curves made of such free curves can be formed (hereinafter, such processing will be referred to as framework processing).

The boundary curve network formed by such framework processing itself represents the rough shape that the designer is trying to design, and the boundary curves surrounding each framework space are used to perform interpolation calculations to create a curved surface that can be expressed by a parametric vector function. If it is possible to do so, it is possible to create a free-form surface designed by the designer as a whole. Here, the curved surfaces stretched in each framework space form basic elements that constitute the entire curved surface, and these are called batches.

The principle of creating a free-form surface will be described with reference to FIG.

Four nodes P in the U direction and the V direction. ,P. , P33
and the shared boundary COMI, C0M2 determined by P03
, C0M3 and C0M4, when considering the parameters U and V in the U direction and V direction along the shared boundary, the cubic Bezier A batch S (
us yl can be formed.

Here E and F are shift operators and batch S Tu
Control point P expressed as a position vector on +vl,
For J, it has the following relationship: (5) (6)

Parameters U and V are calculated using the following formulas % Formula % (7) (8) Therefore, for the boundary curve network connecting a plurality of input nodes, batches S (us
V), many batches S (I
Shape data representing a free-form surface of a desired external shape surrounded by ll v+ +, S(., v)2, . . . can be obtained.

In this way, the external shape that the designer is trying to design can be expressed by a parametric vector function using boundary curves surrounding each framework space, and the free-form surface designed by the designer can be generated as a whole. can.

D Problem to be solved by the invention By the way, when a designer tries to design the external shape of a product using this shape data creation method, the distance between the generated free curve and the set straight line is the shortest. There are cases where it is desired to re-deform the shape of the free curve as necessary by using the position as the reference.

Conventionally, as shown in Fig. 8, the shortest distance d11i11 between the Bezier curve R(t) and a straight line is the distance between the point M on the Bezier curve R(t) and the point M8 on the straight line set by the designer. d squared d! It was detected by finding the values of the parameters tl and , which minimize the equation.

That is, the Bezier curve R expressed using the parameter t
The point M+ on (t) has the parameter value t ”' t
When r, the point M2 on the straight line expressed as the following formula (%) (9) and expressed using the parameter k is the value of the parameter = k.

When , the following formula % Formula % (10) (Here, vector n is the direction vector of straight line L (k))
The square d1 of the distance Md between these two points is generally obtained as the following formula % ()) ()) ()) (11).

Here, by setting equation (11) as a function r(L, k) and partially differentiating the parameters with and k, the following equation (13) is obtained, and these equations (12) and (13) can be reduced to 0 Then, if we solve the following simultaneous equations for the parameter tSk using the Newton-Loughran method, we can calculate the distance 1 between the two points M and Mt.
The parameters t and k that give the extreme value of 111d squared d2 can be found, and using these parameters t and k, the shortest distance d1 between the Bezier curve R(t) and the straight line L(k) can be found. can.

In other words, by performing Taylor expansion of equations (14) and (15), we obtain 2
By eliminating the following terms, it can be expressed as the following formula: Continuing, equation (16) and (
17) When the equation is linearized, the following equation = 0 (16) (LX (k) 10n, Δk) + (Rz (t) - Lz (k))nz)...
-(19) (nX-n, 1+ny0 ny+nz- nz) [(nx(t) Lx(k))nx (1 day) Δk is obtained.

Δ that makes this simultaneous equation converge and Δk (1
The shortest distance d between the Bezier curve R(t) and the straight line is obtained by determining the parameters and the values of k from the initial values of parameters and k.
= n is calculated.

However, the Bezier curve R(
When finding the shortest distance d sin between t) and a straight line,
Depending on the settings of the parameters and the initial value of k, the calculation process will not converge and Δk and Δk cannot be obtained, so the Bezier curve R
There is a possibility that the shortest distance d 111M between (t) and the straight line cannot be determined, and the usability is still insufficient to obtain the free curve intended by the designer.

The present invention has been made in consideration of the above points, and proposes a shape data creation method that can easily and reliably determine the shortest distance between a free curve and a straight line. ) )ny It's a source of sleep.

can be measured.

EMeans for Solving the Problem In order to solve this problem, in the present invention, a sampling point set on the free curve R(t) is passed through,
A plane W1 orthogonal to the free curve R(t) is generated, and the distance d! between the sampling point and the intersection point Q of the plane W with the set straight line is calculated. By obtaining a distance data group representing the distance data group and detecting the minimum value among the distance data group, the free curve R(t)
The shortest distance d,1 between and the straight line is detected.

A sampling point parametrically determined on the F-action free curve R(t), and the intersection point Q! on a straight line. Distance data between d! A distance data group is obtained by calculating distance data d! in the distance data group. By setting the minimum value of the shortest distance d, mu1 between the free curve R(t) and the straight line, the shortest distance d l
An embodiment of the present invention will be described in detail below with reference to the drawings.

This embodiment calculates the shortest path Md, M7 between the straight line set by the designer and the free curve R(t) represented by a Bezier curve, and also calculates the shortest distance d,! Parameter Lai that gives 7, @! at the sampling point! 11, intersection points Q, i, etc., and can be used in the transformation process of the free curve R(t), thereby making it possible to create a free curve with a shape closer to the designer's image. It is.

FIG. 1 shows a case where the shortest distance between a free curved line and a straight line is determined, and the CAD/CAM system 1 includes a free-form surface creation device 2 and a free-form surface cutting tool path creation device each including a central processing bag W (CPU). 3 and an NC milling machine (machining center) 4.

The free-form surface creation device 2 uses a CAD method to generate 3 degrees for each curve segment constituting a free-form curve representing the external shape of the product and each patch S (an v) constituting the free-form surface.

In addition, the free-form surface cutting tool path creation device 3 receives free-form surface data DT consisting of curve segments) Ksc and batches S (un V) generated by the free-form surface creation device 2, and based on the free-form surface data DT. For example, the offset curved surface S for a tool made of a ball end mill,
1IFF is created, and tool path data DTcL is created using a method such as the segment hide method.

Further, the NC milling machine 4 controls the movement of the ball end mill based on the tool path data DTCL input via the floppy disk 5, so that it can cut a product having a free-form external shape. being done.

Incidentally, the free-form surface creation device 2 includes a display device 6, such as a cathode ray tube display, and an input device, such as a keyboard or mouse! 7, and when the designer specifies the shortest distance calculation mode between free curves and straight lines by operating the input device 7 while visually checking the menu screen displayed on the display device 6, the CPU executes the shortest distance calculation mode according to FIG. Find the shortest distance between the free curve and the straight line according to the shortest distance calculation procedure shown below.

That is, the CPU enters the shortest distance calculation processing procedure from step SPI, and in the subsequent step SP2, the designer operates the input device 7 while visually checking the free curve R(t) displayed on the screen, and calculates the free curve R(t). t) and waits for you to set the straight line for which you want to find the shortest distance.

That is, as shown in FIG. 3, when the designer uses a mouse or the like to move the cursor C to a position where a straight line is desired and clicks, the CPU reads the coordinate data of the reference point Q0 from the clicked position.

Next, the designer moves the cursor C in the direction you want to draw a straight line.
When you move and click, the CPU takes in the coordinate data of point Q from the clicked position, then takes in the coordinate components of the direction vector n from the reference point Qo to this newly clicked point Q, and then calculates the coordinates of these two points. The coordinate data of the straight line is taken in from the position information obtained by , and the set straight line is displayed on the display, and the process moves to the next step SP3.

In step SP3, the CPU waits for the curve segment Ksc constituting the free curve R(t) for which the shortest distance is to be determined to be selected and input.

In other words, as shown in FIG.
Move cursor C onto G and click to display the CPU
takes in the position vector R(t) of each point on this clicked curve segment I(sc) as free curve data.

The CPU that has moved to step SP4 has sampling point number i.
The value of the internal counter that counts
t), the shortest distance data d, i% representing the shortest distance between the two points is initially set to a very large value.

Subsequently, the CPU increments the internal counter by "+1" in step SP5 to increase the value of sampling point number i to i=l, and then proceeds to step S.
At P6, it is determined whether the value of the sampling point number i is larger than the set maximum sampling point number 1+ms,x (in this example, it is assumed that it is set to i,,X-100). .

Here, the value of sampling point number i is i=1, and i□
, > 1, the CPU that obtained a negative result moves to Step SP7 and sets the parameter 1+ (0≦1.≦1
) is determined from the following formula (%) (20) to set a value corresponding to the first set point in the t direction.

Next, in step SP8, the CPU executes the parameter 1 set in step SP7 described above. A sampling point Ki on the free curve R(t) is calculated based on the value of . Here parameter 1. Since is defined as shown in equation (20), it is possible to set 100 sampling points over the entire free curve R(t) in steps of t, = 1/99.

When the CPU moves to step SP9, the CPU calculates the differential coefficient representing the tangent vector in the direction of the free curve R(t) at 4 at this sampling point using the following formula, and converts the tangent vector of the free curve into the normal vector N! Find the surface of the plane W that is bound. Since the plane W1 obtained here has infinite extent, it always intersects with the straight line set by the designer in step SP2, and has an intersection point Q.

At this time, the CPU connects the intersection QL on this plane Wi with the free curve 1.
When the distance data di representing the distance to the sampling point KL on #R(t) is calculated based on the following equation (21), the process moves to step 5PIO, and as shown in FIG. step SP9, find... (2
2) (Here, SKV, indicates the X coordinate, y coordinate, and 2 coordinates of the sampling point Ki, and Q, , Q, and Q2 indicate the X coordinate, y coordinate, and 2 coordinate of the intersection point Q) Thus, in step 5PIO, the CPU obtains distance data d! representing the distance between the sampling point Kz and the intersection point Qi of the plane Wi set for the sampling point Kt with the line &iL. Calculate.

In steps SP4 to SP5PIO, the CPU sequentially sets the sampling point KL and the intersection Q! distance md between
Execute the calculation of i.

Next, the CPU moves to step 5P11, and the CPU moves to step 5P11.
The distance data dl obtained by PIO and the stored shortest distance data d, i, (here, the shortest distance data d s
A sufficiently large value is set as the initial value of in)
Compare with. If a positive result is obtained here, this means that the distance data d! obtained in step 5 PIO! is smaller than the conventionally held shortest distance data dsin, and the CPU executes step 5PII to step 5P.
Moving on to step 12, a new value of distance data dm is written in place of the conventional shortest distance data d and i, and the parameter t! The value of is set to L aim, the data of is set to the sampling point, and K m ! Input the data of intersection Q5 into e.
After writing to ehim and resetting each, the process returns to step SP5 through the processing loop LOOP1 and the sampling point number i is incremented by "+1".

This processing loop LOOPI (SPI 1-3P12-
3 P 5-3 P 6-S P 7-S P 8-3
P 9-3PIO-3PII) is calculated in step SP
The process is repeated while a negative result is obtained in step 6 and a positive result is obtained in step 5P11.

If a negative result is obtained, this means that the distance data di obtained in step 5pio is larger than the conventionally held shortest distance data d aiy+, and the CPU passes through the processing loop L00P2. Returning to step SP5, the sampling point number i is increased by "+1". This processing loop LOOP2 (SPl 1-3P
5-3P6-3P7-SF3-3P9-3P 10-3
The operation of P11) is repeated while negative results are obtained in steps SP6 and 5PII.

That is, the CPU determines that the distance data d sequentially calculated in step 5 PIO is the shortest distance data d that has been previously held,
, 7, the processing of processing loop LOOP2 is repeatedly executed, and when a value smaller than the shortest distance data d sin is obtained, processing loop LOOPI is entered from processing loop LOOP2 to repeat the shortest distance data d, 50, etc. Run the settings.

In contrast, if a positive result is obtained in step 5PII while executing the processing of processing loop LOOP 1, the CPU moves from processing loop LOOP l to processing loop L.
Enter OOP2 and execute the above processing.

Eventually, when a positive result is obtained in step SP6,
This means that all sampling points Ki (i.e., i=1.2.3...) set on the free curve R(t)
This means that the calculation of the distance data di at point il, point 8) has been completed, and at this time, the CPU judges that the search for the shortest distance data has been completed and moves to step 5P13, where a free curve and a free curve are displayed on the display screen. A parameter L11iM that displays the shortest distance between straight lines and gives the shortest distance;
After displaying i and the intersection Q1.7 at the sampling point on the screen, the process moves to step 5P14 to end the shortest distance calculation process.

In the above configuration, the CPU performs steps SP2 and SF.
After confirming that the straight line and free curve R(t) have been set and inputted by the designer in step 3, in the subsequent processing steps (SP4 to SP12), the sampling point Kt (in this example) on the free curve R(t) is confirmed. (100 pieces) and the distance data d, representing the distance between the corresponding intersection Q+, are expressed as (2
2) Calculate sequentially based on the formula, and detect the minimum value from the distance data group that is the calculation result.

According to the above configuration, the shortest distance between the free curve and the straight line specified by the designer is set at the intersection point where the straight line intersects the plane whose normal vector is the tangent vector of the free curve at sampling points that are sequentially set on the free curve. By detecting and calculating the minimum value from the distance data group as the minimum value of the distance between the This can be reliably determined, thereby improving the efficiency of free curve creation.

In addition, in the above embodiment, it is possible to obtain not only the shortest distance between the free curve and the straight line, but also information regarding the value of the parameter giving the shortest distance, the sampling point on the free curve, and the intersection point on the straight line. can be used as free curve creation data.

Furthermore, in the above embodiment, by setting the value of the maximum sampling point number t wax to 100, the distance between the free curve R(t) and the straight line is calculated at 100 sampling points for 5. As mentioned,
Alternatively, the maximum sampling point number i, .

In addition, in the above embodiment, the parameter also has a value of (2
0) and obtained from the arithmetic expression, it may be obtained from another relational expression.

In addition, in the above-mentioned embodiment, straight line and free curve R(
I tried to import the data of t) from the coordinate data of the clicked point by moving the cursor using a mouse etc.
The method for specifying the straight line and free curve R(t) is not limited to this, and various methods can be applied.

In the above embodiment, a case was described in which a curve segment represented by a third-order Bezier equation is extended in a three-dimensional space, but it can also be applied to cases of fourth order or higher order, and various free curves such as B-splines can be applied. It can also be widely applied to curved cases.

In the above embodiment, at each sampling point Ki, the distance data di between the free curve R(t) and the straight line is
We have described the case where the shortest distance data d sin conventionally held is compared every time d sin is calculated, but this is not limited to this, and the free curve R(t)
Even if the shortest distance data d m = 11 is searched and found by writing the distance data d between and a straight line into the distance table, and finding the minimum value of the distance data group made up of all the distance data di. good.

H Effects of the Invention As described above, according to the present invention, the shortest distance between the free curve selected by the designer and the set straight line is determined by the sampling points sequentially set on the free curve and the straight line corresponding to the sampling point. By determining the minimum value of the distance data group consisting of the distance data between the above intersection points, the shortest distance between the free curve and the straight line can be easily and reliably obtained.

Engineering (, 4D/CAM system

[Brief explanation of the drawing]

FIG. 1 is a block diagram showing an embodiment of the CAD/CAM system according to the present invention, FIG. 2 is a flowchart showing an embodiment of the shortest distance calculation procedure between a free curve and a straight line according to the present invention, and FIGS. Figure 5 is a route map for explaining the processing procedure in Figure 2, Figure 6 is a route map for explaining free curves, Figure 7 is a route map for explaining free curved surfaces, and Figure 8 is for conventional problems. It is a route map for explaining points. P @ , P (a> I-s・P3・P (1)
l+3 °°°°°° node・P t , P(1), ~
1, P t , P (ri l ~, ... control point,
R(1)...Free curve, K...Sampling point, L...Straight line, Qo...Reference point, n... Direction vector, W,...
Plane, N+... Normal vector, Qi...
・Intersection, d...Distance, C...Cursor. CAD/CAN system's sword 1 戊 1 Figure Shortest distance string -, V calculation processing hand) Koro 2 Figure Free curve and shortest distance # of L latitude Mita f) 5 Figure Free curve expressed by vector function Figure 6 Input of linear data Figure J Figure Yamanaka curved surface Hara distance Figure 7

Claims (1)

[Claims] A plane passing through a sampling point set on a free curve and orthogonal to the free curve is generated, and a distance data group representing the distance between the sampling point and the intersection of the plane with a set straight line is generated. and detecting the shortest distance between the free curve and the straight line by detecting a minimum value among the distance data group.