JPS6286466A - Curved face forming method - Google Patents

Abstract

PURPOSE:To generate a modified curved face in real time by designating a modified vector and a vector field function on the basis of an operating point designated on a modification object curved face to apply partial modification operation only to the modification region designated by the vector field function. CONSTITUTION:A modification vector Vi* is designated to an operating point CPi* designated on a modification object curved face SOR and a coordinate plane SFC in contact with the modification object curved face SOR is formed at the operating point CPi*. The operator uses the coordinate plane SFC and a parameter representing the designation of the modification region VCF and the relative modification distribution with respect to each point in the said modification region is inputted as data designating the vector field function Fi. As a result, the modification object curved face is subjected to modification processing with respect to the curved face position projecting each point of the coordinate plane on the modification object curved face SOR. Thus, the operator uses the coordinate on the coordinate plane SFC in relation to the operating point CPi* to input data and the modification curved face obtained by the inputted data is grasped intuitionally easily by the operator.

Description

[Detailed Description of the Invention] A. Industrial Application Field The present invention relates to a method for creating a curved surface, particularly in computer graphics, in which a curved surface constituting an original surface is locally transformed into a new curved surface. be.

B. Summary of the Invention The present invention provides a method for creating a curved surface in computer graphics, in which a free-form surface can be created by locally specifying and deforming a part of the curved surface, based on the point of action on the curved surface to be deformed. By allowing the operator to specify the deformation data using the deformation data, the operator can easily and intuitively grasp the deformed curved surface.

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. How to get there etc. is used.

D Problems to be Solved by the Invention These conventional methods actually use the external shape of a primitive curved surface as a basic shape, and convert the curved surface based on the basic shape to obtain a desired curved surface. It is believed that it is possible to create a satisfactory curved surface as long as it is applied to express the external shape of a mechanical object.

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 there is, it is possible to easily obtain a curved surface that reasonably matches the curved surface that the operator wants to obtain, so the parameters that the operator sets and inputs and the resulting changes that appear on the curved surface on the display screen are It is desirable to have a correspondence relationship that is easy to understand intuitively.

The present invention has been made in consideration of the above points. For example, when creating a free-form surface that cannot be expressed with a primitive curved surface, such as a curved surface forming a human face, an operator can create a curved surface after deformation. The purpose of this paper is to propose a method for creating a curved surface that can be displayed on a display screen in a manner that is easier to understand intuitively.

EMeans for solving the problem In order to solve the problem, in the first invention,
Specify a point of application CPl'' on the surface to be deformed, specify a deformation vector v positive 9 representing the deformation direction and magnitude at this point of application cpt'', and set the point of application CPl''S to be in contact with the surface to be deformed SOR and A coordinate plane SFC is formed with the point CPi = as a reference, and the coordinates on the coordinate plane SFC are used to determine a predetermined deformation area VCF including the point of action cp, and a deformation vector v at each point within this deformation area VCF.
Determine the vector field function F that represents the deformation rate for i1,
For the curved surface position where each point of the deformation region VCF is projected onto the deformation target surface SOR, the vector field function Fi and the deformation vector v! The deformation target curved surface SOR is deformed based on the product with 9.

Moreover, in the second invention, the point of action CP! is on the curved surface SOR to be deformed! Specify ``,'' specify the deformation vector V,'' representing the direction and magnitude of deformation at the point of application CP,'', and convert the coordinate surface with the point of application CP, as a reference to the deformation target surface SOR.
A vector field function Ft representing a deformation rate for a predetermined deformation region VCF including the point of application CPi" and a deformation vector Vi" at each point within this deformation region VCF is formed using the coordinates on the coordinate curved surface. Then, the surface SOR to be deformed is deformed based on the product of the vector field function F1 and the deformation vectors {circle over (2)} and ''.

The F action vector field function F□ is given as a scalar quantity representing the relative rate of change at each point in the deformation region VCF, and therefore, for each point included in the deformation region VCF,
The position vector V4” *F, which represents the amount of deformation of the curved surface, is
The direction of deformation is the deformation vector v! 1, and has a magnitude corresponding to the relative deformation rate represented by the vector field function Fi as the magnitude of deformation.

