JPS60250403A - Curved surface producing method - Google Patents
Curved surface producing methodInfo
- Publication number
- JPS60250403A JPS60250403A JP59105476A JP10547684A JPS60250403A JP S60250403 A JPS60250403 A JP S60250403A JP 59105476 A JP59105476 A JP 59105476A JP 10547684 A JP10547684 A JP 10547684A JP S60250403 A JPS60250403 A JP S60250403A
- Authority
- JP
- Japan
- Prior art keywords
- point
- cross
- curved surface
- curve
- section
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims description 20
- 239000011159 matrix material Substances 0.000 abstract description 5
- 238000006243 chemical reaction Methods 0.000 abstract description 3
- 230000008878 coupling Effects 0.000 abstract 1
- 238000010168 coupling process Methods 0.000 abstract 1
- 238000005859 coupling reaction Methods 0.000 abstract 1
- 230000009466 transformation Effects 0.000 description 4
- 238000010586 diagram Methods 0.000 description 3
- 238000003754 machining Methods 0.000 description 3
- 238000004364 calculation method Methods 0.000 description 1
- 210000002784 stomach Anatomy 0.000 description 1
Classifications
-
- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/41—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path
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- Engineering & Computer Science (AREA)
- Computing Systems (AREA)
- Theoretical Computer Science (AREA)
- Human Computer Interaction (AREA)
- Manufacturing & Machinery (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Numerical Control (AREA)
Abstract
Description
【発明の詳細な説明】
〈産業上の利用分計〉
本発明は曲面生成方法に係り、特に与えられたいくつか
の断面曲線を用いて曲面を生成する曲面生成方法に関す
る。DETAILED DESCRIPTION OF THE INVENTION <Industrial Application> The present invention relates to a curved surface generation method, and more particularly to a curved surface generation method for generating a curved surface using several given cross-sectional curves.
〈背景技術〉
３次元金型等の設計図面上の曲面は一般に複数の断面曲
線によって表現されており、ある断面曲線と次の断面曲
線間の形状データは存在しない。<Background Art> A curved surface on a design drawing of a three-dimensional mold or the like is generally expressed by a plurality of cross-sectional curves, and shape data between one cross-sectional curve and the next does not exist.
ところで、数値制御加工に際しては乙のように中間の形
状が与えられていないにもかかわらず、上記２つの断面
曲線間をなめらかにつながるように加工することが要求
さオ」る。このことは、換言するならば上記２つの断面
曲線間の曲面を、該断面曲線のデータ等から生成し、該
生成された曲面に関するデータを用いて曲面加工用のＮ
Ｃデータを作成し、該ＮＣデータに基づいて加工しなけ
ればならないことを意味する。このｔこめ、従来より種
々の曲面生成方法が提案されて実用化されている。By the way, when numerically controlled machining is performed, it is required to process the two cross-sectional curves so as to smoothly connect them, even though an intermediate shape is not provided as shown in FIG. In other words, a curved surface between the above two cross-sectional curves is generated from the data of the cross-sectional curve, etc., and data regarding the generated curved surface is used to create the N for curved surface machining.
This means that C data must be created and processed based on the NC data. To this end, various methods of generating curved surfaces have been proposed and put into practical use.
〈発明の目的ン
本発明の目的は与えられた断面曲線に清めらかにつなが
る３次元自由曲面を簡単な方法で生成てきる曲面生成方
法を提供ずろことである。<Object of the Invention> An object of the present invention is to provide a curved surface generation method that can easily generate a three-dimensional free-formed surface that smoothly connects to a given cross-sectional curve.
〈発明の概要〉
本発明は第１の与えられた断面曲線を２つの与えられた
第２、第３の断面曲線に治って変化させながら移動させ
、該移動により形成される曲面を生成する曲面生成方法
であり、乙の方法においては第１の断面曲線をＭ分割し
た時の１番目の中間点Ｐ、ｏの座標値をめるステップ、
第２、第３の断面曲線をそれぞれＮ分割した時の」番目
の各ポイントＰ０．１、Ｐｏｌ、の座標値をめるステッ
プ、第１の断面曲線の始点Ｐ。、。と終点Ｐ工、。と前
記中間点Ｐ、、。の関係を用いて、ポインＩ−Ｐ、、、
ｐ＋＋、Ｊをそれぞれ始点、終点とする中間断面曲線上
の前記中間点Ｐ１．。に対応する中間点Ｐ１８、をめる
ステップ、’％Ｊを変化させて全ポインＩ−Ｐ、Ｊい＝
１．２、・・Ｍ； ｊ＝１．２、・・・Ｎ）により曲面
を生成するステップを有する。この方法によれば、簡単
にいくつかの断面曲線に囲まれた曲面を生成できる。<Summary of the Invention> The present invention provides a curved surface that moves a first given cross-sectional curve while changing into two given second and third cross-sectional curves, and generates a curved surface formed by the movement. This is a generation method, and in the method B, the step of calculating the coordinate values of the first intermediate point P, o when the first cross-sectional curve is divided into M,
Step of calculating the coordinate values of each point P0.1, Pol, when the second and third cross-sectional curves are divided into N parts, and the starting point P of the first cross-sectional curve. ,. and the terminal P-engine. and the intermediate point P, . Using the relationship, point I-P, ,
The intermediate point P1. on the intermediate cross-sectional curve with p++ and J as the starting point and ending point, respectively. . The intermediate point P18 corresponding to , the step of changing '%J and all points I-P, J =
1.2,...M; j=1.2,...N). According to this method, a curved surface surrounded by several cross-sectional curves can be easily generated.
〈実施例〉
第１図は本発明に係る曲面生成方法を説明する説明図、
第２図は処理の流れ図である。第１図において、１１は
３次元曲面体を切断する断面、１１ａは断面１１により
３次元曲面体を切断した場合の断面曲線（動作曲線）、
２１．２２は動作曲線１１ａの始点Ｐ。１１１、終点Ｐ
い、。をそれぞれ含む断面、２１ａ、２２ａばそれぞれ
断面２１．２２により３次元曲面体を切断した場合の断
面曲線（基準曲線）であり、各基準曲線の終点はＰ。Ｎ
ＰＰＭ、Ｉｌである。１３は基準曲線２１ａ１２２ａを
それぞれＮ分割した場合の第３番目のポイントＰ。、４
、ｐＭｌ、を含み、かつポイントＰ、０．より断面２１
に降ろした垂線の足Ｑを含む中間断面である。１３ａは
後述する方法により生成される中間断面曲線、Ｐ、、は
中間断面曲線上の中間点である。<Example> FIG. 1 is an explanatory diagram illustrating a curved surface generation method according to the present invention,
FIG. 2 is a flowchart of the process. In FIG. 1, 11 is a cross section of the three-dimensional curved body, 11a is a cross-sectional curve (operation curve) when the three-dimensional curved body is cut by the cross section 11,
21.22 is the starting point P of the operating curve 11a. 111, end point P
stomach,. The cross sections 21a and 22a are cross-sectional curves (reference curves) obtained when the three-dimensional curved body is cut by the cross sections 21 and 22, respectively, and the end point of each reference curve is P. N
PPM, Il. 13 is the third point P when the reference curve 21a122a is divided into N parts. , 4
, pMl, and points P, 0. Cross section 21
This is an intermediate cross section that includes the foot Q of the perpendicular line drawn down to . 13a is an intermediate cross-sectional curve generated by a method described later, and P is a midpoint on the intermediate cross-sectional curve.
以下、第１図、第２図に従って曲面生成処理を説明する
。The curved surface generation process will be described below with reference to FIGS. 1 and 2.
（１）まず、図示しない曲面生成装置の操作盤から断面
１１．２１．２２、動作曲線１１８１基準曲線２１ａ、
２２ａを特定するデータ、並びに動作曲線１１ａの分割
数Ｍ、基準曲線２１ａ１２２ａの分割数Ｎを入力する。(1) First, from the operation panel of the curved surface generation device (not shown), cross sections 11, 21, 22, operation curve 1181, reference curve 21a,
22a, the number of divisions M of the operating curve 11a, and the number of divisions N of the reference curve 21a122a are input.
（２）プロセッサは１→１．１→Ｊとする。(2) The processor is 1→1.1→J.
（３）ついて、プロセッサは各基準曲線２ ］、 ａ、
２２ａをそれぞれＮ分割した場合の３番目のポイン）Ｐ
。１１、ｐ、、の座標値を演算する。(3), the processor calculates each reference curve 2 ], a,
3rd point when dividing 22a into N parts)P
. 11, calculate the coordinate values of p, .
（４）ポイントＰ。Ｊ Ｎ Ｐ Ｍ、Ｊ演算後、プロセ
ッサは動作曲線１１ａをＭ分割した時の、第１番目のポ
イントＰ、。を演算する。尚、ポイントＰ。１４、Ｐ、
、Ｊ、、Ｐ、。の演算法は周知であり、たとえば特願昭
５６−５４０４４号明細書を参照されたい。(4) Point P. After the J N P M, J operation, the processor calculates the first point P, when the operating curve 11a is divided into M. Calculate. Also, point P. 14.P.
,J., ,P. The calculation method is well known; see, for example, Japanese Patent Application No. 56-54044.
（５）断面１１及び中間断面１３を所定の同一平面（Ｈ
−Ｖ平面・・・第３図参照）に変換する変換マトリクス
Ｍ１、Ｍ２をめる。そして、該変換マトリクスＭ１を用
いて、動作曲線１１ａを含む断面１１を所定の平面に変
換した時の該動作曲線の始点Ｐ。、。、終点ｐ、、１中
間点Ｐ、。の座標値（ＸＯｐ Ｙ ｏ）、（Ｘｌ ｐ
Ｙ□）、ＣＸｐｙ）をそれぞれめ、又変換マトリクスＭ
２を用いて、ポイン）Ｐ。、、ｐ、、を含む中間断面１
３を前記所定平面に変換したときの該ポインｌ−Ｐ、、
、ＰＭｌ、の座標値（ξつ、η０）、（ξ１．η１）を
それぞれめる。(5) The cross section 11 and the intermediate cross section 13 are arranged on the same predetermined plane (H
-V plane...see Figure 3). Then, the starting point P of the motion curve when the cross section 11 including the motion curve 11a is transformed into a predetermined plane using the transformation matrix M1. ,. , end point p,, 1 intermediate point P,. The coordinate values of (XOp Y o), (Xl p
Y□), CXpy) respectively, and the transformation matrix M
2, point) P. Intermediate cross section 1 including ,,p, ,
3 is converted to the predetermined plane, the point l-P,
, PMl, coordinate values (ξ, η0) and (ξ1.η1) are determined, respectively.
（６）しかる後、中間点Ｐ１．．の座標値（ξ、η）を
次式
％式％（１）
（２）
（３）
（４）
（５）
（６）
により演算する。これは、Ｐｏ、。 、。、Ｐｌ、。の
、Ｐ。(6) After that, the intermediate point P1. ．． The coordinate values (ξ, η) of are calculated using the following formula % (1) (2) (3) (4) (5) (6). This is Po. ,. ,Pl,. Of, P.
各座標値に対して、次式
％式％）
）
が成立するからである。以上により中間点Ｐ、。がＰＯ
，０” ＋１．。間を内分あるいは外分している比と同
一の比でＰ。＋ Ｊ ’ Ｐ”＋ Ｊを内分あるいは外
分する中間点Ｐ１．．のＨ−Ｖ平面上の座標値がまるこ
とになる。This is because the following formula %) holds true for each coordinate value. As a result of the above, the intermediate point P. is P.O.
, 0" + 1..P with the same ratio as the ratio that internally or externally divides between P. + J'P" + J' intermediate point P1. ．． The coordinate values on the H-V plane will be a circle.
（７）中間点Ｐ１．４の座標値（ξ、ワ）がまれば、プ
ロセッサは変換マトリクスＭ２の逆変換マトリクスＭ２
−１を用いて、（ξ、η）を断面１３上の座標値に逆変
換して、ポインＩ−Ｐ、、の座標値をめ、メモリに記憶
する。(7) If the coordinate values (ξ, wa) of the intermediate point P1.4 are equal, the processor converts the inverse transformation matrix M2 of the transformation matrix M2
-1, (ξ, η) is inversely transformed into the coordinate values on the cross section 13, and the coordinate values of the points I-P, , are obtained and stored in the memory.
（８）ついで、１−Ｍかどうかを判別し、ｌ〈Ｍてあれ
ばｉ ＋ １→ｌとして、ステップ（４）以降の処理を
繰り返す。(8) Next, it is determined whether 1-M or not, and if l<M, then i + 1→l and the process from step (4) is repeated.
（９）一方、ｉ＝Ｍであれば、ｊ＝Ｎかどうかを判別す
る。ｊ＜Ｎであれば、
ｊ＋１→Ｊ１１→ｌ
により’Ｓ Ｊを更新してステップ（３）以降の処理を
繰り返す。(9) On the other hand, if i=M, determine whether j=N. If j<N, 'SJ is updated by j+1→J11→l and the process from step (3) onwards is repeated.
（１０）ステップ（９）の判別においてｊ＝Ｎであれば
曲面生成の処理は終了し、以後ポイントＰ、、（ｉ＝１
．２、・・・・Ｍ、ｊ＝１．２、・・・・Ｎ）を用いて
曲面加工用のＮＣデータを作成する。(10) If j=N in the determination of step (9), the surface generation process ends, and from now on, points P, , (i=1
．． 2,...M, j=1.2,...N) to create NC data for curved surface machining.
〈発明の効果〉
以上説明したように、本発明によれば第１の断面曲線１
１ａをＭ分割した時の１番目の中間点Ｐ、。<Effects of the Invention> As explained above, according to the present invention, the first cross-sectional curve 1
The first intermediate point P when 1a is divided into M parts.
の座標値をめるステップ、第１、第２の断面曲線２１ａ
、２２ａをそれぞれＮ分割した時の３番目の各ポイント
Ｐ。１１、ｐ、、の座標値をめるステップ、第１の断面
曲線１１ａの始点Ｐ。、０と終点Ｐ、１．。と前記中間
点Ｐ、、ｏの関係を用いて、ポイントＰ。、、ｐ、、を
それぞれ始点、終点とする中間断面曲線１３ａ上の前記
中間点Ｐ、ｏに対応する中間点Ｐ、、Ｊをめるステップ
を有し、１１ Ｊを変化させて全ポイントＰ、Ｊい−１
，２、・・Ｍ、ｊ−１，２、・・・Ｎ）により曲面を生
成するように構成したから、簡単に、かつ与えられた断
面曲線を清めらかに連結する曲面を生成することができ
た。Step of calculating the coordinate values of the first and second cross-sectional curves 21a
, 22a is divided into N parts, each third point P. Step 11: finding the coordinate values of p, , the starting point P of the first cross-sectional curve 11a. , 0 and the end point P, 1. . Point P using the relationship between and the intermediate points P,, o. , , p, , respectively, on the intermediate cross-sectional curve 13a, which corresponds to the intermediate points P and o, are found as intermediate points P, , J, and all points P are obtained by changing J. , J-1
, 2,...M, j-1, 2,...N), it is possible to easily generate a curved surface that smoothly connects the given cross-sectional curves. was completed.
第１図は本発明にかかる曲面生成方法の説明図、第２図
は本発明の処理の流れ図、第３図はＨ−Ｖ平面に変換し
た変換図である。
１１．２１．２２・・・断面
１１ ａ、 ２１ ａ、 ２２ ａ・・・断面曲線１３
・・・中間断面、１３ａ・・中間断面曲線特許出願人
ファナック株式会社
代理人 弁理士 齋藤千幹
第１図
７ 第３図
第２図FIG. 1 is an explanatory diagram of the curved surface generation method according to the present invention, FIG. 2 is a flowchart of the process of the present invention, and FIG. 3 is a conversion diagram of conversion to an HV plane. 11.21.22...Cross section 11 a, 21 a, 22 a...Cross section curve 13
...Intermediate section, 13a...Intermediate section curve patent applicant
FANUC Co., Ltd. Agent Patent Attorney Chiki Saito Figure 1 Figure 7 Figure 3 Figure 2
Claims (2)
第２、第３の断面曲線に沿って変化させ□ながら移動さ
せ、該移動により形成される曲面を生成する曲面生成方
法において、第１の断面曲線をＭ分割した時の１番目の
中間点Ｐ３．。の座標値をめるステップ、第１、第′２
の断面曲線をそれぞれＮ分割した時の１番目の各ポイン
トＰ。、１、 。、。 座標値を゛めるステップ、第１の断面臼□線の始点ｐ、
、ｏと終点Ｐｈ、ｏと前記中間点Ｐ１．。の関係を用い
て、ポイントＰ。、３、ｐ、、をそれぞれ始点、終点と
する中間断面曲線上の前記中間点Ｐ 、 ＋’ｏに対応
する中間点Ｐ１．．をめるステップ、ｉｚ Ｊを変化さ
せ、全ポインｌ−Ｐ、、、、−二１．２、・・Ｍ、ｊ＝
１．２、・・・Ｎ）により曲面を生成するステップを有
する曲面生成方法。(1) In a curved surface generation method that moves a first given t cross-sectional curve while changing it along two given second and third cross-sectional curves, and generates a curved surface formed by the movement. , the first intermediate point P3. when the first cross-sectional curve is divided into M parts. . Step of calculating the coordinate values of 1st and 2nd
Each first point P when dividing the cross-sectional curve into N parts. ,1, . ,. Step of calculating coordinate values, starting point p of the first cross-sectional mill □ line,
, o and the end point Ph, o and the intermediate point P1. . Using the relationship, point P. , 3, p, , respectively, are the intermediate points P1., which correspond to the intermediate points P and +'o on the intermediate cross-sectional curve as the end points. ．． step, change iz J, all points l-P,,,,-21.2,...M,j=
1.2,...N) A curved surface generation method comprising the step of generating a curved surface.
た時の該第１断面曲線の始点、終点及び前記中間点の座
標値をそれぞれ（ｘｏ、 ｙｏ） 、（ｘＩＦす）、（
−７ｐ 、 Ｙ ） 、又前記ポイントＰ。、４、Ｐ、
４、を含？断面を前記所定平面に変換したときの該ポイ
ン）Ｐ、、、Ｐ、、、、の座標値を、それぞれ（ξ。。 η０）、（ξ１． Ｖｌ）とした時、前記所定平面上の
中間点Ｐ１，４の座、標値（ξ、η）をξ＝ （−ｎ、
ｆ０＋町ξ、） ／ （ｍ、−ｎ、）η＝（−ｎ、ηｏ
＋ｍｙη、） ／ （ｍ、−ｎ、）ｍう＝ｘ−ｘ Ｑ ｎＸ＝ｘ−ｘ。 ｍ、＝ｙ−ｙ０ ｎ、：ｙ−ｙ。 より演算し、（ξ、η）をポイントＰ０．４、Ｐｏｌ、
を含む曹記断面上の座標値に逆変換して、ポイン１−Ｐ
、、の座標値をめることを特徴とする特許請求の範囲第
（１）項記載の曲面生成方法。(2) When the cross section including the first cross-sectional curve is converted into a predetermined plane, the coordinate values of the start point, end point, and intermediate point of the first cross-sectional curve are (xo, yo), (xIF), (
-7p, Y), and the above point P. ,4.P.
4. Including? When the coordinate values of the points) P, , P, , , when the cross section is converted to the predetermined plane are (ξ.. η0) and (ξ1. Vl), respectively, the intermediate point on the predetermined plane is The coordinates and values (ξ, η) of points P1, 4 are ξ= (-n,
f0 + town ξ, ) / (m, -n,) η = (-n, ηo
+myη, ) / (m, -n,)m=x-x Q nX=x-x. m,=y-y0 n,:y-y. Calculate (ξ, η) from point P0.4, Pol,
Inversely transform the coordinate values on the Caoji section including
, , , , , , , , , , , , , , , , , , , , , , , , and .
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP59105476A JPH067361B2 (en) | 1984-05-24 | 1984-05-24 | Curved surface generation method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP59105476A JPH067361B2 (en) | 1984-05-24 | 1984-05-24 | Curved surface generation method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPS60250403A true JPS60250403A (en) | 1985-12-11 |
| JPH067361B2 JPH067361B2 (en) | 1994-01-26 |
Family
ID=14408644
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP59105476A Expired - Lifetime JPH067361B2 (en) | 1984-05-24 | 1984-05-24 | Curved surface generation method |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH067361B2 (en) |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS57169814A (en) * | 1981-04-10 | 1982-10-19 | Fanuc Ltd | Forming method of curved surface |
| JPS57211603A (en) * | 1981-06-20 | 1982-12-25 | Fanuc Ltd | Nc data forming method |
| JPS58149507A (en) * | 1982-02-26 | 1983-09-05 | Mitsubishi Electric Corp | Nc automatic programming system |
-
1984
- 1984-05-24 JP JP59105476A patent/JPH067361B2/en not_active Expired - Lifetime
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS57169814A (en) * | 1981-04-10 | 1982-10-19 | Fanuc Ltd | Forming method of curved surface |
| JPS57211603A (en) * | 1981-06-20 | 1982-12-25 | Fanuc Ltd | Nc data forming method |
| JPS58149507A (en) * | 1982-02-26 | 1983-09-05 | Mitsubishi Electric Corp | Nc automatic programming system |
Also Published As
| Publication number | Publication date |
|---|---|
| JPH067361B2 (en) | 1994-01-26 |
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