JPS62276669A - Interpolation device - Google Patents
Interpolation deviceInfo
- Publication number
- JPS62276669A JPS62276669A JP61118404A JP11840486A JPS62276669A JP S62276669 A JPS62276669 A JP S62276669A JP 61118404 A JP61118404 A JP 61118404A JP 11840486 A JP11840486 A JP 11840486A JP S62276669 A JPS62276669 A JP S62276669A
- Authority
- JP
- Japan
- Prior art keywords
- point
- interpolation
- vertex
- segment connecting
- points
- 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.)
- Pending
Links
- 238000000034 method Methods 0.000 description 4
- 238000010586 diagram Methods 0.000 description 3
- 230000000694 effects Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T3/00—Geometric image transformations in the plane of the image
- G06T3/40—Scaling of whole images or parts thereof, e.g. expanding or contracting
- G06T3/4007—Scaling of whole images or parts thereof, e.g. expanding or contracting based on interpolation, e.g. bilinear interpolation
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- Theoretical Computer Science (AREA)
- Complex Calculations (AREA)
- Image Processing (AREA)
Abstract
Description
【発明の詳細な説明】
３、発明の詳細な説明
〔産業上の利用分野〕
本発明は補間に関し、特にＣＡＤ、ＣＡＭ、画像工学等
において与えられた離れた点を結ぶ近似曲線を得るため
の補間装置に関する。Detailed Description of the Invention 3. Detailed Description of the Invention [Field of Industrial Application] The present invention relates to interpolation, and particularly to interpolation for obtaining an approximate curve connecting distant points given in CAD, CAM, image engineering, etc. Relating to an interpolation device.
補間法には座標データ間を直線的に補間する線形補間法
、全区間を単一の多項式で表わして補間するラグランシ
ュ補間法、データ点間を別々の多項式で表わし、補間自
然スプライン補間法等がある。Interpolation methods include linear interpolation, which linearly interpolates between coordinate data, Lagranche interpolation, which interpolates by representing the entire interval with a single polynomial, natural spline interpolation, which represents interpolation between data points with separate polynomials, etc. There is.
上述した各補間法のうち、線形補間はデータ点において
不連続が目立つ欠点があり、ラグランシュ補間法は多く
の乗除算を含むため演算手段が複雑となり、処理時間も
長く、又、大きな振動を生じるという欠点があり、自然
スプライン補間法は、切断べき関数で表わされるため、
その係数を得る連立−次方程式の条件が悪く、演算手段
が煩雑で時間がかかるという欠点がある。Among the above-mentioned interpolation methods, linear interpolation has the disadvantage of conspicuous discontinuities at data points, while Lagranche interpolation involves many multiplications and divisions, which complicates the calculation means, takes a long processing time, and causes large vibrations. However, since the natural spline interpolation method is expressed by a truncated power function,
The disadvantage is that the conditions for the simultaneous equations for obtaining the coefficients are poor, and the calculation means are complicated and time consuming.
本発明は上記各方法の欠点を補い、簡単な演算手段、早
い処理速度そして任意の綱かさという利点のある滑らか
な補間を実現するという補間装置を提供しようとするも
のである。The present invention aims to compensate for the drawbacks of the above-mentioned methods and to provide an interpolation device that realizes smooth interpolation with the advantages of simple calculation means, high processing speed, and arbitrary stiffness.
本発明は上記の問題点を解決するため連続した曲線上に
あるべき、順次設定された第１．第２及び第３の３つの
点の座標データと、前記第２の点に関する、前記第１の
点と第３の点を結ぶ線分の中点の対称点である第１の頂
点の座標データが与えられた場合において、前記第１
（又は第３）の点と第１の頂点を結ぶ線分の中点である
第１１（又は第３１）の頂点を求める第１の演算手段と
、前記第１ （又は第３）の点と第２の点を結ぶ線分の
中点である第１２（又は第３２）の中点を求める第２の
演算手段と、前記第１１ （又は第３１）の頂点と第１
２（又は第３２）の中点を結ぶ線分の中点を求める第３
の演算手段とを備えるようにしたものである。In order to solve the above-mentioned problems, the present invention provides first . Coordinate data of the second and third three points, and coordinate data of the first vertex, which is the symmetrical point of the midpoint of the line segment connecting the first point and the third point, regarding the second point. is given, the first
a first calculation means for calculating an eleventh (or thirty-first) vertex that is the midpoint of a line segment connecting the first (or third) point and the first vertex; a second arithmetic means for calculating a twelfth (or thirty-second) midpoint which is a midpoint of a line segment connecting the second points;
3rd to find the midpoint of the line segment connecting the 2nd (or 32nd) midpoints
The computer is equipped with a calculation means.
以下、本発明の一実施例について図面を参照して詳細に
説明する。Hereinafter, one embodiment of the present invention will be described in detail with reference to the drawings.
第１図は本発明の一実施例の構成を示すブロック図であ
る。FIG. 1 is a block diagram showing the configuration of an embodiment of the present invention.
