JP2920195B2 - Shape conversion method and device - Google Patents
Shape conversion method and deviceInfo
- Publication number
- JP2920195B2 JP2920195B2 JP1058454A JP5845489A JP2920195B2 JP 2920195 B2 JP2920195 B2 JP 2920195B2 JP 1058454 A JP1058454 A JP 1058454A JP 5845489 A JP5845489 A JP 5845489A JP 2920195 B2 JP2920195 B2 JP 2920195B2
- Authority
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- Japan
- Prior art keywords
- shape
- line segment
- model
- arbitrary shape
- approximation
- 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.)
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Description
【発明の詳細な説明】 〔産業上の利用分野〕 本発明は、CAEなどの分野で用いられるコンピュータ
による形状変換方法および装置に係り、特に、形状の分
類、識別を必要とするモデリング、メッシュ分割に好適
な形状変換方法および装置に関する。Description: TECHNICAL FIELD The present invention relates to a method and an apparatus for transforming a shape by a computer used in the field of CAE and the like, and in particular, to modeling and mesh division which require classification and identification of shapes. More particularly, the present invention relates to a shape conversion method and a device suitable for the present invention.
CAEにおいては、境界形状が面−線−点とつながる構
造データ、及び面、線の方程式や点の座標などの幾荷デ
ータで表現されている。In the CAE, the boundary shape is represented by structural data that is connected to a plane-line-point, and several pieces of data such as the equation of a plane and a line and the coordinates of a point.
これらのデータをもとにした形状認識手法として、従
来、最も一般的に用いられてまた方法として、四分木法
(2次元)及び八分木法(3次元)があり、「有限要素
分割のための改良された四分木法」マークエー・エリー
とマークエス・シェファードIEEE CG & A 1983年1月P
39〜46(A Modified Quadtree Approach to Finite Ele
ment Mesh Generation Mark A.Yerry and Mark S.Sheph
ard IEEE CG & A January 1983)にも詳説されてい
る。Conventionally, as a shape recognition method based on these data, the most commonly used methods are the quadtree method (two-dimensional) and the octree method (three-dimensional). Improved Quadtree Method for "Mark A. Ely and Mark E. Shepherd IEEE CG & A January 1983 P
39-46 (A Modified Quadtree Approach to Finite Ele
ment Mesh Generation Mark A. Yerry and Mark S. Sheph
ard IEEE CG & A January 1983).
ここでは、説明を簡単にするため、第17A図に示す2
次元形状を例にとってこの手法を説明する。Here, for the sake of simplicity, FIG.
This method will be described by taking a dimensional shape as an example.
まず、この図形を基準となる正方形(基準正方形)の
中に入れこの正方形の一辺の長さが2nとなるような整数
座標系を設定する。そして、基準正方形を小さな正方形
に4等分して、各領域と前記図形を形成する境界線の関
係を次のように分類する。First, this figure is placed in a reference square (reference square), and an integer coordinate system is set such that the length of one side of the square is 2 n . Then, the reference square is divided into four equal small squares, and the relationship between each area and the boundary line forming the figure is classified as follows.
(1) 正方形が境界線の内側にある (2) 正方形が境界線の外側にある (3) 正方形が境界線を含む ここで、(3)と判定された正方形のみを再び4等分
し、上記のチェックを行う。このような操作を適当な形
状解像度に対応するレベルまで続ける。(1) The square is inside the boundary (2) The square is outside the boundary (3) The square contains the boundary Here, only the square determined as (3) is again divided into four equal parts, Perform the above checks. Such an operation is continued to a level corresponding to an appropriate shape resolution.
正方形の一辺が基準正方形の1/8になるまで分割した
結果が第17B図でこれに対応するツリー構造は第17C図で
表される。また、1ランク解像度を上げると第17D図の
ようになる。The result of division until one side of the square becomes 1/8 of the reference square is shown in FIG. 17B, and the corresponding tree structure is shown in FIG. 17C. When the resolution of one rank is increased, the result becomes as shown in FIG. 17D.
そして、形状認識においては、第17C図のツリー構造
をもとに、形状の概略特性を判定する。Then, in shape recognition, the approximate characteristics of the shape are determined based on the tree structure in FIG. 17C.
第17C図に記入された数字は、分割されてできた正方
形領域と対象図形を形成する境界線との関係を示し、前
記三つの分類に対応している。The numbers entered in FIG. 17C indicate the relationship between the divided square area and the boundary line forming the target graphic, and correspond to the above three classifications.
上記従来技術においては、形状そのものの全体的図形
特性を把握することは困難で登録図形(比較対象となる
図形)から形がゆがんでくると、認識率が累進的に低下
する欠点があった。また、近似モデルを作成するにも、
対象形状の各辺をどの座標軸に平行にするかに関して統
一的な理論は確立されておらず、多分のあいまいさを含
んでいる。In the above prior art, it is difficult to grasp the overall graphic characteristics of the shape itself, and there is a disadvantage that the recognition rate progressively decreases when the shape is distorted from a registered graphic (a graphic to be compared). Also, to create an approximate model,
No unified theory has been established regarding which coordinate axis is parallel to each side of the target shape, and it contains some ambiguity.
本発明の目的は、任意形状の図形特性が保存された近
似モデルを生成する形状変換装置を提供するにある。ま
た、本発明の他の目的は、任意形状を入力することで、
有限要素に分割された任意形状を出力する形状変換装置
を提供することにある。An object of the present invention is to provide a shape conversion device that generates an approximate model in which graphic characteristics of an arbitrary shape are stored. Another object of the present invention is to input an arbitrary shape,
An object of the present invention is to provide a shape conversion device that outputs an arbitrary shape divided into finite elements.
上記の課題は、任意形状を直線線分のみからなる形状
に変換する手段を備えた形状変換装置に、該直線線分を
座標軸に平行な線分に変換する手段を備えることにより
達成される。The above object is achieved by providing a shape conversion device having means for converting an arbitrary shape into a shape consisting only of straight line segments, and having means for converting the straight line segments into line segments parallel to the coordinate axes.
直線線分を座標軸に平行な線分に変換する手段が、メ
ンバシップ関数を用いて演算を行なうあいまい演算部を
備えている請求項1に記載の形状変換装置としてもよ
い。The shape conversion device according to claim 1, wherein the means for converting the straight line segment into a line segment parallel to the coordinate axis includes an ambiguous operation unit for performing an operation using a membership function.
また、上記課題は、任意形状の境界線または稜線を複
数の直線線分で近似し、それぞれの線分の座標軸への近
似度を0から1の変数で表現し、あいまいルールにより
該変数を全体的に修正して各線分をいずれかの座標軸に
平行に割り当て、最終的に一つの近似モデルに収束させ
る形状変換方法によっても達成される。In addition, the above problem is that a boundary line or an ridge line of an arbitrary shape is approximated by a plurality of straight line segments, and the degree of approximation to the coordinate axis of each line segment is expressed by a variable from 0 to 1, and the variable is represented by an ambiguous rule. This is also achieved by a shape conversion method in which each line segment is corrected in parallel and assigned to any of the coordinate axes, and finally converges to one approximate model.
また、任意形状の境界線または稜線を複数の直線線分
で近似し、隣接する線分が、一直線上にあるか、互いに
垂直になるように前記線分を変換して形状を形成する形
状変換方法としてもよい。In addition, a shape conversion that approximates a boundary line or ridge line of an arbitrary shape with a plurality of straight line segments and converts the line segments so that adjacent line segments are on a straight line or perpendicular to each other to form a shape is performed. It is good also as a method.
また、任意形状の境界線または稜線を複数の直線線分
で近似し、それぞれの線分が座標軸となす角度を計算
し、計算された角度および予め設定されたあいまいルー
ルに基づくメンバシップ関数により前記線分をいずれか
の座標軸に平行に割り当てて、前記任意形状の近似モデ
ルを作成する形状変換方法としてもよい。Further, a boundary line or ridge line of an arbitrary shape is approximated by a plurality of straight line segments, an angle between each line segment and a coordinate axis is calculated, and the calculated angle and a membership function based on a preset ambiguous rule are used. A shape conversion method for creating an approximate model of the arbitrary shape by allocating a line segment in parallel to one of the coordinate axes may be used.
また、あいまいルールが、少なくとも、線分となす角
が最も小さい座標軸の方向へなるべく該線分が割り当て
られることと、互に隣接する二つの線分はそのなす角が
一定角よりも小さいほどなるべく異なる方向に、なす角
が一定角よりも大きいほどなるべく同じ方向に割り当て
られることと、を含んでいる請求項5に記載の形状変換
方法としてもよい。Further, the fuzzy rule is that the line segment is assigned at least in the direction of the coordinate axis where the angle formed by the line segment is the smallest, and that the angle between two adjacent line segments is smaller than a certain angle. The shape conversion method according to claim 5, further comprising: assigning an angle to a different direction in the same direction as much as the angle formed is larger than a certain angle.
また、与えられた形状の境界面または境界線の近似モ
デルと、該境界面または境界線に含まれる穴の近似モデ
ルと、を独立に作成したのち、与えられた前記実形状に
おいて穴に関係なく滑らかな格子を形成し、実形状にお
いて穴を形成する頂点がどの格子点に対応するかをもと
にして近似モデルにおける穴の境界形状に対する相対位
置を決定することを特徴とする形状変換方法としてもよ
い。In addition, after independently creating an approximate model of a boundary surface or a boundary line of a given shape and an approximate model of a hole included in the boundary surface or the boundary line, regardless of the hole in the given actual shape, A shape conversion method that forms a smooth grid and determines the relative position of the hole to the boundary shape in the approximate model based on which grid point the vertex that forms the hole in the real shape corresponds to Is also good.
さらに、近似モデルの形状の位相的特性を保持したま
ま、該近似モデルを構成する線分の長さを、単位長さの
最小の整数倍に変換することを特徴とする形状変換方法
としてもよい。Furthermore, the shape conversion method may be characterized in that the length of a line segment forming the approximate model is converted to the minimum integral multiple of the unit length while maintaining the topological characteristics of the shape of the approximate model. .
また、解析対象となる任意形状を入力し、該任意形状
から直交座標系の座標軸に平行な直線線分のみで構成さ
れた任意形状の近似モデルを生成し、該近似モデルから
近時モデルの各直線線分が単位長さの整数倍になるよう
に格子を張った格子形状である写像モデルを生成し、写
像演算を行なうことによって該写像モデルから、任意形
状の解析用メッシュを自動生成するようにしてもよい。Further, an arbitrary shape to be analyzed is input, and an approximate model of an arbitrary shape composed of only straight line segments parallel to the coordinate axes of the orthogonal coordinate system is generated from the arbitrary shape, and each of the recent models is generated from the approximate model. A mapping model having a grid shape in which a straight line segment is gridded so as to be an integral multiple of the unit length is generated, and an analysis mesh of an arbitrary shape is automatically generated from the mapping model by performing a mapping operation. It may be.
任意形状が、直線線分のみからなる形状に変換され、
さらに該直線線分が、いずれかの座標軸に平行に変換さ
れるので、前記任意形状は座標軸に平行な直線のみで構
成された図形に変換される。The arbitrary shape is converted into a shape consisting of only straight line segments,
Further, since the straight line segment is converted to be parallel to any one of the coordinate axes, the arbitrary shape is converted to a figure composed of only straight lines parallel to the coordinate axes.
メンバシップ関数を用いて演算を行うあいまい演算部
は、あらかじめ定められたあいまいルールに従って、そ
れぞれの線分が、どの座標軸に平行に変換されるべきか
を選定する。An ambiguous operation unit that performs an operation using the membership function selects which coordinate axis each line segment should be transformed in parallel to in accordance with a predetermined ambiguous rule.
任意形状の近似モデル作成にあたっては、まず、該任
意形状のすべての稜線(3次元形状の場合)もしくは境
界線(2次元形状の場合)が直線線分によって近似さ
れ、各線分と座標軸(x,y,z軸)とがなす角度が算出さ
れる。次に各線分をどの座標軸に平行にするかの割り当
てを行うにあたり、すくなくとも次の二つの基本となる
あいまいルールが用いられる。In creating an approximate model of an arbitrary shape, first, all ridge lines (in the case of a three-dimensional shape) or boundary lines (in the case of a two-dimensional shape) of the arbitrary shape are approximated by straight line segments, and each line segment and a coordinate axis (x, An angle formed between the y-axis and the y-axis is calculated. Next, at the time of assigning which coordinate axis is parallel to each line segment, at least the following two basic vague rules are used.
各線分はなるべくなす角が最も小さい座標軸の方向
へ割り当てられる。Each line segment is assigned in the direction of a coordinate axis with the smallest angle that can be made.
隣り合う2辺は、そのなす角が一定角よりも小さい
ほど、なるべく異なる座標軸の方向へ割り当てられ、な
す角が一定角よりも大きいほど、なるべく同じ方向に割
り当てられる。Two adjacent sides are assigned to different coordinate axis directions as the angle between them becomes smaller than the fixed angle, and are assigned to the same direction as the angle between the adjacent sides becomes larger than the fixed angle.
そして、このルールの持つあいまいさを表現する為に
ファジィ理論におけるメンバーシップ関数が用いられ
る。まず、各線分の座標軸への近似度が0から1で表さ
れる。この場合、座標軸となす角が0度に近いほど近似
度は1に近づき、なす角が90度に近いほど近似度は0に
近づく。Then, a membership function in fuzzy theory is used to express the ambiguity of this rule. First, the degree of approximation of each line segment to the coordinate axis is represented by 0 to 1. In this case, the degree of approximation approaches 1 as the angle formed with the coordinate axis approaches 0 degrees, and the degree of approximation approaches 0 as the angle formed approaches 90 degrees.
さらに、隣り合う2辺に関して、2辺のなす角をもと
に同方向度が−1から1で表される。この場合、2辺の
なす角が180度に近いほど同方向度は1に近づき、90度
までに−1にまで変化し、90度以下で−1で一定とな
る。Further, with respect to two adjacent sides, the degree of the same direction is represented by -1 to 1 based on the angle formed by the two sides. In this case, the degree of the same direction approaches 1 as the angle between the two sides approaches 180 degrees, changes to -1 by 90 degrees, and becomes constant at -1 below 90 degrees.
次に、隣り合う2辺に関して、座標軸への近似度及び
同方向度をもとに互いの辺への影響度が計算される。こ
の場合、同方向度が正の場合は、例えば影響を与える辺
のX方向近似度は影響を受ける辺のX方向近似度を高く
し、Y,Z方向近似度を低くする働きをする。また、同方
向度が負の場合は、例えば影響を与える辺のY方向近似
度は影響を受ける辺のY方向近似度を低くし、X,Y方向
近似度を高くする働きをする。そして、このような影響
度が数量で表され、この影響度によって、各辺のX,Y,Z
座標軸それぞれへの近似度が修正される。Next, for two adjacent sides, the degree of influence on each side is calculated based on the degree of approximation to the coordinate axis and the degree of the same direction. In this case, when the degree of the same direction is positive, for example, the degree of approximation of the affected side in the X direction acts to increase the degree of approximation of the affected side in the X direction and to decrease the degree of approximation of the Y and Z directions. When the degree of the same direction is negative, for example, the degree of approximation of the affected side in the Y direction lowers the degree of approximation of the affected side in the Y direction and increases the degree of approximation of the X and Y directions. Then, such an influence degree is represented by a quantity, and the X, Y, Z
The degree of approximation to each coordinate axis is modified.
すべての辺の修正が終われば、修正された近似度をも
とに、同様にして隣り合う2辺に関して影響度が算出さ
れ、これにより再び座標軸への近似度が修正される。こ
のような演算が繰り返し行われ、すべての辺に関して、
各座標軸への近似度のうち1方向への近似度が充分1に
近付けば、その状態を収束状態として、各辺の方向割り
当てが決定される。When the correction of all sides is completed, the degree of influence is similarly calculated for two adjacent sides based on the corrected degree of approximation, and thereby the degree of approximation to the coordinate axes is corrected again. Such an operation is repeatedly performed, and for all sides,
If the degree of approximation in one direction among the degrees of approximation to each coordinate axis is sufficiently close to 1, the state is set to a convergence state and the direction assignment of each side is determined.
各辺の方向割り当てが決定すれば、ループ(図形)ご
とに近似モデル上での各辺の長さの決定が行われる。こ
の際、基本的な線長決定の方法として、以下の方法が用
いられる。第15図に示すように、2次元図形が、座標軸
に平行な線分のみで構成されるとループをたどれば各線
分の向きは4方向に分類される。そこで、それぞれの線
分に対応する実形状の線分の各方向成分の線分長の方向
ごとの合計が算出され、実形状での方向1と方向2に対
応する線分の線分長の合計の平均値が近似モデル上での
方向1と方向2を持つ線分の線分長の合計に設定され、
方向3と方向4に関しても同じ操作が行われる。そし
て、近似モデル上での同じ方向の線分の線分長の合計値
が決まれば、この合計値が実形状での線分長の比に応じ
て座標軸に平行に割り当てられた各直線線分の長さとし
て比例配分され、各辺の近似モデル上での長さの決定が
行われる。このようにして、幾何特性及び位相特性をで
きるだけ保存した座標軸に平行な線分のみで構成される
近似モデルが作成される。If the direction assignment of each side is determined, the length of each side on the approximate model is determined for each loop (graphic). At this time, the following method is used as a basic method for determining the line length. As shown in FIG. 15, if the two-dimensional figure is composed of only line segments parallel to the coordinate axes, the directions of the line segments are classified into four directions by following the loop. Then, the total of the line segment lengths of the direction components of the real shape line segments corresponding to the respective line segments is calculated for each direction, and the line segment lengths of the line segments corresponding to direction 1 and direction 2 in the real shape are calculated. The average value of the sum is set to the sum of the lengths of the line segments having the directions 1 and 2 on the approximate model,
The same operation is performed for directions 3 and 4. Then, when the total value of the line segments in the same direction on the approximate model is determined, this total value is assigned to each straight line segment assigned in parallel to the coordinate axis according to the ratio of the line length in the actual shape. , And the length of each side is determined on the approximate model. In this way, an approximation model composed of only line segments parallel to the coordinate axes, in which the geometric characteristics and the phase characteristics are preserved as much as possible, is created.
各構成単位(境界形状及び該形状に含まれる穴)ごと
の近似モデルが構成されたのち、適当な単位長さが決定
され、すべての辺がこの単位長さの整数倍になるように
修正され、この単位長さをもとに境界形状及び穴形状独
立に格子を張られる。そして、近似モデルの境界形状に
格子が張れれば、曲線座標変換法を用いて、この格子が
穴を考慮しない実形状に写像される。After an approximate model is constructed for each constituent unit (boundary shape and holes included in the shape), an appropriate unit length is determined, and all sides are modified so as to be an integral multiple of this unit length. Based on the unit length, a grid can be formed independently of the boundary shape and the hole shape. Then, if a grid is formed on the boundary shape of the approximate model, this grid is mapped to an actual shape that does not consider holes by using the curve coordinate conversion method.
ここで、曲線座標変換法とは、第9図に示すように、
直交格子をもとにして、任意形状に均一な格子を形成す
る数学的手法をいう。Here, the curve coordinate conversion method is, as shown in FIG.
A mathematical method for forming a uniform grid in an arbitrary shape based on an orthogonal grid.
実形状の境界内部に格子が張れれば、穴の特徴点に最
も近い格子点が求められ、近似モデルの境界内部に張ら
れた格子の上での対応が取られ、穴の近似モデルの境界
形状の近似モデルに対する相対位置の最適化が図られ、
穴を含んだ全体的近似モデルが構成される。If a grid is formed inside the boundary of the actual shape, a grid point closest to the feature point of the hole is obtained, and a correspondence is taken on the grid formed inside the boundary of the approximate model, and the boundary of the approximate model of the hole is obtained. Optimization of the relative position with respect to the approximate model of the shape is achieved,
An overall approximation model including the holes is constructed.
全体的近似モデルができれば、第16図に示されるよう
に、近似モデルの位相状態が保持されることを前提に、
各辺が最小の整数値を取るように変換された認識モデル
が構成される。この認識モデルの各辺には対応する近似
モデルの各辺の長さが属性として与えられる。If an overall approximation model is created, as shown in FIG. 16, on the assumption that the phase state of the approximation model is maintained,
A recognition model converted so that each side takes a minimum integer value is configured. The length of each side of the corresponding approximate model is given as an attribute to each side of the recognition model.
認識モデルの認識は、次の手順で行われる。 The recognition of the recognition model is performed in the following procedure.
認識モデルの大きさ(NX,NY)による分類 認識モデルの形状による分類 各辺の対応線分の線長をもとにした比較 以上3段階の認識手順により、もとの任意形状に相当
する登録図形が選び出される。Classification by size of recognition model (NX, NY) Classification by shape of recognition model Comparison based on line length of corresponding line of each side Registration corresponding to the original arbitrary shape by the above three steps of recognition procedure A figure is selected.
第1図は本発明の実施例の全体構成を示すブロック図
である。任意形状設定部8に接続してキーボード2、タ
ブレット3、およびマウス4などの構成要素からユーザ
により形状の直接入力が行われる図形入力部1が設けら
れ、該図形入力部1はさらに、表示制御部6を有するCR
Tディスプレー5に接続されている。前記任意形状設定
部8の入力側には、さらに、形状読取部7が接続され、
任意形状設定部8の出力側には、曲線変換部9や幾何演
算部10で得られた情報をもとに各辺の座標軸への近似度
や隣り合う2辺の同方向度を算出する形状情報生成部11
が接続されている。該形状情報生成部11は、さらに、近
似モデル生成部15に接続され、前記幾何演算部10は形状
情報生成部11および近似モデルを生成部15に接続されて
いる。近似モデル生成部15はさらに全体近似モデル生成
部18に接続され、全体近似モデル生成部18は認識モデル
生成部19に接続されている。認識モデル生成部19は、認
識結果表示部22に接続され、認識結果表示部22はさらに
前記CRTディスプレー5に接続されている。形状情報生
成部11には、さらに、任意形状の稜線(境界線)を直線
近似する曲線変換部9およびファジィ演算を行って決定
された各辺の座標軸方向への方向割当てにより、位相的
に形状が成立するかどうかを確認する整合確認部14が接
続されている。FIG. 1 is a block diagram showing the overall configuration of an embodiment of the present invention. A graphic input unit 1 is provided which is connected to an arbitrary shape setting unit 8 and allows a user to directly input a shape from components such as a keyboard 2, a tablet 3, and a mouse 4. The graphic input unit 1 further includes a display control unit. CR with part 6
Connected to T display 5. A shape reading unit 7 is further connected to an input side of the arbitrary shape setting unit 8,
On the output side of the arbitrary shape setting unit 8, a shape for calculating the degree of approximation of each side to the coordinate axis and the degree of the same direction of two adjacent sides based on the information obtained by the curve conversion unit 9 and the geometric operation unit 10. Information generator 11
Is connected. The shape information generation unit 11 is further connected to an approximate model generation unit 15, and the geometric operation unit 10 is connected to the shape information generation unit 11 and the approximate model generation unit 15. The approximate model generation unit 15 is further connected to an overall approximate model generation unit 18, and the overall approximate model generation unit 18 is connected to a recognition model generation unit 19. The recognition model generation unit 19 is connected to the recognition result display unit 22, and the recognition result display unit 22 is further connected to the CRT display 5. The shape information generation unit 11 further includes a curve conversion unit 9 for linearly approximating a ridge line (boundary line) of an arbitrary shape and a direction assignment in a coordinate axis direction of each side determined by performing a fuzzy operation. Is connected to a matching check unit 14 for checking whether or not the condition is satisfied.
前記近似モデル生成部15には、形状情報をもとに、あ
いまいルールに従って各辺の座標軸への近似度を修正す
るファジィ演算部13および前記整合確認部14が接続さ
れ、ファジィ演算部13には、形状変換を行ううえでの種
々のルールを設定するあいまいルール設定部12が接続さ
れている。幾何演算部10から得られた幾何データおよび
ファジィ演算部13から得られた位相データをもとに近似
モデルを構成する前記近似モデル生成部15には、近似モ
デルに張った正方格子をもとに曲線座標変換法を用いて
実形状に格子を生成する写像演算部16が接続され、該写
像演算部16は、この格子を用いて穴の境界形状に対する
相対位置を検出する相対位置算出部17を介して、前記全
体近似モデル生成部18に接続されている。また、近似モ
デルを認識モデルに変換する前記認識モデル生成部19に
接続して、認識モデルをもとに基本図形データベース21
に登録された図形との照合を行う認識演算部20が設けら
れ、該認識演算部20には、基本図形が登録された基本図
形データベース21が接続されている。認識演算部20はま
た、認識演算部20の演算結果を表示する認識結果表示部
22に接続されている。前記幾何演算部は各直線と座標
軸、及び隣り合う辺がなす角の計算や実形状をもとにし
た近似モデルの各辺の長さの計算を行う。全体近似モデ
ル生成部18は、近似モデル生成部15および相対位置算出
部17から与えられる情報をもとに、境界形状及び穴の近
似モデルを組み合わせて全体的近似モデルを構成する。
前記CRTディスプレイ5は、また任意形状設定部8に接
続されている。Based on the shape information, the approximate model generation unit 15 is connected to a fuzzy calculation unit 13 and the matching check unit 14 for correcting the degree of approximation of each side to the coordinate axis according to the fuzzy rule, and the fuzzy calculation unit 13 An ambiguous rule setting unit 12 for setting various rules for performing shape conversion is connected. The approximation model generation unit 15 that constructs an approximation model based on the geometric data obtained from the geometric operation unit 10 and the phase data obtained from the fuzzy operation unit 13 is based on a square lattice attached to the approximation model. A mapping operation unit 16 that generates a lattice in an actual shape using the curve coordinate transformation method is connected, and the mapping operation unit 16 includes a relative position calculation unit 17 that detects a relative position of the hole with respect to the boundary shape using the lattice. The overall approximation model generation unit 18 is connected via the above. In addition, the basic model database 21 is connected to the recognition model generation unit 19 that converts the approximate model into a recognition model, based on the recognition model.
Is provided with a recognition operation unit 20 for performing comparison with a figure registered in the base figure. The recognition operation unit 20 is connected to a basic figure database 21 in which basic figures are registered. The recognition calculation unit 20 also includes a recognition result display unit that displays the calculation result of the recognition calculation unit 20.
Connected to 22. The geometric operation unit calculates the angle between each straight line and the coordinate axis and the adjacent side, and calculates the length of each side of the approximate model based on the actual shape. The overall approximate model generation unit 18 configures an overall approximate model by combining the boundary shape and the approximate model of the hole based on the information provided from the approximate model generation unit 15 and the relative position calculation unit 17.
The CRT display 5 is connected to an arbitrary shape setting unit 8.
上述のあいまいルール設定部12とファジィ演算部13と
があいまい演算部30Aを形成し、該あいまい演算部30A
と、幾何演算部10と、形状情報生成部11と、整合確認部
14と、近似モデル生成部15とが、直線線分を座標軸に平
行な線分に変換する手段30をなしている。The above-described fuzzy rule setting unit 12 and fuzzy calculation unit 13 form a fuzzy calculation unit 30A, and the fuzzy calculation unit 30A
, A geometric operation unit 10, a shape information generation unit 11, and a matching confirmation unit
The approximation model generation unit 14 and the approximation model generation unit 15 constitute a unit 30 that converts a straight line segment into a line segment parallel to the coordinate axes.
次に、上記実施例の動作を説明する。図形入力部1又
は形状読取部7より任意形状設定部8に第2図に示され
る2次元の形状aが入力されると、曲線変換部9によ
り、その形状の曲線部が直線近似された形状bが生成さ
れる。形状bを構成する各線分がx軸又はy軸に平行な
方向に割り当てられ、第2図の形状cのような近似モデ
ルに変換される。Next, the operation of the above embodiment will be described. When the two-dimensional shape a shown in FIG. 2 is input from the graphic input unit 1 or the shape reading unit 7 to the arbitrary shape setting unit 8, the curve conversion unit 9 linearly approximates the curved portion of the shape. b is generated. Each line segment forming the shape b is assigned in a direction parallel to the x-axis or the y-axis, and is converted into an approximate model such as the shape c in FIG.
この近似モデルの構成方法について説明する。まず、
近似モデルの位相情報(各線分をx,y軸のいずれに平行
に割り当てるかの情報)の生成に関し、次の4つの基本
ルールがあいまいルールとして用いられる。A method of configuring this approximate model will be described. First,
Regarding the generation of the phase information of the approximate model (information on which of the x and y axes each line segment is to be assigned to in parallel), the following four basic rules are used as ambiguous rules.
ルール1:各線はなるべくなす角が最も小さい座標軸の方
向に平行に割り当てられる。Rule 1: Each line is assigned parallel to the direction of the coordinate axis with the smallest possible angle.
ルール2:隣り合う2辺に関して、なす角が別に定められ
る一定角よりも小さいほどなるべく異なる座標軸の方向
に割り当てられ、なす角が前記一定角よりも大きいほ
ど、なるべく同じ座標軸の方向に割り合てられる。Rule 2: With respect to two adjacent sides, the angle formed is assigned to a direction of different coordinate axes as much as smaller than a predetermined fixed angle.As the angle formed is larger than the predetermined angle, the directions are preferably allocated to the same coordinate axis. Can be
ルール3:傾きの変化率の少ない線群は、なるべく1つの
方向に割り当てられる。Rule 3: Line groups with a small change rate of inclination are assigned to one direction as much as possible.
ルール4:平行な線群は、なるべく同じ方向に割り当てら
れる。Rule 4: Parallel lines are preferably assigned in the same direction.
ルール1は各線分が座標軸となす角をもとにして得ら
れる座標軸への近似度の初期設定により実現される。x
軸およびy軸への近似度は第3A図、および第3B図に示さ
れるように、横軸にx軸またはy軸となす角(θx,θ
y)をとり、縦軸にx軸方向又はy軸方向の近似度Px,P
y(0≦Px≦1,0≦Py≦1)をとったメンバーシップ関数
で示される。線分がいずれかの座標軸となす角が0度に
近いほど近似度は1に近ずき、なす角が90゜に近いほど
近似度は0に近ずくように定義される。Rule 1 is realized by initial setting of the degree of approximation to the coordinate axis obtained based on the angle between each line segment and the coordinate axis. x
As shown in FIGS. 3A and 3B, the degree of approximation to the x-axis and y-axis is represented by the angle (θx, θ
y), and the vertical axis represents the degree of approximation Px, P in the x-axis direction or the y-axis direction.
It is represented by a membership function taking y (0 ≦ Px ≦ 1, 0 ≦ Py ≦ 1). The degree of approximation is defined to be closer to 1 as the angle between the line segment and any one of the coordinate axes is closer to 0 degree, and closer to 0 as the angle is closer to 90 °.
また、ルール2は近似度と隣り合う2辺の間の関係で
ある同方向度とをもとにする、各辺の座標軸への近似度
の修正によって実現される。隣り合う2辺の同方向度PR
は、隣り合う該2辺のなす角θRを横軸にとり、同方向
度PR(−1≦PR≦1)1)を縦軸にとった第3C図に示さ
れるようなメンバシップ関数で示される。この場合、同
方向度は2辺のなす角が180度に近ずくほど1に近ず
き、なす角が180度から90度に近ずくにつれ−1にまで
変化し、90度以下では、−1で一定である。Rule 2 is implemented by modifying the degree of approximation of each side to the coordinate axis based on the degree of approximation and the degree of the same direction, which is the relationship between two adjacent sides. The same direction of the two sides adjacent P R
Is membership function as shown an angle theta R of two sides adjacent the horizontal axis, the Figure 3C the same direction of P R (-1 ≦ P R ≦ 1) 1) taken on the vertical axis Indicated by In this case, the degree of the same direction approaches 1 as the angle between the two sides approaches 180 degrees, and changes from -1 to 180 as the angle approaches 180 degrees to 90 degrees. It is constant at 1.
近似度の修正に関し、第4図に示される2本の線分
を例にとって説明する。まず、第3A図により、線分
のx軸近似度Px,y軸近似度Pyはそれぞれ0.8,0.2で線
分のX,Y軸近似度は、それぞれ0.4,0.6であり、2辺の
なす角が108度であることから、第3C図により、線分
の同方向度PRは−0.6であり、これは2辺が異なる
方向の座標軸に割り当てられる強さが0.6であることを
意味する。そこで、これらの値をもとに、まず、線分
から線分への影響度が算出される。なお、影響度は近
似度を修正する度合いを示すものとして定義される。影
響度の算出は、次の4項目の演算を行うことにより実現
される。The modification of the approximation will be described with reference to two line segments shown in FIG. 4 as an example. First, according to FIG. 3A, the x-axis approximation Px and the y-axis approximation Py of the line segment are 0.8 and 0.2, respectively, and the X and Y-axis approximations of the line segment are 0.4 and 0.6, respectively. since There is 108 degrees, the Figure 3C, the same direction of P R of the line segment is -0.6, which means that strength two sides are assigned to different directions of the coordinate axes is 0.6. Therefore, based on these values, first, the degree of influence on a line segment is calculated. Note that the degree of influence is defined as indicating the degree of correcting the degree of approximation. The calculation of the degree of influence is realized by performing the following four operations.
(i)線分のx軸から線分のx軸への影響度 Qxx 線分からなる2辺は、同方向度が前述のように負
のため、線分のxらしさは、線分のxらしさを否定
する。第5A図のように、線分のx軸方向近似度は0.
8、線分の非x軸方向近似度は0.6であるから線分の
x軸から線分のx軸への影響度Qxxは、下記(1)式
により算出される。(I) The degree of influence from the x-axis of the line segment to the x-axis of the line segment Since the two sides of the Qxx line segment have the same negative direction as described above, the x-likeness of the line segment is the x-likeness of the line segment. Is denied. As shown in FIG.5A, the degree of approximation of the line segment in the x-axis direction is 0.
8. Since the degree of approximation of the line segment in the non-x-axis direction is 0.6, the degree of influence Qxx from the x-axis of the line segment to the x-axis of the line segment is calculated by the following equation (1).
Qxx=(線分のx軸方向近似度)×(線分の 非x軸方向近似度)×(同方向度) ……(1) =0.8×0.6×(−0.6)=−0.288 (ii)線分のy軸から線分のx軸への影響度 Qyx 線分からなる2辺は、同方向度が負のため、線分
のyらしさは、線分のxらしさを肯定する。第5B図
のように、線分のy軸方向近似度は0.2、線分のx
軸方向近似度は0.4であるから、線分のy軸から線分
のx軸への影響度Qyxは下記(2)式により算出され
る。Qxx = (degree of approximation of line segment in x-axis direction) x (degree of approximation of line segment in non-x-axis direction) x (degree of same direction) ... (1) = 0.8 x 0.6 x (-0.6) = -0.288 (ii) The degree of influence from the y-axis of the line segment to the x-axis of the line segment Qyx Since the two sides formed by the line segment have the same degree of negative direction, the y-likeness of the line segment affirms the x-likeness of the line segment. As shown in FIG. 5B, the approximation degree of the line segment in the y-axis direction is 0.2, and the line segment x
Since the degree of axial approximation is 0.4, the degree of influence Qyx from the y-axis of the line segment to the x-axis of the line segment is calculated by the following equation (2).
Qyx=(線分のy軸方向近似度)×(線分の X軸方向近似度)×(同方向度×(−1)) ……(2) =0.2×0.4×(−0.6)×(−1)=0.048 (iii)線分のx軸から線分のy軸への影響度 Qxy 線分からなる2辺は、同方向度が負のため、線分
のxらしさは、線分のyらしさを肯定する。第5C図
に示すように、線分のx軸方向近似度は0.8、線分
のy軸方向近似度は0.6であるから、線分のx軸から
線分のy軸のへ影響度Qxyは、下記(3)式により算
出される。Qyx = (degree of approximation of line segment in y-axis direction) × (degree of approximation of line segment in x-axis direction) × (same direction degree × (−1)) (2) = 0.2 × 0.4 × (−0.6) × ( -1) = 0.048 (iii) Influence from the x-axis of the line segment to the y-axis of the line segment Since the two sides composed of the Qxy line segments have the same negative direction, the x-likeness of the line segment is y I affirm the likeness. As shown in FIG. 5C, the degree of approximation of the line segment in the x-axis direction is 0.8, and the degree of approximation of the line segment in the y-axis direction is 0.6. , Calculated by the following equation (3).
Qxy=(線分のx軸方向近似度)×(線分の y軸方向近似度)×(同方向度×(−1)) ……(3) =0.8×0.6(−0.6)×(−1)=0.288 (iv)線分のy軸から線分のy軸への影響度 Qyy 線分からなる2辺は同方向度が負のため、線分
のyらしさは、線分のyらしさを否定する。第5D図の
ように、線分のy軸方向近似度は0.2、線分のy軸
方向近似度は0.4であるから、線分のy軸から線分
のy軸への影響度Qyyは、下記(4)式により算出され
る。Qxy = (degree of approximation of line segment in the x-axis direction) × (degree of approximation of line segment in the y-axis direction) × (same direction degree × (−1)) (3) = 0.8 × 0.6 (−0.6) × (− 1) = 0.288 (iv) The degree of influence from the y-axis of the line segment to the y-axis of the line segment Qyy Since the two sides formed by the line segments have the same degree of the same direction, the y-ness of the line segment is the y-ness of the line segment. Deny. As shown in FIG. 5D, the approximation degree of the line segment in the y-axis direction is 0.2, and the approximation degree of the line segment in the y-axis direction is 0.4. It is calculated by the following equation (4).
Qyy=(線分のy軸方向近似度)×(線分の 非y軸方向近似度)×(同方向度) ……(4) =0.2×0.4×(−0.6)=−0.048 (i)〜(iv)の計算により、線分のx軸方向近似
度への影響度は、 Qxx+Qyx=−0.288+0.048=−0.24 線分のy軸方向近似度への影響度は Qxy+Qyy=0.288−0.048=0.24 となる。近似度の修正は、第3A図、第3B図によって算出
された近似度に(影響度×計算定数)を加えることによ
り実行される。例えば、計算定数0.1のときは、線分
のx軸方向近似度は、0.4から 0.4+(−0.24)×0.1=0.376 に減少し、y軸方向近似度は0.6から 0.6+(0.24)×0.1=0.624 に増加し、線分の方向割り当ては、y軸方向に傾く。
また同様に線分から線分への影響度を計算すること
により、線分の方向割り当てがx軸方向に傾く結果が
得られる。Qyy = (degree of approximation of the line segment in the y-axis direction) × (degree of approximation of the line segment in the non-y-axis direction) × (the same degree of the same direction) (4) = 0.2 × 0.4 × (−0.6) = − 0.048 (i) According to the calculation of (iv), the degree of influence on the x-axis direction approximation of the line segment is Qxx + Qyx = −0.288 + 0.048 = −0.24 The degree of influence on the y-axis direction approximation of the line segment is Qxy + Qyy = 0.288−0.048. = 0.24. The correction of the degree of approximation is executed by adding (influence degree × calculation constant) to the degree of approximation calculated in FIGS. 3A and 3B. For example, when the calculation constant is 0.1, the approximation of the line segment in the x-axis direction is reduced from 0.4 to 0.4 + (− 0.24) × 0.1 = 0.376, and the approximation of the y-axis is 0.6 to 0.6+ (0.24) × 0.1. = 0.624, and the direction assignment of the line segment is inclined in the y-axis direction.
Similarly, by calculating the degree of influence of a line segment on a line segment, a result is obtained in which the direction assignment of the line segment is inclined in the x-axis direction.
上述の演算を対象図形の曲線部が直接近似されて得ら
れた図形(第2図の形状b)における隣り合う2辺のす
べての組に関しておこない、全体的に近似度を修正す
る。次に、修正された近似度をもとに影響度を算出し、
再び近似度を修正する。このような操作を繰返えせば、
各辺(線分)の近似度が一般的にある一つの方向の近似
度(例えばx軸方向近似度)が1に収束し、他の方向の
近似度(例えばy軸方向近似度)が0に収束する。そし
て、この収束状態における方向割り当てを採用すること
により、第2図の形状bから形状cへの変換にみるよう
な、近似モデルの位相情報の生成を実行することができ
る。The above calculation is performed for all pairs of two adjacent sides in the graphic (shape b in FIG. 2) obtained by directly approximating the curved portion of the target graphic, and the degree of approximation is corrected as a whole. Next, the degree of influence is calculated based on the corrected degree of approximation,
Correct the approximation again. By repeating such operations,
In general, the degree of approximation of each side (line segment) converges to 1 in one direction (eg, x-axis direction approximation) and 0 in the other direction (eg, y-axis direction approximation). Converges to Then, by adopting the direction assignment in the convergence state, it is possible to generate the phase information of the approximate model as seen from the conversion from the shape b to the shape c in FIG.
なお、2次元図形に関しては、(x,y)×(x,y)で4
項目の演算により近似度が修正されるが、3次元図形に
関しては、(x,y,z)×(x,y,z)で9項目の演算によ
り、近似度が修正される。For a two-dimensional figure, (x, y) × (x, y)
The degree of approximation is corrected by calculating the items, but for a three-dimensional figure, the degree of approximation is corrected by calculating nine items of (x, y, z) × (x, y, z).
また、上記のように基本的なあいまいルールは4つで
あるが、この他に相互の距離がほぼ等しい二つの線群の
構成線分は、第6図の例に示すように、すべて同じ方向
割り当てとする、3次元のひとつの面に3方向の割り当
てが存在してはならないなどの補助ルールがあり、これ
らのルールを適宜設定することにより、効率的に近似モ
デルが生成される。In addition, although there are four basic vague rules as described above, in addition to these, as shown in the example of FIG. There are auxiliary rules, such as the assignment of three directions that must not exist in one three-dimensional surface to be assigned. By appropriately setting these rules, an approximate model is efficiently generated.
次に上記の方法で得られた方向割り当てによって位相
的に形状が成立するかどうかの判定を行う方法について
第7A図および第7B図を例にとって説明する。任意形状の
対象図形fの曲線部を直線近似した形状が生成され、該
形状から近似モデルを生成するための各線分の方向割り
当てと、該形状を反時計回りに辿る時の線分の方向と
を、x+,y+,x-,y-で表現した。x+,y+はそれぞれ、x軸、
y軸方向に平行で、その数値が増加する方向、x-,y-は
それぞれ、x軸、y軸方向に平行でその数値が減少する
方向に割当てられた線分を示す。第7A図の形状g,iは形
状fに対して割り当てられた線分の方向の例を示し、形
状gと形状iの違いは、形状gにおいては、左上部の線
分がx-を割り当てられているのに対し、形状iにおいて
は対応する線分がy+を等り当てられている点にある。そ
れぞれの図を割り当てられたx軸、y軸に平行な線分で
近似モデル化すると、形状gは形状hに、形状iは形状
jとなる。x軸、y軸に平行な線分のみで構成された図
形を反時計方向に辿るとき、各線分で構成される角のま
わり方は、第7B図に示される8種類のいずれかとなり、
それぞれのまわり方に第7B図のそれぞれの角に記入され
た角記号をつける。形状hおよび形状jの各角部に記入
された数字はこの角番号である。Next, a method of determining whether or not a shape is topologically established by the direction assignment obtained by the above method will be described with reference to FIGS. 7A and 7B as an example. A shape is obtained by linearly approximating the curved part of the target figure f having an arbitrary shape, the direction assignment of each line segment for generating an approximate model from the shape, and the direction of the line segment when the shape is traced counterclockwise. a, x +, y +, x -, y - expressed in. x + and y + are the x axis,
parallel to the y-axis direction, the direction in which the numerical value increases, x -, y -, respectively, showing a line segment x-axis, the numerical value parallel to the y-axis direction is assigned to a decreasing direction. Shapes g and i in FIG. 7A show examples of the direction of a line segment assigned to shape f. The difference between shape g and shape i is that, in shape g, the line segment at the upper left assigns x − . On the other hand, in the shape i, the corresponding line segment is assigned y + . When each figure is approximated by a line segment parallel to the assigned x-axis and y-axis, shape g becomes shape h and shape i becomes shape j. When tracing a figure composed of only line segments parallel to the x-axis and the y-axis in the counterclockwise direction, the corner around each line segment is one of the eight types shown in FIG. 7B,
Mark each corner with the corner symbol written in each corner of Figure 7B. The number written at each corner of the shape h and the shape j is this corner number.
割り当てられた線分の方向で位相的に整合がとれてい
るならば、割り当てられた線分を反時計方向に辿った場
合、角番号の合計は10になり、時計方向に線分を辿った
場合、角番号の合計は−10になるという性質がある。第
7A図に示されるように、この性質をもとに、割り当てら
れた線分方向で構成される図形の位相的整合がとれてい
るかどうかの判定が行われる。If the assigned line segment is topologically aligned, if the assigned line segment is traced counterclockwise, the sum of the corner numbers will be 10 and the line segment will be traced clockwise. In this case, there is a property that the sum of the corner numbers becomes -10. No.
As shown in FIG. 7A, based on this property, it is determined whether or not the topological matching of the figure composed of the assigned line segment directions has been achieved.
なお、位相的整合が得られない場合の対応策の一つと
して、過去の演算結果を参照して、あいまい度の高い辺
から現在の方向割り当てを変更し、整合がとれる割り当
てパターンを探索する方法がある。As a countermeasure in a case where topological matching cannot be obtained, a method of changing the current direction assignment from a side having a high degree of ambiguity with reference to a past calculation result and searching for an assignment pattern that can achieve matching is used. There is.
次に、近似モデルの幾何情報の生成(各辺の長さの決
定)に関して説明する。Next, generation of geometric information of an approximate model (determination of the length of each side) will be described.
第8図の形状mに示すように、ループ(図形を形成す
る境界線)を1方向にたどれば、近似モデルの各辺の向
きは図の〜の4方向に分類され、方向に分類され
る辺の長さの合計と方向に分類される辺の長さの合計
は等しい。第8図の形状nに示すような実形状に関し
て、方向の辺の合計値と方向の辺の合計値の平均値
をとり、これを近似モデルの及び方向に分類される
辺の長さの合計値として設定する。また、方向及び
方向に関しても同様とする。これにより、近似モデルに
おける各方向の辺の長さの合計値は決定されるから、各
方向に関して、実形状における各辺の長さの比をもと
に、合計長さが比例分割されて、近似モデルの各辺の長
さとして設定され、第8図の形状0に示すように各ルー
プごとの近似モデルが完成する。As shown in the shape m of FIG. 8, if the loop (boundary line forming the figure) is traced in one direction, the directions of the sides of the approximate model are classified into four directions (1) to (4) in the figure, and are classified into directions. The sum of the lengths of the sides divided by the direction is equal to the sum of the lengths of the sides classified by the direction. With respect to an actual shape such as shape n in FIG. 8, the average value of the total value of the sides in the direction and the total value of the sides in the direction is calculated, and this is calculated as the sum of the lengths of the sides classified into the approximate model and the direction. Set as a value. The same applies to the direction and direction. Thereby, since the total value of the lengths of the sides in each direction in the approximate model is determined, for each direction, the total length is proportionally divided based on the ratio of the lengths of the sides in the actual shape, The length is set as the length of each side of the approximation model, and the approximation model for each loop is completed as shown in shape 0 in FIG.
ここで、この近似モデルの応用例を述べる。まず、曲
線座標変換法に関して説明する。曲線座標変換法とは、
第9図に示すように、任意形状pとこれに対応する座標
軸に平行な直線のみで構成される格子形状γが設定され
たとき、写像演算を行うことによって、任意形状に均一
な格子を発生させた形状qを得る手法をいう。Here, an application example of this approximate model will be described. First, the curve coordinate conversion method will be described. What is the curve coordinate transformation method?
As shown in FIG. 9, when a grid shape γ composed of only an arbitrary shape p and a straight line parallel to the coordinate axis corresponding to the arbitrary shape p is set, a uniform grid is generated in the arbitrary shape by performing a mapping operation. This is a method for obtaining the shape q.
ゆえに、任意形状が設定されたとき、本発明を用いて
近似モデルを作成し、近似モデルの各辺が単位長さの整
数倍になるように形状を修正し、この単位長さをもとに
格子を張って格子形状として設定し、これに曲線座標変
換法を適用すれば、任意形状の有限要素への自動分割が
行われる。Therefore, when an arbitrary shape is set, an approximate model is created using the present invention, and the shape is corrected so that each side of the approximate model is an integral multiple of the unit length, and based on the unit length, If a grid is set as a grid shape and a curve coordinate conversion method is applied thereto, automatic division into finite elements of an arbitrary shape is performed.
第10図に2次元および3次元の図形の自動分割の例を
示す。FIG. 10 shows an example of automatic division of two-dimensional and three-dimensional figures.
2次元の場合には任意形状u1から、直交座標敬の座標
軸に平行な直線線分のみで構成された任意形状の近似モ
デルu2を生成し、u2の各直線線分が単位長さの整数倍に
なるように格子を張った格子形状である写像モデルを生
成し、該格子形状を任意形状u1に写像するための写像演
算を行うことによって、該写像モデルから、u1に均一な
格子を発生させた解析用メッシュ形状u3を自動生成す
る。In the case of two dimensions, an approximate model u2 of an arbitrary shape composed of only straight line segments parallel to the coordinate axes of the rectangular coordinates is generated from the arbitrary shape u1, and each straight line segment of u2 is an integral multiple of the unit length. By generating a mapping model having a grid shape in which a grid is stretched so as to perform a mapping operation for mapping the grid shape to an arbitrary shape u1, from the mapping model, a uniform grid is generated in u1. The generated analysis mesh shape u3 is automatically generated.
同様に3次元の場合には任意形状v1から、直交座標系
の座標軸に平行な直線線分のみで構成された、上記u2に
相当する任意形状の近似モデルv2を生成し、v2を単位長
さからなる立方体の整数倍の集合になるように分割した
格子形状である写像モデルを生成し、該格子形状を任意
形状v1に写像するための写像演算を行うことによって、
該写像モデルから、v1に均一な格子を発生させた、上記
u3に相当する解析用メッシュ形状v3を自動生成する。な
お、第10図v3では、内部の格子状態までを示すために形
状の一断面における格子のみを表示している。Similarly, in the case of three dimensions, from the arbitrary shape v1, an approximation model v2 of the arbitrary shape corresponding to the above u2, which is composed of only straight line segments parallel to the coordinate axes of the rectangular coordinate system, is generated, and v2 is a unit length. By generating a mapping model that is a grid shape divided so as to be a set of integer multiples of a cube consisting of, by performing a mapping operation to map the grid shape to an arbitrary shape v1
From the mapping model, a uniform grid was generated in v1,
An analysis mesh shape v3 corresponding to u3 is automatically generated. In FIG. 10 v3, only the grid in one cross section of the shape is shown to show the state of the internal grid.
次に、穴を含んだ形状の近似モデルの作成に関して説
明する。まず、第11A図に示すように、近似モデルに関
して、境界形状、及び穴形状独立に各辺が単位長さの整
数倍になるように形状を修正し、この長さをもとに格子
を張る。次に、第11B図に示すように、この格子をもと
に曲線座標変換法を用いて実形状の境界形状に格子を発
生させ、穴の特徴点がどの格子に最も近いかを求め、近
似モデルの境界形状に張られた格子の上での対応をと
る。そして、第11C図に示すように、近似モデルの境界
形状に張られた格子の上で格子を張った穴形状の近似モ
デルを動かし、対応する点どおしの差の合計値が最小に
なる位置が探し出され、穴形状の境界形状に対する相対
位置が決定され、第11D図のような全体的近似モデルが
作成される。Next, creation of an approximate model of a shape including a hole will be described. First, as shown in FIG. 11A, regarding the approximation model, the shape is modified so that each side becomes an integral multiple of the unit length independently of the boundary shape and the hole shape, and a grid is formed based on this length. . Next, as shown in FIG.11B, a grid is generated on the boundary shape of the real shape using the curve coordinate transformation method based on this grid, and the grid to which the feature point of the hole is closest is obtained. The correspondence on the grid attached to the boundary shape of the model is taken. Then, as shown in FIG. 11C, the approximate model of the hole-shaped grid is moved on the grid stretched on the boundary shape of the approximate model, and the total value of the difference between the corresponding points is minimized. The position is found, the relative position of the hole shape to the boundary shape is determined, and an overall approximation model as shown in FIG. 11D is created.
この手法により、穴を持った任意形状の格子形状も自
動作成可能で、これにより、第12図のように穴のあいた
任意形状に関する有限要素分割も自動化される。With this method, it is possible to automatically create an arbitrary lattice shape having holes, and thereby, finite element division relating to an arbitrary shape having holes as shown in FIG. 12 is also automated.
次に近似モデルをもとにした認識モデルの構成方法
と、これを用いた認識方法について説明する。Next, a method of constructing a recognition model based on an approximate model and a recognition method using the same will be described.
全体的近似モデルができれば、第13A図に示すよう
に、近似モデルの位相状態を保持することを前提に、各
辺が最小の整数値をとるように変形された認識モデルが
構成される。この認識モデルの各辺には、対応する近似
モデルの辺の長さが属性として与えられる。If an overall approximation model is created, as shown in FIG. 13A, a recognition model modified so that each side takes a minimum integer value is constructed on the premise that the phase state of the approximation model is maintained. The length of the side of the corresponding approximate model is given as an attribute to each side of the recognition model.
また、穴の相対位置を表現するために、第13B図に示
すように、近似モデルの境界形状、穴形状独立に、最も
左の辺に属するY座標が最小の点が検出され、境界形状
の対応点と各穴形状の対応点との実形状における距離が
属性として設定される。In addition, in order to represent the relative position of the hole, as shown in FIG. 13B, a point having the smallest Y coordinate belonging to the leftmost side is detected independently of the boundary shape of the approximate model and the hole shape independently, and the boundary shape is determined. The distance in the actual shape between the corresponding point and the corresponding point of each hole shape is set as an attribute.
そして、認識モデルをもとに、次の3つの手順に従っ
て認識が実行される。Then, based on the recognition model, recognition is performed according to the following three procedures.
(i)第13C図に示すように認識モデルの大きさ(NX,N
Y)により分類。NX,NYはそれぞれx軸方向、y軸方向の
認識モデルの各辺に与えられている前記属性値の合計さ
れた値である。(I) As shown in FIG. 13C, the size of the recognition model (NX, N
Classified by Y). NX and NY are the sum of the attribute values given to each side of the recognition model in the x-axis direction and the y-axis direction, respectively.
(ii)認識モデルの形状による分類 (iii)モデルに与えられた属性(対応線分の長さ、穴
の相対位置)による比較、 この認識方法の適用例を以下に説明する。(Ii) Classification by shape of recognition model (iii) Comparison based on attributes (length of corresponding line segment, relative position of hole) given to the model, and an application example of this recognition method will be described below.
第14図に示すような、2次元の形状So,toが与えられ
た場合を考える。まず、形状Soに関しては、視点位置の
変更によって、第14図S1,S2に示すように種々の形状変
形が考えられるが、これらはすべて第14図S3で示す同一
の認識モデルに置き換えられる。また、形状toも同じ認
識モデルに置き換えられるが、第14図s,tに示すよう
に、認識モデルの属性により形状Soは形状toとはっきり
区別される。このように、この発明を用いることによ
り、もとの形状からのゆがみによる影響を受けにくい図
形認識が行われる。Consider a case where a two-dimensional shape So, to is given as shown in FIG. First, regarding the shape So, various shape deformations can be considered as shown in FIG. 14 S 1 and S 2 by changing the viewpoint position, but these are all replaced with the same recognition model shown in FIG. 14 S 3 . Can be The shape to is also replaced by the same recognition model, but as shown in FIGS. 14 s and t, the shape So is clearly distinguished from the shape to by the attribute of the recognition model. As described above, by using the present invention, graphic recognition that is not easily affected by distortion from the original shape is performed.
上述の説明では、2次元図形について説明したが、3
次元図形の場合は、図形の稜線をまず、直線線分に近似
し、その後同様の手法が適用される。In the above description, a two-dimensional figure has been described.
In the case of a two-dimensional figure, the edges of the figure are first approximated to straight line segments, and then a similar technique is applied.
第18図に、これまでに述べた、任意形状の入力から図
形認識までの手順をまとめてフローチャートで示した。FIG. 18 is a flowchart summarizing the procedure from the input of an arbitrary shape to the recognition of a figure as described above.
従来、近似モデルの作成にあたっては、画一的な数学
的手法で作成するのは無理であったが、本実施例によれ
ば、メンバシップ関数を用いることにより、形状変換に
関する種々の変換ルールの数学的表現が可能となり、人
のもつあいまいさを含んだ判断を反映した普遍的形状変
換方法が確立された。また、穴形状の境界形状に対する
相対位置の決定にあたっては、曲線座標変換法を用いた
均一格子の生成により境界形状のゆがみによる悪影響が
低減された。さらに近似モデルから変換形成された認識
モデルにより図形認識を行うことにより、ある認識形状
がもとの形状から変形していても、その影響を受けにく
い認識結果が得られるとともに、認識するに際し、その
手順を3段階に分けることにより、認識作業が効率化さ
れた。Conventionally, it was impossible to create an approximate model by a uniform mathematical method. However, according to the present embodiment, by using a membership function, various conversion rules related to shape conversion can be defined. Mathematical expression has become possible, and a universal shape transformation method that reflects judgments involving human ambiguity has been established. In determining the relative position of the hole shape with respect to the boundary shape, the generation of a uniform grid using the curve coordinate conversion method reduced the adverse effects due to the distortion of the boundary shape. Furthermore, by performing graphic recognition using a recognition model converted from an approximate model, even if a certain recognition shape is deformed from the original shape, a recognition result that is less affected by the shape is obtained. By dividing the procedure into three steps, the recognition work was made more efficient.
本発明によれば、任意の形状に対し、座標軸に平行な
直線からなる近似モデルが自動生成されるので、この近
似モデルに格子を張って、曲線座標変換法を適用するこ
とができ、任意形状を自動的に有限要素分割することを
可能にする効果がある。According to the present invention, an approximate model consisting of a straight line parallel to a coordinate axis is automatically generated for an arbitrary shape. Therefore, a grid coordinate conversion method can be applied to this approximate model, and a curve coordinate conversion method can be applied. Has the effect of enabling automatic finite element division.
第1図は本発明を適用した実施例である形状変換装置の
概要構成を示すブロック図、第2図は近似モデルへの変
換手順の例を示す平面図、第3A図〜第3C図はメンバシッ
プ関数の例を示すグラフ、第4図は直線線分と座標軸と
がなす角度の例を示す説明図、第5A図〜第5D図は近似度
の例を示すグラフ、第6図は形状のあいまい処理の例を
示す平面図、第7A図〜第7B図は近似モデルの位相整合の
確認方法の例を示す説明図、第8図は近似モデルの各線
分の長さの決定方法を示す平面図、第9図は曲線座標変
換法の例を示す平面図、第10,12図は図形の有限要素分
割を行った例を示す平面図、第11A図〜第11D図は穴のあ
いた形状の近似モデル作成手順を示す平面図、第13A図
〜第13C図は認識モデルの作成手順を示す平面図、第14
図は近似モデルを用いた図形認識手順を示す平面図、第
15図は近似モデルを構成する線分の方向性を説明する平
面図、第16図は、近似モデルから認識モデルへの変化を
説明する平面図で、第17A図〜第17D図は、従来の図形認
識方法の例を示す図、第18図は本発明を適用して図形認
識を行う場合の手順の例を示すフローチャートである。 30……直線線分を座標軸に平行な線分に変換する手段、
30A……あいまい演算部。FIG. 1 is a block diagram showing a schematic configuration of a shape conversion apparatus according to an embodiment to which the present invention is applied, FIG. 2 is a plan view showing an example of a conversion procedure to an approximate model, and FIGS. 3A to 3C are members. FIG. 4 is an explanatory diagram showing an example of an angle between a straight line segment and a coordinate axis, FIGS. 5A to 5D are graphs showing an example of the degree of approximation, and FIG. FIGS. 7A to 7B are plan views showing an example of the fuzzy processing, FIGS. 7A to 7B are explanatory diagrams showing an example of a method for confirming the phase matching of the approximate model, and FIG. 8 is a plan view showing a method for determining the length of each line segment of the approximate model. FIG. 9, FIG. 9 is a plan view showing an example of the curve coordinate transformation method, FIGS. 10 and 12 are plan views showing an example in which a finite element is divided from a figure, and FIGS. 11A to 11D show shapes with holes. FIG. 13A to FIG. 13C are plan views showing an approximate model creation procedure, and FIG.
The figure is a plan view showing the figure recognition procedure using the approximate model.
FIG. 15 is a plan view for explaining the directionality of the line segments constituting the approximate model, FIG. 16 is a plan view for explaining the change from the approximate model to the recognition model, and FIGS. FIG. 18 is a flowchart showing an example of a graphic recognition method, and FIG. 18 is a flowchart showing an example of a procedure for performing graphic recognition by applying the present invention. 30 ... means for converting a straight line segment into a line segment parallel to the coordinate axes,
30A ... Ambiguous calculation unit.
フロントページの続き (58)調査した分野(Int.Cl.6,DB名) G06F 17/50 G06T 17/20 JICSTファイル(JOIS)Continuation of the front page (58) Field surveyed (Int.Cl. 6 , DB name) G06F 17/50 G06T 17/20 JICST file (JOIS)
Claims (9)
た任意形状の稜線を座標軸のうちいずれの座標軸に平行
な直線線分とするかを決定し、前記任意形状をこの決定
された直線線分からなる形状に変換する手段と、この直
線線分からなる形状に格子を生成する手段とを備えた形
状変換装置。1. A means for inputting an arbitrary shape, and determining which of the coordinate axes a ridge line of the input arbitrary shape is to be a straight line segment parallel to the coordinate axis, and converting the arbitrary shape into the determined straight line A shape conversion device comprising: means for converting into a shape formed by line segments; and means for generating a grid in a shape formed by the straight line segments.
る手段が、メンバシップ関数を用いて演算を行なうあい
まい演算部を備えていることを特徴とする請求項1に記
載の形状変換装置。2. The shape conversion apparatus according to claim 1, wherein the means for converting into a shape composed of line segments parallel to the coordinate axes includes an ambiguous calculation unit for performing calculation using a membership function.
線分で近似する手段と、それぞれの線分の座標軸への近
似度を0から1の変数で表現し、あいまいルールにより
該変数を全体的に修正して各線分をいずれかの座標軸に
平行に割り当て、最終的に一つの近似モデルに収束させ
る手段と、を含んでなる形状変換装置。3. A means for approximating a boundary line or ridge line of an arbitrary shape with a plurality of straight line segments, and expressing the degree of approximation to the coordinate axis of each line segment by a variable from 0 to 1, and using a variable from an ambiguity rule to represent the variable. Means for correcting the whole and assigning each line segment in parallel to any one of the coordinate axes, and finally converging to one approximate model.
線分で近似する手段と、隣接する線分が、一直線上にあ
るか、互いに垂直になるように前記線分を変換して形状
を形成する手段と、を含んでなる形状変換装置。4. A means for approximating a boundary line or ridge line of an arbitrary shape with a plurality of straight line segments, and converting said line segments so that adjacent line segments are on a straight line or perpendicular to each other. Forming means.
線分で近似する手段と、それぞれの線分が座標軸となす
角度を計算し、計算された角度および予め設定されたあ
いまいルールに基づくメンバシップ関数により前記線分
をいずれかの座標軸に平行に割り当てて、前記任意形状
の近似モデルを作成する手段と、を含んでなる形状変換
装置。5. A means for approximating a boundary line or ridge line of an arbitrary shape with a plurality of straight line segments, calculating an angle between each line segment and a coordinate axis, and calculating the angle based on the calculated angle and a preset fuzzy rule. Means for allocating the line segment to any one of the coordinate axes by a membership function to create the approximate model of the arbitrary shape.
ルが、少なくとも、線分となす角が最も小さい座標軸の
方向へなるべく該線分が割り当てられることと、互に隣
接する二つの線分はそのなす角が一定角よりも小さいほ
どなるべく異なる方向に、なす角が一定角よりも大きい
ほどなるべく同じ方向に割り当てられることと、を含ん
でいることを特徴とする請求項5に記載の形状変換装
置。6. The fuzzy rule of the means for creating an approximate model is that at least the line segment is assigned to the direction of the coordinate axis having the smallest angle with the line segment, and that two adjacent line segments are The shape conversion apparatus according to claim 5, wherein the angle is formed in a different direction as much as the angle formed is smaller than the fixed angle, and the same direction is allocated as the angle formed is larger than the fixed angle. .
された任意形状から直交および平行の関係からなる複数
の直線線分で構成されたモデルに格子を張ったモデルを
生成する第2手段と、この生成されたモデルから前記任
意形状に格子を張った任意形状を生成する第3手段と、
を含んでなる形状変換装置。7. A first means for inputting an arbitrary shape, and a second means for generating a model in which a grid is formed from a model formed by a plurality of straight line segments having an orthogonal and parallel relationship from the input arbitrary shape. Means, and third means for generating, from the generated model, an arbitrary shape in which the arbitrary shape is gridded,
A shape conversion device comprising:
行な直線成分のみで構成された任意形状の近似モデルを
生成する手段と、この近似モデルから格子を張った格子
形状である写像モデルを生成する手段とを含むことを特
徴とする形状変換装置。8. The shape conversion apparatus according to claim 7, wherein the second means generates an approximate model of an arbitrary shape composed of only linear components parallel to the coordinate axes of the rectangular coordinate system from the arbitrary shape; Means for generating a mapping model having a lattice shape from the approximate model.
直線成分が単位長さの整数倍となるように格子を張るも
のであることを特徴とする形状変換装置。9. The shape conversion device according to claim 8, wherein the means for generating the mapping model sets a grid so that each linear component of the approximate model is an integral multiple of a unit length. Characteristic shape conversion device.
Priority Applications (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP1058454A JP2920195B2 (en) | 1989-03-10 | 1989-03-10 | Shape conversion method and device |
JP10204887A JPH1196400A (en) | 1989-03-10 | 1998-07-21 | Shape transforming method |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP1058454A JP2920195B2 (en) | 1989-03-10 | 1989-03-10 | Shape conversion method and device |
Related Child Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
JP10204887A Division JPH1196400A (en) | 1989-03-10 | 1998-07-21 | Shape transforming method |
Publications (2)
Publication Number | Publication Date |
---|---|
JPH02236677A JPH02236677A (en) | 1990-09-19 |
JP2920195B2 true JP2920195B2 (en) | 1999-07-19 |
Family
ID=13084871
Family Applications (2)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
JP1058454A Expired - Lifetime JP2920195B2 (en) | 1989-03-10 | 1989-03-10 | Shape conversion method and device |
JP10204887A Pending JPH1196400A (en) | 1989-03-10 | 1998-07-21 | Shape transforming method |
Family Applications After (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
JP10204887A Pending JPH1196400A (en) | 1989-03-10 | 1998-07-21 | Shape transforming method |
Country Status (1)
Country | Link |
---|---|
JP (2) | JP2920195B2 (en) |
Families Citing this family (9)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP3444363B2 (en) * | 1993-09-20 | 2003-09-08 | ソニー株式会社 | Figure editing apparatus and method |
US7174236B2 (en) | 2001-08-16 | 2007-02-06 | Riken | Ultra-precise processing method and apparatus for inhomogeneous material |
WO2003016031A1 (en) * | 2001-08-16 | 2003-02-27 | Riken | Rapid prototyping method and device using v-cad data |
CN1311390C (en) | 2001-12-04 | 2007-04-18 | 独立行政法人理化学研究所 | Method for converting 3-dimensional shape data into cell inner data and conversion program |
WO2003073335A1 (en) | 2002-02-28 | 2003-09-04 | Riken | Method and program for converting boundary data into in-cell shape |
JP3954909B2 (en) | 2002-06-19 | 2007-08-08 | インターナショナル・ビジネス・マシーンズ・コーポレーション | Recognition model generation system, recognition model generation method, program for causing computer to execute recognition model generation method, computer-readable recording medium on which program is recorded, and structural mesh generation system |
JP4381743B2 (en) | 2003-07-16 | 2009-12-09 | 独立行政法人理化学研究所 | Method and program for generating volume data from boundary representation data |
JP4657042B2 (en) * | 2005-07-19 | 2011-03-23 | 富士通株式会社 | Printed circuit board analysis model generation apparatus and program |
JP4783100B2 (en) | 2005-09-12 | 2011-09-28 | 独立行政法人理化学研究所 | Method of converting boundary data into in-cell shape data and its conversion program |
Family Cites Families (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPH0623991B2 (en) * | 1985-09-26 | 1994-03-30 | 株式会社日立製作所 | Coordinate grid generation support method and apparatus |
JPS63656A (en) * | 1986-06-20 | 1988-01-05 | Hitachi Ltd | Supporting method for generation of coordinate grid |
-
1989
- 1989-03-10 JP JP1058454A patent/JP2920195B2/en not_active Expired - Lifetime
-
1998
- 1998-07-21 JP JP10204887A patent/JPH1196400A/en active Pending
Also Published As
Publication number | Publication date |
---|---|
JPH1196400A (en) | 1999-04-09 |
JPH02236677A (en) | 1990-09-19 |
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