JPH0687266B2 - Curve generator - Google Patents
Curve generatorInfo
- Publication number
- JPH0687266B2 JPH0687266B2 JP14080585A JP14080585A JPH0687266B2 JP H0687266 B2 JPH0687266 B2 JP H0687266B2 JP 14080585 A JP14080585 A JP 14080585A JP 14080585 A JP14080585 A JP 14080585A JP H0687266 B2 JPH0687266 B2 JP H0687266B2
- Authority
- JP
- Japan
- Prior art keywords
- curve
- distance
- points
- feature point
- point
- 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.)
- Expired - Lifetime
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- Numerical Control (AREA)
- Digital Computer Display Output (AREA)
- Image Generation (AREA)
Description
【発明の詳細な説明】 産業上の利用分野 本発明は、電子式文字図形発生装置等に用いることがで
きる曲線発生装置に関するものである。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a curve generator that can be used in an electronic character / graphics generator or the like.
従来の技術 近年、電子式文字図形発生装置は情報端末機器、放送機
器等に広く用いられるようになっていている。その中で
用いられる曲線発生装置は、折れ線近似、円弧近似によ
るものから、滑らかな曲線の接線による近似へと進歩し
てきている。2. Description of the Related Art In recent years, electronic character / graphics generators have been widely used in information terminal equipment, broadcasting equipment and the like. The curve generating device used therein has been progressing from a polygonal line approximation and an arc approximation to a smooth curve tangent line approximation.
以下、図面を参照しながら従来の３次曲線近似による曲
線発生装置について説明する従来の曲線発生装置で発生
された曲線と、その曲線を決定するために必要な特徴点
を第２図に示す。従来の装置においては、与えられた特
徴点の間を、互いに隣接する曲線が境界点において１
次、２次の微分係数が等しくなるような３次関数で表現
する方法がとられている。（例えば、山口富士夫著「コ
ンピュータディスプレイによる形状処理光学Ｉ」、P170
〜） このような従来の装置における方式においては、曲線を
滑らかに表現することに重点をおいている。FIG. 2 shows a curve generated by a conventional curve generating device for explaining a conventional curve generating device using a cubic curve approximation with reference to the drawings, and characteristic points necessary for determining the curve. In the conventional device, curves that are adjacent to each other between the given feature points are 1 at the boundary points.
A method of expressing with a cubic function such that the second and second differential coefficients are equal is adopted. (For example, Fujio Yamaguchi, "Shape processing optics by computer display I", P170
) In such a conventional system, emphasis is placed on smoothly expressing a curve.
発明が解決しようとする問題点 しかしながら、このような方式では、曲線発生装置で発
生される曲線を決定するために必要な特徴点の与え方に
よって、曲線の変曲点の制御を行うことは困難である。
また、この曲線は、特徴点の与え方によっては第３図に
示すように曲線に不必要な振動が生じる場合があるが、
この曲線を、文字図形発生装置が発生する漢字等の文字
の骨格として用いる場合、このような振動は文字の品位
を劣化させ、ひいては文字図形発生装置の品位を劣化さ
せることになる。DISCLOSURE OF THE INVENTION Problems to be Solved by the Invention However, in such a method, it is difficult to control an inflection point of a curve depending on how to provide a characteristic point necessary for determining a curve generated by the curve generator. Is.
Also, depending on how the characteristic points are given, this curve may cause unnecessary vibrations as shown in FIG. 3,
When this curve is used as a skeleton of a character such as a Chinese character generated by the character / graphics generator, such vibration deteriorates the quality of the character, and thus deteriorates the quality of the character / graphics generator.
このような振動を抑えるためには、試行錯誤によって特
徴点を見出す必要があり、文字や図形表示のためのデー
タ入力作業に大きな負担をかけることになる。In order to suppress such vibration, it is necessary to find the characteristic points by trial and error, which imposes a heavy burden on the data input work for displaying characters and figures.
本発明はかかる点に鑑みてなされたもので、簡単なデー
タ入力作業により、不必要な振動の生じない曲線を、発
生することのできる曲線発生装置を提供することを目的
としている。The present invention has been made in view of the above points, and an object of the present invention is to provide a curve generator capable of generating a curve that does not cause unnecessary vibration by a simple data input operation.
問題点を解決するための手段 本発明は、上位問題点を解決するため、連続する第1,第
2,第３の特徴点座標の入力により、第１と第３の特徴点
間の距離Ｌ、第２の特徴点から第１と第３の特徴点を結
ぶ線分に下ろした垂線の高さｈ、距離Ｌに対する前記第
１の特徴点と垂線の足の距離の比ｔを出力する特徴点演
算手段と、距離Ｌと高さｈと距離の比ｔから区分関数の
係数を求める係数演算手段と、係数演算手段の結果を区
分関数発生手段に入力することにより所望の曲線を発生
する曲線発生装置からなる。Means for Solving Problems In order to solve the higher-ranking problems, the present invention provides continuous first, first
2, by inputting the coordinates of the third feature point, the distance L between the first and third feature points, the height of the perpendicular line drawn from the second feature point to the line segment connecting the first and third feature points h, a characteristic point calculating means for outputting a ratio t of the distance between the first characteristic point and the foot of the perpendicular to the distance L, and a coefficient calculating means for obtaining a coefficient of the piecewise function from the ratio t of the distance L, the height h and the distance. And a curve generating device for generating a desired curve by inputting the result of the coefficient calculating means to the piecewise function generating means.
作用 本発明は上記の構成により、特徴点を結ぶ区間内に変曲
点を持たない区分関数を発生させることができるので、
変曲点は必ず特徴点上にあり、このために、特徴点で変
曲点の制御を容易に行うことができ、文字骨格等の曲線
発生に際し、そのデータの作成を極めて容易に行うこと
ができる。Action The present invention can generate a piecewise function having no inflection point in the section connecting the feature points by the above configuration,
Since the inflection point is always on the feature point, it is possible to easily control the inflection point at the feature point, and it is extremely easy to create the data when a curve such as a character skeleton is generated. it can.
実施例 第１図は、本発明の一実施例で用いられる区分関数発生
手段が発生する曲線の表現方式を示す図である。第１図
において１は始点、２は終点、３は最大変位点、４は最
大変位点３から点１、２を結ぶ線分に下ろした垂線の足
である。点１から最大変位点３に至る曲線は、区分関数
発生手段が発生する区分曲線であり、このような曲線を
区分関数発生手段によって複数個発生させ、それらを接
続することによって、３つの点を通過する曲線が生成さ
れる。本実施例では、区分関数を、点１、３間、点３、
２間をそれぞれ表現する２つの３次関数ｙ＝f1（Ｘ）、
ｙ＝f2（ｘ）とし、f1（ｘ）、f2（ｘ）はそれぞれ点
１、及び点２、３を通り、かつ最大変位点３におけるf1
（ｘ）とf2（ｘ）の傾きは等しい。さらに、f1（ｘ）、
f2（ｘ）は点１、３間及び点２、３間に変曲点を有さな
い。すなわち、区分関数発生手段は以下の条件を満足す
るf1（ｘ）、f2（ｘ）を決定する。Embodiment FIG. 1 is a diagram showing an expression system of a curve generated by a piecewise function generating means used in an embodiment of the present invention. In FIG. 1, 1 is a start point, 2 is an end point, 3 is a maximum displacement point, and 4 is a foot of a perpendicular line drawn from the maximum displacement point 3 to a line segment connecting the points 1 and 2. The curve from the point 1 to the maximum displacement point 3 is a piecewise curve generated by the piecewise function generating means. By generating a plurality of such curves by the piecewise function generating means and connecting them, three points are obtained. A passing curve is generated. In the present embodiment, the piecewise function is set between points 1 and 3, point 3,
Two cubic functions y = f 1 (X), which respectively represent the two,
When y = f 2 (x), f 1 (x) and f 2 (x) pass through points 1 and 2 and 3, respectively, and f 1 at the maximum displacement point 3
The slopes of (x) and f 2 (x) are equal. Furthermore, f 1 (x),
f 2 (x) has no inflection point between points 1 and 3 and between points 2 and 3. That is, the piecewise function generating means determines f 1 (x) and f 2 (x) that satisfy the following conditions.