In the first invention, the deformation vector v!' is designated at the point of application CPU'' specified on the deformation target surface 5OR, and the deformation target surface SOR is designated at the application point CPi''.
A coordinate plane SFC tangent to is formed. Using this coordinate plane SFC, the operator specifies the deformation area VCF and the parameters representing the relative deformation rate distribution for each point within the deformation area using the vector field function F! Input as data to specify. As a result, the deformation target curved surface is transformed at the curved surface position obtained by projecting each point on the coordinate plane onto the deformation target curved surface SOR.

Therefore, by allowing the operator to input data using the coordinates on the coordinate plane SFC related to the point of application CPi, the operator can easily and intuitively understand the deformed surface obtained by the input data. Become.

Further, in the second invention, data for obtaining the deformed curved surface is input using a coordinate curved surface formed on the deformed curved surface SOR. Therefore, data can be input in a manner that allows the operator to more easily understand the curved surface after deformation.

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

As shown in FIG. 1, the method for creating a curved surface according to the present invention is based on the point of application CP! on the curved surface SOR to be deformed! Specify the position vector representing ", and transform the deformation area VC including the relevant point of action CP!"
A computer executes calculations for deforming the curved surface only within the range of F. The calculation result is displayed on the display device CRT (second
It is possible to display the transformed screen SCH on the display screen DSP shown in FIG.

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), Pi' is a position vector representing each point of the deformed surface formed in three-dimensional space (9), and this position vector Pi* is the position vector of the corresponding point on the deformed surface SOR. P□-1'' and the amount of deformation V from the position vector Pi-1'' before the deformation! ” *Ft
It is expressed as the sum of (Pi−+ ”, CPt ”) and (7).

This amount of deformation is the vector field function Fi (Pi−+ ”
, CPi'') by the deformation vector 19.

Here, the deformation vector v1 is defined as the point of action c
The direction and magnitude of the deformation to be applied to the deformation target surface SOR at pi'' is expressed as a vector quantity, so that the point of action crt'' on the deformation target surface SOR is separated by the deformation vector ■50 from the deformation target surface SOR. It will undergo a deformation that will cause it to be lifted up.

Also, the vector field function Fi (Pt-+ ”, CPt
") is the deformation area V determined including the point of action cp,"
It represents the relative deformation rate distribution that determines how much deformation is given to each point P1-1'' of CF (its size can be specified by setting and inputting parameters). This relative deformation rate distribution has a value only inside the deformation region VCF, and has a distribution of scalar quantities that "becomes 0" or "converges to 0" toward the periphery.

In this way, the amount of deformation Vi"*Fi (Pi-+",
CPi'' is a position vector representing the amount of deformation at each point in the deformation area VCF, its direction is parallel to the deformation vector ■i3, and its size is the same as the size of the deformation vector V!'' and the vector It has a multiplication value (scalar quantity) with the relative deformation rate distribution represented by the field function Fi. In this way, the deformation of the curved surface of the deformation region VCF occurs at the point of action c
The change in the deformation rate of the vector field function F□ occurs in the direction and magnitude of the deformation vector Vi's in the direction and magnitude of the deformation vector Vi's at p, occurs with a magnitude that varies in response to the

Here, if a function is assigned as the vector field function F1, such as a glass distribution function, which gradually converges symmetrically to the 0 level as it goes outward from the center point, the amount of deformation Vi''*Fi is The vector V has a maximum value in the direction of 11 at the position of the point of action CPU, and the point of action CP
! '' to the outer periphery, a deformed surface is obtained which has the direction of vector V, 11 and whose size gradually converges to O.

In this way, with one conversion operation, the amount of deformation is V! ”
IF( is calculated, and this is added to the position vector Pt1'' before transformation to obtain the position vector P1'' after transformation. In the same way, each time a transformation operation is performed, (1)
By calculating the recurrence formula expressed by the equation, a position vector representing the deformed surface is repeatedly and recursively calculated based on the position vector before deformation.

As a result of repeating this recursive calculation N times, the position vector representing the final deformation point PN* is determined by the initial deformation target surface 5OR(
This is called the original picture) point P. It is determined as a position vector obtained by adding the sum of the deformation amounts (i.e., the total deformation amount) sequentially obtained by N times of deformation calculations (i-1 to N) to the position vector representing .

Thus, according to equation (2), the operator determines the point P of the first deformation target surface SOR (that is, the original image). When performing N deformation operations sequentially from ``, by specifying the point of action CPi'' for the deformation target surface SOR each time, the curved surface P before deformation! -1", the position to be deformed can be arbitrarily specified based on the operator's judgment. Also, by respecifying the parameters that determine the vector field function F+ and the deformation vector ■t1, the size of the deformation area VCF, the deformation surface Similarly, the deformation rate distribution and the direction of deformation can be arbitrarily reset based on Oberet's judgment.

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

Therefore, as is clear from equation (1), the position vector P! before deformation! -1” to position vector P after conversion
! To obtain ``, it is sufficient to simply add the deformation amount V, IF1 to the position vector Pi-11 before deformation, so the calculation speed can be shortened enough for practical use (according to experiments, it is less than 1 second). Obtained). And the amount of deformation Vi” *F
Regarding the calculation to obtain i, the vector field function Fl is selected to be limited to the deformation region VCF so that it converges to O or becomes 0 as it approaches the periphery, so that the deformation vector The multiplication operation with Vl" can be shortened to +1 minute to the extent that it can be practically called real-time processing (according to experiments, it was possible to shorten it within 1/30 second).
.

Therefore, according to the curved surface creation method 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, thereby making it possible to perform repeated image transformation operations interactively on a computer. It can be executed.

Therefore, as described above regarding equation (2), the operator must By re-entering the deformation parameters through trial and error, it is possible to continue deforming the surface obtained by the previous deformation operation while evaluating the effect of the transformation.
After each transformation operation, the next operation to transform is to determine "at what position", "in what width", "in what direction", and "what size" of the curved surface. Parameters can be set while considering what deformation should be performed, and thus a free-form surface that is closest to the surface that one ultimately desires to obtain can be easily obtained.

The new point of action CPl'', vector field function Fi, and deformation vector Vi1 during this deformation operation are specified as follows.

In the case of the first embodiment, the deformation target curved surface SOR formed by the previous deformation operation is represented by a position vector Pi,' as shown in FIG.

A new point of application cpi''' is selected on the deformation target curved surface SOR, and the deformation vector
is set.

Here, at the point of action CPa'', an xy orthogonal coordinate plane SFC consisting of a tangential plane orthogonal to the deformation vector v19 is formed, and the unit vectors in the X-axis and y-axis directions and ni* are
It is determined based on the unit vector n1 of the deformation vector v positive 1 on the axis.

Here, the deformation vector vi8 is expressed by the following equation (%) (3), in which the unit vector n'k is multiplied by the scalar amount V.

The coordinates (x,
Y), vector field function F, (Pi−+ ”
, CPi''), it is possible to determine the distribution of deformation rates for the deformation region VCF specified on the coordinate plane SFC using the vector field function.

The coordinates (x, y) on the coordinate plane SFC are x−j”, (
Pt-+ "CPi")""...(4) Y=k
” , (Pt-+ “CPt”)・・・・・・(
5), which can be obtained by the inner product of the vector of the difference between the position vector Pi-10 representing the deformation target curved surface SOR and the new point of application CPi'', and the unit vectors j'' and k''. In a relationship.

And the unit vector j″′, kg, n” is expressed by the following formula N”
, k", n") = ru) (R) (I7) - [R] ...... (6) As expressed by the following, a three-dimensional rotation matrix (
R). Also, the three-dimensional rotation matrix (R)
is the difference vector (P+-+” CF
4'') around the X axis by an angle γ to obtain a vector on the XZ plane (the third term on the right side of equation (7)), then rotate this vector around the y axis by an angle δ. By doing this, the direction of the deformed pect J and y, + can be found (the second term on the right side of equation (7)).

In this way, the direction from the point of action CP (''' of the unit vector n'' can be determined, and the unit vector j
1 and * are formed. Therefore, by rotating this unit pectoral bi and k'' by an angle θ around two axes, it is possible to align the unit pectoral bi and k'' in the X and y-axis directions of the tangent plane SFC (the first right-hand side of equation (7) section)
.

In this way, the operator can actually input the data about the vector from the position vector Pi-1'' on the deformation target curved surface 5OR to the point of action CP411 as data about the parameters, and then change the angles T, δ, and θ. If you input the data, the coordinate plane SFC tangent to the point of application CPi0
You will be able to set

Therefore, if we input the parameters of the deformation area VCF on this coordinate plane SFC and also input the data about the scalar quantity V of the deformation vector Vi4 at the point of action CPi'', the equation can be expressed by the second term of equation (1). amount of deformation Vi”
This means that *Fi (Pi-+'', CP1') has been specified.

As a result, the deformation that occurs in the deformation target curved surface SOR is determined by the deformation rate formed for the deformation region VCF at each point where each coordinate point of the deformation area VCF formed on the coordinate plane SFC is projected onto the deformation target curved surface SOR. Deformation occurs in the direction of unit vector n* by the amount of deformation corresponding to the distribution.

In this way, according to the method shown in Fig. 3, the vector field function F□ can be set for the coordinate plane SFC, so it is possible to directly determine how much the deformation target curved surface 5OR can be deformed. It is possible to set parameters that can be predicted in advance, and thus it is possible to realize a free-form surface creation device that allows an operator to easily grasp the deformation of a curved surface intuitively.

In practice, when specifying each position on the coordinate plane SFC,
If the vector field function Fi is selected so that the circle can be specified as a unit, the parameter to be set is the point of action CPi
”, which means that it is only necessary to set a one-dimensional parameter.

On the other hand, in general, the coordinate plane S on the xy plane
In order to specify each position of the FC, it is necessary to input two-dimensional data in the X and y directions.

In addition, in FIG. 3, a case was described in which a tangential plane was used as the coordinate plane SFC, but instead of this, by changing the direction of the deformation vector V%, the deformation target curved surface SO
Even if the angle of the coordinate plane SFC with respect to R is tilted by a necessary amount, a vector field function can be formed for a specified position on the coordinate plane SFC.

When inputting the parameters for the amount of deformation using the method shown in Figure 3, as shown in Figure 4, specify the point of action CP' on the front curved surface 5ORI to form a coordinate plane SFC, and The deformation vector vi′ formed in and the deformation distribution rate Vi ” *F,
It is possible to input data for deforming the surface-side deformation target curved surface 5ORI based on .

However, in this case, the vector field function F on the coordinate plane SFC
1 onto the deformation target surface SOR, if there is a deformation target curved surface 5OR2 on the back side in this projection direction, this is also undesirably deformed by the vector field functions y and m pieces Fi. The result is that

In order to prevent such deformation of the curved surface 5OR2 to be deformed on the back side, the first deformed curved surface SOR, that is, the texture coordinate system on the original image is used, and as for the curved surface parts that may overlap each other as shown in FIG. It is sufficient to set conditions in advance to limit the influence of the vector field number F1. In this way, the problem shown in FIG. 4 can be easily solved.

FIG. 5 shows another embodiment of the invention. In the case of Figure 3,
By projecting the deformation area and deformation rate distribution determined based on the vector field number Fl set on the coordinate plane SFC that is in contact with the point of action CP+3 onto the deformation target curved surface SOR, the corresponding points on the deformation target curved surface SOR are The specification and the amount of deformation can now be specified. On the other hand, in the case of Fig. 5, a coordinate surface SFD consisting of coordinate axes U and V extending through the point of action cp,'' and extending onto the deformation target surface SOR is set,
The curved surface S to be deformed specified by these coordinate axes U and V
A vector field function F1 is set for each position on the OR.

Here, the coordinate axes U and V are set to be perpendicular to each other at the position of the point of action CPl'', and by specifying the coordinates of the coordinate axes U and V, each It is possible to specify a point.

In this way, the operator can directly specify the deformation area VCF and the vector field function Fi for the deformation target surface SOR to be deformed, so that the operator can more easily and intuitively determine the deformation result. This means that the transformation operation can be performed while predicting.

In this case as well, using the U and V coordinate axes, the point of action C
The vector field function F can be specified by specifying a point at a certain distance (distance measured along the surface of the deformation target curved surface SOR) from "PU".
! If you select , you can specify the point to be deformed by setting one-dimensional parameters. Otherwise, by specifying the U-axis and v-axis values as two-dimensional parameters. Points to be transformed can be specified by simple operations.

In addition, according to the method shown in FIG. 5, there is no need for processing such as projecting the deformation data on the coordinate plane onto the deformation target curved surface SOR as in the case of FIG. As described above, there is no fear that the projection of data to the front side deformation target curved surface 5OR1 will affect the rear side deformation target curved surface 5OR2, and therefore, the configuration as a branch body without the need to take countermeasures can be simplified.

In the above-mentioned method for creating a curved surface, for example, in an embodiment in which a curved surface for a human face is created, a Gaussian distribution function is used as the vector field function F dog in equations (1) and (2) above, and the deformation region VCF A circular or elliptical shape can be selected as the shape.

For example, in the case of the first embodiment described above with reference to FIG.
is (8) corresponding to equations (1) and (2), respectively.
It becomes as shown in the equation and the equation (9).

P i ” (X% y) = P t-+ ”
(X-=3')α5p! PM ” (xl y)=P6 ” (xl y)
As expressed by the formula % formula % (10), the point of action (xi, Yi) on the xy plane
Centered on , the radius in the X direction and the y direction is α and β,
As shown in FIG. 6, the ellipse exhibits a Gaussian distribution function in the X direction and the y direction.

When doing this, the operator uses the vector field function F
1, the parameters of the point of action CPt” are expressed as coordinates (X!
, Y, and the diameters α and β in the X and Y directions are set as the parameters of the deformation region VCF, and the parameters of the deformation vector v5'1 are set.

Thus, the operator determines the point of action CPz"(Xt, Yz)
With respect to the circular or elliptical deformation area VCF with radius α and β, centering on the deformation vector ■!” in the direction of the deformation vector v! A deformed surface whose deformation rate smoothly converges to O can be obtained by drawing a Gaussian distribution curve as it approaches the periphery.

Therefore, the position vector Pm'' (x, y) or P
The curved surface represented by M'' (X%y) has a smooth shape as shown by a Gaussian distribution function in the direction of the deformation vector vI* for a local area centered on the point of application CPi'' of the curved surface to be deformed. The surface becomes a free-form surface.

(Thus, for a free-form surface with softness such as a human face, it is possible to create a curved surface that does not cause unnaturalness by adapting to this.

The above explanation has been about the case where the vector field function shown in FIG. 6 is applied to the coordinate plane SFC of FIG. 3, but it can be similarly applied to the coordinate curved surface SFD of FIG. 5,
In this case, the parameters may be specified using coordinates determined by the coordinate axes U and V.

The curved surface creation method described above with reference to FIGS. 1 to 5 is as follows:
This can be realized by a curved surface creation device configured as shown in FIG. Note that in this case, the vector field function F! is set to have a deformation rate distribution expressed by a Gaussian distribution function for the elliptical deformation region.

In FIG. 7, reference numeral 1 denotes a computer-configured curved surface calculation device, in which position information obtained as a result of calculations based on equations (8) and (9) is converted into a video signal by a curved surface display control device 2, and then transferred to a cathode ray tube. displayed on the display device 3 of the configuration.

The curved surface operation bag W1 is provided with a mouse 4, levers 5, 6, 7, and a trackball 8 as input operators for inputting parameters necessary for calculating equations (8) and (9). .

Mouse 4 inputs parameters X+ and Yi for setting the point of action CPi on the xy plane, and thereby
) and (9), the point of action CP! ”(Xi, Y
).

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 (8) and (
The radius α1 and β radius in the X direction and the y direction in Equation 9) can be set.

Further, the lever 7 is used to set the deformation vector V11, and can set parameters regarding the direction and height of the deformation vector V11 set at the point of action crt,'' (X□, Yl).

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 completing the settings using the mouse 4 and the levers 5 to 7, the curved surface calculation device 1 executes the calculations of equations (8) and (9).

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 deformation area VC set by the levers 5 and 6 is displayed, centering on the point of action CPa'' (Xi, Yi) set by the mouse 4.
Regarding F, the center part rises by an amount corresponding to the direction and height of the deformation vector vi'' set by the lever 7, and as it goes to the periphery, it gradually converges to O and undergoes deformation such as (row). A curved surface will be displayed.

Is this transformation operation a surface calculation bag? fl is obtained by executing the processing procedure shown in FIG. 8 by the CPU.

That is, the CPU of the curved surface calculation device 1 starts the processing procedure in step SPl, and then executes the process in step SP2.
A position vector P representing the first deformation target curved surface SOR, that is, the original image. ' is set in the curved surface data memory 12 (FIG. 9(A)) provided in the curved 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 XL,
Y! Input the radius data αL using levers 5 and 6.
and β5, and use lever 7 to change the deformation vector V%
Enter.

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 calculation regarding equation (8). Here, the position vector Pi−+” before deformation
(X, y) are those set in the surface data memory 12, and each parameter α, βi, Xi
% Yt, V4'' 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! ′
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 curved surface calculation device 1
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. Thereafter, the CPU moves to the next step SP8 and determines 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-
Using the loop LOOPI of 3P4-3P5-3P6-3P7-3P8-3P3, the point of action CP! is repeated until the operator can make the transformation that meets his/her requirements. ”, the size of the deformation area VCF, the direction and height of the deformation vector 18 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 W1 moves to the next step SP9 and calculates the set data αpositive, βi, Xs, Yt. ,■,'' are stored in the command list memory provided in the surface calculation device 1 (Fig. 9(B)
)11, α1, β+, Xs, YI, Vr are stored in the parameter memory area N-1 corresponding to the first setting operation of 11.
After storing it as ''', proceed to step 5 PIO, add "+1" to the number of operations l (i = 2), and step 5p
Move to i1.

This step 5PII is a step for confirming whether the operator has finished the deformation operation, and when the operator has not inputted an operation end command, the CPU of the surface calculation device 1 obtains a negative result in step 5P11. Therefore, the process returns to step SP3 described above, and a state awaits the second transformation operation (i=2) by the operator.

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, with the intention of creating a new curved surface. Thus, the point of action CP transformed by the first transformation operation,
For the point of action different from "crt", the operator can again perform the transformation operation to suit his 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 step SP5 and SF3, the position vector Pg" (xSy) is calculated using equation (8), and then the curved surface is displayed on the display device 3. This transformation operation is performed in step S
PiSP4-3P5-3P6-3P7-3P8-3P3
The loop LOOP1 is repeated until the operator is satisfied.

When the end of the deformation operation by the operator is confirmed in step SP8, the surface calculation device 1 proceeds to step S.
Parameter data α2 newly input in P9,
βz, -3), proceed to step 5P11.

Similarly, 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 the process of OOP 1, the set parameter data is stored in the command list memory 11, and the position vector P8'' obtained as a result of the transformation calculation is stored and updated in the curved surface data memory. The data memory 12 stores a curved surface PM" (x, y) ((
9) Equation) is obtained.

Eventually, when the operator finishes all the transformation processing, the CPU of the surface calculation device 1 executes steps 5P11 to 5P12.
and exit the program.

Therefore, according to the curved surface creation device shown in FIG.
When performing transformation operations, use mouse 4, lever 5.6.7.
By inputting transformation parameters into the curved surface creation device 1 while operating the trackball 8, the curved surface can be transformed. In this way, as mentioned above for equations (1) and (2) or equations (8) and (9), the calculation time required for the transformation calculation is about 1 second at most, so the operator is practically free. As soon as the transformation operation is performed, the transformation result can be displayed on the display screen of the display device 3, so that the operator can select a part of the curved surface before transformation as necessary and set parameters to transform it into a desired shape. Settings can be input, and in this way, a desired curved surface can be created for the interrafting as a whole while making partial modifications.

Further, the curved surface creation device shown in FIG. 7 has the command list memory 11 as shown in FIG. 9(B), so that the newest deformed position vector P ), read the parameters used in the previous transformation process, calculate the amount of deformation added by the previous transformation operation, and subtract it from the data in the surface data memory. It is possible to reproduce the curved surface before performing the deformation operation. In this way, since it is sufficient to have the screen data memory 12 for one frame as the data memory, the structure of the entire curved surface creation device can be simplified.

In the above embodiment, an example was described in which a Gaussian distribution function was used as the vector field function F1 in equations (8) and (9) (formula (10)), but this However, various functions such as those described below can be used.

And such various vector field functions F! If a surface creation device is constructed that can select By performing deformation while combining deformed surfaces with various characteristics, it is possible to create a curved surface that can optimally adapt to the operator's requirements.

Incidentally, switching the deformed surface as necessary is
It is possible to produce an effect similar to that of carving a surface by sequentially changing the shape of a chisel with a different cutting edge.

Figure 10 shows the case where the deformation region VCF in the xy plane uses a vector field function F representing the outer surface of a cylinder made of a circle or an ellipse, and the vector field function F is F1=1
...... (12), and when F1=0 ...... (14)
becomes.

If we use the vector field function Fi as shown in Fig. 10,
It is possible to obtain a deformed curved surface having the shape of a neighbor on a cylindrical surface while exhibiting a distribution of deformation rates that has a maximum value in the center of the deformed region VCF and becomes zero all at once in the periphery, and therefore, A desired curved surface can be created by repeatedly performing deformation operations while dividing the deformation region into small sections.

FIG. 11 shows an example in which a vector field function F1 in which the deformation area VCF on the xy plane is rectangular is used. In this case, the vector field function Fi is -a:! in the X-axis and y-axis directions. ax≦a ・・・・・・(1
5)-b≦y≦b ・・・・・・(1
6) When F5 = 1 (17)
becomes. On the other hand, for areas other than the deformation area VCF, -a≦X≦a (18)
y<-b, y>b (19
), then F, = 0 (20)
And x<-aSx>a −・= (21)−
When b≦y≦b (22), i”i-0 (23), and x<-a, x>a (2
4) y<-b, y>b ・・・・・・(
25) When F! =0 (26)
becomes.

If such a vector field function Fi is used, it is possible to deform the curved surface before deformation by a prismatic deformation surface that locally makes the surface shape of a quadrangular prism.

Fig. 12 shows an example in which a function representing the surface of a cone whose shape on the xy plane is a circle or an ellipse is used as the vector field function F4, and when the vector field function Fi is... (28) and then FA=0...(30)
becomes.

This allows the curved surface before deformation to be deformed by the deformed curved surface having the shape of the surface of the cone expressed by Equation (28), only within the range of the deformation region VCF expressed by Equation (27). can. Therefore, the distribution of the deformation rate in this case is maximum at the center of the deformation region VCF, and converges to O as it goes to the periphery.

Fig. 13 shows an example in which a function representing the outer surface of a cone erected against a deformation area VCF whose shape on the xy plane is a quadrilateral is used as the vector field function F. In this case, the vector field function F is The number Fi is -a≦X≦a ・・
...(31)-b≦y≦b...
When (32)... (33) A vector field function Fl expressed as follows is used. On the other hand, for areas other than the deformation area VCF, -a≦X≦a
......(34) y<-b, y>
When b ・・・・・・(35), F,=0 ・・・・・・(36)
And x<-a, x>a ・・・・・・(37
)-b≦y≦b ・・・・・・(38
), then F, = 0 (39)
Then, z < −a Sx > a ・=
-(40)y<-b, y>b...
...When (41), F(=0 ......(42)
become.

Thus, in this example, for the curved surface before deformation,
The curved surface can be deformed using a deformed curved surface having the shape of the outer surface of a pyramid.

Figure 14 shows an example in which a function representing a spherical surface whose shape on the xy plane is a circle or an ellipse is used as the vector field function Fi. In this case, the vector field function Fi is for the deformation area VCF expressed by , ......(44) becomes.

On the other hand, for other areas, when F! -0...(46) becomes.

In this way, a relatively soft deformation can be applied to the undeformed curved surface using the deformed curved surface having a spherical external shape.

FIG. 15 shows an example in which a function representing the outer surface of a prism-shaped column whose deformation region VCF on the xy plane has a quadrilateral shape is used as the vector field function F. In this case, the vector field function F is , -a≦X≦a (47)
−b≦y≦b (48)
It happens when On the other hand, the vector field function F1 for other areas is -a≦X≦a (50)
y<-b, y>b (51
), then Fi-0...(52), and x<-a,,x>a...(
53)-b≦y≦b ・・・・・・(
54) When F! =0 (55)
Then, x<-a, x>a (56
)y<-bSy>b ・・・・・・(5
7) When F! =O...(58).

In this way, it is possible to deform the curved surface using a directional deformation curved surface that has the shape of the outer surface of the brism-shaped column and has a ridge line in the y-axis direction, relative to the curved surface before deformation. can.

Figure 16 shows the shape of the curved surface constituting the vector field function Fi compared to Figure 15 by rotating the extension direction of the ridgeline by 90°
In this example, the vector field function Fi is changed to extend in the axial direction, and in this case, the vector field function Fi is -a≦X≦a
・・・・・・(59)-b≦y≦b
...... (60), whereas for other areas -a:
5x≦a...(62)y<
-b, y>b (63) then F4=o (
64), and x<-a, x>a ......(65
)-b≦y≦b ・・・・・・(66
) when Ft=0...
(67), and x<-a, x>a ......(6
8) y<-b, y>b ・・・・・・(
69), then Fi=0 ・・・・・・(
70).

Even in this case, the same effect as described above with respect to FIG. 15 can be obtained.

H Effects of the Invention As described above, according to the present invention, the point of action CP□′ on the curved surface SOR to be deformed is specified, and the deformation vector v! 1 and the vector field function Fi, the vector field function F! By performing a partial deformation operation only in the deformation area specified by , a deformed curved surface can be generated substantially in real time.

Thus, in particular according to the invention, the point of action CPi′
, the shape and size of the deformation area VCF, and the direction and size of the deformation vector ■i' can be set on the deformation target surface SOR if coordinates are determined based on the deformation target surface SOR. Accordingly, the operator can easily and intuitively predict the curved surface after deformation by setting and inputting parameters, and thus it is possible to easily realize a curved surface creation device that is easier to use when creating a free-formed surface.

[Brief explanation of drawings]

1 to 3 are route maps for explaining the first embodiment of the curved surface creation method according to the present invention, FIG. 4 is a route map for explaining the operation mode, and FIG. 5 is a route map for explaining the second embodiment. FIG. 6 is a route map for explanation of the vector field function Fl. FIG. 7 is a block diagram showing a curved surface creation device that implements the curved surface creation method of the present invention, and FIG. 8 shows the processing procedure. The flowchart shown in FIG. 9 is the curved surface calculation device 1 shown in FIG.
10 to 16 are route maps showing other examples of the vector field number F1. 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) (a) Specify the point of action on the curved surface to be deformed, (b)
specifying a deformation vector representing the direction and magnitude of deformation at the point of action, (c) forming a coordinate plane that is in contact with the curved surface to be deformed at the point of action and with the point of action as a reference; (d) determine a predetermined deformation area including the point of application and a vector field function representing the relative deformation rate with respect to the deformation vector at each point in this deformation area; (d) apply the deformation to each point in the deformation area; A method for creating a curved surface, characterized in that the curved surface to be transformed is transformed based on the product of the vector field function and the deformation vector, with respect to a curved surface position projected onto the target curved surface. (2) (a) Specify the point of action on the curved surface to be deformed, (b)
specifying a deformation vector representing the direction and magnitude of deformation at the point of action, (c) forming a coordinate curved surface based on the point of action on the deformation target curved surface, and using the coordinates on the coordinate curved surface to perform the above action; (d) determining a predetermined deformation region including a point and a vector field function representing a relative deformation rate with respect to the deformation vector at each point within this deformation region; A curved surface creation method characterized by transforming the curved surface to be transformed.