JPH01277966A - Design data delivery device - Google Patents

Abstract

PURPOSE:To improve the function of the whole of a design system by converting control point position data, by which parameter data is multiplied, to vector coefficient data and converting vector coefficient data to control point position data to output them as design data of two systems. CONSTITUTION:When receiving Beziers system free curved surface design data DFB from a Beziers design device 2, a design data delivery device 1 converts control point position data to corresponding vector coefficient data to convert data DFB to Ferugson system free curved surface data DFF and sends this data to a Ferugson design device 3. When receiving data DFF from the device 3, the device 1 converts vector coefficient data to corresponding control point position data to convert data DFF to data DFB and sends this data to the device 2. Thus, shape data of different data systems concerning an object designed by devices 2 and 3 are freely and efficiently used as the whole to perform the design work.

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. Conventional technology Problems to be solved by the invention E. Means for solving the problems F. Effects G. Example (G1) Delivery of free-form surface data FIG. Figure 2) (
G2) Delivery of free curve data (Fig. 3) (G3) Other embodiments H Effect of the invention
(computer aided design)
, CAM (computer aided man)
It can be applied to a design system that designs the shape of an object by ufacturing.

B. Summary of the Invention According to the present invention, by converting control point position data and vector coefficient data in a design data transfer device, it is possible to easily transfer Bezier type design data and Ferguson type design data.

C Conventional technology For example, when designing the shape of an object with a free-form surface (one that cannot be defined by a quadratic function) using a CAD method (geometric modeling), the designer generally creates a three-dimensional space through which the curved surface should pass. By specifying multiple points (these are called nodes) in , and having a computer calculate a boundary curve network connecting the specified multiple nodes using a predetermined vector function, a curved surface expressed in a so-called wire frame is created. Create. In this way, a large number of framework spaces surrounded by boundary curves can be formed (such processing is called framework processing).

The boundary curve network formed by such framework processing itself represents the rough shape that the designer intends to design, and a curved surface that can be expressed by a predetermined vector function is calculated using interpolation using the boundary curves surrounding each framework space. If possible, a free-form surface designed by the designer as a whole can be generated. Here, the curved surfaces stretched in each framework space form basic elements constituting the entire curved surface, and these are called patches, and the lines that serve as basic elements stretched between two points in the framework space are called segments.

As a method that allows patches with curved surfaces that have conventionally unique features to be stretched so that the distance between them is as smooth as possible, and at the same time does not increase the amount of time required for computer processing, Bezier (
Bezier's equation and Ferguson's
), a method has been proposed in which a parametric vector function expressed as a third-order tensor product is used to form a patch consisting of a free-form surface under the condition of continuous tangent plane. No. 60-277448, patent application No. 60-29
No. 0849, Patent Application No. 1986-298638, Patent Application No. 1983
-15396, patent application No. 1983-33412, patent application No. 1983
1-59790, Japanese Patent Application No. 61-64560, Japanese Patent Application No. 61-96368, Japanese Patent Application No. 61-69385).

D Problems to be solved by the invention By the way, as a mathematical representation of a patch in the framework space formed by framework processing, we use design data when a free-form surface is created using the Bezier formula, and design data when a free-form surface is created using the Ferguson formula. The created design data is configured to represent the position vector of a point on the patch by a polynomial formed by the sum of products of parameter data and coefficient data, both of which have the same definition area.

However, in reality, the mathematical expressions in the Bezier formula and the mathematical expressions in the Ferguson formula have different data processing systems with different expression formats, so they are created using a design device that handles the Bezier formula (this is called a Bezier molding design device). The created design data can be input directly into a design device that handles the Ferguson method (this is called a Ferguson molding design device), or conversely, the design data created by the Ferguson molding design device can be input into a Bezier molding design device. Even if you try,
There is a problem in that the transmitted design data cannot be accepted.

For example, when designing the shape of an object consisting of multiple parts and their bodies, it is necessary to select either the Bezier type design device or the Ferguson molded design device depending on the object to be designed (i.e., the body, parts). If you prepare various design devices as design devices and build a design system that can mutually process each design data, it will be possible to handle a wide variety of design objects as a whole. It is believed that it is possible to realize a design device that can do the following.

