JPH01120674A - Production of free curved surface - Google Patents
Production of free curved surfaceInfo
- Publication number
- JPH01120674A JPH01120674A JP62278756A JP27875687A JPH01120674A JP H01120674 A JPH01120674 A JP H01120674A JP 62278756 A JP62278756 A JP 62278756A JP 27875687 A JP27875687 A JP 27875687A JP H01120674 A JPH01120674 A JP H01120674A
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- interpolated
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- 239000013598 vector Substances 0.000 claims abstract description 12
- 238000000034 method Methods 0.000 claims description 19
- 230000002411 adverse Effects 0.000 abstract 1
- 238000010586 diagram Methods 0.000 description 4
- 230000000694 effects Effects 0.000 description 2
- 229910017435 S2 In Inorganic materials 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000002349 favourable effect Effects 0.000 description 1
- 238000003754 machining Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
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Abstract
Description
【発明の詳細な説明】
〔産業上の利用分野〕
本発明は自由曲面作成方法に関し、ＣＡＤ／ＣＡＭにお
ける３次元形状モデリングに用いて最適なものである。DETAILED DESCRIPTION OF THE INVENTION [Industrial Application Field] The present invention relates to a free-form surface creation method, and is most suitable for use in three-dimensional shape modeling in CAD/CAM.
自由曲面上の離れている２つの面素の間の空間に各面素
の制御点情報を基にした２点を定め、そ０５２点を制御
点として各面素の境界端点間に３次ベジェ曲線を生成し
、各面素の他側の境界端点間にも同様にして３次ベジェ
曲線を生成し、各曲線を補間すべき面素の境界線（辺）
とすることを特徴とし、面素の除去、補間により目的の
自由曲面が容易に且つ高速に得られるようにした自由曲
面作成方法である。Two points are defined in the space between two separate surface elements on the free-form surface based on the control point information of each surface element, and a cubic Bezier is created between the boundary end points of each surface element using the 052 point as a control point. Generate a curve, and similarly generate a cubic Bezier curve between the boundary end points on the other side of each surface element, and determine the boundary line (edge) of the surface element to which each curve should be interpolated.
This free-form surface creation method is characterized in that a desired free-form surface can be easily and quickly obtained by removing and interpolating surface elements.
計算機内部で３次元自由曲面のデータを扱い、これらの
データから最終的な製品又は金型をＮＣ工作機械等で自
動加工するためのＮＣデータ（工具経路データ）を生成
するＣＡＤ／ＣＡＭシステムが実用化されつつある。A CAD/CAM system that handles three-dimensional free-form surface data inside a computer and generates NC data (tool path data) for automatically machining final products or molds using NC machine tools, etc. is now in practical use. It is becoming more and more popular.
計算機内で製品外形等の曲面を扱う場合、形状の制御性
が良い（変形や修正が容易）とか計算が容易であると云
った設計に好ましい性質を持つベジェ（Ｂ≦ｚｉｅｒ）
式とかＢ−スプライン（Ｓｐｌｉｎｅ）式を用いたパラ
メトリックな表現形式が良く使われている。３次元モデ
ルは、これらの弐によって計算することができる線素で
構成された面素（パンチ）の集合として表される。When handling curved surfaces such as product external shapes in a computer, Bezier (B≦zier) has favorable properties for design, such as good shape controllability (easy deformation and modification) and easy calculation.
Parametric expression formats using equations or B-spline equations are often used. A three-dimensional model is represented as a set of surface elements (punch) made up of line elements that can be calculated using these two.
自由曲面を設計する過程で、形状が意図通りでないとい
う理由で１つの面素（曲面パッチ）を削除してしまうと
、形状設計の初期段階に戻らなければならない、従って
再び曲線から構成される境界線網（パッチの集合）を生
成し、曲面を生成すると云う手順を取り、大変手間がか
かる。In the process of designing a free-form surface, if one surface element (surface patch) is deleted because the shape is not as intended, it is necessary to go back to the initial stage of shape design, and the boundary composed of curves must be returned to the initial stage of shape design. The procedure of generating a line network (a collection of patches) and then generating a curved surface is very time-consuming.
