JPH01277969A - Free curve drawing method - Google Patents

Abstract

PURPOSE:To smoothly deform a free curve by moving a nodal point shared between two curve segments and adjacent control points in the same direction by the same extent of movement and connecting new curve segments on the condition of tangential continuation. CONSTITUTION:Plural curve segments KSG1-KSG3 consisting of arbitrary plane Beziers curves are connected to form a free curve. When this free curve formed by connecting segments on the condition of tangential continuation is deformed, nodal points P(0)1 and P(3)2 (P(0)2 and P(3)3) shared between two curve segments KSG1 and KSG2 (KSG2 and KSG3) and control points P(1)1 and P(2)2 (P(1)2 and P(2)3) adjacent to these nodal points are moved in the same direction by the same extent (m) of movement. New curve segments KSG1N and KSG2N (KSG2N and KSG3N) are formed and connected on the condition of tangential continuation.

Description

[Detailed description of the invention] The present invention will be explained in the following order.

A: Industrial field of application B: Outline of the invention C: Conventional technology: Problems to be solved by the invention E: Means for solving the problem (Figs. 2 and 3) F: Effects (Figs. 2 and 3) Figure) G Example (G1) Principle of free curve (Figure 2) (G2) Example of free curve creation (Figures 1 to 7) (G
3) Other embodiments H Effects of the invention A Field of industrial application The present invention relates to a free curve creation method, for example CAD (c
os+puter aided design)%
or CAM (c.

mputer aided +manufactory
ng), it is suitable for application when deforming the shape of the generated free curve.

B. Summary of the Invention The present invention provides a free curve creation method for deforming a free curve formed by connecting a plurality of Bezier curve segments on a plane. By moving the nodes shared by two curve segments and the control points adjacent to those nodes by the same amount of movement in the same direction, a new curve segment is formed while maintaining the tangent continuity condition. The free curve can be smoothly deformed while maintaining the atmosphere of the curved shape.

C Conventional technology For example, when designing the shape of an object with a free-form surface using a CAD method (geometric n+od
e1ing), designers generally specify 3 that the curved surface should pass through.
By specifying multiple points in a dimensional space (these are called nodes) and having a computer calculate a boundary curve network connecting the specified multiple nodes using a predetermined vector function, it can be expressed in a so-called wire frame. Create a curved surface. In this way, it is possible to form a large number of framework spaces surrounded by boundary curves (such processing is hereinafter referred to as framework processing).

The boundary curve network formed by such framework processing itself represents the rough shape that the designer intends to design, and a curved surface that can be expressed by a predetermined vector function is calculated using interpolation using the boundary curves surrounding each framework space. If it is possible to do so, it is possible to generate a free-form surface (which cannot be defined by a quadratic function) that is designed by the designer as a whole. Here, the curved surfaces stretched in each framework space form basic elements that constitute the entire curved surface, and these are called batches.

Conventionally, in this type of CAD system, easy-to-calculate vector functions representing boundary curve networks, such as the Bezier equation and B-spline, have been used.
A third-order tensor product formed by the equation (ne) is used, and is considered to be optimal for mathematically expressing a free-form surface that does not have any special features in terms of shape, for example.

In other words, a free-form surface that has no special features in shape is
When points given in space are projected onto the xy plane, the projected points are often arranged regularly in a matrix, and when the number of projected points is expressed as mxn, the framework space It is known that it can be easily stretched using a quadrilateral patch expressed by a cubic Bezier equation.

However, when this conventional mathematical expression is applied to a curved surface with characteristic shapes (for example, a curved surface with a greatly distorted shape), it is difficult to connect the patches, and it requires advanced mathematical calculation processing. Since it is necessary to execute the method, there is a problem that the calculation processing by the computer becomes complicated and enormous, and the calculation time becomes long.

As a way to solve this problem, we find internal control points that satisfy the condition of tangent plane continuity for the shared boundaries of adjacent framework spaces, and use a vector function that represents the free-form surface determined by the internal control points to A method of applying patches made of curved surfaces has been proposed (Japanese Patent Application No. 60-277)
No. 448, Patent Application No. 1984-290849, Patent Application No. 1983-
No. 298638, Japanese Patent Application No. 15396, 1983, Japanese Patent Application No. 1983
1-33412, Japanese Patent Application No. 61-59790, Japanese Patent Application No. 61-64560, Japanese Patent Application No. 61-96368, Japanese Patent Application No. 61-69385).

Problems that the invention aims to solveIn reality, in the design work of a designer, it is normal to approach the shape that the designer has imagined step by step by repeating local corrections. The free-form surface generated as described above is also repeatedly modified to approximate the shape envisioned by the designer.

In other words, as a method for modifying such a free-form surface, the designer cuts the free-form surface at a desired cross section on the display screen, visually confirms the cross-sectional shape of the resulting free-form surface, and expresses the cross-sectional shape as a cubic shape. A method is used that locally modifies the details of a free curve in which multiple curve segments are connected using Bezier curves expressed by the Bezier equation, and then generates a free-form surface again based on its cross-sectional shape. (Patent Application No. 1982-276925, Patent Application No. 62-278
No. 694).

However, when a designer modifies a free-form surface using such a method, the designer inflates the entire free-form curve by a small amount without drastically deforming the cross-sectional shape of the free-form curve. There are times when you want to correct or check the shape of a free curve by making it indented or concave.

In such cases, conventionally, for each curve segment of the free curve, the nodes and internal control points, etc. are moved in any direction to transform the curve shape for each curve segment, and then the curve shape is transformed again to the adjacent curve segment. By resetting internal control points to satisfy the tangent continuity condition, designers must smoothly connect adjacent curve segments to form a new curve, which is an extremely complicated design task for designers. The problem was that it was needed.

The present invention has been made in consideration of the above points, and it is possible to maintain the original free curved atmosphere with simple designer operations.
This paper attempts to propose a free curve creation method that can smoothly deform the free curve.

E Means for Solving the Problem In order to solve this problem, in the present invention, a curve segment Kscl − consisting of a Bezier curve is formed on an arbitrary plane.
,K3゜2,K,. In a free curve creation method that transforms a free curve formed by connecting a plurality of curve segments, 3cl,
KsGz, Ks. When transforming a free curve consisting of 2
three curve segments Ksr, l, Ksat (Kst
at , KsG3). , IP(nt
cP+. ,2,P(!ts) and its node P,. , IP
1ull! Control point P (111% P , t+t (P n>t) adjacent to (P (012, Pa5ss)
-, P (Create a new curve segment by moving the lily in the same direction by the same amount m and maintaining the condition of tangent continuity) Ksats, K 5GZN (K 5azNs
K 5csu> was formed.

F action two curve segments Ksa+ % Kstat (
Ksat, KSG3). )iP(s
+t(P(.,!,Pa3+3) and its node P,.>
Is P < 3) z (P t., t, control point adjacent to P (313) P (1) P (z + z (P (11
! , P, t, and ri are moved in the same direction by the same amount itm and a new curve segment KSGIN% Ksats CKsc, zNzK is created while maintaining the condition of tangent continuity.
3G1.4), the free curve can be smoothly deformed while maintaining the atmosphere of the original curve shape.

G example An embodiment of the present invention will be described in detail below with reference to the drawings.

(G1) Principle of free curve In this example, the free curve is as shown in Figure 2.
Nodes Po and P3 (P(
011 and P (y) 1% P (011 and P (3)
2%P. , 3 and P. , 3) multiple curve segments Ksa (Ks., KsGz , Ksa3)
will be connected. This curve segment KSG is calculated using the third-order Bezier equation as follows, R(t)=
(1-t+tE)'Po... Expressed by a parametric space curve R(t) expressed as (1).

Here, t is the curve segment Ksa from one node P0
It is a parameter that changes from a value of 0 to a value of 1 as expressed by the following equation (2) in the direction along the direction until reaching the other node P.

In this way, the curve segment 3r expressed by the third-order Bezier equation is changed to the nodes P6 and 2 by the shift operator E.
By specifying two control points P1 and P2 between 1 and 2, each point on the curve segment KEG is expanded by the following formula% +3(1-t)t''Pt+t'P1... (3) It is expressed as a position vector R(t) from the origin O of the xyz space by the formula.

Here, the shift operator E has the following relationship with the control point P on the curve segment KSG as shown in the following equation (4). Therefore, by expanding equation (1) and substituting the relationship in equation (4), we get the following equation R(t)=(1-t+tE)3P.

= ((1-t)'+3(1-t)"tE+3(1-t
) t"E" + t 'E31 p.

=(1-t)3Po+3(1-t)"tEP.

+3(1-t)tZE” P, + M 3 E
3 p 0 = (1-t)'po+ 3 (1-t)"
t P++3(1-t)t2P, +t''P.

...... It can be calculated as shown in (6), and as a result, each curve segment on the free curve KSGI, K
sGz and Kstas are two nodes and a control point P, respectively, based on equation (3). ,1~3,P(Ill~
3, Puz~, and P(311~, and each curve segment Ksa+ , Ksr, z , K
By expressing the free curve using SG:l, each curve segment Ksc+% KsGz・KSG
Nodes and control points P C01+-s, P(1
1+-3, P Hl 1-3 and PC311-3 can be used to express a free curve.

(G2) Example of Free Curve Creation As shown in FIG. 2, this example consists of three curve segments Ksc+
% KsGz and KSG3, an attempt is made to create a free curve that smoothly bulges upward while maintaining the atmosphere of the original shape.

The central processing unit (CPU) of the free curve creation device executes the curve deformation processing program SPO shown in FIG. 1 in accordance with the designer's instructions, and uses the method shown in FIG. 3 to create three curve segments Ksa+, KsGt,
The shape of the first curve segment Ksc+ of KsG3 is changed, and the curve deformation processing program SPO is sequentially executed for the second and third curve segments 1 (scz and KSG3) as shown in FIGS. In total, three curve segments are obtained by executing .,Ksa
t and Ksaff, it is possible to create a free curve that smoothly bulges upward while maintaining the atmosphere of the original shape under the condition of tangent continuity.

That is, the CPU enters the curve deformation processing program SPO and, in step SPI, waits for the designation of the curve segment (Ksc) on which the deformation process is to be performed from the designer.

Here, the designer uses, for example, a mouse to select the three curve segments Ksc+% of the free curve as shown in FIG.
Ksat, K2O2, 30. in the first curve segment. When the cursor is moved upward and the mouse is clicked, the CPU in the next step SP2 sets the node P, which will be the reference for the transformation process, to the first curve segment specified by the designer. , 1 or P. , waits for selection of 1.

In this state, when the designer uses the mouse to move the cursor to one of the nodes P(.) on the first curve segment and clicks the mouse, the CPU will move the mouse to the node P(.) in the next step SP3. ., waits for the designer's designation as to whether to use the input value of the movement vector or specify it on the display screen as the movement direction and movement distance for I.

If a negative result is obtained here (that is, this word indicates that the designer sets the moving direction and moving distance on the display screen), the CPU moves to the next step SP4 and accepts the designation of the moving direction and moving distance from the designer. wait.

In this state, the designer visually checks the display screen and selects the node P using the mouse. , I when you stop the cursor at the desired position and click the mouse, the CPU displays the specified movement vector m on the display screen,
The process moves to the next step SP6.

Further, when the CPU obtains a positive result in step SP3 described above (that is, this indicates that the designer inputs the movement direction and movement distance as vector information from, for example, a keyboard), the CPU moves to step SP5 and inputs the movement direction and movement distance as vector information from the designer. Waits for designation of movement direction and movement distance.

In this state, if the designer inputs the position to which the node P(.)1 should be moved as vector information from the keyboard, etc.,
The CPU displays the movement vector m resulting from the designation on the display screen, and proceeds to the next step SP6.

In this step SP6, the CPU selects the node P(.1
．． and the control point P(Il+
is moved by the movement path Mm in the movement direction specified by the designer to create a new node P(.)1. l and a new control point P(IIIN) are calculated, and then (
1) Node P, using the method described above for equations 2 to (6). )IN and pHl control point P(111N and P(
A new first curve segment KsGIN is calculated on Zll.

Subsequently, in the next step SP7, the CPU displays on the display screen the new first curve segment obtained by calculation, as shown in FIG.
In P8, it is determined whether or not the curve deformation process has ended, and if a positive result is obtained here (this indicates that the designer has instructed the end of this curve deformation process), the CPU proceeds to the next step SP9. Then, the curve deformation processing program SPO is ended.

If a negative result is obtained in this step SP9 (this indicates that the designer has instructed m-continuation of this curve deformation process), the CPU returns to the above-mentioned step SPI and performs steps 5P2-3P3-3P4-3P5. -3P
6-3 Execute the process of P7.

In this way, the CPU executes the processing loop of the curve deformation processing program SPO once according to the instructions from the designer, thereby converting the original first curve segment) Ksc+
While maintaining the atmosphere of the shape, this is smoothly expanded upward to create a new first curve segment) (
sGg)I can be created.

In this embodiment, the designer also selects the original first curve segment l''K3 while the new first curve segment KsGIN is displayed on the display screen, as shown in FIG.
Select the second curve segment KSG2 adjacent to G+ and add 3,1 nodes P(.1
．． Node P located at the same position as . , 2, and the above-mentioned node P, as the moving distance. 1. If we use values equal to the moving direction and moving distance m, as shown in Fig. 5,
While maintaining the atmosphere of the shape of the original second curve segment (Ks, z) in the same way as the new first curve segment, a new second curve segment is created by smoothly expanding it upward. A curve segment KS62N can be created. .

Furthermore, in the second and third curve segments, .

And to! 63, if the same procedure is applied as described above, the second and third curve segments (as shown in FIGS. 6 and 7)
Kscz andni! While maintaining the atmosphere of the G3 shape, this is a new second model that smoothly expands upward.
and in the third curve segment. 1N and KsaxN can be created.

It should be noted that in this case two curved segments KsGl and K,G are connected to each other under the condition of tangential continuity.

The node Plt that (Kscz and Kscs) share with each other
l) I and P 13) 2 (P (012 and Pa1e
Regarding s) - It is configured to move in the same direction and by the same amount of movement i1m, thereby creating two new curve segments KsGIN while maintaining the condition of tangent continuity.
and K 5GZN (K 302N and 3G:1)l
), and thus any part of the curved shape containing $GI, Kscz −, K2O:l as a whole into multiple curved segments can be smoothly bulged upward while maintaining the atmosphere of the original shape. You can create free curves.

According to the above method, the node shared by two curve segments connected to each other under the condition of tangent continuity and the control point adjacent to that node are moved in the same direction by the same amount of movement, and the condition of tangent continuity is By forming two new curve segments while maintaining the above, it is possible to create a free curve that smoothly bulges upward while maintaining the atmosphere of the original curve shape. .

Also, if this new free curve is moved by the same amount of movement with the sign reversed, it can easily return to the shape of the original free curve, and if it is further moved by the amount of movement in the negative direction,
A new free curve can be created by smoothly recessing the free curve while maintaining the atmosphere of the original curve shape.

(By repeating the above-mentioned free curve creation method, the overall curve shape can be arbitrarily changed by a minute amount without changing the detailed shape of each curve segment through complicated operations.) As a result, the usability of the designer in model creation, free curve design, etc. can be greatly improved.

(G3) Other embodiments (1) In the above embodiments, a case was described in which a curved segment represented by a cubic Bezier equation is stretched on an arbitrary plane, but the order of the equation is not limited to this. It may be of fourth order or higher.

(2) In the above embodiment, a case was described in which curved segments represented by the Bezier equation were stretched;
It is also possible to use other vector functions such as the equation, the Furgason equation, etc.

H Effects of the Invention As described above, according to the present invention, when a free curve consisting of a plurality of curve segments connected to each other under the condition of tangential continuity is deformed, the nodes shared by the two curve segments and their nodes are By moving the control points adjacent to the curve by the same amount in the same direction and forming two new curve segments while maintaining the tangent continuity condition, the atmosphere of the original curve shape can be maintained. However, it is possible to create a free curve by smoothly deforming the free curve.

In this way, it is possible to realize a free curve creation method that can significantly save the designer's design work.

[Brief explanation of the drawing]

FIG. 1 is a flowchart showing one embodiment of the present invention, and FIG.
Figure 3 is a route map for explaining the curved segments, Figure 3 is a route map for explaining the deformation of the first curved segment, Figure 4 is a route map for explaining the transformation of the first curved segment,
7 to 7 are route maps for explaining the process of deforming a free curve formed by first to third curve segments. K. + s, Ksaz,, KsGff...
・Original curve segment, K, G, , K 3GZN%
K 5GsN"'"'New curve segment・P
(011~3・P (311~ko・P(ozN~2
N・P<3128~. N...Node, Po
, 1-1, p, H-3, P (11IN -zs -,
P lt, zH-38""" control point, m...Movement vector.

Claims (1)

[Claims] A free curve creation method for deforming a free curve formed by connecting a plurality of curve segments formed by Bezier curves on an arbitrary plane, comprising: a plurality of curve segments connected to each other under the condition of continuous tangents; When transforming the above free curve formed by
By moving the nodes shared by two curve segments and the control points adjacent to the nodes by the same amount of movement in the same direction,
A free curve creation method characterized in that a new curve segment is formed while maintaining the condition of tangent continuity.