The present invention has been made in consideration of the above points, and it is an object of the present invention to propose a design data transfer device that can correctly transfer design data between a Bezier mold design device and a Ferguson mold design device. be.

E Means for Solving the Problem In order to solve this problem, in the present invention, control point position data P,. . ,~P(3U1,P,.,~P,3
．． and parameter data (
The first patch S (un vl or segment L) is obtained by the sum of data of multiple terms consisting of the products of u, v) and t.

, with the Bezier outcome design data identifying the position on the
Vector coefficient data a,. , ~a, 1sl and parameter data (u-, V) that can specify a predetermined defined area,
When receiving Bezier resultant design data based on the Ferguson-style design data that specifies the position on the second patch R (un vl or segment Mat>) by the sum of data of multiple terms multiplied by t, Among the multiple terms of the Bezier design data, control point position data P, . When the Ferguson type design data is received, the vector coefficient data a, . . .
Control point position data P(..., ~P) corresponding to a(1%)
(331, P, . . . . ~P+z+) to send Bezier result design data.

The F-action Bezier result design data and the Ferguson formula design data are each formed as a data string consisting of multiple term data based on parameter data (U, v) and L that specify a predetermined defined area, and each term is multiplied. Power control point position data P,. . ,~P,31,P,. , ~P131 (or vector coefficient data a, ., ~atls)), vector coefficient data a 11+1~a (Is) (or control point position data P (0@l ~PT331, P (
By converting into @l~P(s)), Bezier result design data and Ferguson style design data can be easily converted and transferred. In this way, it is possible to easily construct a design system that can effectively utilize design data of different design data series in design devices having different types of data processing systems.

G example An embodiment of the present invention will be described in detail below with reference to the drawings.

(G1) Delivery of free-form surface data In FIG. 1, the DSG shows a design system as a whole and has a design data delivery device 1.

The design data delivery device 1 is the Bezier molding design device 2.
When receiving Bezier free-form surface design data DFI from , Ferguson free-form surface design data DFF is received.
It is configured to convert the data into 3D data and send it to Ferguson Molding Design System W3.

At the same time, when the design data delivery device 1 receives the Ferguson-type free-form surface design data DFF from the Ferguson molding design device 3, it converts this into Bezier-type free-form surface design data D□ and sends it to the Bezier molding design device 2. do.

Here, the Bezier molding design device 2 calculates the boundary curve representing the boundary line of the quadrilateral framework space subjected to framework processing and the patch S (un v) stretched in each quadrilateral framework space using the following formula % formula % - (1 -u+uE)'-(1-vlvF)'P+oo,
・・・・・・ As shown in (1), it is expressed using design data consisting of a vector function expressed by cubic Bezier 2. In equation (1), P (001 is a curved surface stretched across two adjacent frame spaces, that is, the first quadrilateral patch S (u+ vl + and the second quadrilateral patch S Lu
, vl 2 is a position vector representing the position of one end of the boundary (this is called a shared boundary) held together, and a position vector P representing the position of the other end. 1. and the first patch S
(u+ vl 1 position vector P(3°, 1, P(
331+ and the position vector PL3°12, P+:l.2 of the second patch S(u+lZ) constitute a node specified during framework processing.

Thus, the first and second patches S (u+V) I
and S (u+ vl z are the nodes P fooJ
P (3011-P (33r + P (os
) P fooJ and P (GoJ P (30) z
-P+3°2-P,. It can be seen that it is surrounded by four boundary curves of 31P(...).

Node P, among these boundary curves. . , and P(.,〉
The boundary curve between the two control points P, constitutes a shared boundary COM. 1. and P(.2. defines the cubic Bezier 2.

On the other hand, the first patch S (node P of u+ v□,
. . , and P. The boundary curve between 011, P(3°, 1 and P(33, 1, PCl31+ and P(o*
The boundary curves between are each two control points (P, 1°)
5, P (2011), (P + sr, l % P tx
t, l), (P + z2+ I, P (1°1).