図において、入力手段１より入力された、連続した曲線
上にあるべき順次設定された第１．第２及び第３の３つ
の点の座標データと、前記第２の点に関する、前記第１
の点と第３の点を結ぶ線分の中点の対称点である第１の
頂点の座標データは第１の記憶手段２に格納される。In the figure, the first . coordinate data of the second and third three points; and the coordinate data of the first point regarding the second point.
The coordinate data of the first vertex, which is the symmetrical point of the midpoint of the line segment connecting the point and the third point, is stored in the first storage means 2.
そしてまず、前記第１ （又は第３）の点と第１の頂点
の座標データからその２点を結ぶ線分の中点である第１
１ （又は第３１）の頂点の座標データが第１の演算手
段３により与えられる。First, from the coordinate data of the first (or third) point and the first vertex, the first
The coordinate data of the 1st (or 31st) vertex is given by the first calculation means 3.
一方、前記第１ （又は第３）の点と第２の点の座標デ
ータからその２点を結ぶ線分の中点である第１２ （又
は第３２）の中点の座標データが第２の演算手段４で演
算される。On the other hand, from the coordinate data of the first (or third) point and the second point, the coordinate data of the 12th (or 32nd) midpoint, which is the midpoint of the line segment connecting the two points, becomes the second point. It is calculated by the calculation means 4.
次いで前記第１１ （又は第３１）頂点と第１２（又は
第３２）の中点の座標データからこの２点を結ぶ線分の
中点の座標データが第３の演算手段５により演算され、
この中点が第１ （又は第３）の点と第２の点の間の補
間点である。この補間点の座標データは第２の記憶手段
６に格納され出力手段７により出力される。Next, from the coordinate data of the 11th (or 31st) vertex and the 12th (or 32nd) midpoint, the coordinate data of the midpoint of the line segment connecting these two points is calculated by the third calculation means 5,
This midpoint is the interpolation point between the first (or third) point and the second point. The coordinate data of this interpolation point is stored in the second storage means 6 and outputted by the output means 7.
このようにして、第１ （又は第３）の点と第２の点の
間の補間点が算出される。In this way, the interpolation point between the first (or third) point and the second point is calculated.
次に、２次′元の直交座標における演算を、第２図を参
照して具体的に説明する。例えば第１の点Ｐ、（０，Ｏ
）、第２の点ｐ、（１００，２００）と第３の点ｐ、（
３００，Ｏ）そして第１の頂点Ｔ、（５０，４００）に
ついて考える。Next, calculations in two-dimensional orthogonal coordinates will be specifically explained with reference to FIG. For example, the first point P, (0, O
), the second point p, (100,200) and the third point p, (
300, O) and consider the first vertex T, (50, 400).
ここで、第１の頂点Ｔ、（５０，４００）が、第２の点
ｐ２ （１００，２００）に関して、第１の点Ｐ、
（０，Ｏ）と第３の点Ｐ、（３００，Ｏ）を結ぶ線分の
中点（１５０，０）に対して対称であることを確認する
。Here, the first vertex T, (50,400) is the first point P, with respect to the second point p2 (100,200).
Confirm that it is symmetrical with respect to the midpoint (150,0) of the line segment connecting (0,O) and the third point P, (300,O).
まず、第１の点Ｐ、（０，０）と第１の頂点Ｔ、 （
５０，４００）の中点である第１１の頂点Ｔ１、（２５
，２００）が第１の演算手段３より求まる。First, the first point P, (0,0) and the first vertex T, (
50,400), the 11th vertex T1 is the midpoint of (25
, 200) are determined by the first calculation means 3.
一方、第１の点Ｐ、（０，０）と第２の点Ｐ２（１００
，２００）の中点である第１２の中点Ｃ，２（５０，１
００＞が第２の演算手段４より求まる。On the other hand, the first point P, (0,0) and the second point P2 (100
,200) is the midpoint of the 12th midpoint C,2(50,1
00> is determined by the second calculation means 4.
この第１１の頂点Ｔ１． （２５，２００）と第１２の
中点Ｃ，ｚ（５０，１００）の中点（３７，５゜１００
）が第３の演算手段５より求まる。This eleventh vertex T1. (25,200) and the 12th midpoint C,z (50,100) midpoint (37,5°100
) is determined by the third calculation means 5.
このようにして、３点ＰＩ、Ｐ２．Ｐ３に関して、第１
の点Ｐ、（０，０）と第２点Ｐｚ （１００゜２００
）の間に補間点■１□（３７，５，１００）を得る。In this way, 3 points PI, P2. Regarding P3, the first
The point P, (0,0) and the second point Pz (100°200
), the interpolation point ■1□ (37, 5, 100) is obtained.
同様にすれば、第２の点ｐ、（１００，２００）と第３
の点Ｐｚ （３００，０）の間にも補間点（１８７，
５、１５０）が得られる。Similarly, the second point p, (100, 200) and the third point
There is also an interpolation point (187, 0) between the points Pz (300, 0)
5,150) is obtained.
さらに細かく補間点をとる場合には、新しく得られた補
間点をデータ点とみなし、その補間点を含むさらに細い
隣接する３点と、対応する頂点について上記演算を行う
、以上を繰り返すことで任意の細かさまで補間点を求め
ることができる。If you want to take even finer interpolation points, consider the newly obtained interpolation point as a data point, and perform the above calculation on three thinner adjacent points including the interpolation point and the corresponding vertex. It is possible to find interpolation points up to the level of detail.
最初の補間において、３点だけが与えられ、頂点が与え
られていない場合には、第２の点に関し、第１の点と第
３の点を結ぶ線分の中点と対称な点を求め、これを第１
の頂点とする方法がある。In the first interpolation, if only three points are given and no vertex is given, find a point that is symmetrical about the second point to the midpoint of the line connecting the first and third points. , this is the first
There is a way to make it the vertex of
以上説明したように、本発明は簡単な演算手段で、高速
に、任意の細かさまで滑らかに補間できる効果がある。As explained above, the present invention has the advantage of being able to perform smooth interpolation to arbitrary fineness at high speed using a simple calculation means.
第１図は、本発明の実施例のブロック図。
第２図は、本発明装置によって実行される補間′の説明
図である。
１・・・入力手段
２・・・第１の記憶手段
３・・・第１の演算手段
４・・・第２の演算手段
５・・・第３の演算手段
６・・・第２の記憶手段
７・・・出力手段FIG. 1 is a block diagram of an embodiment of the present invention. FIG. 2 is an explanatory diagram of interpolation' executed by the apparatus of the present invention. 1... Input means 2... First storage means 3... First calculation means 4... Second calculation means 5... Third calculation means 6... Second storage Means 7: Output means
Claims (1)
及び第３の３つの点の座標データと、前記第２の点に関
する、前記第１の点と第３の点を結ぶ線分の中点の対称
点である第１の頂点の座標データが与えられている場合
において、前記第１（又は第３）の点と第１の頂点を結
ぶ線分の中点である第１１（又は第３１）の頂点を求め
る第１の演算手段と、前記第１（又は第３）の点を結ぶ
線分の中点である第１２（又は第３２）の中点を求める
第２の演算手段と、前記第１１（又は第３１）の頂点と
第１２（又は第３２）の中点を結ぶ線分の中点を求める
第３の演算手段とを備えることを特徴とする補間装置。The first and second sets should be on a continuous curve.
and the coordinate data of the third three points, and the coordinate data of the first vertex, which is the symmetrical point of the midpoint of the line segment connecting the first point and the third point, regarding the second point are given. in the case where a second calculating means for calculating the 12th (or 32nd) midpoint, which is the midpoint of the line segment connecting the 1st (or 3rd) point; or (32)) third calculation means for calculating the midpoint of a line segment connecting the midpoints.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP61118404A JPS62276669A (en) | 1986-05-24 | 1986-05-24 | Interpolation device |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP61118404A JPS62276669A (en) | 1986-05-24 | 1986-05-24 | Interpolation device |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| JPS62276669A true JPS62276669A (en) | 1987-12-01 |
Family
ID=14735810
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP61118404A Pending JPS62276669A (en) | 1986-05-24 | 1986-05-24 | Interpolation device |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JPS62276669A (en) |
-
1986
- 1986-05-24 JP JP61118404A patent/JPS62276669A/en active Pending
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| JPH02278290A (en) | Method for applying curve to shape shown by linear short vector train | |
| JPS62276669A (en) | Interpolation device | |
| JP2684609B2 (en) | Graphic display method in graphic data processing device | |
| JPH01217562A (en) | System for generating computing grid | |
| JPH01166177A (en) | Thick line drawing system for dda circuit | |
| JPH1125266A (en) | Method for converting picture and device therefor | |
| JPH02118782A (en) | Method for processing picture | |
| JP2740484B2 (en) | Graphic processing method | |
| JPH0368086A (en) | Linear interpolating circuit | |
| JP2000132712A (en) | Device and method for generating two-dimensional finite element mesh using triangular six node higher order element | |
| JPH06314341A (en) | Eliiptic interpolating method and arithmetic unit for elliptic interpolation | |
| US6995764B1 (en) | Automatic application task placement procedure in a signal processing machine | |
| JPS6286460A (en) | Two-dimensional fourier transform calculator | |
| JPH0664618B2 (en) | Clipping circuit | |
| JP4089806B2 (en) | Curve generating device and method, and storage medium | |
| JPH02194477A (en) | Mesh generator by mapping method | |
| JPS62182841A (en) | Square root arithmetic system | |
| JPH07311841A (en) | Method and device for synthesizing picture | |
| JPH0261779A (en) | Coordinate data processing unit | |
| JP2000306116A (en) | Method for deriving continuous rotational angle from continuous rotational matrix and storage medium storing program related to the method | |
| JPH07107710B2 (en) | Two-dimensional distance calculation device for image processing device | |
| JPH0449473A (en) | Image interpolating and contracting system | |
| JPH02159679A (en) | Rapid filtering system for image data | |
| JPH0520404A (en) | Three-dimensional graphic processing system | |
| JPS5952379A (en) | Interpolating device |