JPS622372A - Curve generation device - Google Patents
Curve generation deviceInfo
- Publication number
- JPS622372A JPS622372A JP14080585A JP14080585A JPS622372A JP S622372 A JPS622372 A JP S622372A JP 14080585 A JP14080585 A JP 14080585A JP 14080585 A JP14080585 A JP 14080585A JP S622372 A JPS622372 A JP S622372A
- Authority
- JP
- Japan
- Prior art keywords
- point
- curve
- inflection
- feature
- generated
- 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
Landscapes
- Numerical Control (AREA)
- Digital Computer Display Output (AREA)
- Image Generation (AREA)
Abstract
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。DETAILED DESCRIPTION OF THE INVENTION Field of the Invention The present invention relates to a curve generator that can be used in electronic character/figure generators and 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きている。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、滑らかな曲線の接続により近似へと進歩し
てきている。2. Description of the Related Art In recent years, electronic character/figure generators have come to be widely used in information terminal equipment, broadcasting equipment, and the like. The curve generation devices used therein have progressed from those based on polygonal line approximation and circular arc approximation to those based on smooth curve connection.
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、山口冨士夫著「コ
ンピュータディスプレイによる形状処理工学■」、P
170〜)
発明が解決しようとする問題点
このような従来の装置における方式においては、曲線を
滑らかに表現する事に重点をおいている。Hereinafter, a conventional curve generation device using cubic curve approximation will be described with reference to the drawings. FIG. 2 shows a curve generated by a conventional curve generator and characteristic points necessary to determine the curve. In conventional devices, adjacent curves between given feature points are connected to one another at the boundary point.
A method is used to express it by a cubic function in which the second-order and second-order differential coefficients are equal. (For example, “Shape processing engineering using computer displays” by Fujio Yamaguchi, p.
170~) Problems to be Solved by the Invention In the systems of such conventional devices, emphasis is placed on expressing curves smoothly.
しかしながら、特徴点の与え方によって曲線の変曲点の
制御を行うことが困難である。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、漢字等の文字の骨格の表
現に用いる場合、このような振動は文字の品位を劣下さ
せる原因となる。However, it is difficult to control the inflection point of the curve depending on how the feature points are given. Also, depending on how the feature points are assigned, unnecessary vibrations may occur in the curve as shown in Figure 3, but when used to express the skeleton of characters such as kanji, such vibrations can be avoided. This causes deterioration in the quality of characters.
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 vibrations, it is necessary to find feature points through trial and error, which places a heavy burden on 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 problems, and an object of the present invention is to provide a curve generation device that can generate a curve without unnecessary vibrations by a simple data input operation.
問題点を解決するための手段
本発明は、上記問題点を解決するため、曲線の特徴点間
を、その区間内に変曲点を持たない区分関数を用いて表
現するものである。Means for Solving the Problems In order to solve the above problems, the present invention expresses the feature points of a curve using a piecewise function that does not have an inflection point within its section.
作用
本発明は、上記した構成により、特徴点間に変曲点を有
さない曲線の接続により全体の曲線を表現しているため
、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。Effect The present invention, with the above-described configuration, expresses the entire curve by connecting curves that do not have inflection points between feature points, so the inflection points are always on the feature points. Inflection points can be easily controlled using feature points, and data can be created extremely easily when generating curves such as character skeletons.
実施例
第1図は、本発明の一実施例で用いられる曲線の表現方
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3から1.2を結ぶ線分に下
ろした垂線の足である。1から3に至る曲線は、全体の
曲線を表すための区分曲線であり、このような曲線を複
数個接続することによって、全体の曲線を表現する。本
実施例では区分関数をさらに1.3間、3.2間を表す
2つの3次間数y=r、(x)、y=fz (x)で
表現している。fz (x)、fz (X)は、そ
れぞれ1.3及び2.3を通り、かつ3における、fl
(x)とfZ (X)の傾きは等しい。さらに!
+ (X)、fz (X)は1.3間及び2.3間
に変曲点を有さない。すなわち、以下の条件を満足する
ようにfl (x)、fz (X)を決定する。Embodiment FIG. 1 is a diagram showing a method of expressing a curve used in an embodiment of the present invention. In FIG. 1, 1 is the starting point, 2 is the ending point, 3 is the maximum displacement point, and 4- is the foot of the perpendicular line drawn from 3 to the line segment connecting 1.2. The curves from 1 to 3 are segmented curves for expressing the entire curve, and the entire curve is expressed by connecting a plurality of such curves. In this embodiment, the piecewise function is further expressed by two cubic numbers y=r, (x) and y=fz (x) representing 1.3 and 3.2. fz (x) and fz (X) pass through 1.3 and 2.3, respectively, and fl at 3
The slopes of (x) and fZ (X) are equal. moreover!
+ (X), fz (X) has no inflection point between 1.3 and 2.3. That is, fl (x) and fz (X) are determined so as to satisfy the following conditions.
fl (0)=O,,f+ (tL)=hfZ(L
)=0、fz (tL) =hf、 (tL) =
fz (tL) =hf+’(tL) =fz’(t
L) =Ofl”(X)<0 (0≦X≦tL)
fz’(x)<0 (tL≦X≦L)
または、
f+’(x)>0 (0≦X≦tL)
f +”(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
の比であり、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fl ’ (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、fl (X) 、fZ
(X)は以下のように求めることができる。fl (0)=O,,f+ (tL)=hfZ(L
) = 0, fz (tL) = hf, (tL) =
fz (tL) =hf+'(tL) =fz'(t
L) = Ofl”(X)<0 (0≦X≦tL) fz'(x)<0 (tL≦X≦L) or f+'(x)>0 (0≦X≦tL) f +” (x) > 0 (tL≦X≦L) where L is the distance between 1 and 2, t is the ratio of the distance between 1 and 4 to L, and h is the distance between 3.4 . Under this condition, there remains a degree of freedom in the coefficients of the curve, but it is important to make this piecewise curve connect as smoothly as possible to the previous and succeeding piecewise curves. By choosing the value closest to the value set by the slope, the coefficients of the curve can be uniquely determined. From the above conditions, fl (X), fZ
(X) can be determined as follows.
ここで、
+fz’(0)x
ここで、
前後の区分曲線から、f、’ (0)とr2 ’
(L)を前記条件の範囲内で決定し、入力された特徴点
1.2.3よりt、L、hを求め、fl (x)、f
Z(X)の係数を計算する。前記係数を3次曲線発生器
に人力すれば所望の曲線を発生することができる。Here, +fz'(0)x Here, from the front and rear piece curves, f,' (0) and r2'
(L) is determined within the range of the above conditions, t, L, h are determined from the input feature points 1.2.3, fl (x), f
Calculate the coefficients of Z(X). A desired curve can be generated by manually inputting the coefficients to a cubic curve generator.
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 this embodiment, the piecewise curve is expressed by two cubic functions, but any curve that does not have an inflection point within the section can be used as the piecewise curve.
発明の効果
以上述べてきたように、本発明によれば、極めて容易に
入力できるデータをもとに、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、このことは多種類の曲線
パターンを入力し、発生する事が要求される際に重要で
ある。Effects of the Invention As described above, according to the present invention, a free curve that does not generate unnecessary vibrations can be generated based on data that can be inputted extremely easily. This is important when a pattern is entered and required to occur.
第1図は、本発明の一実施例で用いられる区分実施例に
よって発生された曲線を示す図である。
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、5〜1)・・・・・・特徴点、
12〜22・・・・・・特徴点。
代理人の氏名 弁理士 中尾敏男 はか1名第1図FIG. 1 is a diagram illustrating curves generated by a segmented embodiment used in one embodiment of the present invention. 1...Starting point, 2...Ending point, 3...
・・Maximum displacement point, 4・・・・ Leg of the perpendicular line drawn from 3 to the line segment connecting 1.2, 5 to 1)・・・・・Feature point,
12-22...Feature points. Name of agent: Patent attorney Toshio Nakao (1 person) Figure 1
Claims (2)
内に変曲点を持たない区分関数を用いて表現することを
特徴とする曲線発生装置。(1) A curve generation device characterized in that an arbitrary curve is expressed using a piecewise function whose shape is determined by inputting three points and which does not have an inflection point within an interval.
とを特徴とする特許請求の範囲第(1)項記載の曲線発
生装置。(2) The curve generating device according to claim (1), wherein the piecewise function is expressed by a combination of two cubic functions.
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 true JPS622372A (en) | 1987-01-08 |
JPH0687266B2 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) |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPS647207A (en) * | 1987-06-30 | 1989-01-11 | Fanuc Ltd | Spline interpolating system |
WO1989003074A1 (en) * | 1987-09-22 | 1989-04-06 | Fanuc Ltd | Numerical control apparatus |
-
1985
- 1985-06-27 JP JP14080585A patent/JPH0687266B2/en not_active Expired - Lifetime
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JPS647207A (en) * | 1987-06-30 | 1989-01-11 | Fanuc Ltd | Spline interpolating system |
WO1989000306A1 (en) * | 1987-06-30 | 1989-01-12 | Fanuc Ltd | Spline interpolation method |
WO1989003074A1 (en) * | 1987-09-22 | 1989-04-06 | Fanuc Ltd | Numerical control apparatus |
Also Published As
Publication number | Publication date |
---|---|
JPH0687266B2 (en) | 1994-11-02 |
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