本発明はこの問題にかんがみ、削除したパッチの隣接パ
ッチから形状的及び位置的に整合（連続）する新たなパ
ンチを生成（補間）することを目的とする。In view of this problem, an object of the present invention is to generate (interpolate) a new punch that matches (continuously) shapely and positionally from patches adjacent to a deleted patch.
本発明の自由曲面作成方法は、自由曲面の離れている２
つの面素ｓ、、３２間に面素を補間する方法である。The free-form surface creation method of the present invention is characterized in that two free-form surfaces are separated from each other.
This is a method of interpolating surface elements between two surface elements s, , 32.
まず補間すべき面素Ｓ、に接する一方の面素Ｓ。First, one surface element S that is in contact with the surface element S to be interpolated.
め境界線Ｃ８の端点Ｐ１において、端点のまわりの制御
点を通るベクトルと逆向きのベクトルを形成し、その長
さを、点Ｐ、とこの点に対応する他方の面素Ｓ２の端点
Ｐ２との間の距離の数分の１とし、その終点を制御点Ｑ
、として求める。At the end point P1 of the boundary line C8, a vector in the opposite direction to the vector passing through the control points around the end point is formed, and its length is defined as the point P and the end point P2 of the other surface element S2 corresponding to this point. The end point is the control point Q
, is obtained as .
次に他方の面素Ｓ２の端点Ｐ２において、上記過程と同
様な処理を行って制御点Ｑ２を求める。Next, at the end point P2 of the other surface element S2, a process similar to the above process is performed to obtain a control point Q2.
次に点Ｐ、、Ｐ、を端点とし、点Ｑ＋ 、Ｑｔを制御点
とする３次ベジェ曲線Ｃ３を生成する。Next, a cubic Bezier curve C3 is generated, with points P, , P, as end points and points Q+ and Qt as control points.
更に面素Ｓ１、Ｓ２の他側端点Ｐ３ 、Ｐａに関し、上
記の過程を行って、端点間に３次ベジェ曲線Ｃ２を生成
する。Furthermore, the above process is performed regarding the other end points P3 and Pa of the surface elements S1 and S2 to generate a cubic Bezier curve C2 between the end points.
上記曲線Ｃ，，Ｃ，と、これらに連なる面素ｓｌ、Ｓ２
の境界線Ｃ８、Ｃ４とを４辺とする双３次ベジェ曲面か
ら成る補間面素Ｓ、を生成する。The above curves C,,C, and the surface elements sl and S2 connected to these
An interpolated surface element S, which is a bicubic Bezier surface whose four sides are boundary lines C8 and C4, is generated.
自由曲面上の離れた２つの面素の夫々を構成する４辺の
端点、制御点を使用して、ベジェ曲面から成る補間面素
を直接生成する。離れた面素と補間面素とは、位置的及
び形状的に整合し、接線連続でなめらかにつながる。An interpolated surface element consisting of a Bezier surface is directly generated using end points and control points of four sides constituting each of two separate surface elements on a free-form surface. The separated surface elements and the interpolated surface elements match in position and shape, and are smoothly connected by continuous tangents.
第１図に面素Ｓ、、Ｓ、の間に新たな補間面素Ｓ、を補
間する一方法を示す、また第２図に生成手順のフローチ
ャートを示す。FIG. 1 shows a method for interpolating a new interpolated surface element S, between the surface elements S, , S, and FIG. 2 shows a flowchart of the generation procedure.
面素Ｓｒ、Ｓｔはこの例では４辺形で構成され、その各
辺は第３図に示すように４つの制御点Ｐ０〜Ｐ３でパラ
メータ表現される３次ベジェ曲線で表されている。In this example, the surface elements Sr and St are composed of quadrilaterals, each side of which is represented by a cubic Bezier curve expressed as parameters by four control points P0 to P3, as shown in FIG.
３次ベジェ曲線のテンソル式は、 Ｒ（ｔ）−（１−ｔ＋ｔＥ）３Ｐ。The tensor formula of cubic Bezier curve is R(t)-(1-t+tE)3P.
−（１−ｔ）’Ｐｏ＋３（１−ｔ）ｚＥＰ。-(1-t)'Po+3(1-t)zEP.
＋３（１−ｔ）ｔ”ｔ！”Ｐ ＋ｔ’Ｅ’Ｐｏ−−−
−・−・・・−・−−−−・・−（１）で表される。ｔ
は両端点Ｐ、、Ｐ２（節点）間で０〜ｌの値を取るパラ
メータである。またＥは各制御点を示すシフト演算子で
あって、Ｐ＋””ＥＰｏ、Ｐ ｚ −Ｅ仲。、Ｐ３ ＝
２３Ｐ、である。+3(1-t)t"t!"P +t'E'Po---
−・−・・・−−−−・・−(1) t
is a parameter that takes a value of 0 to l between both end points P, , P2 (nodes). Further, E is a shift operator indicating each control point, P+""EPo, Pz-E. , P3 =
It is 23P.
４辺形面素は、ｕＳｖをパラメータとして、第４′図に
示すように１６個の制御点１〜１６による双３次ベジェ
式、
Ｓ （ｕ、 ｖ） ＝ （１−ｕ ＋ ｕＥ） ３（１
−ｖ ＋ＶＦ） ’ＰＯＱ −−−−−−−−（２）
で表される。The quadrilateral surface element is a bicubic Bezier equation with 16 control points 1 to 16 as shown in Figure 4', with uSv as a parameter, S (u, v) = (1-u + uE) 3 (1
-v +VF) 'POQ ----------(2)
It is expressed as
まず第１図及び第２図に示すように、ステップＳ１で面
素Ｓ１の一つのコーナ（制御点又は端点）Ｐｌから延び
、Ｐ、に連なる面素Ｓ１の辺の制御点Ｐ、′へのベクト
ルａ （制御辺ベクトル）に対して逆向きの単位ベクト
ルをｎｌとする。次にステップＳ２で、面素Ｓ１のコー
ナの端点ＰＩ と面素Ｓ２の対向するコーナの端点Ｐ２
との間の直線距離１１を求め、次のステップＳ３で、点
Ｐ＋にβ１
− ｎ 、を加えて、その終端を新たな制御点Ｑ１とす
る。なお１１の除数は適宜に定めてよく、３〜５が好ま
しい。First, as shown in FIGS. 1 and 2, in step S1, the control point P,' of the side of the surface element S1 extending from one corner (control point or end point) Pl of the surface element S1 and continuing to P, Let nl be a unit vector in the opposite direction to vector a (control side vector). Next, in step S2, the end point PI of the corner of the surface element S1 and the end point P2 of the opposite corner of the surface element S2
In the next step S3, β1 − n is added to the point P+, and its terminal point is set as a new control point Q1. Note that the divisor of 11 may be determined as appropriate, and is preferably 3 to 5.
次にステップＳ４で、面素Ｓ２について前記ステップ８
１〜Ｓ３と同様な処理を行い、新たな制御点Ｑ２を得る
。そしてステップＳ５で、点Ｐ５、β２を端とし、Ｑ＋
、Ｑｚを制御点とする３次ベジェ曲線Ｃ１を求める。Next, in step S4, the step 8 for the surface element S2
Processing similar to steps 1 to S3 is performed to obtain a new control point Q2. Then, in step S5, point P5, with β2 as the end, Q+
, Qz as the control points, a cubic Bezier curve C1 is obtained.
同様にして、ステップＳ６で面素５ＩＳＳｔの他のコー
ナ点の端点Ｐ、 、β４について、ステップ３１〜Ｓ４
を行い、新たな制御点Ｑ３ 、Ｑ、を得て、点Ｐ３、β
４を端とし、Ｑｌ、Ｑ４を制御点とする３次ベジェ曲線
Ｃ２を得る。このようにして出来た曲線Ｃ１、Ｃｔと、
面素Ｓｔ、Ｓｔの本来の境界線Ｃｓ、Ｃａを夫々４辺と
する双３次ベジェ曲面Ｓ３を補間面素として生成する（
ステップ３７）。なお第４図のｍｌ素内部の制御点６．
７．１０．１１については、４角におけるツイストベト
クルを零とするか、又は曲率に相当する量を零とするこ
とにより決めることができる。Similarly, in step S6, for other corner points P, , β4 of surface element 5ISSt, steps 31 to S4
and obtain new control points Q3, Q, and set the points P3, β
A cubic Bezier curve C2 with Ql and Q4 as control points is obtained. The curves C1 and Ct created in this way,
A bicubic Bezier surface S3 whose four sides are the original boundaries Cs and Ca of the surface elements St and St, respectively, is generated as an interpolated surface element (
Step 37). Note that the control point 6 inside the ml element in FIG.
Regarding 7.10.11, it can be determined by setting the twist vector at the four corners to zero, or by setting the amount corresponding to the curvature to zero.
この補間面素の生成方法の特徴は、第５図に示すように
、段違いとなっている面素間を補間する場合でも、自然
につながる曲面Ｓ、が生成されることである。The feature of this method of generating interpolated surface elements is that, as shown in FIG. 5, even when interpolating between surface elements that are at different levels, a naturally connected curved surface S is generated.
また補間面素Ｓ、の各コーナＰ、〜Ｐ４においては接線
連続となる。Furthermore, each corner P, to P4 of the interpolated surface element S is a continuous tangent.
本発明は上述のように、離れている２つの面素間に各面
と連続したベジェ曲面から成る補間曲面を生成できるよ
うにしたので、面素の集合から成る幾何モデルの一つの
面素を削除し、これを新たな面素で補間する場合に、モ
デル設計の初期段階に戻ることなく、ベジェ曲面を直接
的に部分生成することが可能になり、形状モデリング設
計の自由度及び能率が著しく向上する。As described above, the present invention makes it possible to generate an interpolated surface consisting of a continuous Bezier surface between two separated surface elements, so that one surface element of a geometric model consisting of a set of surface elements can be generated. When deleting a surface element and interpolating it with a new surface element, it is now possible to directly generate a partial Bezier surface without having to go back to the initial stage of model design, greatly increasing the freedom and efficiency of shape modeling design. improves.
第１図は本発明の一実施例の補間面素生成方法を示す線
図、第２図はその手順を示すフローチャート、第３図は
ベジェ曲線とその制御点を示す線図、第４図は１６個の
制御点から成るベジェ曲線の一面素を示す線図、第５図
は段差のある面素間を補間する様子を示す線図である。
なお図面に用いた符号において、
ｓ、、 ５ｒ−−−−−−−−−−・面素Ｓ ３−−−
−−−−−−−−−・・・・−補間面素Ｐ Ｉ”＝ Ｐ
＊’−・・・・−・−制御点（端点）ｑ、〜Ｑ 、、
−−−−−−−−−一制御点ａ・−−−−一−−−−−
・−一−−−−−制御辺ベクトルである。FIG. 1 is a diagram showing a method for generating interpolated surface elements according to an embodiment of the present invention, FIG. 2 is a flowchart showing the procedure, FIG. 3 is a diagram showing Bezier curves and their control points, and FIG. FIG. 5 is a diagram showing one surface element of a Bezier curve consisting of 16 control points, and FIG. 5 is a diagram showing interpolation between surface elements with steps. In addition, in the symbols used in the drawings, s,, 5r------・Surface element S 3---
−−−−−−−−−・・・・−Interpolated surface element P I”= P
*'−・・−・−Control point (end point) q, ~Q ,,
----------1 control point a・-----1-------
・−1−−−− Control edge vector.
Claims (1)
素を補間する方法であって、 補間すべき面素Ｓ＿３に接する一方の面素Ｓ＿１の境界
線Ｃ＿３の端点Ｐ＿１において、端点のまわりの制御点
を通るベクトルと逆向きのベクトルを形成し、その長さ
を、点Ｐ＿１とこの点に対応する他方の面素Ｓ＿２の端
点Ｐ＿２との間の距離の数分の１とし、その終点を制御
点Ｑ＿１として求める第１過程と、 他方の面素Ｓ＿２の端点Ｐ＿２において、上記第１過程
と同様な処理を行って制御点Ｑ＿２を求める第２過程と
、 点Ｐ＿１、Ｐ＿２を端点とし、点Ｑ＿１、Ｑ＿２を制御
点とする３次ベジエ曲線Ｃ＿１を生成する第３過程と、 面素Ｓ＿１、Ｓ＿２の他側端点Ｐ＿３、Ｐ＿４に関し、
上記第１〜第３過程を行って、端点間に３次ベジエ曲線
Ｃ＿２を生成する第４過程と、 上記曲線Ｃ＿１、Ｃ＿２と、これらに連なる面素Ｓ＿１
、Ｓ＿２の境界線Ｃ＿３、Ｃ＿４とを４辺とする双３次
ベジエ曲面から成る補間面素Ｓ＿３を生成する第５過程
とから成る自由曲面作成方法。[Claims] A method of interpolating a surface element between two separated surface elements S_1 and S_2 of a free-form surface, the end point of the boundary line C_3 of one surface element S_1 touching the surface element S_3 to be interpolated. At P_1, form a vector in the opposite direction to the vector passing through the control point around the end point, and make its length a number of times the distance between the point P_1 and the end point P_2 of the other surface element S_2 corresponding to this point. 1 and its end point is determined as the control point Q_1; A second process is performed at the end point P_2 of the other surface element S_2 to obtain the control point Q_2 by performing the same process as the first process; and the point P_1. , P_2 as the end point and the points Q_1 and Q_2 as the control points, and the third process of generating the cubic Bezier curve C_1, and the other end points P_3 and P_4 of the surface elements S_1 and S_2,
a fourth step of performing the first to third steps above to generate a cubic Bezier curve C_2 between the end points; and a surface element S_1 connected to the above curves C_1 and C_2;
, a fifth step of generating an interpolated surface element S_3 consisting of a bicubic Bezier surface whose four sides are boundary lines C_3 and C_4 of S_2.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP62278756A JP2737127B2 (en) | 1987-11-04 | 1987-11-04 | Object surface shape data creation method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP62278756A JP2737127B2 (en) | 1987-11-04 | 1987-11-04 | Object surface shape data creation method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH01120674A true JPH01120674A (en) | 1989-05-12 |
| JP2737127B2 JP2737127B2 (en) | 1998-04-08 |
Family
ID=17601754
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| JP62278756A Expired - Fee Related JP2737127B2 (en) | 1987-11-04 | 1987-11-04 | Object surface shape data creation method |
Country Status (1)
| Country | Link |
|---|---|
| JP (1) | JP2737127B2 (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO1999014061A1 (en) * | 1997-09-12 | 1999-03-25 | Petio Co., Ltd. | Three-dimensional shape data processing device, carved plate and carving device |
| US6373491B1 (en) | 1998-04-09 | 2002-04-16 | Sony Computer Entertainment, Inc. | Image processing device, image processing method and program distribution medium and data distribution medium for processing images |
| CN104741994A (en) * | 2015-03-25 | 2015-07-01 | 华南理工大学 | Precise curved-surface grinding method for grinding wheel with any curved surface |
| CN106527940A (en) * | 2016-11-03 | 2017-03-22 | 青岛海信电器股份有限公司 | Handwriting determination method and apparatus |
-
1987
- 1987-11-04 JP JP62278756A patent/JP2737127B2/en not_active Expired - Fee Related
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO1999014061A1 (en) * | 1997-09-12 | 1999-03-25 | Petio Co., Ltd. | Three-dimensional shape data processing device, carved plate and carving device |
| US6373491B1 (en) | 1998-04-09 | 2002-04-16 | Sony Computer Entertainment, Inc. | Image processing device, image processing method and program distribution medium and data distribution medium for processing images |
| US7084883B2 (en) | 1998-04-09 | 2006-08-01 | Sony Computer Entertainment Inc. | Image processing device, image processing method and program distribution medium and data distribution medium for processing images |
| CN104741994A (en) * | 2015-03-25 | 2015-07-01 | 华南理工大学 | Precise curved-surface grinding method for grinding wheel with any curved surface |
| CN104741994B (en) * | 2015-03-25 | 2017-04-19 | 华南理工大学 | Precise curved-surface grinding method for grinding wheel with any curved surface |
| CN106527940A (en) * | 2016-11-03 | 2017-03-22 | 青岛海信电器股份有限公司 | Handwriting determination method and apparatus |
| CN106527940B (en) * | 2016-11-03 | 2019-12-10 | 青岛海信电器股份有限公司 | Handwriting determining method and device |
Also Published As
| Publication number | Publication date |
|---|---|
| JP2737127B2 (en) | 1998-04-08 |
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