Also, the node P of the second patch Sf*+v)2. . ,
and the boundary curve between P+to+z, P (3012 and P
(: boundary curve between 131K, P (33) 2 and P,
. The boundary curves between 31 and 31 each have two control points (P 1
1012, P (201K), (P (:+, z
, P nnz ), (P (231g , P ns+z
).

In addition to this, the first and second patches S fu+ v)
The internal shape of H and S (u+ vl z is the internal control point (P(II□, P, 2゜l , P (2□11, P(
+□)1) and (P u++z , P+znz , P+
It is defined by zz+z, P(1212).

In addition, in equation (1), E and F are shift operators in the U direction and V direction, and the control point P (ijl On the other hand, the following formula, E-P +i=+ = P u-+ j+(i, j=o
, 1.2) ...... (2) F' P (ijl
-P (i +411(i, j=o, 1.2)...
...has the relationship (3).

Here, U and V are parameters for the U direction and ■ direction, 0≦U≦1 ・Old...(4) 0≦V
≦1 Defined in the range of 0 to 1, as in (5).

(As shown in FIG. 2, the first and second patches S
(u+V) l and S (u+vl For Z, respectively, from the nodes P, . . ., use the coordinates (u, v) that take the U axis in the horizontal direction and the V axis in the vertical direction to create a patch S.
(u+V) l and S (coordinates on a free-form surface within u+v□ can be expressed.

In this way, the two patches S (u+ v) I and S (u+ v) t each have 12 control points (including nodes, called control points) set along the four boundary curves and the patch. The position on the four boundary curves of each patch and the internal free-form surface surrounded by the boundary curve are determined by a polynomial expression consisting of the product sum of the four internal control points set inside and the parameters u and v. can be determined by specifying the values of parameters U and V.

By the way, if formula (1) is expanded with respect to the parameters U and
1) u+(3P(0016P++o++3P+za+)
u”+ (P toot + 3 P <to) 3 P
, zortenP <5ob) u' + (-3P(..l"3Pl.++) V+(9P(..

, 9P(1019P(.1゜+9P tz))u
v + (9P(0@l+18P(1019P+to++9P
,. u 18P(II) +9 P +z++)u”v +(3P(..) 9P(lot+9Puo+3
Pn. ) 3P(.,, + 9P(I 1
+9 P (tl) + 3 P t3++)u3V+
(3P (6016P <on + 3P (ot+
)V”+(9P(@(11+9P(10)+18P(0
1) 18P (++1-9 P (oz) + 9 P ++z+) u v2 + (9P (00) 18P (lot + 9
P < go + 18P (011 + 36P ol, 1
8P, t.

+ 9 P (+1!+ 18P (41+ 9 P
Hl)) u”v” +(-3P,..+ +9 P u.l 9Pn..

+ 3 P txo> + 6 P (
6 violet 1 18P (eyes)”18Pnu 6
P(3113P(021+ 9 P ＜+□) 9
P (tt++ 3 P (Hl)) u ” v
”+(P (001+ 3 P (01+ 3
P toz)” P 102)) V 3 +(3P(.., 3P(1019P(.1+9P+
++>+9P (az) QPtth) 3 P tos+
+3 P (13)) u v '+(3P (00
1+6P (11113P tzo.

+9P(.++ 18P (II) + 9P
<tl)-9P,. z+ + 18P <+ゎ-9P
Ht.

+3P(.s, 6 P (131 +3 P (zz+)u”V' + (P no+ -3P (101+ 3 P (2
01-P(,.1 3PT.+)+9 PL
' + +9 P on + 3 P <s, + 3
P <ot)9 P ut+ +9 P uz+ 3
P upP (os+ + 3 P ＜+s+
3 P tts+”P (33+)u”V3 −
− The reference control point P, as in (6). . , and the parameters u, , u2, u'', V, uV, u''
V% u”V.

v, uv, uv, uv
, v'', uv', u''v3, u3v3, and the sum of products of control points P+601 to P(33). In the end, the Bezier hole design device 2 allows the designer to specify and input the control point data P(. Bezier resultant free-form surface design data D□ can be created, and the shape of the patch can be modified and designed by changing the boundary curve or internal control points of the patch as necessary.

On the other hand, the Ferguson hole design device 3 calculates the patch R(uv vl by the following formula % % ” ” +121 ”” a (+z) u
v 3 + a (141u”V'+a (
+5) u3V' ・As in =-(7), the reference vector coefficient a,. , and the parameter u
−, u”, u3, V, uv, u” v, u3■,■
, uv2, u ■ , u ■ , v 1uv' , u''
vco, u' vco and vector coefficient a (0) ~a
(It can be organized into 151 product-sum terms. After all) As in the case of equation (6), the Ryo-Gason type design device 3 has parameters U & V and 16 vector coefficients a (Ill
It is expressed by a polynomial expression of the sum of products with ~a(151).

(7) As is clear from Part 2, the Ferguson large-system free-form surface design data DFF is not the control point data that defines the internal surface or boundary curve of a patch, as in the case of the Bezier resultant free-form surface design data DFI. Different vector coefficients a,. , ~a (151) allows the designer to specify points on the boundary curve of the patch and points inside the patch, thereby designing the shape of the patch as a free-form surface that can be modified as necessary. be able to.

The design data delivery device 1 determines one coordinate point (U) of the patch S (u+v) using the Bezier resultant free-form surface design data D□ expressed by equation (6).

■) is specified, for the same point, the value of the coordinate point (U, ■) on the patch R(u+vl) represented by the Ferguson large system free-form surface design data D□ is the same value. The coefficient data corresponding to is converted and transferred between the Bezier type mold design device 2 and the Ferguson type mold design device 3.

In other words, the design data delivery device 1 has (6)2 and (7)
) patch S Iu+ v) and R given by the formula
Assume that (u+v) are equal to each other as shown in the following formula (8).

In order for the relationship in equation (8) to hold true, the parameters u, v
Since the coefficient data of the corresponding terms should be equal to each other, in the Bezier type design device 2, the control points P,
. . , ~P(3,, this is a, ., -P, . . . . . .
(9) a(++= 3P+oo++3Pna+
--(10)a (Zl = 3P C001-6P
t+o+ + 3 P, zo+...(11
) a (31= P toor +3 P (1013
PC2010P, 3゜, ・・・・・・
・(12) a +41= 3 P (00+ + 3
P 111 -- (13) a +s+= 9 P
(00+ 9 P C1ot 9 P ton+
9PCIl+ ・・・・・・(14)a
tb+ = 9P toor +18P (10
19P (zo++9P,.u 18P (Ill
+ 9 P tz++・・・・・・ (15) a (71= 3 P (oo, 9 P (+01 +
9 P, zo.

−3P <zo, 3 P (Ill1 + 9 P I
ll19 P u++ + 3 P (31) ・
... (16) a+a+=3Pcoo+ 6
P(O11+3P(0゜・・・・・・(17) a n+ = 9 P ((lot + 9 P
no)+18P ton18P (llll 9 P
C0t+ + 9 P (121... (1
8) aflol=9p toot-18P(lot+9P+
zo+-18P(.+1"36P u+, 18P
tz+.

+9P,. z+ -18P, +z, +9P (2
□.

・・・・・・ (19) an++= 3P(061+9P(1019P+z
o++ 3 P (3°) + 6 P +. ++
18P++.

+18P (21+ 6P, zn 3P
(.2゜+ 9 P (+z)9 P (tz)+
3 P (321... (20) a (12) = P (001+ 3 P (6
113P toz)+p,. 8.
・・・・・・ (21) a++3+=3P too, 3
Ptto+ 9P Ca1l+9P(II)+9P
(.z>9P tax)-3P,. 31 +
3 P (+ 31 ...... (22)a
(+41 = 3 P (oo+
+ 6 P (1013P (to++ 9
P (01118P (1++ +9 P tt+)9
P (on +18P (1!l 9 P nz
)” 3 P (03) 6 P (+3. +
3 P (zs+... (23) a +151 =P (0013P LIo, +3 P
(2(11P tso+ 3P <on +
9 P < t ++ 9 P < tn + 3 P (:
lll +3 P (0219P <+z+ + 9
P nz) 3 P (321P <os+ + 3 P
(I:u 3 P (231+P(33)
・・・・・・ Like (24),
16 vector coefficients a, in the Ferguson result free-form surface design data DFF. , ~a(Is).

