JP2591476B2 - Surface creation method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for creating a curved surface, and more particularly to a computer graphic in which a curved surface constituting an original surface is locally deformed into a new curved surface.

[0002]

SUMMARY OF THE INVENTION The present invention provides a method for creating a curved surface in computer graphics, in which a part of a curved surface is locally specified and a recurrence formula is repeatedly calculated to deform the surface to create a free-form surface. Thus, in practice, a desired curved surface can be formed in a step-by-step manner by an interactive operation in real time.

[0003]

2. Description of the Related Art In a conventional computer graphic, as a method of generating a three-dimensional curved surface, data of a basic curved surface such as a cylinder or a sphere (hereinafter referred to as a primitive curved surface) is prepared in advance. A method of creating a new surface by combining primitive surfaces as needed, or specifying points on a surface to be newly created as control points, and using a surface passing through these control points using a spline function For example, a method of interpolation is used.

[0004]

In these conventional methods, a desired curved surface is formed by actually taking the outer shape of a primitive curved surface as a basic shape and deforming the curved surface based on the basic shape. It is considered that a satisfactory curved surface can be created as long as it is applied to the case of expressing the appearance of a mechanical object in practical use.

[0005] Even when a curved surface is created using a spline function, a large number of control points must be actually set. Therefore, a primitive curved surface is used to form the large number of control points, By combining the figures, the control points are set within a practically acceptable range, and therefore, also in this case, the same characteristics as in the case of combining the primitive surfaces are also practically used. .

However, a curved surface that gives a soft impression like a curved surface representing a human face and becomes unnatural unless represented by a curved surface different from the primitive curved surface (referred to as a free curved surface). Is not practically sufficient to use a conventional curved surface creation method in which the influence of the characteristic of a primitive curved surface is strong in principle.

When a new curved surface is created, the correlation between the image displayed on the display screen by the image data processed by the computer and the data to be controlled and set by the operator is intuitive. The parameters set and input by the operator and the result display screen are considered in view of the fact that the operator can easily obtain a curved surface that is moderately suitable to the curved surface that the operator wants to obtain if it is easy to grasp. It is desirable to have a correspondence such that the change appearing on the upper curved surface is easily intuitively grasped.

The present invention has been made in view of the above points. For example, a free-form surface that cannot be expressed by a primitive surface, such as a surface forming a human face, can be created. When an operator sets a parameter, a method for creating a curved surface is proposed in which a change that occurs on an image due to this setting can be displayed on a display screen at a high speed and in a manner that is easy to intuitively grasp. What you want to do.

[0009]

According to the present invention, in order to solve the above-mentioned problem, the surface SOR before the deformation processing is
Designating a predetermined deformation area VCF including the action point CP _i ^* ,
A vector field function F _i indicating the relative relationship between the deformation rates of the points in the deformation area VCF is determined, and a deformation vector V _i ^* indicating the deformation amount and direction at the action point CP _i ^* of the deformation area VCF is specified. , position vector to obtain a position vector V _i ^* * F _i representing the amount of deformation of the curved surface modification in the vector V _i ^* and the vector field function F _i O connexion deformation area by multiplying the VCF, represents the surface of the pre-deformation treatment P _i-1 ^* and a curved position vector V _i represents the amount of deformation of ^* * F _i position vector representing the curved surface of the deformed and P _i ^* consists of a recurrence formula ^{_{P i * = P i-1}} * + V i * * so as to obtain the position vector P _i ^* representative of a curved surface after the desired deformation by repeating the calculation of F _i.

[0010]

The vector field function F _i is given as a scalar quantity indicating the relative change rate at each point in the deformation area VCF. Therefore, for each point included in the deformation area VCF, the deformation of the curved surface is performed. position vector V _i ^{* *} F _i representing the amount
Has the direction of the deformation vector V _i ^* as the direction of deformation, and has a magnitude corresponding to the relative deformation rate represented by the vector field function F _i as the magnitude of the deformation.

However, since the position vector V _i ^** F _i representing the amount of deformation of the curved surface has a value only inside the deformation area VCF, an operation of the vector field function F _i and the deformation vector V _i ^* is performed. Can be calculated only for points in the deformation area VCF. Therefore, the calculation time is practically real-time, and it is considered that the operator wants to obtain by performing the repetition calculation using the recurrence formula. A suitable deformed image can be obtained appropriately and easily.

[0012]

BRIEF DESCRIPTION OF THE DRAWINGS FIG.

The curved surface creating apparatus according to the present invention, as shown in FIG. 1, has an action point CP _i on an original surface SOR on an xy plane.
A position vector representing ^* (= X _i , Y _i ) is designated, and the computer performs the deformation operation of the surface only in the range of the deformation area VCF including the action point CP _i ^* . The calculation result is displayed on the display screen DSP on the display device CRT (FIG. 2).
Above, it is possible to display as a converted image SCH similar to the case where the deformed curved surface is viewed from an arbitrarily determined viewpoint position.

The deformation of the curved surface in the deformation region VCF is represented by the following recurrence formula.

(Equation 1) Is calculated recursively using a conversion formula represented by (1)
In the equation, P _i ^* is a position vector representing each point of the deformed curved surface formed in the three-dimensional space.
_i ^* is a position vector P _i-1 ^* of a corresponding point on the original surface SOR before deformation and a position vector P _i-1 before the deformation.
^* The amount of deformation of the ^{_{V i * * F i (P}} i-1 *, CP i *) is represented by the sum of the.

The amount of deformation is expressed by a vector field function F _i (P
_i-1 ^* , CP _i ^* ) by a deformation vector V _i ^* . Here, when the action point CP _i ^* is specified in the original surface SOR before the deformation processing, the deformation vector V _i ^* is the direction and magnitude of the deformation to be given to the original surface SOR at the action point CP _i ^* . Is expressed as a vector quantity, and the original surface SO
The action point CP _i ^* of R undergoes a deformation that can be lifted by the deformation vector V _i ^* .

The vector field function F _i (P _i-1 ^* , CP
_i ^* ) is relative to each point P _i-1 ^* of the deformation area VCF determined by including the action point CP _i ^* (its size can be specified by setting and inputting parameters). Represents the distribution of the relative deformation rate that determines whether or not to apply the deformation. The distribution of the relative deformation ratio has a value only inside the deformation region VCF, and “0” in the periphery.
Has a distribution of scalar quantities such as "is converged to 0".

[0017] accordance go-between, the amount of deformation ^{_{V i * * F i (P}} i-1 *,
CP _i ^* ) is a position vector representing the amount of deformation at each point in the deformation area VCF, and its direction is the deformation vector V _i
^* Has a direction parallel to ^* and the size is the deformation vector V
_It has a multiplied value (scalar amount) of the magnitude of _i ^* and the distribution of the relative deformation rate represented by the vector field function F _i .
Thus, the deformation of the curved surface of the deformation area VCF is caused by the action point CP _i
Resulting in deformation vectors V _i ^* direction and magnitude of the ^*, in accordance connexion deformation vector V _i ^* direction to go to the periphery of the action point CP _i ^*, and the change of the deformation rate of the vector field function F _i It occurs at a correspondingly varying magnitude.

Here, when a function that gradually converges symmetrically as going outward from the center point, such as a Gaussian distribution function, is assigned as the vector field function F _i , the deformation amount V _i ^* * F _i has a maximum value of the deformation vector V _i ^* direction in the point CP _i ^* position, follow to go to the outer circumferential portion from the point CP _i ^* connexion variation vector V _i ^*
, And a deformed surface whose size gradually converges to 0 is obtained.

[0019] Thus, once modified by connexion deformation amount V _i ^{* *} F _i in the operation is found, this is the position vector P _i after position vector P _i-1 ^* and is summed deformed before deformation
^* Is required. In the same manner, every time a deformation operation is performed in the same manner, a position vector representing a deformed surface is repeatedly and gradually calculated based on the position vector before deformation by calculating a recurrence formula expressed by Expression (1). It is calculated chemically.

As a result of repeating such a recursive operation,
The position vector representing the final deformation point P _N ^* is

(Equation 2) , The deformation amount sequentially obtained by N times of deformation operations (i = 1 to N) with respect to the position vector representing the point P ₀ ^* of the original surface SOR before the start of the deformation. (I.e., the total deformation amount) is obtained as a position vector.

Thus, according to the equation (2), the operator designates the action point CP _i ^* for the curved surface before the deformation each time the deformation operation is sequentially performed N times from the point P ₀ ^* of the original surface SOR. Thus, the position to be deformed from the curved surface P _i-1 ^* before the deformation can be arbitrarily specified based on the judgment of the operator. Also, the vector field function F _i and the deformation vector V _i
^By re-designating the parameter for determining ^* , the size of the deformation area VCF, the deformation rate distribution of the deformation surface, and the direction of the deformation can be arbitrarily set similarly based on the judgment of the operator.

Thus, every time the operator executes one deformation operation, the operator moves the deformed surface to a desired position with respect to the curved surface before the deformation.
Operations for applying a deformation having a desired size in a desired direction can be gradually stacked.

In this way, as is apparent from the equation (1), the position vector P _i ^* after the transformation is obtained from the position vector P _i-1 ^* before the transformation.
Since it is sufficient to simply add the deformation amount V _i ^** F _i to _i−1 ^* , the operation speed can be made sufficiently short for practical use (according to an experiment, it could be set to 1 second or less). In order to hide
Regarding the calculation for obtaining the deformation amount V _i ^** F _i , the vector field function F _i converges to 0 as it goes to the periphery, or is selected as a function that becomes 0 as the function is changed. The multiplication operation with the vector V _i ^* can be shortened to a time short enough to be practically called real-time processing (it can be shortened to 1/30 seconds according to experiments).

Therefore, according to the curved surface creation method according to the present invention, every time the operator performs the deformation operation, the converted image can be displayed on the display screen in real time in practical use. Therefore, the image deformation operation can be performed on the computer. To perform interactively. By obtaining the position vector P _i ^* representing the deformed surface for each deformation operation by the recurrence formula (1), the operator visually checks the deformation process of the image displayed on the display screen. By doing so, the image can be appropriately and easily deformed.

Then, as described above with respect to equation (2),
While stacking N deformation operations until the final deformation position vector P _N ^* is obtained from the position vector P ₀ ^* of the original surface SOR, the operator re-inputs the deformation parameters by trial and error. With respect to the curved surface obtained by the previous deformation operation, the deformation operation can be continued while evaluating the effect of the deformation. Thus, each time one operation is completed, the next operation to be deformed is It is possible to set parameters while considering the “what position”, “what size”, “what direction”, and “what size” deformation of the curved surface. Thus, it is possible to easily obtain a curved surface closest to the curved surface that the user wants to finally obtain.

In the above-described method for creating a curved surface, as an example of creating a curved surface for a human face, for example, a Gaussian distribution function is used as the vector field function F _{i in} the above-mentioned expressions (1) and (2), and A circular or elliptical shape can be selected as the region VCF. At this time, the deformation position vectors P _i ^* (x, y) and P
_N ^* (x, y) is as shown in equations (3) and (4), corresponding to equations (1) and (2), respectively.

[0027]

(Equation 3)

(Equation 4) In this case, the vector field function F _i is given by

(Equation 5) As shown in the following expression, the action point (X _i , Y _i ) on the xy plane
As shown in FIG. 3, a Gaussian distribution function is exhibited in the x direction and the y direction with respect to the ellipse having the diameters α _i and β _i in the x direction and the y direction.

In doing so, the operator sets the parameters of the action point CP _i ^* to the coordinates (X _i , Y _i ) for the vector field function F _i , and sets the parameters in the x direction and y as the parameters of the deformation area VCF. The direction diameters α _i and β _i are set, and the parameters of the deformation vector V _i ^* are set. Thus, the operator can determine the point of action (X _i , Y _i )
Centering on the deformation vector V _i ^{* in} the direction of the deformation vector V _i ^* set at the action point (X _i , Y _i ) for the circle or ellipse deformation region VCF of diameters α _i and β _i Thus, it is possible to obtain a deformed curved surface in which the deformation rate smoothly converges to 0 so as to draw a Gaussian distribution curve toward the periphery.

Accordingly, the deformed position vector P _i ^* (x,
y) or a curved surface represented by P _N ^* (x, y) has a Gaussian distribution in the direction of the deformation vector V _i ^* for a local region around the action point CP _i ^* in the original surface before deformation. It becomes a curved surface that exhibits a smooth free-form surface as shown by the function. Thus, for a free-form surface having softness such as a human face, a curved surface that does not cause unnaturalness can be created.

The method for creating a curved surface described above with reference to FIGS. 1 to 3 can be realized by a curved surface creating device having a configuration as shown in FIG. In this case, the vector field function F _i is set so as to have a deformation rate distribution represented by a Gaussian distribution function for an elliptical deformation area.

In FIG. 4, reference numeral 1 denotes a computer-configured surface calculation device, which converts position information obtained as a result of calculation based on the expressions (3) and (4) into a video signal by a surface display control device 2. Thereafter, it is displayed on the display device 3 having a cathode ray tube configuration. The curved surface calculation device 1 is provided with a mouse 4, levers 5, 6, 7, and a track ball 8 as input operators for inputting parameters required for the calculations of the equations (3) and (4). .

The mouse 4 inputs parameters X _i , Y _i for setting the action point CP _i ^* on the xy plane, whereby the action points (X _i , Y) are obtained in the equations (3) and (4).
_i ). The levers 5 and 6 are connected to the deformation area VC.
A parameter for determining the size of F is input, and the diameters α _i and β _i in the x and y directions in the equations (3) and (4) can be set.

Further, the lever 7 sets a deformation vector V _i ^* , and can set parameters regarding the direction and height of the deformation vector V _i ^* set at the action point (X _i , Y _i ). Further, the track ball 8 is for setting a viewpoint position with respect to a curved surface, and the curved surface viewed from the viewpoint position set by the track ball 8 is displayed on the display device 3.

When the setting by the mouse 4 and the levers 5 to 7 is completed, the curved surface calculation device 1 executes the calculations of the equations (3) and (4). The calculation result is rotationally converted based on the viewpoint position information input from the track ball 8, and is displayed on the display device 3 via the curved surface display control device 2. The thus display device 3 on the display screen, by the mouse 4 connexion set working point (X _i, Y _i) around a,
With respect to the deformation area VCF set by the levers 5 and 6, the deformation vector V _i ^* set by the lever 7
The height of the central portion rises by an amount corresponding to the direction and height of the image, and a curved surface deformed such that it gradually converges to 0 as it goes to its peripheral portion is displayed.

Such a deforming operation is obtained by the curved surface calculation device 1 executing the processing procedure of FIG. 5 by its CPU. That is, after starting the processing procedure in step SP1, the CPU of the curved surface calculation device 1 then executes the position vector P ₀ ^* representing the original surface SOR in step SP2 ^.
Is set in the surface data memory 12 (FIG. 6A) provided in the surface calculation device 1.

Subsequently, the CPU proceeds to the next step SP3, and fetches the parameters set by the operator. At this time, the operator inputs the action point data X _i , Y _i with the mouse 4, the diameter data α _i and β _i with the levers 5 and 6, and the deformation vector V _i ^* with the lever 7. Enter

At the next step SP4, the CPU of the curved surface calculation device 1 fetches the viewpoint position data input from the trackball 8 by the operator, and then proceeds to step SP5. This step SP5 executes the calculation described above with respect to equation (3). Here, the position vector P _i-1 ^* (x, y) before deformation uses the one set in the surface data memory 12, and the parameters α _i , β _i ,
X _i , Y _i , and V _i ^* use those set in step SP3.

Subsequently, the curved surface calculation device 1 proceeds to step SP6.
In step S5, the display device 3 displays the curved surface represented by the deformed position vector P _i ^* calculated in step SP5 via the curved surface display control device 2.

In this state, the CP of the curved surface calculation device 1
By continuing the display of the curved surface P _i ^* , U checks at the next step SP7 whether the degree of deformation conforms to the operator's request while checking the display on the display device 3. Thereafter, the CPU proceeds 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 curved surface calculation device 1 returns to the above-described step SP3 to return to a state of waiting for the setting of a new parameter. At this time, the operator re-sets new parameters in steps SP3 and SP4 so that steps SP5 and SP
Display device 3 after recalculating the deformation operation formula in P6
At step SP8, and again asks the operator whether the deformation is as requested.

Thus, the CPU of the curved surface calculation device 1 executes steps SP3-SP4-SP5-SP6-SP7-SP8.
-The position of the action point CP _i ^* until the operator can deform according to his / her needs by the loop of SP3;
The size of the deformation area VCF, the direction and the height of the deformation vector V _i ^* can be reset.

When the operator is satisfied with his setting operation and inputs a setting end signal to the surface computing device 1, the CPU of the surface computing device 1 proceeds to the next step SP9 and sets the data α _i and β _i. , X _i , Y _i , and V _i ^* are stored in a command list memory (FIG. 6) provided in the surface arithmetic device 1.
(B)) α ₁ , β ₁ , X ₁ , Y ₁ , and V are stored in the parameter memory area N = 1 corresponding to the 11th first setting operation.
After storing as ₁ ^* , the process proceeds to step SP10, where "+1" is added to the number of operations i (i = 2).
Move to 1.

This step SP11 is a step for checking whether or not the operator has finished the deformation operation. When the operation end command is not input from the operator, the CPU of the curved surface calculation device 1 returns a negative result in step SP11. By returning to step SP3 described above,
It is in a state of waiting for the second deformation operation (N = 2) by the operator.

In this state, the operator can perform a second deformation operation on the curved surface created by the first deformation operation of the curved surface with a new intention. Thus, the action point CP deformed by the first deformation operation
₁ ^* for different working point CP ₂ ^* A, the operator again may perform deformation operations to suit their needs.

That is, when the operator sets the parameters in steps SP3 and SP4, the curved surface calculation device 1 executes the calculation of the position vector P ₂ ^* (x, y) for the equation (3) in the following steps SP5 and SP6. The curved surface is displayed on the display device 3. This deformation operation is performed in steps SP3-SP4-SP5-SP6-SP7.
Repeated until the operator is satisfied by the loop of -SP8-SP3.

In step SP8, when the end of the deformation operation by the operator is confirmed, the curved surface calculation device 1 in step SP9 executes the newly input parameter data α ₂ , β ₂ , X ₂ , Y ₂ , V _{After 2} ^* is stored in the parameter memory area N = 2 corresponding to the second setting operation of the command list memory 11, step S
In P10, “+1” is added to the operation count i (i =
3), proceed to step SP11.

In the same manner, the CPU of the curved surface calculation device 1
Means that each time the operator performs a new deformation operation, the above-described deformation processing loop SP3-SP4-SP5-SP6-SP7
After executing -SP8-SP3, the set parameter data is stored in the command list memory 11, and the position vector P _i ^* obtained as a result of the deformation operation is stored and updated in the surface data memory. Accordingly, the curved surface data memory 12 stores the curved surface P _N ^* (x, y) ((4)) which has been deformed by the total deformation amount generated by the N times of deformation operations.
Equation) is obtained.

When the operator finishes all the deformation processing, the CPU of the curved surface calculation device 1 proceeds to step SP12.
Then, the program is terminated. Therefore, according to the curved surface creating apparatus shown in FIG. 4, the operator performs a single deformation operation by using the mouse 4, the levers 5, 6, 7, and the track ball 8.
By inputting the conversion parameters to the surface calculation device 1 while operating the, the surface deformation processing can be executed. As described above, as described above with respect to the expressions (1) and (2), or the expressions (3) and (4), the operation time required for the transformation operation is at most about one second. Immediately after the deformation operation, the conversion 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 deformation as necessary and deform the parameter to a desired shape. Settings can be input, and thus a desired curved surface can be created as a whole while partially modifying the interactive surface.

Further, the curved surface creating apparatus of FIG. 4 has the command list memory 11 as shown in FIG. 6B, so that the newest deformed position vector P _N ^* ((4 ), The parameters used in the immediately preceding deformation process are read out, the amount of deformation added by the immediately preceding deformation operation is calculated, and subtraction is performed from the data in the surface data memory 12. Thus, it is possible to reproduce the curved surface before executing the previous deformation operation. In this case, the data memory only needs to have the screen data memory 12 for one frame, so that the configuration of the entire curved surface creating apparatus can be simplified.

In the embodiment described above, the embodiment using the Gaussian distribution function as the vector field function F _{i in the} equations (3) and (4) has been described (Equation (5)). _{The function i} is not limited to this, and various functions as described below can be used. And if constituting the surface generating device can be selected such various vector field function F _i, deformation processing loop described above with reference to FIG. 5 SP3-SP4-SP5-SP6 -SP7-SP8-
In SP3, the transformation operation formula (step SP5) in each transformation loop is sequentially switched, so that the transformation of the curved surface is performed while combining the transformed surfaces having various characteristics, thereby allowing the operator to perform the transformation. A curved surface that can be optimally adapted to a request can be created.

By switching the deformed surface as needed, it is possible to produce the same effect as engraving a surface while sequentially changing chisels having different cutting edges. it can.

FIG. 7 shows a vector field function F representing the outer surface of a cylinder whose deformation area VCF in the xy plane is a circle or an ellipse.
_{When i} is used, the vector field function F _i is

(Equation 6) When

(Equation 7) And again

(Equation 8) When

(Equation 9) Becomes

By using the vector field function F _i as shown in FIG. 7, a cylinder having a maximum value at the center of the deformation region VCF and a distribution of the deformation rate at the periphery at a stroke of 0 is obtained. A deformed curved surface having an approximate shape to the surface can be obtained. Therefore, a desired curved surface can be created by repeatedly performing the deforming operation while finely dividing the deformed region.

FIG. 8 shows an embodiment in which a vector field function F _{i in} which the deformation area VCF on the xy plane is rectangular is used.
In this case, the vector field function F _i is expressed as follows in the x-axis and y-axis directions.

(Equation 10)

[Equation 11] When

(Equation 12) Becomes On the other hand, for regions other than the deformation region VCF,

(Equation 13)

[Equation 14] When

(Equation 15) And again

(Equation 16)

[Equation 17] When

(Equation 18) And then

[Equation 19]

(Equation 20) When

(Equation 21) Becomes

If such a vector field function F _i is used, the curved surface before deformation can be deformed by a prism-shaped deformed curved surface that locally has the surface shape of a quadrangular prism. As Figure 9 shows the vector field function F _i, in the embodiment when the shape of the xy plane with a function representing the surface of the circular or elliptical cone, the vector field function F _i,

(Equation 22) When

(Equation 23) And again

(Equation 24) When

(Equation 25) Becomes

As a result, the curved surface before deformation is deformed by the deformed curved surface having the shape of the surface of the cone shown in Expression (23), limited to the range of the deformation region VCF expressed by Expression (22). Let me go. Therefore, the distribution of the deformation rate in this case is
The maximum value is at the center of the deformation region VCF, and converges to 0 as it goes to the periphery.

FIG. 10 shows xy as a vector field function F _i .
In the embodiment in which a function representing the outer surface of a cone set up with respect to a deformation region VCF having a quadrilateral shape on a plane is used. In this case, the vector field function F _i is

(Equation 26)

[Equation 27] When

[Equation 28] Using the vector field function F _i, expressed in. On the other hand, for regions other than the deformation region VCF,

(Equation 29)

[Equation 30] When

(Equation 31) And again

(Equation 32)

[Equation 33] When

(Equation 34) And then

(Equation 35)

[Equation 36] When

(37) become.

Thus, in the case of this embodiment, the curved surface can be deformed by using a deformed curved surface having the shape of the outer surface of the pyramid with respect to the curved surface before deformation. FIG. 11 shows the vector field function F
_In the embodiment in which a function representing a spherical surface whose shape on the xy plane is a circle or an ellipse is used as _i , in this case, the vector field function F _i is

(38) For the deformation area VCF represented by

[Equation 39] become.

On the other hand, for other areas,

(Equation 40) When

[Equation 41] Becomes Thus, a relatively soft deformation can be applied to the curved surface before deformation by using a deformed curved surface having a spherical outer shape.

FIG. 12 shows xy as the vector field function F _i.
In the embodiment in which the shape of the deformation region VCF on a plane uses a function representing the outer surface of a prismatic prism having a quadrilateral shape, the vector field function F _{i in} this case is

(Equation 42)

[Equation 43] When

[Equation 44] become. On the other hand, for other regions, the vector field function F _i is

[Equation 45]

[Equation 46] When

[Equation 47] And again

[Equation 48]

[Equation 49] When

[Equation 50] And then

(Equation 51)

(Equation 52) When

(Equation 53) Becomes In this way, the curved surface can be deformed by using a deformed curved surface having a directional line having a ridge line in the y-axis direction with the shape of the outer surface of the prism-shaped column relative to the curved surface before deformation. it can.

FIG. 13 shows a vector field function F
_{In the} embodiment in which the shape of the curved surface forming _i is changed so that the extension direction of the ridgeline is rotated by 90 ° to extend in the x-axis direction, the vector field function F _{i in} this case is

(Equation 54)

[Equation 55] When

[Equation 56] Whereas for other areas,

[Equation 57]

[Equation 58] When

[Equation 59] And again

[Equation 60]

[Equation 61] When

(Equation 62) And then

[Equation 63]

[Equation 64] When

[Equation 65] Becomes Even in this case, the same effect as described above with reference to FIG. 12 can be obtained.

[0062]

As described above, according to the present invention, a vector field function F _i that can be deformed by specifying a partial area of a curved surface before deformation is specified, and this vector field function F _i is specified. On the other hand, by forming the deformed surface by multiplying by the deformed vector V _i ^* , the deformed surface can be generated substantially in real time, and can be set while viewing the screen as a parameter, that is, Since the position of the action point, the deformation area, and the direction and the size of the deformation vector can be used, the parameter setting operation can be performed intuitively. In addition, by obtaining the position vector P _i ^* representing the deformed surface for each deformation operation by the recurrence formula of equation (1), the deformation process of the image displayed on the display screen can be performed. The image can be appropriately and easily deformed by the visual confirmation by the operator.

[Brief description of the drawings]

FIG. 1 is a schematic diagram for explaining the principle of a curved surface creation method according to the present invention.

FIG. 2 is a schematic diagram illustrating the principle of a curved surface creation method according to the present invention.

FIG. 3 is a schematic diagram for explaining a position vector representing a curved surface after deformation.

FIG. 4 is a block diagram showing a curved surface creating apparatus for implementing the method of the present invention.

FIG. 5 is a flowchart showing a curved surface deformation processing procedure.

FIG. 6 is a schematic diagram illustrating a surface data memory and a command list memory provided in the surface calculation device 1 of FIG. 4;

FIG. 7 is a schematic diagram showing an embodiment in the case of using a circular or elliptic cylinder type vector field function F _i .

FIG. 8 is a schematic diagram showing an embodiment when a prismatic vector field function F _i is used.

FIG. 9 is a schematic diagram showing an embodiment when a circular or elliptical cone type vector field function F _i is used.

FIG. 10 is a schematic diagram illustrating an example in which a pyramidal vector field function F _i is used.

FIG. 11 is a schematic diagram illustrating an example in which a spherical vector field function F _i is used.

FIG. 12 is a schematic diagram illustrating an embodiment when a prism type vector field function F _i is used.

FIG. 13 is a schematic diagram showing an embodiment when a prism type vector field function F _i is used.

[Explanation of symbols]

1 ... Surface calculation device, 2 ... Surface display control device, 3 ... Display device, 4 ... Mouse, 5-7 ... Lever, 8 ... Track ball.

Claims (1)

(57) [Claims] 1. A position including an action point with respect to a surface before deformation processing.
Designate a fixed deformation area and change the deformation rate of each point in the above deformation area
Field function F representing the relative function of_iAnd the deformation amount and direction at the action point in the deformation area are displayed.
S deformation vector V_i ^*And the deformation vector V_i ^*And the vector field function F_iTo
By multiplying, the amount of deformation of the surface within the deformation area is calculated.
A position vector representing the surface before the deformation process is obtained._i-1 ^*And on
Position vector V representing the amount of deformation of the curved surface_i ^** F_iAnd above
Position vector P representing the surface after deformation_i ^*Recursion consisting of
Formula P_i ^*= P_i-1 ^*+ V_i ^** F_i  By repeating the above calculation, the desired curved surface after the deformation is obtained.
The position vector P to represent_i ^*ToGet The position vector P _i ^* Display the surface after deformation based on
Show A method for creating a curved surface, characterized in that: