JPS62251975A - Curved face forming method - Google Patents

Abstract

PURPOSE:To form a free curved face having shape intended by an operator easily by obtining positional vector that indicates a curved face after transformation from positional vector indicated by transform positional information and positional vector indicating the face before transformation. CONSTITUTION:A vector field function Fi is set for a transformed area of an ellipse in variable distribution expressed by a Gaussian distribution function, and transform vector Vi* that indicate the amount of transformation and direction at a point of application is designated. By multiplying the transform vector Vi* and the function Fi, a preliminary transform positional vector PD(i-1)* that indicates preliminary transformation of the curved face in the transformed area is obtained. By adding a position transform function PEX(i-1)* to it a positional vector Pi* that indicates a final transformed curved face is obtained. Thus, by determining the direction of positional change and magnitude on transformation points P1, P2 - etc. making a point of application P0 a center using the function PEX(i-1)*, a free curved face intended by an operator can be formed.

Description

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

A: Industrial field of application B: Overview of the invention C: Conventional technology D: Problems to be solved by the invention E: Means for solving the problem (Figs. 1 to 11) F: Effects (Figs. 1 to 11) Figure) G Example (G1) Basic configuration (Figures 7 to 9) (G2) Structure of characteristic parts (Figures 7 to 9, Figures 10, 11) (G3) Curved surface creation device Example (Fig. 12, Fig. 13)
H Effects of the Invention A Industrial Field of Application The present invention relates to a method for creating a curved surface, particularly in computer graphics, in which a curved surface constituting an original image is locally transformed into a new curved surface.

B. Summary of the Invention The present invention is a method for creating a curved surface in computer graphics, in which a free-form surface can be created by locally deforming a part of the curved surface based on deformation position information obtained through a position transformation function. This makes it possible to form the desired curved surface in steps with a relatively large degree of freedom.

C. Conventional technology Conventionally, in computer graphics, a method for generating three-dimensional curved surfaces is to prepare data for basic curved surfaces such as cylinders and spheres (these are called primitive curved surfaces) in advance, and to generate these primitive curved surfaces. You can create a new surface by combining them as necessary, or you can specify points on the newly created surface as control points and interpolate the surface passing through these control points using a spline function. rows (methods, etc.) are used.

D. Problems to be Solved by the Invention These conventional methods actually use the outer shape of a primitive curved surface as a basic shape, and obtain a desired curved surface by deforming the curved surface based on the basic shape. It is believed that it is possible to create curved surfaces that can be added with grooves, as long as it is applied to express the external shape of mechanical objects.

Incidentally, even when creating a curved surface using a spline function, it is actually necessary to set a large number of control points.
Control points are set within a practically acceptable range by combining cross-sectional views, and therefore this case also has the same characteristics as the combination of primitive curved surfaces.

However, for example, we are trying to create a curved surface that gives a soft impression, such as a curved surface that represents a human face, and that would be unnatural if it were not expressed by a curved surface that is different from a primitive curved surface (this is called a free-form surface). In such cases, it is practically insufficient to use the conventional curved surface creation method, which in principle is strongly influenced by the characteristics of the primitive curved surface.

Furthermore, when creating a new curved surface, it is easy to intuitively understand the correlation between the image displayed on the display screen using image data processed by the computer and the data that the operator should set for the control. If so, the parameters that the operator sets and inputs and the resulting changes that appear on the curved surface on the display screen, from the viewpoint of easily obtaining a curved surface that closely matches the curved surface that the operator wants to obtain. It is desirable to have a correspondence relationship that is easy to understand intuitively.

As a way to solve this problem, the patent application 1986-16
As disclosed in No. 6312, the surface S before deformation processing
A predetermined deformation region V including the point of application CP i with respect to OR
CF, determine the vector field function I-bow that represents the relative deformation rate at each point in this deformation region VCF, and calculate the deformation hector vl'' that represents the amount and direction of deformation at the point of action CP1' in the deformation region VCF. Specify the deformation vector■
(9 and a position vector V representing the amount of deformation of the curved surface in the deformation area VCF by multiplying by the vector field function Fi,
" *Fi is obtained, and a position vector V representing the amount of deformation of this curved surface is obtained.") Based on IIFi and a position vector Pi-1* representing the surface SOR before transformation processing, a position vector P3 representing the curved surface after transformation is determined. A method for creating a curved surface has been proposed.

In this surface creation method, the vector field function Fi is
It is given as a scalar quantity representing the relative rate of change at each point within the deformation area VCF, and therefore the deformation area VCF
For each point included in It has a size corresponding to the deformation rate.

