JPH0682384B2 - Curved surface creation device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention will be described in the following order.

A Industrial Field B Outline of the Invention C Prior Art D Problems to be Solved by the Invention E Means for Solving Problems (Fig. 1) F Action (Fig. 1) G Example (1st) (Fig. 10) (G1) Principles applied by this curved surface creation device (Fig. 2-5)
Fig.) (G2) Example (Fig. 1) (G3) Animation creation device applying this curved surface creation device (Figs. 6 to 10) H Effect of the invention A Industrial field Regarding the device, it is particularly applicable to an animation creating device and a special effect device.

B Outline of the Invention According to the present invention, in a curved surface creation device in a computer graphics, it is possible to create a data representing a new curved surface by multiply-add operation of curved surface information data indicating a plurality of curved surfaces and an interpolation coefficient or an extrapolation coefficient. By doing so, various curved surfaces can be created, and moreover, the curved surface can be continuously changed.

C Conventional Technology In the animation creating device and the special effect device, the curved surface creating device in computer graphics is used. Conventionally, as a curved surface creating method applied to this type of curved surface creating apparatus, data of basic curved surfaces such as cylinders and spheres (referred to as primitive curved surfaces) is prepared in advance, and these primitive curved surfaces are required. Method such as creating a new curved surface by combining according to
A method is used in which points on a curved surface to be newly created are designated as control points, and a curved surface passing through these control points is interpolated using a spline function.

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

Even when creating a curved surface using the spline function, many control points must be set in practice, so in order to form that many control points, you can use a primitive curved surface or a cross-sectional view. By combining them, the control points are set within a practically permissible range. Therefore, in this case as well, in practice, the characteristics are the same as in the case of combining the primitive curved surfaces.

As described above, according to the conventional curved surface creating method, since a new curved surface is created by combining primitive curved surfaces, the set of newly formed curved surfaces is limited, and the curved surface as intended by the operator is created. There are many cases where you do not get it.

Also, if the set of newly formed curved surfaces is limited,
Even if this curved surface creating device is applied to an animation creating device or a special effect device, it may not be possible to obtain a smooth curved surface deformation, and the applicable curved surface deformation pattern is limited to a narrow range.

The present invention has been made in consideration of the above points, and it is possible to create various curved surfaces from primitive curved surfaces, and
An object of the present invention is to provide a curved surface forming apparatus that can easily respond to obtaining a continuously changing curved surface.

In the present invention for solving means above problems to solve E problems, a storage unit 1 ₁ 1n for storing curved surface information data P ₁ to PN showing a plurality of curved surfaces P ₁ to PN, curved information The data P _{1 to} Pn and the interpolation coefficient Ii (where Ii satisfies 0 <Ii <1 of I _{1 to} In) or the extrapolation coefficient Ij (where Ij is Ij <0 or Ij <of I _{1 to} In).
Product-sum operation means (2 ₁ to generate the data indicating the new curved surface P and ones) that satisfies 1 and sum operation to 2n, so that provision of the 3) and.

F action A plurality of curved surfaces P _{1 to} Pn are represented by a set of position information of points on the surface, and when the number of points on each curved surface is the same, information on the plurality of curved surfaces P _{1 to} Pn can be associated. .

The position information of the corresponding points on the two curved surfaces is divided into inner and outer parts (hereinafter,
By performing interpolation or extrapolation around this time), a curved surface made up of a set of points having new position information can be obtained.

It is possible to obtain various curved surfaces by repeatedly performing such interpolation or extrapolation processing on a plurality of curved surfaces or created curved surfaces. Here, repeating the interpolation or extrapolation processing a plurality of times means that in the relation between the final curved surface P and the plural curved surfaces P _{1 to} Pn, the interpolation or extrapolation corresponding to the information of the plural curved surfaces P _{1 to} Pn. This is the same as obtaining the final curved surface P by executing the sum of products operation with the insertion coefficients I _{1 to} In.

Therefore, the product-sum operation means (2 ₁ to 2n, 3), and so as to execute the product-sum operation ((12) see formula).

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

(G1) Principle applied to the curved surface creating apparatus First, the principle of the present invention will be described. The present invention is shown in FIG.
As shown in, two primitive curved surfaces Pa and Pb (curved surface is represented by a set of position vectors of points on the surface) are interpolated or extrapolated (corresponding points of both curved surfaces Pa and Pb are internally divided or extrapolated). This means that a new created curved surface Pab is obtained by performing the division. Therefore, the newly created curved surface Pab can be expressed by the following equation Pab = (1-k) Pa + kPb (1). Here, k is an interpolation extrapolation coefficient and represents interpolation when the value is in the range of the following expression 0 <k <1 (2), and the range of the following expression k <0, 1 <k (3) The value of indicates extrapolation.

By selecting this interpolation / extrapolation coefficient k as a predetermined value, one new created curved surface Pab can be obtained. Therefore, various new curved surfaces Pab can be obtained from the two primitive curved surfaces Pa and Pb according to the interpolation / extrapolation coefficient k.

For example, if the interpolation coefficient k is set to 0.5 and the interpolation is
From the cylindrical first primitive curved surface Pa and the spherical second primitive curved surface Pb, as shown by the broken line in FIG. 2 (B), the body part that retains the information of the original primitive curved surface as a new created curved surface Almost barrel-shaped curved surface Pa
You can get bi. Also, the same primitive curved surface
Even if Pa and Pb are used and the extrapolation coefficient k is selected to −1 and extrapolated, as shown by the broken line in FIG. 2 (C) and as shown in FIG. 2 (A), Unexpected from the primitive curved surface that becomes a nearly drum-shaped curved surface Pabo
Can be obtained.

Here, the corresponding points of the two primitive curved surfaces Pa and Pb can be defined as follows.

All primitive curved surfaces stored in the curved surface database have a fixed number (for example, 600) regardless of the curved surface shape.
It is represented by the set of position vectors of the points. For example, write a grid pattern on the original screen IMP as shown in FIG.
If the spherical and cylindrical primitive curved surfaces Pac and Pbc shown in FIGS. 3 (B) and (C) are created by modifying them, the intersection points (hereinafter referred to as grid points) C on the original screen IMP
It can be represented by a set of position vectors after the transformation of RS. Therefore, the points on the primitive curved surfaces Pac and Pbc obtained by transforming the same lattice points on the original screen IMP are the corresponding points.

The mapping of the primitive curved surfaces Pac and Pbc with respect to the original screen IMP is not uniquely determined, and for example, as shown in FIG. 4 (A), one coordinate axis direction, that is, y
The deformation points PCH of the grid points CRS may be mapped in the same direction so that the deformation points PCH of the grid points CRS are equal on the primitive curved surfaces Pac and Pbc as shown in FIG. 4B. You may map so that it may become a space.

Therefore, the corresponding points of the primitive curved surfaces Pac and Pbc may have the same value in the y direction depending on the mapping method, and may have different values in any case, but in any case, as shown in FIGS. 4 (A) and 4 (B). As shown in, a new created curved surface can be obtained by interpolation and extrapolation.

In this way, when a newly created curved surface is formed from two curved surfaces by interpolation extrapolation, the original curved surface need not be limited to the primitive curved surface, and a curved surface already created by interpolation extrapolation is used. You can also

Therefore, for example, as shown in FIG. 5, a drum-shaped creation curved surface P _AB is obtained from the cylindrical primitive curved surface P _A and the spherical primitive curved surface P _B by interpolation and extrapolation (first step). Conical primitive surface P of surface P _AB
A curved surface P _ABC of a trapezoid shape that gradually expands from one end to the other end is obtained from _C and by interpolation and extrapolation (second
(Step), and further, from this created curved surface P _ABC and a substantially cylindrical primitive curved surface P _D with axially repeated concave and convex portions, insert and extrapolate to gradually expand from one end to the other end. It is also possible to go (third step) so as to obtain a created curved surface P _ABCD whose side surface has unevenness repeatedly.

That is, by repeating the interpolation extrapolation several times (hereinafter referred to as multiple interpolation extrapolation), a plurality of primitive curved surfaces P _A ,
A desired created surface P _ABCD can be obtained from P _B , P _C and P _D.

In the modification shown in FIG. 5, assuming that the interpolation extrapolation coefficient in the first step is α, the extrapolation extrapolation coefficient in the second step is β, and the interpolative extrapolation coefficient in the third step is γ, each step. The curved surfaces P _AB , P _ABC , and P _ABCD created in are the following equations P _AB = (1-α) P _A + αP _B ...... (4) P _ABC = (1-β) P _AB + βP _C ...... (5) P _ABCD = (1−γ) P _ABC + γP _D (6)

By substituting equations (4) and (5) into equation (6) and rearranging, the final curved surface P _ABCD is the following equation P _ABCD = I _A P _A + I _B P _B + I _C P _C + I _D P _{As in D} (7), it can be represented by the sum of products of the primitive curved surfaces P _A , P _B , P _C , P _D and the multiple interpolation extrapolation coefficients I _A , I _B , I _C , I _D.
Here, the multiple interpolation extrapolation coefficients I _A , I _B , I _C , and I _D are respectively the following formulas I _A = (1-α) (1-β) (1-γ) (8) I _B = α (1-β) (1-γ) (9) I _C = β (1-γ) (10) I _D = γ (11)

Therefore, by generalizing the equation (7), the n multiple extrapolation coefficients are calculated from the n primitive curved surfaces P ₁ , P ₂ ... Pn.
The value of I ₁ , I ₂ , ... It can be seen that a new created curved surface P can be created by multiple interpolation and extrapolation by executing the product-sum operation of

(G2) Example FIG. 1 shows an example of a curved surface forming apparatus according to the present invention to which the above-described curved surface forming principle is applied.

In FIG. 1, n large-capacity primitive curved surface information memories 1 ₁ , 1 ₂ , ... 1n respectively include primitive curved surface information P ₁ , P ₂ , which is a set of position vectors at points on the surface of the curved surface. ...... Pn is stored, and the multiplier 2 ₁ , to which this primitive surface information P ₁ , P ₂ , ... Pn corresponds,
2 ₂ , ... 2n is given as the first multiplication input. Each of the multipliers 2 ₁ , 2 ₂ , ..., 2n is used as a second multiplication input, and is a multiple interpolation extrapolation coefficient I ₁ , I ₂ which is a scalar quantity corresponding to each of the primitive surface information P ₁ , P ₂ ,. , …… In is given.

Thus, from each of the multipliers 2 ₁ , 2 ₂ , ... 2n, the multiple interpolation extrapolation coefficient corresponding to each of the primitive surface information P ₁ , P ₂ ,.
I _1, I _2, multiplication value I ₁ of the _{...... In P 1, I 2 P} 2, ...... InPn is obtained, which is given to the adders 3.

The adder 3 obtains the sum of the respective multiplication values I ₁ P ₁ , I ₂ P ₂ , ... InPn, that is, calculates the above equation (12) and newly creates curved surface information by multiple interpolation extrapolation. P is obtained and given to the created music information memory 4 to be stored.

In the above configuration, a predetermined primitive curved surface P ₁ , P ₂ , ... Pn is selected by the operator and stored in the primitive curved surface information memory 11 ₁ , 12 ₂ , ... 1n, and a predetermined multiple interpolation is performed by the operator. extrapolation factor I _1, I _2, when ...... in is selected, surface generating device by the multiplier 2 ₁ to 2n and an adder 3 to a desired created curved surface P running (12) integral calculation of formula create.

The created curved surface P created in this way is stored in the created curved surface memory 4 and displayed on the display device as required.

If there is an unnecessary primitive curved surface for creating the desired created curved surface P, the multiple interpolation extrapolation coefficient corresponding to the primitive curved surface may be set to zero.

According to the above-described embodiment, various new curved surfaces can be obtained by changing the selection of the primitive curved surfaces P _{1 to} Pn and changing the values of the multiple interpolation extrapolation coefficients I _{1 to} In. . Also, a continuously changing curved surface can be obtained by continuously changing the multiple interpolation / extrapolation coefficients I _{1 to} In, which is easy for an animation creation device or a special effect device that wants a continuously changing curved surface. Can be met.

For To write, if Hakare faster constitutes a multiplier 2 ₁ to 2n and an adder 3 in parallel processor, as to be in accordance with real time if the operator has changed the multiplexed within挿外interpolation factor I ₁ -In Can be

(G3) Animation creation device to which this curved surface creation device is applied Next, an example in which the curved surface creation device of the present invention is applied to an animation creation device is shown by the same reference numerals in FIG. The figure will be described.

As shown in FIG. 7, the host computer 10 as an animation creation control device has N (N> N) as shown in FIG.
n) Primitive surface database 11 composed of, for example, a hard disk, which stores a number of different primitive surfaces.
The host computer 10 selects n primitive curved surfaces P ₁ , P ₂ , ... Pn according to the curved surface selection signal coming from the keyboard input device 12, and selects the curved surface information memories 1 ₁ , 1 ₂ , …… Stored in 1n.

Further, the host computer 10 has a trackball device 13 as a key frame input device for inputting curved surface images (hereinafter referred to as key frames) KY1 to KY5 which are keys in the change of animation as shown in FIG. .
The trackball device 13 is the time axis of the key frames KY1 to KY5.
Time axis setting mode selection button 13a for selecting the time axis setting mode for setting the positions t1 to t5 on the AXS and creation of key frames KY1 to KY5 View point moving mode for selecting the view point moving mode for changing the viewpoint position for viewing the curved surface Select button 13b
And the multiple interpolation extrapolation coefficient I ₁ in the key frames KY1 to KY5
To In are recorded in the multiple interpolation / extrapolation coefficient memory 14 shown in detail in FIG. 9 and a key frame registration button 13c. Further, the trackball device 13 rotates to move the time axis AXS when the time axis setting mode is selected, and rotates when the viewpoint moving mode is selected to move the viewpoint ball 13d. Have.

A display device 15 is connected to the host computer 10. The display device 15 displays the created curved surface P (key frames KY1 to KY5) stored in the curved surface information memory 4 for the created curved surface, and also displays the time axis AXS, for example, on the lower side of the tube surface. When the time axis setting mode selection button 13a is operated, the cursor 16 is displayed close to the time axis AXS displayed on the display surface of the display device 15, and the track ball 13d is rotated to move the cursor 16 to the time axis. It moves along AXS, and you can select and select the time point of the key frame.

Furthermore, the host computer 10 has n levers 17 ₁ , 1 for setting multiple interpolation extrapolation coefficients I ₁ , I ₂ , ... In.
7 ₂ , ..., 17n are provided, and when the keyframe registration button 13c is pressed, the multiple interpolation extrapolation coefficient I that specifies the curved surface for creating the keyframe at the time point specified by the cursor 16 on the display device 15 is provided. The set values of the levers 17 _{1 to} 17 n as _{1 to} In are stored in the multiple interpolation / extrapolation coefficient memory 14.

Here, the multiple interpolation / extrapolation coefficient memory 14 stores, for example, multiple interpolation / extrapolation coefficients I _{1 to} In for each frame as shown in FIG. 9, and the frames Ft ₁ and F of the key frames KY _{1 to} KY 5 are stored.
t _2, ...... Ft ₅ stores set values by the lever 17 ₁ ~17n for also for frames other than the key frame KY1~KY5 is multiplexed in挿外interpolation coefficient of the nearest key frame prior to the frame The host computer 10 interpolates and stores the multiple interpolation extrapolation coefficient of the closest key frame after the frame, according to the time with the key frames. Therefore, in the multiple interpolation / extrapolation coefficient memory 14, the multiple extrapolation / extrapolation coefficients I _{1 to} In between adjacent frames differ only to the extent that the curved surface deformation can be seen sufficiently smoothly when visually observed.

Further, the host computer 10 has a viewpoint position information memory 18 for storing, for example, viewpoint position information for each frame, and this viewpoint position information memory 18 is a key frame registration button 13c.
The viewpoint position information by the track ball 13d when is pressed is stored, and for the frames other than the key frame, the host computer 10 interpolates the viewpoint position information of the key frame similarly to the multiple interpolation extrapolation coefficient memory 14. The calculated viewpoint position information is stored.

In the above configuration, the animation is created according to the processing procedure shown in FIG.

That is, when the processing is started in step SP1, the host computer 10 uses it for the animation selected by the operator from the N primitive curved surfaces stored in the primitive curved surface database 11 through the keyboard input device 12 in the next step SP2. n-number of primitive curved surfaces P _1, P _2, stores ...... Pn the curved surface data memory 1 ₁ 1n.

After that, the operator selects the time axis setting mode selection button.
When 13a is pressed, it moves to the next step SP3 and the display device 15
The cursor 16 is displayed above, the cursor 16 is moved according to the rotation of the track ball 13d, and the time point on the time axis AXS where the cursor 16 is stopped is set as the time point t1 of the first key frame KY1.

The host computer 10 displays the created curved surface P based on the multiple interpolation extrapolation factors I _{1 to} In given from the levers 17 _{1 to} 17n on the display device 15 at step SP4 almost in parallel with this step SP3. At this time, when the levers 17 _{1 to} 17 n are operated by the operator, the created curved surface P is deformed and displayed accordingly. When the operator pushes the viewpoint movement mode selection button 13b and then rotates the track ball 13d, a curved surface viewed by moving the viewpoint of the curved surface P created by the multiple interpolation / extrapolation coefficient is displayed.

In this way, the curved surface of the key frame KY1 is selected in step SP4 by selecting the multiple interpolation / extrapolation coefficients I _{1 to} In and the viewpoint position.
If it is decided by
Press 13c. As a result, the host computer 10 proceeds to the next step SP5 at the multi-interpolation coefficients I _{1 to} In at that time.
Is stored in the frame column Ft ₁ of the multiple interpolation / extrapolation coefficient memory 14 corresponding to the time point t ₁ , and similarly, the position information of the viewpoint is stored in the frame column of the viewpoint position information memory 18.

Next, the host computer 10 determines whether or not the next key frame is designated in step SP6. When the setting result is obtained, the procedure returns to the above-mentioned step SP3, and the step SP3
~ Execute SP5 to determine and register the curved surface of the next key frame KY2. For example, as shown in FIG. 8, when determining and registering five key frames KY1 to KY5,
The processing of SP3 to SP5 is repeated about 5 times to register 5 frames.

The curved surface determination and registration operations for all the key frames KY1 to KY5 to be set are completed, and, for example, the keyboard input device 12
When the operator gives an end command to the effect that the input operation of the key frame is completed, the host computer 10 moves to the next step SP7 and the multiple interpolation extrapolation coefficient I ₁ ~ In and the viewpoint position information are sequentially obtained by interpolating the multiplex interpolation extrapolation coefficient of the key frame and the viewpoint position information, and stored in the multiplex interpolation extrapolation coefficient memory 14 and the viewpoint position information memory 18, respectively.
After that, the processing ends at step SP8.

Next, based on such a processing procedure, as shown in FIG. 8, a curved surface having a rectangular shape is rounded so that a pair of opposite edges gradually approach each other, and both edges are separated by a predetermined distance. From the time when it became a round shape, the center part became concave and the central part became depressed, and from the time when it became a drum-shaped curved surface with both end edges overlapping, the upper part was sandwiched and the lower part expanded, and a lappa-shaped curved surface was obtained. A case will be described in which an animation is created that gradually changes from side to side so that irregularities are formed on the side surface in the axial direction. In this case, the viewpoint position is always fixed.

In this case, the operator needs the primitive surfaces needed to create each surface in this series of animations,
That is, the cylindrical curved surface P ₁ and the spherical curved surface shown in FIG.
N primitive surfaces including P ₂ , a conical curved surface P ₃ , a rectangular curved surface P ₄ and a cylindrical curved surface Pn having unevenness on the side surface.
Select P _{1 to} Pn and operate the keyboard input device 12 to store them in the primitive curved surface information memories 1 ₁ to 1n.

Next, the operator selects the time axis setting mode selection button 13a.
After pressing, turn the track ball 13d to set the rectangular curved surface (key frame) KY1 that is the curved surface at the time of start, determine the time t1, and then operate the levers 17 _{1 to} 17n to visually check the display device 15. While checking, get the curved surface of the key frame KY1. At this time point t1, since the primitive curved surface P4 becomes the key frame KY1 as it is, among the multiple extrapolation coefficients, the one (I ₄ ) corresponding to the primitive curved surface P4 is 1 and the other multiple extrapolation coefficients. I ₁ ~ I ₃ , I ₅ ~
The levers 17 ₁ to 17 n may be operated so that In becomes 0.

After that, by pressing the keyframe registration button 13c,
The coefficients I _{1 to} In are stored in the memory area of the multiple interpolation extrapolation coefficient memory 14 corresponding to the time point t1.

Next, in a series of changes, the operator determines and registers the curved surface of the key frame KY2 that is the key next to the rectangular shape. The both ends of the rectangular shape go round and the curved surface of the shape that has come close to a predetermined distance is the second key frame KY2
Then, the operator selects the first key frame KY1 to 2
Considering the time t1 to t2 required to change to the second key frame KY2, time axis setting mode selection button 13a
After pressing, turn the trackball 13d to move the cursor 16
And set time t2.

After that, operate the levers 17 ₁ to 17 n to operate the desired key frame KY.
2 curved surfaces are obtained, and the desired key frame KY2 is displayed on the display device 15
Is pressed, press the keyframe registration button 13c. As a result, the time t2 in the multiple interpolation extrapolation coefficient memory 14 is
To the frame field Ft ₂ corresponding to the lever 17 _{1 to} 17n at that time
The value of is stored. Here, since the curved surface of the key frame KY2 is obtained by, for example, interpolating the cylindrical primitive curved surface P ₁ and the rectangular primitive curved surface P ₄ by 0.5, the stored content of the memory 14 at that time is the coefficient I. ₁ , I ₄
Is 0.5 for 0 and 0 for the other coefficients I ₂ , I ₃ , I _{5 to} In.

Similarly, the operator registers the hourglass-shaped curved surface as the third key frame KY3 at time t3, the trumpet-shaped curved surface as the fourth key frame KY4 at time t4, and has the unevenness on the side surface at time t5. Register the trapezoidal curved surface as the last key frame KY5.

After registering the last key frame KY5, the operator gives an instruction to end the input operation via the keyboard input device 12. In this way, the host computer 10
For each frame between adjacent key frames, the multiple interpolation extrapolation coefficients I _{1 to} In of the key frame are interpolated to obtain the multiple extrapolation extrapolation coefficients I _{1 to} In and stored in the memory 14. For example, as for the frame at the intermediate time point t34 between the key frames KY3 and KY4, as shown in FIG. 9, the values of the multiple interpolation extrapolation coefficients I _{1 to} In of the key frame KY3 are 2, -1, 0, 0, ... , 0 and the values of the multiple interpolation extrapolation coefficients I _{1 to} In of the key frame KY 4, 1, −0.5, 0.
Intermediate value of 5, 0, ..., 0 is 1.5, -0.75, 0.25, 0, ...
..., 0 is stored in the memory 14.

In this way, by reading out the multiple interpolation extrapolation coefficients I _{1 to} In stored in the multiple extrapolation extrapolation coefficient memory 14 for each frame and displaying the curved surface P created by the coefficients,
It is possible to obtain an animation that gradually changes from a rectangular curved surface (KY1) to a trapezoidal curved surface (KY5) having unevenness on the side surface.

As described above, according to the animation creating apparatus to which the curved surface creating apparatus according to the present invention is applied, it is possible to obtain an animation image that continuously and smoothly changes.

Per To write, create a multiplier 2 ₁ to 2n and an adder 3 be constituted by a parallel processor, multi-in挿外interpolation factor I ₁ -In and viewpoint data in real time for each frame be varied for each frame A curved surface can be obtained and real-time animation can be easily realized.

Although FIG. 6 shows the curved surface creating apparatus of the present invention applied to an animation creating apparatus, it can also be applied to a special effect apparatus in a television transmission system, for example.

H Effect of the Invention As described above, according to the present invention, a new curved surface is created by the product sum of the curved surface information data indicating a plurality of curved surfaces and the interpolation coefficient or the extrapolation coefficient. A variety of curved surfaces can be created by selection, selection of interpolation coefficient or extrapolation coefficient, and continuous and smooth curved surface can be obtained by continuously changing interpolation coefficient or extrapolation coefficient. It is possible to obtain a curved surface forming apparatus which can easily meet the requirements of the apparatus.

[Brief description of drawings]

FIG. 1 is a block diagram showing an embodiment of a curved surface forming apparatus according to the present invention, FIG. 2 is a schematic diagram for explaining interpolation and extrapolation of two primitive curved surfaces, and FIGS. 3 and 4 are interpolated. FIG. 5 is a schematic diagram for explaining the correspondence of points on the primitive curved surface for extrapolation, FIG. 5 is a schematic diagram for explaining multiple interpolation extrapolation of a plurality of primitive curved surfaces, and FIG. FIG. 7 is a schematic diagram showing an animation creating device, FIG. 7 is a schematic diagram showing a method of selecting a primitive curved surface, FIG. 8 is a schematic diagram showing a relationship between a key frame and a time axis, and FIG. FIG. 10 is a schematic diagram for explaining the stored contents of the extrapolation / extrapolation coefficient memory, and FIG. 10 is a flow chart showing the procedure for creating the animation. 1 _{1 to} 1n …… Primitive curved surface information memory, 2 _{1 to} 2n …… Multiplier, 3 …… Adder, 4 …… Created curved surface information memory, P ₁ ～
Pn …… Primitive surface (primitive surface information), P
…… Created surface (created surface information), I _{1 to} In …… Multiple interpolation extrapolation coefficient.

Claims (1)

[Claims] 1. A storage means for storing curved surface information data indicating a plurality of curved surfaces, and a sum of products for generating a data indicating a new curved surface by multiply-accumulate the curved surface information data and an interpolation coefficient or an extrapolation coefficient. A curved surface creating apparatus characterized by comprising a computing means.