By doing this, the Bezier molding design device 2
Bezier resultant free-form surface design data D□ sent from
is converted into Ferguson result free-form surface design data DFF by the design data delivery device 1, and is thereby imported into the Ferguson molding design device 3, and is used as design data similar to the design data formed inside the Ferguson large-scale design device 3. It is processed.

On the other hand, the Ferguson result free-form surface design data D formed in the Ferguson molding design device 3
When the FF is sent to the design data delivery device 1,
The design data delivery device l is calculated using the following formula % formula % (25) ...... (34) P (3z+ = a (1) a (2+ ”)
a (x)+ a (41+-an+1
...... (36)P (03) -
a (01+ a (41+ a) (Ill
+ a (121... (37) ...... (38) J ” a (141... (39) P (zs
)= a (11” a +z) + 4 a 〈o+
a (s) + a f6) ” a (71
+ 4 3 (111+ a (?)+ a
(lot + 4 a nz) + a (1:11 +
a (141+a (1,1... (40)
Vector coefficients a, inputted to the Ferguson molding design device 3 as follows. , ~a (16 control points P in 16 Bezier large-system free-form surface design data DFI based on data of 151, ..., ~P (converted to data of 331).

Bezier large system free-form surface design data DFI obtained by converting in the design data delivery device 1 in this way
is received in the Bezier molding design device 2, and
It is processed using the same method as the Bezier large-system free-form surface design data formed inside the Bezier molding design device 2.

According to the above embodiment, the Bezier large-system free-form surface design data D□ and the Ferguson result free-form surface design data D have different data processing systems with different mathematical expressions.
, so that they are compatible with each other in the design data delivery device 1, the design data formed in the Bezier molding design device 2 and the design data formed in the Ferguson molding design device 3 can be mutually effectively used. As a result, the functionality of the design system DSG as a whole can be further improved.

(G2) Delivery of free curve data The design data receiving device 1 receives the Bezier result free curve data DL11 formed in the Bezier molding design device 2 and the Ferguson result free curve design data formed in the Ferguson molding design device 3. I
) ty and perform mutual transfer processing so that they are compatible with each other.

Here, as shown in FIG. 3, the Bezier molding design device 2 uses the following formula L+t+=(1t+tE)3P(., . . . with the origin 0 of the XYZ orthogonal coordinate system as a reference).
...The segment represented by (41) is defined as two control points P (1) between the end points P (.) and P (1) at both ends.
1 and P(2).

Here, E is a shift operator in the U direction, and segment L+
Control point P1. expressed by the position vector corresponding to t+.
．． % has the following relationship.

Also, t is a parameter in the direction along segment L+t+, 0≦t≦1 (43)
It is defined in the range of 0 to 1, as shown in FIG.

Thus, the segment L(tl is defined by the endpoint P(., and P
(When two control points P(,) and P(!, are set between 11 and 11, by specifying the parameter t, the position on the segment L(. It can be formed as

Segment of equation (41))L(tl is the following equation if expanded and organized by parameter t), where parameter t and control point P. ,~P(
3) It can be expressed by a polynomial that is the sum of products.

On the other hand, the Ferguson molding design device 3 uses the following formula: %formula% The parameter t and the four coefficient vectors a, as follows.

, ~a(3), each point on the segment M<t) can be expressed by a polynomial formed by the sum of products. Therefore, the designer used the Ferguson molding design device 3.
Coefficient vector a, based on the shape of the free curve that we want to obtain. )
By specifying and inputting ~a +31 as necessary, a free curve can be designed.

The design data delivery device 1 is the Bezier molding design device 2.
Bezier result free curve design data formed based on the equation (44) by the position on the segment L+t+ which can be found by tm, and the segment formed based on the equation (45) by the Ferguson molding design device 3) The conversion process is performed so that the following equation (46) is established so that the positions on M+t+ are equal to each other. That is, when the design data delivery device 1 receives the Bezier result free curve design data DLI from the Bezier molding design device 2,
From the relationship that the coefficients of each term in equations (,44) and (45) are equal, a (01= P (o)・” −(47) a (+1
= 3 (P < n P (+11)...
・-(48) a <tl = 3 (P <
z+ -2P (ll'+ P (111)・
(50) Control point data P, which the designer inputs into the Bezier molding design device 2 based on the following. , ~P(11 is converted into coefficient vector a, .) ~aH).

Thus, the Bezier result free curve design data DLJ is
By converting into the Ferguson result free curve design data DLF in the design data delivery device 1,
The receiver is placed in the Ferguson mold design device 3.

On the other hand, when the Ferguson molding design device 3 receives the Ferguson type free curve design data DLF, the design data delivery device 1 receives (47) 2 ~ (5
0) Expression organized for the control point P (11~P cx+ , P, ., -a, ., ......(
51) P n+ = (3a +01 +a, I+
) −・” (52)P(21= (a+z)+
23++++33to+)・・・・・・(53) P (31” a (31+ a (!l)
+ a fil + a Nil...
...(54) The coefficient hector a, which the designer inputs into the Ferguson molding design device 3. , ~a (21 data is converted into control point data P(., ~P11.).

Thus, Ferguson large system free curve design data DL
F is converted into Bezier result free curve design data DLI by the design data delivery device 1, and then received by the Hezier type design device 2.

In this way, the design data delivery device 1 mutually transfers the Bezier result free curve design data DLI+ formed by the Hezier type design device 2 and the Ferguson large-scale free curve design data DLF formed by the Ferguson molded design device 3. It is possible to perform a conversion operation that is compatible with the design system DSG, thus further improving the functionality of the design system DSG as a whole.

(G3) Other embodiments (1) In the above embodiments, the case where a patch or segment expressed by a third-order Hezier equation or a third-order Ferguson equation is stretched in the framework space can be carried out, but the order of the formula is not limited to this, and may be of fourth order or higher.

(2) In the above-described embodiment, the present invention is applied to the case where a free-form surface is generated using a quadrilateral patch, but the present invention is not limited to this, and the present invention is applied to a case where a trigonal patch is used, It can also be widely applied to cases where design data is transferred, such as when patches and quadrilateral patches are mixed.

H Effects of the Invention As described above, according to the present invention, control point position data and vector coefficient data to be multiplied by parameter data are mutually converted and output as Ferguson result design data or Bezier result design data. As a result, it is possible to easily realize a design system that can perform design work by freely and efficiently using the shape data of different data systems for objects designed by the Bezier molding design device and the Ferguson molding design device as a whole.

[Brief explanation of the drawing]

Fig. 1 is a block diagram showing a design system using the design data delivery device according to the present invention, Fig. 2 is a route map showing an example of Bezier result patch design data, and Fig. 3 is a route map showing Bezier result segment design data. It is. 1...Design data delivery device, 2...
・Bezier molding design device, 3...Ferguson molding design device.

Claims (1)

[Claims] A Bezier formula that specifies the position on the first patch or segment by the sum of multiple terms of data that is the product of control point position data and parameter data that can specify a predetermined defined area. A Ferguson-style system design that specifies a position on a second patch or segment by the sum of multiple term data that is the product of system design data, vector coefficient data, and parameter data that can specify a predetermined defined area. When the Bezier design data is received, the control point position data of the plurality of terms of the Bezier design data is converted into the corresponding vector coefficient data. When transmitting the Ferguson type design data and receiving the Ferguson type design data, converting the vector coefficient data among the data of the plurality of terms of the Ferguson type design data into the corresponding control point position data. A design data delivery device characterized in that the Bezier style design data is transmitted by: