JPS6274159A - Curved surface forming device - Google Patents

Abstract

PURPOSE:To form various curved surfaces, and also to cope with even the continuous variation of the curved surface by forming a new curved surface by bringing the curved surface information of plural primitive curves surfaces to multiple interpolation and extrapolation. CONSTITUTION:Plural primitive curved surfaces P1-Pn are shown by the collection of position information of points of the surface, and when the number of points related to each curved surface coincides, the information of plural primitive curves surfaces P1-Pn can be made to correspondence. Multiple interpolation and extrapolation coefficients I1-In corresponding to each primitive curved surface P1-Pn, and curved surface information of the primitive curved surfaces P1-Pn are brought to a product sum operation by product sum operating means 21-2n and 3, and a new curved surface P by the multiple interpolation and extrapolation of plural primitive curved surfaces P1-Pn is formed.

Description

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

A. Industrial field of application B. Overview of the invention C. Conventional technology Problems to be solved by the invention E. Means for solving the problems (Fig. 1) F. Effects (Fig. 1)
Figure) G Example (Figures 1 to 10) (G1) Principle applied by this curved surface creation device (Figures 2 to 5)
Figure) (G2) Example (Figure 1) (G3) Animation creation bag W to which the present curved surface creation device is applied (Figures 6 to 10) Regarding devices, the present invention is particularly applicable to animation creation devices and special effects devices.

B Summary of the Invention The present invention is a curved surface creation device for computer graphics that creates new curved surfaces by multiple interpolation and extrapolation of surface information of a plurality of primitive curved surfaces, thereby making it possible to create various curved surfaces. , which can respond to continuous changes in the curved surface.

C. Conventional Technology Curved surface creation devices for computer graphics are used in animation creation devices and special effects devices. Conventionally, the surface creation method applied by this type of surface creation device is to prepare data for basic curved surfaces such as cylinders and spheres (these are called primitive surfaces) in advance, and then to create these primitive surfaces as needed. You can use methods such as creating a new surface by combining them according to the method, or specifying the second point of the new surface to be created as a control point and interpolating the surface passing through these control points using a spline function. (methods, etc.) are used.

D Problems to be Solved by the Invention In these conventional methods, a desired curved surface is obtained by using the external shape of an actual primitive curved surface as a basic shape and converting the curved surface based on the basic shape. It is believed that it is possible to create a satisfactory curved surface as long as it is applied to expressing the appearance and shape of mechanical objects such as practical vehicles.

Incidentally, even when creating a curved surface using a spline function, it is actually necessary to set a large number of control points I-, so in order to form the large number of control points, it is necessary to use a primitive curved surface,
Control points are set within a practically acceptable range by combining cross-sectional views, and therefore, in this case as well, practical soil has the same characteristics as when combining Primilive curved surfaces.

As shown below, in the conventional surface creation method, a new surface is created by combining primitive surfaces, so the set of newly formed surfaces is limited, and it is difficult for the operator to create the surface as intended. In many cases, it is not possible to create one.

Also, if the set of newly formed curved surfaces is limited,
Even if this curved surface creation device is applied to an animation creation device or a special effects device, it may not be possible to obtain smooth curved surface deformation, and the applicable curved surface deformation patterns are 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
It is an object of the present invention to provide a curved surface creation device that can easily respond to the creation of continuously changing curved surfaces.

E Means for Solving the Problem In order to solve this problem, the present invention uses a plurality of pre-formed primitive curved surfaces P.

The surface information of ~P, , and each primitive curved surface Pl~P,
The product-sum calculation means (21 to general, 3) executes the product-sum calculation with the multiple interpolation-extrapolation coefficients II to In corresponding to A curved surface P is created.

F action A plurality of primitive curved surfaces P1 to P1 are represented by a set of positional information of points on the surface, and if the number of points on each curved surface is the same, the information of the plurality of primitive curved surfaces P, -P, is expressed as a corresponding image. ] You can do it.

When position information of corresponding points on two primitive curved surfaces is internally or externally divided (hereinafter referred to as interpolation and extrapolation in this section),
A curved surface consisting of a set of points having new position information can be obtained.

This interpolation/extrapolation process can be applied to multiple primitive surfaces,
By repeating the process on the created curved surface, various curved surfaces can be obtained. Here, repeating the interpolation/extrapolation process multiple times means that the plurality of primitive curved surfaces P is used in the relationship between the final curved surface P and the plurality of primitive curved surfaces P1 to P7.

This is similar to obtaining the final curved surface P by performing a product-sum operation of the information of ~P7 and the corresponding multiple interpolation and extrapolation coefficients 11~In.

Therefore, the product-sum calculation means (2+ to 2.l, 3) are configured to execute the product-sum calculation (see equation (12)).

G example Hereinafter, one embodiment of the present invention will be described in detail with reference to the drawings.

(G1) Principle applied by the wooden curved surface creation device First, the present invention will be explained in detail. The present invention, as shown in FIG. 2 (A>),
Interpolation or extrapolation of two primitive surfaces pm and pb (a surface is represented by a set of position vectors of points on the surface) (internally or externally dividing the corresponding points of biconvex surfaces P, , P) By doing this, a new created surface Pab is obtained. Therefore, the newly created curved surface Pab can be expressed by the following formula (1). Here, I( is an interpolation-extrapolation coefficient and represents interpolation when the value is in the range of the following formula % formula % (2), and the following formula k < 0, l < k ...... (3)
It represents extrapolation when the value is in the range of .

By selecting this interpolation-extrapolation coefficient k to a predetermined value, one newly created curved surface pub can be obtained.

Therefore, various newly created surfaces P and b can be obtained from the two primitive surfaces p, Pb, according to the interpolation-extrapolation coefficient k.

For example, if the interpolation coefficient k is selected to be 0.5 and interpolation is performed, the first primitive curved surface P has a cylindrical shape.

from the second spherical primitive curved surface Pb in Fig. 2 (B
), a substantially barrel-shaped curved surface Pmbi with a bulging body can be obtained as a newly created curved surface, which retains the information of the original primitive curved surface. In addition, even if the same primitive curved surfaces P,
As shown by the broken line in , and as shown in FIG. 2(A), it is possible to obtain a curved surface p abo that is approximately in the shape of a drum and has a concave central portion, which is unexpected from the original primitive curved surface.

Here, the corresponding points of the two primitive curved surfaces pH,'p can be determined as follows.

All primitive surfaces stored in the surface database have a fixed number (for example, 600), regardless of the surface shape.
) is represented by a set of position vectors of points. For example, the third
As shown in Figure (A), a grid pattern is drawn on the original screen IMP, and by deforming it, a spherical or cylindrical primitive curved surface Pllc as shown in Figures 3 (B) and (C) is created.
% When pbe is created, position back 1 of the post-transformation position of the intersection point (hereinafter referred to as grid point) CR3 on the original screen IMP
It can be expressed as a set of Hell. Therefore, the original screen I
Points on the primitive curved surface Pllc%Pbc obtained by deforming the same lattice point on MP become corresponding points.

Primitive surfaces p ac, Pb for the original screen IMF
The mapping with C is not uniquely defined; for example, as shown in Figure 4 (A), one coordinate axis direction,
That is, mapping may be performed so that the deformation points PCH of the grid point CR3 are equally spaced in the y direction.
), mapping may be performed so that the deformation points PCH of the lattice point CR5 are equally spaced on the primitive curved surfaces P and Pbc.

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

In this way, when creating a new created surface from two surfaces by interpolation and extrapolation, the source surface does not have to be limited to a primitive surface, and a surface that has already been created by interpolation and extrapolation can be used. You can also do that.

Therefore, for example, as shown in FIG. 5, a drum-shaped created surface PAR is obtained by interpolation and extrapolation from a cylindrical primitive curved surface PA and a spherical primitive curved surface PI (first step), and this created curved surface P□ By interpolation and extrapolation from and the conical primitive curved surface Pc, a trumpet-shaped curved surface PAll that gradually expands from one end to the other end is created.
c (second step), and furthermore, this created surface PAI
By interpolation and extrapolation from C and a roughly cylindrical primitive curved surface P with repeated unevenness in the axial direction on the side surface, the surface gradually expands from one end to the other end and the side surface has repeated unevenness. It is also possible to obtain the created curved surface P All CD (third step).

That is, by repeating interpolation and extrapolation several times (hereinafter referred to as multiple interpolation and extrapolation), multiple primitive curved surfaces PA
, Pg , Pc , Pn to create a desired surface P All
You can get a CD.

Here, in the modification shown in Fig. 5, let α be the interpolation-extrapolation coefficient in the first step, β be the interpolation-extrapolation coefficient in the second step, and γ be the interpolation-extrapolation coefficient in the third step. Created surface P in 41% PAII
C% PAmco can be expressed by the following formula 1 (4).

By substituting equations (4) and (5) into equation (6) and arranging them, the final created surface PAllcD is expressed as the following equation 1%.
It can be expressed as the sum of products of Pl, multiple interpolation coefficient IA, summer 5, and IC1ID. Here, multiple interpolation extrapolation coefficient IA
, 1. ．． IC,in are each expressed by the following formula 1 % (1 Therefore, by generalizing formula (7), n multiple interpolation and extrapolation from n primitive surfaces P+ , Pz...P, , A new created surface P is created by multiple interpolation and extrapolation by appropriately selecting the values of the interpolation coefficients II, I2, ...In and executing the product-sum operation of the following formula % formula % (12) I know what I can do.

(G2) An embodiment of the curved surface creation apparatus according to the present invention to which the curved surface creation principle described above is applied is shown in FIG.

In FIG. 1, n large-capacity primitive surface information memories 10.1□, . p, , p, ,...
・P, , is stored, and this primitive surface information f
Ilp, , Pg, . . . P7 are respectively applied to corresponding multipliers 23.2□, . . . 2 as first multiplication inputs. Each multiplier 28.2□,...
. . 2n are multiple interpolation and extrapolation coefficients 1. ．． 12,...
I7 is given.

Thus, from each multiplier 23.2□,...27,
Each primitive surface information P+, Pz,...P7
and the corresponding multiple interpolation and extrapolation coefficients ■1, I2,...
I.

The multiplication value 1+ P+ , It P2 , "'-I-p
H is obtained, which is applied to the adder 3, respectively.

The adder 3 receives each of the given multiplication values I, P1, l2P2, .
... Find the sum of I and Pn, that is, (
12) Calculate the equation to obtain new created surface information P by multiple interpolation and extrapolation, and give it to the created surface information memory 4 for storage.

In the above configuration, the predetermined primitive curved surfaces P1, P2,...P7 are selected by the operator, and the primitive curved surface information memory 11.1□,...1
．． , and predetermined multiple interpolation and extrapolation coefficients 1+, Iz, . . . ■ by the operator. is selected, the surface creation device uses multiplier 2. ~2n and the adder 3 execute the product-sum operation of equation (12) to create the desired created surface P.

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

Incidentally, if there is an unnecessary primitive curved surface when creating the desired curved surface P, the multiple interpolation and extrapolation coefficient corresponding to the primitive curved surface may be set to zero.

According to the above-described embodiment, the selection of the primitive surfaces PI to Pゎ can be changed, and the multiple interpolation and extrapolation coefficients can be changed! 1-I
By changing the value of 7, various new curved surfaces can be obtained. In addition, by continuously changing the multiple interpolation and extrapolation coefficients ■1 to ■7, a continuously changing curved surface can be obtained, making it easy for animation creation devices and special effects devices that require continuously changing curved surfaces. can be accommodated.

In this case, if the multipliers 21 to 2 and the adder 3 are configured with parallel processors to increase the speed, the operator can process the multiple interpolation and extrapolation coefficients II to 1. It is possible to respond in real time when changes occur.

(G3) Animation creation device to which the present curved surface creation device is applied Next, regarding FIG. 6, an example in which the curved surface creation device of the present invention is applied to an animation creation device is shown by assigning the same reference numerals to corresponding parts as in FIG. 1. explain.

In FIG. 6, the host computer 10 as an animation creation control device has N (
A primitive curved surface database 11 consisting of, for example, a hard disk is provided which stores N>n) different primitive curved surfaces, and the post computer 10 selects n primitive curved surfaces in response to a surface selection signal received from the keyboard input device 12. P,,P, ,・・・・・・
Select P and l and save the surface information memory 1. ．． 1. ,...
...Stored in IR.

In addition, as shown in FIG. 8, the host computer 10 also uses a trackball device f as a key frame input device for inputting curved surface images (hereinafter referred to as key frames) KYI to KY5 that are keys in animation changes.
l has 3. The trackball device 13 has a time axis setting mode selection button 13a for selecting a time axis setting mode for setting positions t1-t5 on the time axis AXS of key frames KYI to KY5, and a viewpoint for viewing the creation curved surface of key frames KYI to KY5. A viewpoint movement mode selection button 13b for selecting a viewpoint movement mode for changing the position, and multiple interpolation and extrapolation coefficients ■, ~ at key frames KYI to KY5.
■Multiple interpolation and extrapolation coefficient memory 14 whose details are shown in Fig. 9.
It has a key frame registration button 13c for recording. Further, when the time axis setting mode is selected, the trackball device 13 rotates to set the time axis A.
It has a trackball 13d that moves the XS and rotates to move the viewpoint when the viewpoint movement mode is selected.

Further, a display device 15 is connected to the host computer 10. The display device 15 displays the created curved surface P (key frame KYI) stored in the curved surface information memory 4 for created curved surfaces.
~KY5), and the time axis AXS is displayed, for example, on the lower side of the screen.

When the time axis setting mode selection button 13a is operated, a cursor 16 is displayed close to the time axis AXS displayed on the display surface of the display device 15, and by rotating the trackball 13d, the cursor 16 is moved to the time axis AXS. It is possible to move along the AXS and select a key frame point.

Furthermore, the host computer 10 has multiple interpolation and extrapolation coefficients 1. , Ig, . . . n levers 1711172, . . . 17° for setting the bow are provided. When the key frame registration button 13c is pressed, The setting values of the levers 171 to 17n are stored in the multiple interpolation and extrapolation coefficient memory 14 as the multiple interpolation and extrapolation coefficients 1 to 1 to specify the surface for creating a key frame at the point specified by the cursor 16. being done.

Here, the multiple interpolation and extrapolation coefficient memory 14 stores, for example, multiple interpolation and extrapolation coefficients 1 to T for each frame, as shown in FIG.
It memorizes the settings made by levers 171 to 1711 for keep [/-), frames KYI to KY5, Fv+-Ftz, ......Fts, and also stores key frames other than key frames KYI to KY5. For frames, the multiple interpolation-extrapolation coefficients of the closest keyframes before the relevant frame and the multiple interpolation-extrapolation coefficients of -1, which is the closest to the frame after the relevant frame, are combined with those keyframes. The host computer 10 performs interpolation calculations according to time and stores them. Therefore, multiple interpolation and extrapolation coefficient memory 14
Multiple interpolation and extrapolation coefficients 11~ between adjacent frames in
In is different only to the extent that the curved surface deformation appears sufficiently smooth when visually observed.

The boss computer 10 also has a viewpoint position information memory 18 that stores viewpoint position information for each frame, for example, and this viewpoint position information memory 18 stores the viewpoint position information obtained by the trackball 13d when the key frame registration button 13C is pressed. is stored, and for frames other than key frames, viewpoint position information obtained by interpolating the viewpoint position information of each frame by the boss 7 viewer 10 is stored, similarly to the multiple interpolation and extrapolation coefficient memory 14. Ru.

In the following configuration, animation creation is the 10th step.
This is carried out according to the processing procedure shown in the figure.

That is, when the process is started in step SPI, in the next step SP2, the host computer 10 selects n primitive surfaces to be used for animation selected by the operator via the keyboard input device 12 from N primitive surfaces stored in the primitive surface database 11. The primitive curved surfaces Pl, P2, . . . P, l are stored in the surface information memories 1° to 1o.

After that, the operation! When the time axis setting mode selection button], 3 a is pressed, the next step S l)3
, display the cursor I6 on the display device 15F, move the cursor 16 according to the rotation of the trackball 13d, and set the time point on the time axis AXS, h at which the cursor ]6 stopped as the first key frame KYIO time point t1. Set.

Almost parallel to step SP3 of the host computer 10, in step SP4, the levers 171-1
The created curved surface P based on the multiple interpolation and extrapolation coefficients 11 to I given from 77 is displayed on the display device 15. At this time, lever 17. 17, 1 is operated by the operator, the created curved surface P is transformed and displayed accordingly. Further, when the operator presses the viewpoint movement mode selection button 13b and then rotates the trackball 13d, a curved surface obtained by moving the viewpoint and viewing the curved surface P created by the multiple interpolation and extrapolation coefficients is displayed.

In this way, the surface of the key frame KYI has a multiple interpolation and extrapolation coefficient of 1. ~I7 and the viewpoint position are selected and determined in step SP4, the operator presses the key frame registration button 13C.

This causes the host computer 10 to perform the next step S.
At P5, the multiple interpolation/extrapolation coefficients I, ~7 at that time are stored in the frame field Ft+ corresponding to time t1 of the multiple interpolation/extrapolation coefficient memory 14, and the viewpoint position information is similarly stored in the viewpoint position information memory 18. is stored in that frame field.

Next, the host computer 10 determines whether the next key frame is specified in step S6. If a positive result is obtained, the process returns to step SP3 described above, and steps SP3 to SP5 are executed to determine and register the surface of the next key frame KY2. For example, as shown in FIG. 8, when five key frames KYI to KY5 are determined and registered, the process of steps SP3 to SP5 is repeated five times to register the five frames.

When surface determination and non-registration operations for all key frames KYI to KY5 to be set are completed, and an end command is given by the operator via the keyboard input device 12, for example, to indicate that the manual operation of the key frames has ended, the host computer 10 moves to the next step SP7 and calculates the multiple interpolation and extrapolation coefficient ■1 for each frame between key frames.
~ I, l and viewpoint position information are obtained through multiple interpolation of key frames (interpolation coefficients and viewpoint position information are interpolated and obtained sequentially, and stored in the multiple interpolation extrapolation coefficient memory 14 and viewpoint position information memory 18, respectively) Then, the process ends at step SP8.

Next, based on such a processing procedure, as shown in Fig. 8, a rectangular curved surface is rounded so that a pair of opposing edges gradually approach each other, and both edges are kept at a predetermined distance from each other. From this point onwards, it becomes rounded and the center becomes concave, and from the point at which both edges overlap to form a drum-shaped curved surface, the upper part narrows and the lower part widens, and from the point at which a trumpet-shaped curved surface is obtained. This explains the case where an animation is created in which the side surface changes as unevenness is gradually repeated in the axial direction. Note that in this case, the viewpoint position is always fixed.

In this case, the operator selects the primitive surfaces necessary to create each surface in this series of animations,
That is, n primitive curved surfaces P1 to 1 include a cylindrical curved surface P1, a spherical curved surface P2, a conical curved surface P3, a rectangular curved surface P4, and a cylindrical curved surface P1 having unevenness on the side surface shown in FIG. Select P9, keyboard input bag M12
The primitive curved surface information memory II-1. Store it in l.

Next, the operator presses the time axis setting mode selection button 13.
After pressing a, rotate the trackball 13d to determine the time t1 for setting the rectangular curved surface (key frame) KYI that is the starting curved surface, and then move the levers 17+ to 17.
．． , to obtain the curved surface of the key frame KY1 while visually checking the display device 15. At this point t
1, the primitive surface P4 directly becomes the key frame KYI, so among the multiple interpolation-extrapolation coefficients, the one (■,) corresponding to the primitive surface P4 is 1, and the other multiple interpolation-extrapolation coefficients II~ Turn the levers 171 to 17 so that Is, Is to ■7 become 0. All you have to do is operate.

Thereafter, by pressing the key frame registration button 13c, the coefficients 11 to Ill are stored in the memory area of the multiple interpolation/extrapolation coefficient memory 14 corresponding to time t1.

Next, in a series of changes, the operator determines and registers the curved surface of key frame KY2, which is the next key after the rectangular shadow shape. Both ends of the rectangular shape are rounded, and the curved surface of the shape that approaches a predetermined distance is set as the second key frame K.
Y2, the operator selects the first keyframe KYI
After pressing the time axis setting mode selection button 13a, taking into consideration the time t1 to t2 required for the change from to the second key frame KY2, rotate the track pole 13d to move the cursor 16. , time t2 is set.

Thereafter, the levers 171 to 17 are operated to obtain the curved surface 2 at a desired key frame, and when 2 is displayed on the display device 15 at the desired key frame, the key frame registration button 13c is pressed. This allows multiple interpolation and extrapolation coefficient memory 14
The values of the levers 171 to 17a at that time are stored in the frame field FLZ corresponding to the time t2. Here, the curved surface of the key frame KY2 is, for example, a cylindrical primitive curved surface P1 and a rectangular primitive curved surface P4.
Since it is obtained by interpolating in units of 5, the contents stored in the memory 14 at that time are 0.5 for the coefficients 1t and Ia, and 0 for the other coefficients It, I3, and Is~17.

Thereafter, in the same way, the operator registers the drum-shaped curved surface as the third key frame KY3 at time t3, registers the trumpet-shaped curved surface as the fourth key frame KY4 at time t4, and registers the trumpet-shaped curved surface as the fourth key frame KY4 at time t5. The trumpet-shaped curved surface is registered as the last key frame KY5.

After registering this last key frame KY5, the operator instructs the end of the input operation via the keyboard input device 12. In this way, host computer 1
0 is the multiple interpolation and extrapolation coefficients 11 to 1.0 by interpolating the key frame multiple interpolation and extrapolation coefficients 11 to 1. is calculated and stored in the memory 14. For example, for the frame at the intermediate time point t34 between key frames KY3 and KY4, as shown in FIG.
110.0,..., O and key frame KY4
The multiple interpolation coefficient ■, ~1. The value of 1, -0.5.0.
5, O,..., intermediate value between 0 and 1.5, -0.
75.0.25.0, ..., 0 is memory 14
is stored in

By reading out the multiple interpolation and extrapolation coefficients ■1 to I stored in the multiple interpolation and extrapolation coefficient memory 14 in this way for each frame and displaying the curved surface P created by the coefficients, the rectangular shape An animation that gradually changes from a curved surface (KYl) to a trumpet-shaped curved surface (KY5) having unevenness on the side surface can be obtained.

In this way, according to the animation creation device to which the curved surface creation device according to the present invention is applied, it is possible to obtain an animation image that changes continuously and smoothly.

Therefore, multiplier 2. ~2ゎ and if adder 3 is configured with a parallel processor, multiple interpolation and extrapolation coefficients 11~■,
And even if the viewpoint position information changes from frame to frame, frame 1
, it is possible to obtain curved surfaces created in real time for each time, and real-time animation can be easily realized.

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

H Effects of the Invention As described above, according to the present invention, a new surface is created by multiple interpolation/extrapolation of multiple primitive surfaces. It is possible to create various curved surfaces by selecting coefficients, and it is easy to use for devices that require continuous and smoothly changing curved surfaces by continuously changing the multiple interpolation and extrapolation coefficients. It is possible to obtain a curved surface creation device that can meet the requirements.

[Brief explanation of drawings]

Fig. 1 is a block diagram showing an embodiment of a curved surface creation device according to the present invention, Fig. 2 is a route diagram for explaining interpolation and extrapolation of two primitive curved surfaces, and Figs. 3 and 4 are interpolation and extrapolation. A route map for explaining the correspondence of points on a primitive curved surface for interpolation, Figure 5 is a route map for explaining multiple interpolation and extrapolation of multiple primitive curved surfaces, and Figure 6 is an animation creation using the present invention. Figure 7 is a route map that does not show the equipment, Figure 7 is a route map that does not show how to select primitive surfaces, Figure 8 is a route map that shows the relationship between key frames and time axis, and Figure 9 is a multiple interpolation and extrapolation coefficient memory. Route map for explaining the memory contents of 10th
The figure is a flowchart showing the animation creation procedure. ■, ~17... Primitive surface information memory,
21-2□... Multiplier, 3... Adder, 4... Creation surface information memory, P, ~P, l.
...Primitive surface (primitive surface information)
, P... Creation surface (creation surface information), ■1 to I
,,...Multiple interpolation and extrapolation coefficients.

Claims (1)

[Claims] A product-sum calculation means executes a product-sum calculation of surface information of a plurality of pre-formed primitive surfaces and multiple interpolation-extrapolation coefficients corresponding to each of the primitive surfaces, thereby performing multiple interpolation of the plurality of primitive surfaces. A curved surface creation device characterized in that a new curved surface is created by extrapolation.