f1（０）＝０、f1（tL）＝ｈ f2（Ｌ）＝０、f2（tL）＝ｈ f1（tL）＝f2（tL）＝ｈ f1′（tL）＝f2′（tL）＝０ f1″（ｘ）＜０（０≦ｘ≦tL） f2″（ｘ）＜０（tL≦Ｘ≦Ｌ） または、 f1″（ｘ）＞０（０≦ｘ≦tL） f1″（ｘ）＞０（tL≦ｘ≦Ｌ） ここでＬは１、２間の距離であり、ｔはＬに対する１、
４間の距離の比があり、ｈは３、４間の距離である。こ
の条件では、曲線の係数に自由度が残っているが、この
区分曲線が前後の区分曲線とできるだけ滑らかに接続す
るようにすること、すなわちf1′（０）の値を直前の曲
線の終点における傾きによって設定される値に最も近い
値を選ぶことにより、曲線の係数は一意に決定すること
ができる。前記した条件より、f1（ｘ）、f2（ｘ）は以
下のように求めることができる。f 1 (0) = 0, f 1 (tL) = h f 2 (L) = 0, f 2 (tL) = h f 1 (tL) = f 2 (tL) = h f 1 ′ (tL) = f 2 ′ (tL) = 0 f 1 ″ (x) <0 (0 ≦ x ≦ tL) f 2 ″ (x) <0 (tL ≦ X ≦ L) or f 1 ″ (x)> 0 (0 ≦ x ≦ tL) f 1 ″ (x)> 0 (tL ≦ x ≦ L) where L is a distance between 1 and 2, t is 1 with respect to L,
There is a ratio of distances between 4 and h is the distance between 3 and 4. Under this condition, the coefficient of the curve still has a degree of freedom, but it is necessary to connect this piecewise curve to the piecewise curves before and after as smoothly as possible, that is, to set the value of f 1 ′ (0) to the end point of the immediately preceding curve. The coefficient of the curve can be uniquely determined by choosing the value closest to the value set by the slope at. From the above conditions, f 1 (x) and f 2 (x) can be calculated as follows.
ここで、 ここで、 前後の区分曲線から、区分関数発生手段は、f1′（０）
とf2′（Ｌ）を前記条件の範囲内で決定する。 here, here, From the front and back piecewise curves, the piecewise function generating means is f 1 ′ (0)
And f 2 ′ (L) are determined within the above conditions.
次に第４図を用いて本発明の実施例における曲線発生装
置について説明する。第４図において、41,42,43はそれ
ぞれ３つの特徴点を表す第１の特徴点、第２の特徴点、
第３の特徴点の座標入力を示すものであり、これらは第
１図における特徴点1,特徴点3,特徴点２の座標（x,y）
の入力を意味する。Next, the curve generator in the embodiment of the present invention will be described with reference to FIG. In FIG. 4, reference numerals 41, 42, and 43 denote a first feature point, a second feature point, and three feature points, respectively.
The coordinate input of the third feature point is shown. These are the coordinates (x, y) of feature point 1, feature point 3, and feature point 2 in FIG.
Means input.
44は、特徴点座標41,42,43の入力により、所定の出力、
すなわち特徴点間の距離L,垂線の高さh,距離の比ｔの出
力とする特徴点演算手段である。44 is a predetermined output by the input of the feature point coordinates 41, 42, 43,
That is, it is a feature point calculation means that outputs the distance L between the feature points, the height h of the perpendicular, and the distance ratio t.
46は、特徴点演算手段44により演算されたL,h,tそれぞ
れの値45の入力により、区分関数f1（ｘ）,f2（ｘ）の
係数を算出する係数演算手段であり、得られた係数47は
区分関数発生手段48に入力され、最終的に所望の曲線49
が発生される。46 is a coefficient calculation means for calculating the coefficients of the piecewise functions f 1 (x), f 2 (x) by inputting the respective values 45 of L, h, t calculated by the feature point calculation means 44, and The obtained coefficient 47 is input to the piecewise function generating means 48, and finally the desired curve 49 is obtained.
Is generated.
本実施例では、区分曲線を２個の３次関数で表現してい
るが、区間内に変曲点を持たない任意の曲線を区分曲線
として用いることができる。In the present embodiment, the piecewise curve is represented by two cubic functions, but any curve having no inflection point in the section can be used as the piecewise curve.
発明の効果 以上のように本発明は、３つの特徴点の座標を特徴点演
算手段に入力し、第１と第３の特徴点間の距離Ｌと、第
２の特徴点から第１と第３の特徴点を結ぶ線分に下ろし
た垂線の高さｈと、距離Ｌに対する第１の特徴点と垂線
の足の距離の比ｔを求め、それぞれの値を係数演算手段
に入力することにより、区分関数の係数を演算し、その
結果を区分関数発生手段に入力するという構成により、
不必要な振動を生じない自由曲線を発生することができ
る。EFFECTS OF THE INVENTION As described above, according to the present invention, the coordinates of three feature points are input to the feature point calculating means, and the distance L between the first and third feature points and the first to the first feature point from the second feature point. By calculating the height h of the perpendicular line drawn to the line segment connecting the three feature points and the ratio t of the distance between the first feature point and the foot of the perpendicular line to the distance L, and inputting each value to the coefficient calculating means. , By calculating the coefficient of the piecewise function and inputting the result to the piecewise function generating means,
It is possible to generate a free curve that does not cause unnecessary vibration.
さらに、この曲線を漢字等の文字の骨格として用いる曲
線発生装置に適用すれば、不必要な振動の生じない極め
て文字品位の高い装置を提供することができる。Further, if this curve is applied to a curve generator that uses a skeleton of a character such as a Chinese character, it is possible to provide a device with extremely high character quality in which unnecessary vibration does not occur.
第１図は、本発明の一実施例で用いられる区分曲線を示
す図、第２図は従来の一実施例で用いられる曲線とその
特徴点を示す図、第３図は従来の一実施例によって発生
された曲線を示す図であり、第４図は本発明の実施例に
おける曲線発生装置の構成を示す図である。 １……始点、２……終点、３……最大変位点、４……３
より１、２を結ぶ線分に下ろした垂線の足、５〜11……
特徴点、12〜22……特徴点。FIG. 1 is a diagram showing a segmental curve used in one embodiment of the present invention, FIG. 2 is a diagram showing a curve used in one conventional embodiment and its characteristic points, and FIG. 3 is a conventional one embodiment. It is a figure which shows the curve generated by FIG. 4, and FIG. 4 is a figure which shows the structure of the curve generator in the Example of this invention. 1 ... Start point, 2 ... End point, 3 ... Maximum displacement point, 4 ... 3
Foot of a perpendicular line drawn on a line segment connecting 1 and 2, 5-11 ……
Characteristic points, 12 to 22 ... Characteristic points.
───────────────────────────────────────────────────── フロントページの続き (72)発明者 吉田 純 大阪府門真市大字門真1006番地 松下電器 産業株式会社内 (72)発明者 浅原 重夫 大阪府門真市大字門真1006番地 松下電器 産業株式会社内 (56)参考文献 特開 昭60−500385（ＪＰ，Ａ) 特開 昭60−22280（ＪＰ，Ａ) 特開 昭57−29087（ＪＰ，Ａ) ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Jun Yoshida 1006 Kadoma, Kadoma City, Osaka Prefecture Matsushita Electric Industrial Co., Ltd. (72) Inventor Shigeo Asahara, 1006 Kadoma, Kadoma City, Osaka Matsushita Electric Industrial Co., Ltd. 56) References JP-A-60-500385 (JP, A) JP-A-60-22280 (JP, A) JP-A-57-29087 (JP, A)
Claims (1)
各区間内の曲線を表わす区分関数を求めて、所望の曲線
を発生する曲線発生装置において、 連続する第1,第2,第３の特徴点座標の入力により、前記
第１と第３の特徴点間の距離Ｌ、前記第２の特徴点から
前記第１と第３の特徴点を結ぶ線分に下ろした垂線の高
さｈ、前記距離Ｌに対する前記第１の特徴点と前記垂線
の足の距離の比ｔを出力する特徴点演算手段と、 前記距離Ｌと前記高さｈと前記距離の比ｔから区間内の
二次微分係数が常に負となる条件の下に前記区分関数の
係数を求める係数演算手段と、 この係数演算手段の結果に基づき所望の曲線を発生する
区分関数発生手段とを備えた曲線発生装置。1. A curve generator that generates a desired curve by obtaining a piecewise function having a plurality of characteristic points and representing a curve in each section of the plurality of characteristic points, and a continuous first, second By inputting the coordinates of the third feature point, the distance L between the first and third feature points and the perpendicular line drawn from the second feature point to the line segment connecting the first and third feature points A feature point calculating means for outputting a ratio t of the height h and the distance between the first feature point and the foot of the perpendicular to the distance L, and within a section from the ratio t between the distance L, the height h, and the distance. A curve generating device is provided with a coefficient calculating means for obtaining the coefficient of the piecewise function under the condition that the second derivative of is always negative, and a piecewise function generating means for generating a desired curve based on the result of the coefficient calculating means. apparatus.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP14080585A JPH0687266B2 (en) | 1985-06-27 | 1985-06-27 | Curve generator |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP14080585A JPH0687266B2 (en) | 1985-06-27 | 1985-06-27 | Curve generator |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPS622372A JPS622372A (en) | 1987-01-08 |
| JPH0687266B2 true JPH0687266B2 (en) | 1994-11-02 |
Family
ID=15277149
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP14080585A Expired - Lifetime JPH0687266B2 (en) | 1985-06-27 | 1985-06-27 | Curve generator |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPH0687266B2 (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS647207A (en) * | 1987-06-30 | 1989-01-11 | Fanuc Ltd | Spline interpolating system |
| JPS6481012A (en) * | 1987-09-22 | 1989-03-27 | Fanuc Ltd | Numerical controller |
-
1985
- 1985-06-27 JP JP14080585A patent/JPH0687266B2/en not_active Expired - Lifetime
Also Published As
| Publication number | Publication date |
|---|---|
| JPS622372A (en) | 1987-01-08 |
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