Here, the position vector Vi ” representing the amount of deformation of this curved surface
*Fi has a value only inside the deformation region VCF, so the vector field function Fi and the deformation vector V, 1''
Since it is only necessary to calculate wJ for the points within the deformation area VCF, the calculation time is practically real time.

In addition, the position vector PI0 representing the curved surface after deformation is calculated by calculating a recurrence formula consisting of the position vector Pi-1'' representing the curved surface before the deformation process, and the position vector ■,!F! representing the amount of deformation of the curved surface. Therefore, when creating a surface, you can create a deformed surface by accidentally deforming the surface one step at a time locally. Therefore, it is possible to interactively create a free-form surface that closely approximates the surface that the operator wants to obtain in practice.

However, according to the surface creation method disclosed in Japanese Patent Application No. 60-166312, the deformation area VCF and its deformation amount are directly controlled by specifying the parameters of the vector field function Fi as the Mi1 means. Therefore, it has a small degree of freedom as a control means, and in practice, in order to create a desired curved surface, it is necessary to repeat many deformation operations, so it is still insufficient as a means to create a free-form surface. .

The present invention has been made in consideration of the above points, and aims to propose a free-form surface creation method that further expands the degree of freedom of the operator's deformation operation (1) when creating a free-form surface. It is.

E Means for solving problem Based on the position of each deformation point P4-1'' of Specify 0 and change the deformation vector V%
A preliminary deformation position vector PD (4-t) representing the amount of preliminary deformation of the curved surface in the deformation region VCF is obtained by multiplying the vector field function FA by the vector field function FA. Position conversion function P.

, Mu-I,I to generate converted position information,
A position vector PLI representing the curved surface after deformation is obtained based on the position vector represented by this converted position information and the position vector Pi-1' representing the surface SOR before deformation processing.

The amount of preliminary deformation of the F action surface can be determined by the position vector v,**Fi, and this position vector V,'' *F
! has a value only within the deformation area VCF, so the calculation between the vector field function Fl and the deformation vector y,+ only needs to be performed for points within the deformation area VCF, so the calculation Time becomes practically real time.

Thus, in particular according to the invention, the preliminary deformation position vector P! 1(!-1)”, the position transformation function pEx
By calculating the transformed position information obtained by ``
When calculating, the operator can insert parameters that can be arbitrarily controlled as necessary, and the shape can be practically matched to the shape that the operator wants to create with a larger free width. The amount of deformation can be easily generated.

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

(G1) Basic configuration The method for creating a curved surface according to the present invention is as shown in FIG.
The point of application Crt” (
-(xt,)'i))), and specify the point of action CP! The computer executes the deformation calculation of the curved surface only within the range of deformation area CF including ".The calculation result is displayed on the display screen DSP on the display device CRT (Figure 8) from an arbitrarily determined viewpoint position. It can be displayed as a converted screen SCH similar to when viewing the curved surface after deformation.

The deformation of the curved surface in the deformation region VCF is calculated recursively using a conversion formula expressed by the following recursive formula %.

In equation (1), Pio is a position vector representing each point of the curved surface after deformation formed in three-dimensional space, and this position vector Pi' is the position vector Pi of the corresponding point on the original image SOR before deformation. , ''' and the amount of deformation VL from the position vector Pi, ' before the deformation *F4 (Pi-I
I, Crt”).

This amount of deformation is determined by the vector field function Fi(Pt-+ ”, C
It is expressed as a position vector obtained by multiplying the deformation vector Vi* by the deformation vector Vi*.

Here, the deformation vector v4° is the original image SO before deformation processing.
In R, when the point of action crt" is set, the direction and magnitude of the deformation to be applied to the original image SOR at the point of action cp," is expressed as a vector quantity, and this causes the point of action CPl of the original image SOR to be ” is a deformation vector■
It will be deformed so that only i9 will be lifted.

Also, the vector field function Ft (P !-1”, CP
(''') is relative to each point pi-t''' of the deformation area VCF (its size can be specified by setting and inputting parameters) that is determined including the application points CP and ''. It represents the distribution of the relative deformation rate that determines the degree of deformation.This distribution of the relative deformation rate is
It has a distribution of scalar quantities that has values only inside the deformation region VCF, and that "becomes 0" or "converges to 0" toward the periphery.

Deformation amount V, I*Fi(Pi-1", Cp
t'') is a position vector representing the amount of deformation at each point in the deformation area VCF, whose direction is parallel to the deformation vector y%, and whose magnitude is equal to the deformation vector vI'
, and the relative deformation rate distribution represented by the vector field number Fi (scalar quantity). Thus, the deformation of the curved surface of the deformation region VCF is the deformation vector It occurs in the direction and magnitude of 0, and as it goes from the point of action CPt9 toward the periphery, it occurs in the direction of the deformation vector 50, and with a magnitude that changes in accordance with changes in the deformation rate of the vector field function Fi.

Here, if the vector field function F+ is assigned a function such as a Gaussian distribution function that gradually converges symmetrically to 0 as it goes outward from the center point, the amount of deformation V = "" F t has a maximum value in the direction of the deformation vector y% at the point of action CP!', and the deformation vector V
, 11 directions and whose size gradually converges to O is obtained.

In this way, with one transformation operation, the amount of transformation V,
*Fi is calculated, and this is the position vector Pi- before deformation.
1'' is added to obtain the post-deformation position vector P,'.Every time a similar deformation operation is performed, (1
), by operating the recurrence formula represented by the formula
A position vector representing the deformed surface is repeatedly and recursively calculated based on the pre-deformation position 'II vector.

As a result of repeating such recursive calculations, the position vector representing the final deformation point PN' is the point P of the original image SOR before the start of deformation, as expressed by the following equation. . N transformation operations (
1-1 to N)) is obtained as a position vector obtained by adding the sum of the deformation amounts (i.e., the total deformation amount).

Thus, according to equation (2), when the operator sequentially performs N deformation operations from point P, 9 of the original image SOR, each time, by specifying the point of application CP1° for the curved surface before deformation, The position to be deformed from the curved surface P l-1'' can be specified arbitrarily based on the operator's judgment.Also, by respecifying the parameters that determine the vector field function Fi and the deformation vector V%, the deformation area V
The size of CF, the deformation rate distribution of the deformed surface, and the direction of deformation are
Similarly, the settings can be arbitrarily reset based on the operator's judgment.

In this way, each time the operator performs one deformation operation, the operator gradually accumulates operations that apply deformation to the undeformed curved surface at a desired position, in a desired direction, and with a desired magnitude. be able to.

(As is clear from equation (1), the position vector Pi-1° before transformation is changed from the position vector P after transformation
When obtaining the straight 0, position vector p t-+ * before deformation
Since it is sufficient to simply add the deformation 1v, "*Ft," the calculation speed can be made sufficiently short for practical purposes (according to experiments, it was possible to reduce it to less than 1 second).Then, the deformation amount Vi "
* Regarding the operation to obtain [i', the vector field function Fi converges to 0 as it goes to the periphery, or 0
By selecting a function such that ).

Therefore, according to the method for creating a curved surface according to the present invention, a transformed image can be displayed on the display screen in practical real time every time the operator performs a transformation operation, and therefore the image transformation operation can be performed interactively on a computer. It is possible.

Therefore, as described above regarding equation (2), the operator uses the deformation parameters by trial and error while accumulating N deformation operations until obtaining the final deformation position vector PNI from the position vector P@' of the original image SOR. By re-inputting , it is possible to continue the transformation operation while evaluating the effect of the transformation on the curved surface obtained by the previous transformation operation, and in this way, after each operation,
Next, while thinking about the operations that should be performed on the curved surface, ``at what position,'' ``in what area,'' ``in what direction,'' and ``what size?'' , parameters can be set, and in this way it is possible to easily obtain a curved surface that is closest to the curved surface that one ultimately wishes to obtain.

In the above curved surface creation method, as an example of creating a curved surface for a human face, the above equation (1) and (
2) A Gaussian distribution function may be used as the vector field function Fi in the equation, and a circular or elliptical shape may be selected as the deformation region VCF. At this time, sit! Deformed position vector P+” (XSy) and PM for point II (xSy)
' (X% y) is shown in equations (3) and (4) in correspondence with equations (1) and (2), respectively.

Pl"(X% y)-pt-+"(xSy)αi PN"(X, y)-P a"(xSy)αi 2Fr = ...... (5) , the point of action on the xy plane (Xt, Yt)
As shown in FIG. 9, an ellipse with diameters α1 and β in the X direction and X direction exhibiting a Gaussian distribution function in the X direction and the X direction.

When doing this, the operator uses the vector field function F
For i, point of action CP! ” parameters as coordinates (xt
. Thus, the operator determines the point of application CPi ” (X
For a circular or elliptical deformation region ■CF with diameters α and β perpendicular and centering on i , Yl), the point of application CPi ” (
In the direction of 1°, the deformation vector ■ is set at 0 (Xi 1Yt), and the deformation rate smoothly converges to O so that it draws a Gaussian distribution curve as it moves toward the periphery. A deformed surface can be obtained.

Therefore, the curved surface represented by the position vector P+" (x, y) or P." (X%y) after deformation is the layer surface S before deformation.
For a local region of the OR centered on the point of application CPI', a curved surface exhibits a smooth free-form surface as shown by a Gaussian distribution function in the direction of the deformation vector I'.

In this way, it is possible to create a curved surface that does not cause unnaturalness by adapting to a soft free-form surface such as a human face.

(G2) Structure of characteristic parts As mentioned above, the present invention has the basic structure, for example (1
), for example, the point of action c
If we specify the position vector Pi-1 before deformation for this point of action CpH with reference to p,", then the vector field number F! According to the deformation rate distribution defined in the coordinate system in which +', the position vector P1' after deformation can be obtained, and the free-form surface after deformation can be specified by the position vector P50 after deformation.

In the present invention, in addition to this basic configuration, (
1) Preliminary deformation position vector P, by deformation processing based on Eq. −1,′ is obtained, and this preliminary deformation position vector P
D(!-11" is further converted into position conversion function P EX (1-
11'' to obtain the final deformed position vector p,*.
In order to control the shape of the free-form surface represented by this position vector P1°, a new parameter is interposed, thus further improving the degree of freedom in deformation operations using parameters.

In other words, by the transformation processing method using equation (1), the following equation %formula% A preliminary deformation position vector P, □-3, expressed by is obtained.

Then, for this preliminary deformation position vector PO (1-11'', add the position conversion function PEX (4-113) expressed by the following formula % formula %),
Thus, the position vectors p, I representing the final deformed surface expressed by the following formula
get.

(6) If the calculations of equations (2) to (8) are executed, the position vector P representing the deformed surface can be obtained! . is the position vector Pi− before deformation
1* to the positions shown in FIGS. 10 and 11.

In other words, the preliminary deformation position vector Poct-n'' is the first
As shown in Figure 0, the point of action CP! ”, the deformation point p,
When −, * is specified, the second term of equation (6) lifts the object in the direction along the deformation vector ■1°.

On the other hand, the position transformation function PEXTi-11'' is (
7) As shown in the equation, the difference vector Pi−,”−CPi
has a direction along ''' and has a vector field function FE
It is a vector whose size is obtained by multiplying X (PL-1'', Crt'') and by the position conversion coefficient J.

Here, the vector field function Ftx (P+-+ ”, C
Pl'') represents the relative position loss rate assigned to each deformation point in the deformation region VCF, and thus the position transformation number PEX(!-11'' is the vector field function F!x
As a value determined by (Pt-+9, CPl"), the value converges to 0 as it goes to the periphery with the point of action CP!" as the center (the difference vector Pi-+ "-CPt
” will be multiplied by

On the other hand, the position conversion coefficient J has 0, a positive value, and a negative value, and when J=0, the position conversion function Ptxtt-n
” becomes 0, the final position of the curved surface P,.

From equation (8), becomes Poti-+, and thus the position that is not subjected to position change from the preliminary deformation position vector pH+1-1)'' becomes the position of the final position vector P,''.

On the other hand, when the value of the position conversion coefficient J becomes a positive value, the number P between position conversions. o-01 is the preliminary deformation position vector r'DT1-1 in the direction along the difference vector pi-+''-CPi' indicating the position of the deformation point P, -10 with respect to the point of application CPi'' as shown in FIG. )''' as a reference and the position converted in the direction away from the point of action crt''' is the final position of the position vector PI0.

Conversely, when the value of the position conversion function J becomes a negative value,
Position conversion function P! XLI-11” is the difference vector Pi-+
In the direction along "-CPI", the point of action CP!
By having a vector that approaches ``, the position vector PL0 representing the final deformed surface will be converted to a position that approaches the point of action CP,'' with the preliminary deformation position vector PD(!-11'' as a reference) .

In this way, using the position transformation function PEX (T11''), as shown in FIG. - If the number and size of position transformations are determined for P-z, P-3..., then the position vector P after transformation is the value of the position transformation coefficient J in equation (7). or vector field function FEx(PL1 ”
,CPz'') as necessary.As a result, even if the same pattern position is specified as the deformation point P!-1' in the deformation area VCF, different position vectors P, * can be controlled. It is possible to generate a curved surface with

As a result, using the method based on the basic configuration described above for equation (1), the free-form surface before conversion is transformed into a local deformation region VC.
Even if you specify the same deformation point as when F is deformed by °ζ,
Position conversion function P. l! -1) ''' (Formula (7)) can be deformed into different free-form surfaces depending on the parameter selection, and in this way, when an operator wants to form a desired free-form surface, the surface can be created with a large degree of freedom. The device can be realized.

Here, as mentioned above regarding equations (3) and (4),
Transformation position Hector P! 9, the deformation point P+-+ specified for the deformation area VCF on the xy seat rod.
When (X, y) is used, the position conversion function P! of equation (7) is used. x(,-n ” (XtxLl-n
-, Vtx+i-++ ), the position conversion formula in the X and X directions is expressed as the following formula:
9) )' Exci-++ -J * (y Yt)...
...(10) A conversion function as expressed by the following can be applied.

This position conversion function xEX(t-11 and Ytxt+-n
As the vector field function FIX in equation (7),
and the diameter in the X direction is α. 1 and β. , the transformation region V of the ellipse
In CF, draw a Gaussian distribution curve.

In this case, the difference vector Pi-1°-CP in equation (7)
The position vector from the point of action CP+'' (Xi, Yt) to the deformation point Pi-+'' (x, y) is taken as the value 0.

In this way, by selecting the value and sign of the position conversion coefficient J as 0, a positive value, or a negative value as necessary as the position degree (negative function , input position X of deformation point P!-1°(x,y)
and the preliminary deformation position vector P! corresponding to y! 1(i-1
From this, it is possible to obtain transformed position information that is moved by the position transformation function P□(i-1)' so as to remain unchanged, diffuse, and converge, respectively.

If such a position conversion method is used, the deformation area VCF
The same deformation point can be deformed into different curved surfaces depending on how the parameters are selected. Regarding this point, next, the position conversion function PCII+! For example, consider the conversion function for the component X!

In addition, in the case of this example, the position conversion function Ptx+1
-tt'', the diameters α, 1 and β, are selected to be equal to the diameters α and β of the deformation region VCF.

First, when we set J-0 in equation (9), the position transformation function XtXN-11 becomes 0 as XEX(!-11-0"" (11). This means that the pattern of deformation points determined as I in is directly mapped onto the coordinates of X EX (t-11).

Therefore, when the position transformation coefficient J is J-0, in order to form a free-form surface represented by the position vector Pi0 of equation (8), if a deformation point on the deformation area VCF is set, the specified deformation position Preliminary deformation position vector PDI of equation (6) for ! -0' position vector P, based only on the calculation result. is required. As a result, as shown in FIG. 1, the curved surface Pi-1'' before transformation can be deformed in the deformation region VCF so as to draw a Gaussian distribution curve determined by the vector field function F of equation (5).

However, when the position conversion coefficient J is set to a negative value in equation (9), the position conversion function PI! of the second term in equation (8) changes. X(
+-11' Therefore, the position conversion function X EX (T1) is
Preliminary deformation position vector pH+! deformed based on the value of X set as the deformation point! From the position of -11'', we will perform an operation to shift the position vector P0 to converge to 0, and as a result, as shown in Figure 2,
The pattern of deformation points designated on the X coordinate is mapped as a reduced pattern in the direction of the point of action CPI'' as a position vector P1' on the deformation surface.

As a result, when a deformed position pattern similar to that shown in FIG. 1 is given on the X coordinate, the deformed position vector P! draws a Gaussian distribution curve as shown in FIG. 1! ” (
x, y), but as shown in Figure 2, the deformed position vector PL changes in the same way as if the Gaussian distribution curve were crushed in the X direction with the point of action (x-0) as the center.
(X% y).

On the other hand, if the position conversion coefficient J in equation (9) is selected as a positive value, the deformation position numerical value xEll+1-11 becomes the preliminary deformation position vector pH (i-th 0
An operation is performed to shift the position vector P1' outward from the point of action (x-0) as the center. As a result, when the position pattern of the deformation point is specified on the is mapped to the position vector Pi9.

As a result, the deformed position vector Pi'' obtained when the same position information as in Fig. 1 is given on the X axis
(x, y) does not result in drawing a Gaussian distribution curve as in the case of Figure 1, but instead draws this Gaussian distribution curve at the point of action (
This results in a deformed curved surface that appears to be expanded outward with X-0) as the center.

In this way, the preliminary deformation position vector P D obtained based on the position information X about the deformation point on the curved surface before deformation
(1-11′″, position conversion function xE of equation (9))l
The position vector P after the transformation is moved by the negative variable 1 obtained by (g1)! By selecting the value of the position transformation coefficient J as 0, a negative value, or a positive value, even if the same deformed position information is given, the obtained In addition to the reference deformed curved surface, it is possible to freely create deformed curved surfaces that are pushed outward or compressed inward around the point of action of this reference deformed curved surface.

The degree of expansion or contraction can be arbitrarily selected by changing the value of the position conversion coefficient J as necessary, and in this way, the deformed curved surface can be changed from a curved surface with a relatively sharp tip to a curved surface with a relatively sharp tip.
Free-form surfaces of various shapes can be created, up to a wide trapezoidal shape.

Note that in the above description, the position conversion function P is used. +! -11", the X-direction component expressed by equation (9) Similarly, by arbitrarily selecting the value of the position conversion coefficient J, various deformation curves can be obtained in the y-axis direction.

In this way, various deformed curved surfaces can be formed for the two-dimensional deformed region VCF on the xy coordinates on the curved surface before deformation.

According to experiments, with the configuration of the above-described embodiment, a deformed curved surface Pi'' (x, y ) was confirmed to be able to be created.

Figure 4 shows the deformed surface when the position conversion coefficient J in equations (9) and (10) is set to J=O, and the position vector PH'' (X%y) representing the deformed surface has a Gaussian distribution surface. There is.

Furthermore, Fig. 5 shows the case where a negative value is set as the negative coefficient J (position), and the position vector Pi representing the deformed surface in this case
* (X% y) is compared with the deformed surface in Fig. 4,
It was possible to obtain a curved surface with a large sharpness at the tip centering on the point of application (x-0, y=0).

On the other hand, FIG. 6 shows the deformation surface Pi'' (X%y) when a positive value is set as the position conversion coefficient J, and the point of action (x -0,y-0)
We were able to obtain a deformed surface that looks like a rounded shape around .

(G3) Example of curved surface creation device The above-described curved surface creation method can be realized by a curved surface creation device configured as shown in FIG.

In this case, the vector field function FA is set to have a deformation rate distribution expressed by a Gaussian distribution function for the elliptical deformation region VCF, as described above for equations (3) and (4), and the position transformation Function P. (i-+1' is (9
) and (1o), similarly,
The elliptical deformation region VCF is set so as to be able to perform enlargement and reduction transformation expressed using a Gaussian distribution function.

In FIG. 12, numeral 1 denotes a computer-configured surface calculation device, which calculates equations (9) and (10), as well as equations (3) and (
4) After converting the position information obtained as a result of calculation based on the formula into a video signal by the curved surface display control device 2,
It is displayed on a display device 3 composed of a cathode ray tube.

The surface calculation device l has a mouse 4 and levers 5 and 6 as input operators for inputting parameters necessary for calculating equations (9) and (10), and equations (3) and (4).
．． 7. A trackball 8 is provided.

Mouse 4 is the point of action CP on the xy plane! ”, enter the parameter XI%Y! to set
In equations and equations (10), and equations (3) and (4), the point of action cp59 (X!, Yl) is assumed.

In addition, levers 5 and 6 are used to input parameters for determining the size of the deformation area VCF, and are used to input parameters for determining the size of the deformation area VCF, and are used for formulas (3) and (
4) The diameters α and β in the X direction and the y direction in the equation can be set.

Furthermore, the lever &-7 is used to set the deformation vectors V and I, and the parameters for the direction and height of the deformation vector v! set at the point of action CPmu''(xi, yi), and the position conversion coefficient PI. !X(i-110 position conversion coefficient J
You can set the value of .

Furthermore, the trackball 8 is used to set a viewpoint position with respect to the curved surface, and the curved surface viewed from the viewpoint position set by the trackball 8 is displayed on the display device 3.

After the settings using the mouse 4 and the levers 5 to 7 are completed, the curved surface calculation device 1 executes calculations of equations (9) and (10), as well as equations (3) 2 and (4). The calculation result is rotationally converted using viewpoint position information input from the trackball 8 and then displayed on the display device 3 via the curved surface display control device 2. Thus, on the display screen of the display device 3, the points of action cp set by the mouse 4,
” (X!, Yi), the center part is raised by an amount corresponding to the direction and height of the deformation vector v, set by lever 7, with respect to the deformation area VCF set by levers 5 and 6. A curved surface that has been deformed in such a way that it swells and gradually converges to 0 toward the periphery is displayed, and the sharpness of the central part of this deformed curved surface is determined by the position conversion coefficient J set by the lever 7. Become.

Such a deformation operation is obtained by the surface calculation device 1 executing the processing procedure shown in FIG. 13 using its cPU.

That is, after starting the processing procedure in step SPI, the CPU of the surface calculation device 1 starts the processing procedure in step SP2.
In this step, the position vector pH* representing the prototype SOR is set in the surface data memory provided in the surface calculation device 1.

Subsequently, the CPU moves to the next step SP3 and takes in the parameters set by the operator. At this time, the operator uses the mouse 4 to select the point of action data Xt,
Input Yi and use levers 5 and 6 to obtain diameter data αi
and β1, and input the position conversion coefficient J and deformation vector Vl* using the lever 7.

The CPU of the curved surface calculation device 1 takes in the viewpoint position data input by the operator from the trackball 8 in the next step sP4, and then moves to step SP5.

This step SP5 executes the above-mentioned calculations for equations (9) and (10), and equations (3) and (4). Here, the position vector Pi−+ ” before deformation
(x, y) are those stored in advance in the internal curved surface data memory, and each parameter α1, βtsXt
SYt, Vto, and J are those set in step SP3.

Subsequently, in step SP6, the curved surface calculation device 1 calculates the position vector P after the deformation calculated in step SP5! 0
The curved surface represented by is displayed on the display device 3 via the curved surface display control device 2.

In this state, the CPU of the surface calculation device 1 calculates the surface P,
. By continuing to display the next step SP7
At this point, the operator checks the display on the display device 3 to confirm whether the degree of deformation is appropriate to the operator's requirements. The ficPU is then sent to the next step SP8.
Then, it is determined whether or not the operator has input a confirmation signal.

If a negative result is obtained here, the CPU of the surface calculation device 1
The process returns to step SP3 described above to wait for new parameter settings.

At this time, the operator resets the new parameters in steps SP3 and SF3, recalculates the modified calculation formula in steps SP5 and SF3, displays it on the display device 3, and then prompts the operator again in step SP8. The students are asked to judge whether the deformation is as requested or not.

Thus, the CPU of the surface calculation device 1 performs step 5P3-
3P4-3P5-3P6-3P? -3P8-3P3 loop LOOP 1 allows the operator to repeat the action point CP! until the operator can make the transformation that meets his/her requirements. "Position of,
The size of the deformation area VCF, the value and sign of the position conversion coefficient J, and the direction and height of the deformation vector I0 can be reset.

When the operator is satisfied with his setting operation and inputs a setting end signal to the surface calculation device 1, the CPU of the surface calculation device 1 moves to the next step SP9 and processes the set data α1, βi, Xi, Yi, V,”,J to the first command list memory provided in the surface calculation unit rrtl.
In the parameter memory area corresponding to the first setting operation,
After storing α1, β1,
” is added (i=2), and the process moves to step 5PII.

This step 5pit is a step for checking whether the operator has finished the deformation operation, and when the operator has not given an instruction to finish the operation manually, the CPU of the surface calculation device 1 obtains a negative result in step 5P11. The above step SP is passed through the loop L00P2.
Returning to step 3, the operator performs the second transformation operation (N
-2).

In this state, the operator can perform a second curved surface transformation operation on the curved surface created by the first curved surface transformation operation based on a new transformation intention. Thus the first
Regarding the point of action CP, ``'', which is different from the point of action CP,'' that has been transformed by the second transformation operation, the operator can again perform the transformation operation that meets his/her requirements.

That is, the surface calculation device 1 allows the operator to perform step SP.
3. After setting the parameters in SF3, in the following steps SP5 and SF3, the position vector P is calculated for equations (9) and (10), and equations (3) and (4).
After performing the calculation of t'' (x5y), the curved surface is displayed on the display device 3.

This transformation operation is performed in steps 5P3-3P4-3P5-3
P6-5P? -3P8-3P3 loop L00P1 is repeated until the operator is satisfied.

Eventually, in step SP8, when the end of the deformation operation by the operator is confirmed, the curved surface calculation device 1 converts the newly manually entered parameter data α2, βt, Xi, Ya, Vz'', Jz into a command list in step SP9. After storing it in the parameter memory area corresponding to the second setting operation in the memory, "+1" is added to the number of operations i (i=3) in step 5PIO, and there are many sheep in step 5PIf.

Thereafter, in the same way, the CPU of the surface calculation device 1 executes the above-mentioned transformation processing loop L every time the operator performs a new transformation operation.
After executing OOP 1, the set parameter data is stored in the command list memory, and the position vector P1'' obtained as a result of the transformation calculation is stored and updated in the surface data memory. The curved surface PM'' (x, y) (Equation (4)) that has been deformed by the total amount of deformation caused by N times of deformation operations is obtained.

Eventually, when the operator finishes all the transformation processing, the CPU of the surface calculation device 1 moves to step 5PI2 and
The Pig program will be completed this winter.

Therefore, according to the curved surface creation device shown in FIG. 12, the operator uses the mouse 4, the lever 5.
．． 7. Curved surface creation device 1 while operating the trackball 8
By inputting transformation parameters into , the curved surface can be transformed. Therefore, (1)
Regarding Equation and Equation (2), as mentioned above, the calculation time required for the transformation calculation is about 1 second at most, so virtually as soon as the operator performs the transformation operation, the transformation result is displayed on the display 3. By being able to display it on the display screen, the operator can select a part of the curved surface as necessary and manually set parameters to transform it into the desired shape, making the entire surface interactive. A desired curved surface can be created by making partial modifications.

Therefore, after obtaining the preliminary deformation position vector pH (!-1) based on the deformation points P,' in the deformation area VCF, the position is transformed by the position transformation function PEX (i-11°). By doing so, the operator can increase the degree of freedom in setting parameters.

H Effects of the Invention As described above, according to the present invention, a vector field function F that can specify and deform a part of a curved surface before deformation is obtained.
By specifying + and multiplying this vector field function Fi by the deformation vector VH'' to form the deformed surface, the deformed surface can actually be generated in real time. Since it is possible to use parameters that can be set while looking at the curved surface, that is, the position of the point of action, the deformation area, the direction and magnitude of the deformation vector, and the position conversion coefficient, the parameter setting can be done intuitively.

(Particularly, according to the present invention, the position represented by the preliminary deformation position vector obtained based on the position information of the deformation point is transformed using the position transformation function P. By obtaining the position vector representing the deformed surface, the operator can insert parameters when calculating the position deformation function Hp. In this way, a free-form surface having the shape the operator has in mind can be created even more easily.

[Brief explanation of drawings]

1 to 3 are characteristic curve diagrams showing an embodiment of the position conversion method used in the curved surface creation method according to the present invention, and FIGS. 4 to 6 show curved surfaces created by the curved surface creation method according to the present invention. A perspective view shown by a wire frame, FIGS. 7 and 8 are route diagrams for explaining the basic principle of the method of creating a curved surface according to the present invention, and FIG. 9 is a characteristic curve for explaining the vector field function used when generating a deformed curved surface. Figure, 1st
0 and 11 are route maps for explaining the position conversion function, FIG. 12 is a block diagram showing a curved surface creation device that implements the curved surface creation method according to the present invention, and FIG. 13 is a flowchart showing the data processing procedure. be. 1... Curved surface calculation device, 2... Curved surface display control device, 3... Display device, 4...
...Mouse, 5-7...Lever, 8...
...Trackball.

Claims (2)

[Claims] (1) Specify a predetermined deformation area including the point of application for the surface before deformation processing, and a vector representing the relative deformation rate at each position of the curved surface based on the position of each deformation point within the deformation area. Determine the field function F_i, specify a deformation vector V_i^* representing the amount and direction of deformation at the point of application of the deformation region, and multiply the deformation vector V_i^* by the vector field function F_i to perform the deformation. Obtain a preliminary deformation position vector representing the amount of preliminary deformation of the curved surface in the area, transform the position represented by the preliminary deformation position vector using a predetermined position conversion function to generate transformed position information, and generate transformed position information represented by the transformed position information. A method for creating a curved surface, the method comprising: obtaining a position vector representing a curved surface after deformation based on a position vector and a position vector representing the surface before the deformation process. (2) The position conversion function multiplies a difference vector representing the position of the deformation point with respect to the point of application by a position conversion coefficient consisting of a parameter representing 0 and a value of a negative sign and/or a positive sign. The method has a configuration that transforms the position in a direction along the direction of the difference vector based on the position of the preliminary deformation position vector, and changes the shape of the curved surface after the deformation by selecting the position conversion coefficient. A method for creating a curved surface according to claim 1, wherein the curved surface is created by: