JPH11213175A - Production of program and program recording medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To produce an object program including a part to calculate a three- dimensional rotary matrix by using data of a four-way number to represent each position of a three-dimensional object. SOLUTION: A source program including the part to calculate the three- dimensional rotary matrix is generated by using data on the Euler angle provided from a motion capture 100, the data is transformed to the data of four- way number (16) when the data is compiled, the source program is transformed to the object program (170 and a library to calculate the three-dimensional rotary matrix by using the data of four-way number is incorporated in the object program as it is.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[0001] The present invention relates to a program manufacturing method for manufacturing an animation program for executing an animation or the like using a three-dimensional rotation matrix.

[0002]

2. Description of the Related Art In order to create an animation program, data representing a three-dimensional position of a three-dimensional object to be modeled and data representing a three-dimensional angular position are taken by using a measuring device called a motion capture. Make an exercise model. In the motion capture, data representing the Euler angle of an object is generally output as data representing a three-dimensional angular position of the object from a historical background. In order to change and display the position and angle of the object, it is necessary to calculate a three-dimensional rotation matrix related to the three-dimensional angular position of the object.

To calculate a three-dimensional rotation matrix using Euler angles, it is necessary to calculate trigonometric functions of sine and cosine with respect to the Euler angles. When a trigonometric function is calculated using a general arithmetic unit capable of executing the four arithmetic operations, it takes a long calculation time.

A table storing the values of trigonometric functions calculated in advance for various Euler angles is prepared as an arithmetic unit. When calculating the value of a trigonometric function at a certain Euler angle, this table is referred to and the trigonometric function is referred to. A method of calculating a function value at high speed is also known. However, storing the table requires a large-capacity memory.

As another method for calculating a three-dimensional rotation matrix at high speed, a method of calculating a trigonometric function by an approximate polynomial is known. An arithmetic unit for calculating an approximate polynomial at high speed can be realized by a relatively compact circuit.

On the other hand, a quaternion is known as another data representing a three-dimensional angular position of an object. It is known that when the angular position is represented by this quaternion, a three-dimensional rotation matrix can be calculated only by addition and subtraction and multiplication without using a trigonometric function (for example, S. Shoemake: Animating Rotation with Qua
ternion Curves, Proc.Siggraph '85, Computer Graph
ics, Vol. 19, No. 3, pp. 245-254, 1985).

[0007]

Problems to be Solved by the Invention 3
Conventional methods of calculating the dimensional rotation matrix are computationally time consuming or require relatively large circuits. The arithmetic unit required by the conventional method of calculating a trigonometric function by an approximate polynomial can be realized by a relatively compact circuit.
However, an arithmetic unit that requires a method of calculating a three-dimensional rotation matrix using a quaternion is simpler. On the other hand, motion capture, which is currently often used for creating animation programs, outputs Euler angle data as data representing a three-dimensional angular position of an object. Therefore, it is desirable that an animation program can be manufactured using the Euler angle data output by the motion capture. Alternatively, it is desirable that motion capture be improved so that quaternion data can be output as data representing a three-dimensional angular position of an object, and an animation program can be manufactured using the output.

[0008] Therefore, the object of the present invention is to provide an object 3
Including Euler angle data as data representing a three-dimensional angular position of an object, which can be conventionally created using motion capture that outputs Euler angle data as data representing a three-dimensional angular position, An object of the present invention is to provide a method for producing an animation program including a part for calculating a three-dimensional rotation matrix using a quaternion from a source program for animation including a part for calculating a three-dimensional rotation matrix using the same.

It is another object of the present invention to provide a method for producing an animation program for calculating a three-dimensional rotation matrix using motion capture capable of outputting a quaternion.

Still another object of the present invention is to include a part for calculating a three-dimensional rotation matrix using an Euler angle, a part for calculating a three-dimensional rotation matrix using a source program for animation or a quaternion. An object program that calculates a three-dimensional rotation matrix using an arithmetic unit that can calculate the value of a trigonometric function from an animation source program at a relatively high speed, or a three-dimensional object using addition, subtraction, and multiplication of quaternion data It is an object of the present invention to provide a program manufacturing method capable of manufacturing by switching an object program for calculating a rotation matrix.

[0011] Other objects of the present invention will be more apparent from the embodiments described below.

[0012]

A first aspect of the present invention is directed to an animation for animation including Euler angle data representing a three-dimensional angular position of an object and including a part for calculating a three-dimensional rotation matrix using the data. Use the source program of the above as the source program.

First, the Euler angle data is converted into quaternion data representing the same angular position. This conversion is performed, for example, when compiling the source program. Thereafter, the source program is converted into an object program including a part for calculating a three-dimensional rotation matrix using the obtained quaternion data, thereby producing an animation program.

Since the data is provided from a conventionally available motion capture, the source program can be created using such a conventional motion capture. Therefore, according to the first aspect of the present invention, an object program including a part for calculating a three-dimensional rotation matrix using quaternion data while using a source program created using such motion capture Can be manufactured.

Further, in the second invention of the present application, motion capture for outputting quaternion data as data representing a three-dimensional angular position of a three-dimensional object used as a model is used. This data is repeatedly captured by a computer by changing the angular position of the object. A source program for animation including a part for calculating a three-dimensional rotation matrix using quaternion data obtained by each capture is generated by an operator operation on a computer. Then, the source program is converted into a corresponding object program by a computer so as to include a part for calculating the three-dimensional rotation matrix by addition, subtraction, and multiplication of quaternion data, thereby producing an animation program. By using the new motion capture in this manner, an object program including a part for calculating a three-dimensional rotation matrix using quaternion data can be easily manufactured.

Further, the third invention of the present application provides an animation source program including Euler angle data representing a three-dimensional angular position of an object and including a part for calculating a three-dimensional rotation matrix using the data. Any of the animation source programs including a quaternion data representing a three-dimensional angular position of an object and a part for calculating a three-dimensional rotation matrix using the data may be used as a source program. forgive. The computer executes one of the following two steps (a) and (b) on these source programs.

(A) When the data is Euler angle data, the Euler angle data is converted into quaternion data representing the same angular position before an object program corresponding to the source program is manufactured. .

An object program including a part for calculating a three-dimensional rotation matrix using addition, subtraction, and multiplication with respect to quaternion data obtained by the conversion is manufactured from the source program after the conversion.

(B) When the data is quaternion data, an object program including a part for calculating a three-dimensional rotation matrix by using addition, subtraction, and multiplication on the quaternion data, Convert the program.

By executing one of the above steps (a) and (b) in this manner, from either of these two types of source programs, three types of data can be obtained by using addition and subtraction and multiplication using quaternion data. An object program including a part for calculating a dimensional rotation matrix can be manufactured.

Further, in the fourth invention of the present application, one of the following two steps (a) and (b) is executed by a computer for the two types of source programs used in the third invention.

(A) Using the arithmetic unit as an object program, calculate a plurality of trigonometric functions for the Euler angle data, and calculate a three-dimensional rotation matrix using the calculated values. Convert the above source program to one containing the part.

(B) converting the Euler angle data to quaternion data representing the same angular position before manufacturing an object program corresponding to the source program;
Further, the source program is converted into an object program including a part for calculating a three-dimensional rotation matrix by using addition, subtraction, and multiplication on quaternion data obtained by the conversion.

As a result, from either of the above two types of source programs, two types of computers can be executed by a computer using an arithmetic unit capable of calculating the value of the trigonometric function at a relatively high speed and a computer not using the arithmetic unit. It can be manufactured by switching object programs.

Further, in the fifth invention of the present application, the following three steps (a) and (b) are executed by a computer for the two types of source programs used in the third invention of the present application.
Execute one of (c).

(A) When the data is Euler angle data, a plurality of trigonometric function values for the Euler angle data are calculated using the arithmetic unit, and further, the calculated values are used. Then, the source program is converted into an object program including a part for calculating a three-dimensional rotation matrix.

(B) When the data is Euler angle data, the Euler angle data is converted into quaternion data representing the same angular position before manufacturing an object program corresponding to the source program. The source program is converted into an object program including a part for calculating a three-dimensional rotation matrix by using addition, subtraction, and multiplication on quaternion data obtained by the conversion.

(C) When the data is quaternion data, an object program including a part for calculating a three-dimensional rotation matrix by using addition, subtraction and multiplication on the quaternion data, Convert the program.

As a result, when the data included in the source program is Euler angle data, an object program for a computer using an arithmetic unit capable of calculating the value of a trigonometric function at a relatively high speed and the use of the arithmetic unit An object program for a computer that does not use a computer can be manufactured from the source program, and when the data included in the source program is quaternion data, an object program that can be executed by a computer that does not use the arithmetic unit can be manufactured.

[0030]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Before describing an embodiment of the present invention, two kinds of parameters, ie, Euler angles and quaternions, representing three-dimensional angular positions of an object and a three-dimensional rotation matrix will be described. .

The Euler angle is an angle formed between a three-dimensional coordinate axis defined on the object and a coordinate axis stationary in space. Specifically, as shown in FIG. 2, the rotation O of the object (rigid body) is fixed. It is assumed that the stationary coordinate system (x, y, z) fixed in space and the coordinate axes (ξ, η,
ζ), the angle formed by the ζ axis with respect to the z axis is θ,
An angle formed by an intersection line OL between the xy plane and the ξ plane with respect to the η axis is defined as ψ, and an angle formed with respect to the y axis is defined as φ. These angles are called Euler angles. However, although there are various ways of determining the Euler angle, any Euler angle can be used in the present invention. As shown in FIG. 3, these angles φ,
θ and ψ can be considered as a rotation angle around the z axis, a rotation angle around the y axis, and a rotation angle around the ζ axis, respectively. For each rotation, the coordinates (x, y, z) are (ξ, η,
ζ) to convert to three-dimensional matrix Rz (φ), Ry
(Θ), Rζ (ψ) are defined. These matrices are shown in FIG.
As shown in FIG. Therefore, three angles φ, θ,
When all the rotations by ψ are performed, a three-dimensional rotation matrix R for this rotation is given by a product Rζ (ψ) Ry (θ) Rz (φ) of these three matrices as shown in FIG. Can be The coordinates (x, y,
By multiplying by z), the coordinates (ξ, η, ζ) on the rotated object are obtained.

The quaternion consists of four parameters representing the angular position of a rotating object, and is well known per se. Usually, a quaternion is often represented by four parameters (w, x, y, z). Here, x, y, and z are stationary coordinates (x, y, z).
y, z).

A specific quaternion (w, x, y, z) corresponds to a specific Euler angle (φ, θ, ψ). The relationship between the two is as shown in FIG. When a quaternion (w, x, y, z) is used for the three-dimensional rotation matrix, FIG.
It is expressed as (c). As can be seen, each element of the three-dimensional rotation matrix can be calculated by addition, subtraction, and multiplication, and can be calculated at a high speed by an arithmetic unit in an ordinary computer without using a special arithmetic unit.

Hereinafter, the program manufacturing method according to the present invention will be described in more detail with reference to some embodiments shown in the drawings. In the following, the same reference numerals represent the same or similar ones. Also,
In the second and subsequent embodiments of the invention, only the differences from the first embodiment of the invention will be mainly described.

<Embodiment 1> In the present embodiment, a motion capture which outputs Euler angle data representing a three-dimensional angular position of a model object is used, and Euler angle data output therefrom is used. , A source program for animation is generated so as to include a part for calculating a three-dimensional rotation matrix. The source program is converted into an object program including a part for calculating a three-dimensional rotation matrix by addition, subtraction, and multiplication using quaternion data corresponding to the Euler angle data. This provides an object program that calculates a three-dimensional rotation matrix by addition, subtraction and multiplication while using conventional motion capture.

In FIG. 1, motion capture 1
Reference numeral 00 denotes an apparatus that outputs Euler angle data representing a three-dimensional angular position of a model object. Specifically, the apparatus measures an image input unit 101 including a camera or the like that captures an object (not shown) to be a model, and measures the coordinates of each pixel of an output image of the image input unit 101. Image coordinate measurement analysis unit 102 for analyzing the coordinates of a plurality of representative points of the object and detecting the angular position of the object, and an Euler angle output conversion unit for converting the detected angular position of the object into Euler angle data and outputting the data 103.

The programmer of the animation program changes the position and orientation of the object manually or by another method, and sequentially loads the data representing the coordinates of the object and the data representing the angular position into the computer 200. The programmer creates a motion model of the object that he / she wants to use for the animation by repeating this loading.

The programmer prepares a source program for animation for displaying a moving image using this data,
An input is made to the computer 200 using the input device 260 and the display device 250. A program sentence for calculating a three-dimensional rotation matrix using the data taken into the computer 200 is also input. The source program 21 is written on the computer 300 using an intermediate language that does not depend on the model. For example, a high-level language such as C or an intermediate language such as Java may be used.

FIG. 5 schematically shows the source program 21 generated in this manner. Here, reference numeral 22 denotes Euler angle data taken from the motion capture 100, and reference numeral 29 denotes a call statement for calling a function rotate3d for calculating an element of a three-dimensional rotation matrix. Here, each call statement 29 has an argument dadd
Using r1 and daddr2, return values are stored in arrays r1 and r2.
Substitute for

FIG. 6 shows an example of such a source program described in the C language. Here, reference numeral 24 denotes a declaration statement for incorporating the function rotate3d for calculating a three-dimensional rotation matrix. Reference numeral 25 denotes a declaration sentence relating to the size of the data 22. For input parameters, an address pointer (daddr) where data is stored
To be specified. Then the number of parameters is 3
It is possible to cope with both cases. Array data data [LDAT for input parameters of a three-dimensional rotation matrix
A] (22) is secured by the array statement 26. Statement 25
Indicates the size of this array.

For a natural motion animation,
The programmer measures in advance the required rotational motion arrangement of the model by the motion capture 100. The layout of the drawing scene of the model is interactively determined, and the rotation operation of the model is selectively designated by the parameter daddr. A coordinate transformation is performed using the three-dimensional matrix calculated by the three-dimensional rotation matrix function, and a model is drawn. In practice, the calculation of the movement of the position of the model is performed in conjunction with the rotation calculation, and the above-described coordinate transformation is performed using the results of these two calculations. However, in this specification, the description of the movement calculation is omitted for simplification.

Statement 28 includes the sequence data [LDATA] 2
2. The address of the data to be quoted on
dr1 (or daddr2) is specified, and a three-dimensional rotation matrix calculation function rotate3d (daddr1 (or d
addr2)) (29) is a function for calculating the three-row, three-column component of the three-dimensional rotation matrix using the three components of the Euler angle data stored at the specified address.

Referring back to FIG. 1, the source program for animation produced in this manner is converted into an object program for calculating a three-dimensional rotation matrix using quaternion data by a compiler 400 running on a computer 300. I do. The compiler 400 first converts the Euler angle data 22 included in the source program into 4
The data is converted to the original number data (16). This conversion can be performed by the procedure shown in FIG. Three consecutive elements data (i) and data (i +
It is assumed that 1) and data (i + 2) (i = 0, 1, 2,...) Respectively hold three parameters (φ, θ, ψ) belonging to the same Euler angle. 1/2 of these three parameters, φ / 2, θ / 2, ψ / 2, si
Calculate n and cos. Thereafter, the corresponding quaternion (w, x, y, z) is calculated using the relational expression shown in FIG. 4 (b), and each of the quaternions is calculated as four consecutive elements tdata (j ), Tdata (j + 1), td
Data are stored in data (j + 2) and tdata (j + 3) (201, 202). Total number of elements of array data LDAT
4/3 times A is calculated as the total number of elements of the array tdata, and then the array tdata is copied to the array data (203). In this way, a new array tdata is obtained from the original array data, and finally the array data is updated.

Returning to FIG. 1, the source program is converted into an object program for a specific computer (17).

Thereafter, a library for calculating a three-dimensional rotation matrix based on a quaternion is incorporated into this object program (20). More specifically, for the source program of FIG.
The compiler 300 is prepared in advance to execute d. This library may perform a three-dimensional rotation matrix for quaternion data in accordance with FIG. Specifically, the data da of the quaternion obtained earlier is
ta may be performed as shown in FIG. The calculation of the elements r [1,1] to r [3,3] of the three-dimensional rotation matrix can be executed by multiplication and addition / subtraction as shown in FIG. Therefore, the animation object program created in this way can be executed at high speed even by a computer having no arithmetic unit for trigonometric functions.

As a result, a three-dimensional rotation matrix for quaternion data is calculated from a source program including Euler angle data output from motion capture and having a part for calculating a three-dimensional rotation matrix. An object program including a part can be manufactured.

It should be noted that the conversion of the array 20 may not be performed at the time of compilation, but may be performed earlier.
However, as in the present embodiment, it is easier to perform this conversion when compiling.

<Embodiment 2 of the Invention> In this embodiment, a novel motion capture that outputs quaternion data representing a three-dimensional angular position of a model object is used.
A source program for animation is generated so as to include a part for calculating a three-dimensional rotation matrix for the data output therefrom. The source program is converted into an object program including a part for calculating a three-dimensional rotation matrix by addition, subtraction, and multiplication using quaternion data. Thus, by using the new motion capture, an object program that calculates a three-dimensional rotation matrix by addition, subtraction, and multiplication is obtained.

In FIG. 9, motion capture 1
For 00, a quaternion output converter 104 is used instead of the Euler angle output converter 103 described above. The Euler angle output conversion unit 103 converts the output of the image coordinate measurement analysis unit 102 into Euler angle data. However, it is not possible to configure the quaternion output conversion unit 104 so that the former output becomes a quaternion. It is equally possible. The solution based on the quaternion is already known (for example, DW Eggert: Estim
ating 3-D rigid body transformations: a comparison
of four major algorithms, Machine Vision and Appl
ications, 1997, 9, pp. 272-290).

The subsequent creation of the source program is basically the same as that of the first embodiment except for the data output from the motion capture 100. At this time, the example of the source program created in the C language differs from that shown in FIG. 6 only in the value of each element of the array data and the number of elements.

When compiling the source program thus created by the compiler 400, it is not necessary to execute the data conversion procedure (16 (FIG. 1)) in the first embodiment, that is, the source program is converted into an object program. (17), then 4
A library for calculating a three-dimensional rotation matrix based on the element number may be incorporated into this object program (20).

As a result, a quaternion data is output from the motion capture, and a source program including this data and having a part for calculating a three-dimensional rotation matrix can be manufactured. Further, from this source program, an object program including a part for calculating a three-dimensional rotation matrix for quaternion data can be manufactured. Such an object program can be executed by a computer having no arithmetic unit for calculating a trigonometric function, as in the embodiment.

<Third Embodiment of the Invention>
Either the Euler angle data representing the three-dimensional angular position of the object used in the first embodiment or the quaternion data representing the three-dimensional angular position of the object used in the second embodiment From a source program including a part for calculating a three-dimensional rotation matrix using the data, a plurality of types of computers, in particular, a computer having a trigonometric function calculator and a computer not having one An executable object program for animation can be manufactured using the same compiler.

More specifically, the compiler of the present embodiment uses the Euler angle data and
From a first type source program including a part for calculating a three-dimensional rotation matrix, a first type object program for animation for calculating a three-dimensional rotation matrix using quaternion data can be manufactured. . This first type of object program can also calculate a three-dimensional rotation matrix at high speed even with a computer having no trigonometric function calculator.

Further, the compiler of the present embodiment can produce a second type of object program for calculating a three-dimensional rotation matrix from the first type of source program by using a trigonometric function calculator. it can. This object program can be executed by a computer having a trigonometric function calculator.

As described above, the compiler according to the present embodiment uses these two
By using the function of manufacturing various types of object programs, animation software of the same theme can be easily manufactured for different computers.

Further, the compiler according to the present embodiment
For an animation that calculates a three-dimensional rotation matrix using quaternion data from a second-type source program that includes data of an enumeration and a part that calculates a three-dimensional rotation matrix using the data Can be manufactured.

Therefore, the first type program can be manufactured from the first type source program and the second type source program by the same compiler. The first type of source program can be created using conventional motion capture. A second type of source program can be created using the new motion capture proposed in the second embodiment of the present invention. Therefore, the compiler according to the present embodiment can manufacture an object program using quaternion data from any source program.

Furthermore, the compiler according to the present embodiment, when producing a first-type object program, converts an object program that can be executed by a computer having no trigonometric function calculator into a computer program having no trigonometric function calculator. However, in practice, this object program can be configured by different codes corresponding to a plurality of computers having different architectures such as instruction systems. The compiler according to the present embodiment has a common feature in that when a second type of object program is manufactured, an object program that can be executed by a computer having a trigonometric function operation unit has a trigonometric function operation unit.
Actually, this object program can be constituted by different codes corresponding to a plurality of computers having different architectures such as an instruction system. Therefore, with these functions, an object program for animation of the same theme can be easily manufactured for various computers.

According to the present embodiment, even if the configuration of the arithmetic unit of each target computer is different from the others, and the format of the input parameters of the three-dimensional rotation matrix is different,
This is effective in unifying the development of an object program having a part for calculating a three-dimensional rotation matrix composed of codes corresponding to the respective target computers under a low-cost development environment such as a personal computer. It is also useful for easily porting animation software of the same title to these target computers.

In FIG. 10, the source program 21
Is manufactured using motion capture that outputs Euler angle data representing a three-dimensional angular position of the model object as in the first embodiment, or the model object is manufactured as in the second embodiment. It is manufactured using a motion capture that outputs quaternion data representing the three-dimensional angular position of. Unlike the first or second embodiment, the source program 21 includes various information 28 for specifying the conversion operation of the compiler 400. FIG. 10 includes, as an example, a sentence for identifying whether the data 22 included in the source program 21 is Euler angle data or quaternion data.

FIG. 11 shows a specific example of the source program 21, which is described in C language. Where the variable EUL
ER indicates whether the data 22 is Euler angle data or quaternion data. Variable SCSUP
Is that the computer that should use the compilation results is a sine,
It indicates whether or not there is a calculator for calculating a trigonometric function called cosine. This arithmetic unit may use a memory that stores the value of the trigonometric function, may calculate the value of the trigonometric function by polynomial approximation, or may be of another type. Furthermore, E
ULANG indicates whether or not to manufacture an object program that uses a computing unit when a computer that should use the compilation result has a computing unit for calculating trigonometric functions such as sine and cosine. MACN
Is an identification number assigned to a computer (target computer) that uses the result of the compiler 40. The operator causes the above-mentioned conversion operation designation information to be included in the source program 21 before or after newly creating the source program 21. Such information may be added to a source program that has already been created. Variables other than the identification number MACN have the value 1 or 0.

Returning to FIG. 10, a library group 8 for calculating a three-dimensional rotation matrix is prepared in the computer 300 in advance. Compiler 400 compiles source program 21 to produce one of object programs 23 to 27 for different computers. These include data 33 to 37 and appropriate libraries 93 to 97 included in library group 8.

As shown in FIG.
First, the user inputs the source program 21 (10).
It is determined whether the data 22 included in the source program 21 is Euler angle data or quaternion data (10).
This determination is made depending on whether the variable EULER is 0 or 1 in the case of the source program 21 in FIG. If the data 22 is an Euler angle, the compiler 400 determines whether or not the target computer includes a calculator for calculating trigonometric functions such as sine and cosine (12).
This determination is made in the case of the program of FIG.
This is performed depending on whether P is 1 or not. If the target computer does not have this operator, the compiler 400
Converts the data 21 into corresponding quaternion data (16). This conversion is performed in the same manner as in the first or second embodiment. After that, the source program 21 is converted into an object program consisting of codes corresponding to the target computer (17). This processing 17
Is executed in exactly the same manner as in the first embodiment. Note that the target computer is the program of FIG.
It is identified by the identification number MACN. Next, the obtained 4
A library for calculating a three-dimensional rotation matrix using the data of the element number is selected from the library group 8 (FIG. 11) and incorporated into the object program. In the case of the program shown in FIG. 11, the library prepared for the target computer determined by the identification number MACN is selected from the library group 8. This library also calculates the elements of this matrix using multiplication and addition / subtraction, as in the first embodiment. Thus, in the same manner as in the first embodiment, the three-dimensional rotation matrix is calculated from the Euler angle data and the source program for calculating the three-dimensional rotation matrix using the data using the quaternion data. An object program for the target computer to be calculated is manufactured.

As a result of the determination in step 11, the data 22
Are determined to be quaternion data, steps 17 and 20 are executed. As a result, in the same manner as in Embodiment 2, quaternion data and a source program for calculating a three-dimensional rotation matrix using the data,
Calculate a three-dimensional rotation matrix using the data of the element numbers,
An object program for the target computer is manufactured.

As a result of the determination in step 12, when it is determined that the above-described arithmetic unit is included in the target computer, the compiler 400 determines whether or not to manufacture an object program using the arithmetic unit. (1
3). In the case of the program shown in FIG.
This is performed based on the value of ULANG. If an object program using the arithmetic unit is not manufactured, steps 17 and 20 described above are executed.

When it is determined in step 13 that an object program using the above-described arithmetic unit is manufactured, the compiler 400 calculates the sine and cosine of the three parameters of the Euler angles using the arithmetic unit. Then, a library prepared for the target computer for calculating a three-dimensional rotation matrix using the calculation results is incorporated in the object program (19). This library may calculate a three-dimensional rotation matrix according to FIG. More specifically, the calculation may be performed using the data 22 as shown in FIG.

Thus, the source program including the Euler angle data and the part for calculating the three-dimensional rotation matrix using the data includes the part for calculating the three-dimensional rotation matrix using the arithmetic unit. An object program is manufactured. This object can be used when it is desired to execute the source program 21 by a computer having the arithmetic unit.

The conversion operation specifying information may be specified by the user by another method instead of the information included in the source program shown in FIG. For example, compiler 400
However, a user of the compiler may input information necessary for determinations 11, 12, and 13 by using a display device and an input device (both not shown) connected to the computer 300.

<Embodiment 4> Embodiments 1 and 2
Alternatively, in 3, in the generated object program, a part for calculating a three-dimensional rotation matrix using quaternion data can be executed by multiplication and addition / subtraction, and is usually included in a computer. It is described that the processing is executed at high speed by using an arithmetic unit. In the present embodiment, 4
Provided is an arithmetic unit for calculating a three-dimensional rotation matrix based on an element at a higher speed. When this arithmetic unit is included in a computer that executes the object program, the calculation of the matrix can be performed at higher speed.

In FIG. 14, the arithmetic unit comprises three multipliers 60, 61, 62, adders 70, 71, 72, 73 and other circuits. The quaternions w, x, y, z are
The registers 50, 51, 52, and 53 are loaded from memories (not shown). The parameter w is supplied from the register 50 to the multiplier 60. The selector 54 sequentially supplies the parameters z, y, and x from the registers 53, 52, and 51 to the multiplier 60, and causes the multiplier 60 to calculate a product with the parameter w.
As a result, the multiplier 60 sequentially outputs the products wz, wy, and wx. The selectors 55 and 56 include registers 53, 52,
From 51, the parameter pair xy, xz, yz is sequentially multiplied by 6
1 to calculate the product of the two parameters belonging to each pair. As a result, the multiplier 61 outputs the product xy, x
z and yz are output in order. The selector 57 selects the register 5
The parameters x, y, and z are sequentially supplied from 1, 52, and 53 to the multiplier 62, and the respective squares are calculated. As a result, the multiplier 62 sequentially outputs the products xx, yy, and zz. The selectors 54, 55, 56, 57 operate in synchronization with each other. The same applies to the multipliers 60, 61, and 62. Therefore, wz, xy, and xx are output in parallel in a certain machine cycle from the multipliers 60, 61, and 62, and wy, xz, and yy are output in the next machine cycle. In the next machine cycle, wx, yz, and zz are output in parallel.

The adder 70 adds the outputs of the multipliers 60 and 61. The adder 71 operates as a subtractor, and subtracts the output of the multiplier 60 from the output of the multiplier 61. Adder 7
0, 71 operate synchronously.

First two outputs wz, x of multipliers 60 and 61
y, an addition result xy + wz is given from the adder 70, and a subtraction result xy-wz of those two outputs is obtained by the subtractor 7
1 at the same time. The addition result and the subtraction result are output to the shifter 7 connected to the outputs of the adders 70 and 71.
The register 8 is shifted left by 1 bit by
0 and 81 are set respectively. That is, 2 (xy + wz) and 2 (xy−wz) are stored in the registers 80 and 81.
Is set. These data are represented by a three-dimensional rotation matrix R
R (2,1) and R (1,2).

In the second machine cycle, the multiplier 6
Similarly, 2 (xz
+ Wy) and 2 (xz-wy) are the registers 80 and 81
Is set to These data represent the elements R (1,3) and R (3,1) of the three-dimensional rotation matrix R.

Further, in the third machine cycle, the outputs wx and yz of the multipliers 60 and 61 are used to calculate 2 (y
z + wx) and 2 (yz−wx) are the registers 80 and 8
Set to 1. These data are represented by a three-dimensional rotation matrix R
R (3,2) and R (2,3).

On the other hand, in the first machine cycle, the shifter 78 shifts the output xx of the multiplier 62 to the left by one bit, and outputs 2x to the adder (which operates as a subtractor) 72.
Supply as x. The selector 76 selects the constant 1.0 in the first machine cycle and supplies it to the subtractor 72. The subtracter 72 subtracts 2xx from the constant 1.0. The multiplexer 79 sets the subtraction result 1-2xx in the register 82. Thus, in the first machine cycle, the operation result 1-2xx is stored in the register 82.

The selector 76 selects the register 82 in the second machine cycle. In this machine cycle, the selector 78 is supplied with twice the output yy of the multiplier 62 from the selector 78, and the selector 76 outputs 1-2x
x is supplied. As a result, the subtractor 72 outputs 1-2xx-
2yy is output. The multiplexer 79 sets the result of the subtraction in the register 84. Thus, in the second machine cycle, the operation result 1-2 is stored in the register 84.
xx-2yy is stored, and the element R of the three-dimensional rotation matrix R
Used as (3,3).

The selector 76 selects the register 82 also in the third machine cycle. In this machine cycle, the selector 78 is supplied with twice the output zz of the multiplier 62 from the selector 78, and the selector 76 outputs 1-2x
x is supplied. As a result, the subtractor 72 outputs 1-2xx-
2zz is output. The multiplexer 79 sets the subtraction result in the register 82. Thus, in the third machine cycle, the operation result 1-2 is stored in the register 82.
xx-2zz is stored, and the element R of the three-dimensional rotation matrix R is stored.
Used as (2,2).

On the other hand, in the second machine cycle, the output 2yy of the selector 78 is also supplied to the subtractor 73.
The selector 77 supplies the constant 1.0 to the subtractor 73. The subtractor 73 outputs 1-2yy to the register 83. In the third machine cycle, the selector 78 selects the multiplier 6
2 is output to the subtractor 73. The selector 77 subtracts the data 1-2yy in the register 83 from the subtractor 73.
To supply. Thus, the subtractor 73 has 1-2yy-2z
z is stored in the register 83. This data is used as an element R (1, 1) of the three-dimensional rotation matrix R.

As described above, in this operation unit, the register 8
All the elements of the three-dimensional rotation matrix 17 based on the quaternion are obtained in 0, 81, 82, 83, 84. These data are stored in a memory (not shown). Moreover, these data are obtained in three machine cycles.

The loading of data w, x, y, z from a memory (not shown) to the registers 50, 51, 52, 53 is performed in the same manner as for the preceding quaternion data. The operation of storing the result data obtained in 82, 83, and 84 in the memory is executed in a manner overlapping the pipeline.

Since this arithmetic unit has three multipliers and four adders as main components, its structure is relatively simple. In addition, conventional computer computing units include:
Many have four multipliers and one adder 70 for the product-sum operation. In the present embodiment, such a computer uses three of the four multipliers and the adder 70, and further realizes the adders 71, 72, 73, and the wiring and control additionally. it can. Therefore, this arithmetic unit can be realized by adding a few circuits to the arithmetic unit in the conventional computer.

Even if such a special arithmetic unit is provided in each target computer, the three-dimensional rotation matrix calculation formula 17
Is simple, so that it is easy to write and output a code for calculating a three-dimensional rotation matrix using this calculator for each target computer. For this reason, it is possible to develop a program using this arithmetic unit in a unified environment.

[0084]

As described above, according to the present invention, an animation including Euler angle data representing a three-dimensional angular position of an object and a part for calculating a three-dimensional rotation matrix using the data. From the source program for
An animation program including a part for calculating the three-dimensional rotation matrix using a quaternion can be manufactured.

Further, according to the present invention, it is possible to manufacture an animation program for calculating a three-dimensional rotation matrix using motion capture capable of outputting a quaternion.

Further, according to the present invention, an animation source program or a quaternion including a part for calculating a three-dimensional rotation matrix using Euler angles is used.
From an animation source program that includes a part that calculates a three-dimensional rotation matrix, to an object program that calculates a three-dimensional rotation matrix using a calculator that can calculate trigonometric function values at relatively high speed, or quaternion data It can be manufactured by switching an object program that calculates a three-dimensional rotation matrix using addition, subtraction, and multiplication.

Further, according to the present invention, an animation program for a computer having the above-described arithmetic unit or an animation program for a computer having no such arithmetic unit can be developed in a unified environment.

[Brief description of the drawings]

FIG. 1 can calculate a matrix using quaternion data corresponding to the data from a source program created to calculate a three-dimensional rotation matrix using the Euler angle data. 9 is a flowchart of a procedure for manufacturing an object program.

FIG. 2 is a diagram illustrating an Euler angle.

FIG. 3 is a view for explaining three three-dimensional matrices used to calculate a three-dimensional rotation matrix using Euler angles.

FIG. 4A is a diagram illustrating a three-dimensional rotation matrix calculated using Euler angles. (B) is a diagram showing the relationship between Euler angles and quaternions. (C) is calculated using quaternion 3
The figure which shows the rotation matrix of a dimension.

FIG. 5 is a diagram schematically showing a source program used in the procedure of FIG. 1;

FIG. 6 is a view showing a specific example of a source program used in the procedure of FIG. 1;

FIG. 7 is a diagram showing a procedure used to convert the Euler angle into a quaternion used in the procedure of FIG. 1;

FIG. 8 is a diagram illustrating a procedure for calculating a three-dimensional rotation matrix using a quaternion, which is used in the procedure of FIG. 1;

FIG. 9 calculates a matrix using quaternion data from a source program created to calculate a three-dimensional rotation matrix using the output of a motion capture capable of outputting a quaternion. 5 is a flowchart of a procedure for manufacturing an object program that can be used.

FIG. 10 is a flowchart of a procedure of manufacturing object programs for various target computers from various source programs using a common compiler.

FIG. 11 is a view showing a specific example of a source program used in the procedure of FIG. 10;

FIG. 12 is a flowchart showing a processing procedure of a compiler used in the procedure of FIG. 10;

FIG. 13 is a diagram showing a procedure for calculating a three-dimensional rotation matrix using Euler angles, which is used in the procedure of FIG. 10;

FIG. 14 is a schematic configuration diagram of an arithmetic unit suitable for calculating a three-dimensional rotation matrix using a quaternion.

[Description of Signs] 21... Source program including a calculation program for a three-dimensional rotation matrix.

Claims (20)

[Claims] An object program is produced from an animation source program including Euler angle data representing a three-dimensional angular position of an object and a part for calculating a three-dimensional rotation matrix using the data. A method in which the following steps are performed by a computer. The above Euler angle data represents the same angular position as 4
The data is converted into element data, and the source program is converted into an object program including a part for calculating a three-dimensional rotation matrix using the data of the quaternion obtained by the conversion to produce an animation program. 2. A part for calculating a three-dimensional rotation matrix in the source program includes a call statement for calling a program routine for calculating a three-dimensional rotation matrix, and the conversion of the source program includes an object called by the call statement. The program manufacturing method according to claim 1, further comprising a step of incorporating a routine as a part of the object program, wherein the object routine is a routine for calculating the three-dimensional rotation matrix by addition, subtraction, and multiplication of quaternion data. 3. A computer which captures quaternion data representing a three-dimensional angular position of a three-dimensional object to be modeled by motion capture, and repeats the above capturing by changing the angular position of the object. An animation source program including a part for calculating a three-dimensional rotation matrix using the quaternion data obtained by the capture is generated by an operator operation on a computer, and the above-described quaternion data is added and subtracted and multiplied by multiplication. A program manufacturing method for manufacturing an animation program by converting the source program into a corresponding object program by a computer so as to include a part for calculating a three-dimensional rotation matrix. 4. A part for calculating a three-dimensional rotation matrix in the source program includes a call statement for calling a program routine for calculating a three-dimensional rotation matrix, and the conversion of the source program includes an object called by the call statement. 4. The method according to claim 3, further comprising the step of incorporating a routine as a part of the object program, wherein the object routine is a routine for calculating the three-dimensional rotation matrix by adding, subtracting, and multiplying quaternion data. 5. A method according to claim 1, wherein a plurality of arithmetic units that can be used are different from an animation source program including data representing a three-dimensional angular position of the object and a part for calculating a three-dimensional rotation matrix using the data. A program manufacturing method for manufacturing an object program for any one of a computer, wherein the computer switches between the following two and executes the object program. (A) when the data is Euler angle data, convert the Euler angle data to quaternion data representing the same angular position before manufacturing an object program corresponding to the source program; The source program is converted into an object program including a part for calculating a three-dimensional rotation matrix by using addition / subtraction and multiplication on the obtained quaternion data. (B) when the data is quaternion data,
The above source program is converted into an object program including a part for calculating a three-dimensional rotation matrix by using addition and subtraction and multiplication on the data of the element number. 6. A part for calculating a three-dimensional rotation matrix in the source program includes a call statement for calling a program routine for calculating a three-dimensional rotation matrix, and is manufactured in the step (a) or (b). The part for calculating the three-dimensional rotation matrix in the object program includes the object routine called by the above call statement, and the object routine calculates the three-dimensional rotation matrix using addition, subtraction, and multiplication on quaternion data. The program manufacturing method according to claim 5, wherein the program is a routine for performing a program. 7. An operation unit that can be used from an animation source program including Euler angle data representing a three-dimensional angular position of an object and a part for calculating a three-dimensional rotation matrix using the data. A program manufacturing method for manufacturing an object program for any one of a plurality of different computers, wherein the following two steps (a) and (b) are switched by a computer and executed. (A) Using a calculator capable of calculating the value of the trigonometric function at a relatively high speed, calculating the values of a plurality of trigonometric functions with respect to the Euler angle data, and further using the calculated values to obtain 3
The source program is converted into an object program including a part for calculating a dimensional rotation matrix. (B) Before manufacturing the object program corresponding to the source program, the Euler angle data is converted into quaternion data representing the same angular position, and the quaternion data obtained by the conversion is converted. The source program is converted into an object program including a part for calculating a three-dimensional rotation matrix using addition and subtraction and multiplication. 8. A part for calculating a three-dimensional rotation matrix in the source program includes a call statement for calling a program routine for calculating a three-dimensional rotation matrix, and a part of the object program in the object program manufactured in the step (a). The part for calculating the three-dimensional rotation matrix includes a first object routine called by the above-mentioned call statement, and the first object routine uses the arithmetic unit to generate a plurality of trigonometric functions for the Euler angle data. Is a routine for calculating a three-dimensional rotation matrix using the calculated value, and a part for calculating the three-dimensional rotation matrix in the object program manufactured in the step (b) is: A second object routine that is called by the above call statement; 8. The method according to claim 7, wherein the routine is a routine for calculating a three-dimensional rotation matrix using addition, subtraction, and multiplication on quaternion data. 9. An animation source program including data representing a three-dimensional angular position of an object and including a part for calculating a three-dimensional rotation matrix using the data, wherein a plurality of usable arithmetic units differ from each other. A program manufacturing method for manufacturing an object program for an arbitrary one of computers, wherein the computer executes the following three steps (a), (b), and (c) by switching. (A) When the data is Euler angle data, a plurality of trigonometric function values for the Euler angle data are calculated using an arithmetic unit capable of calculating the value of the trigonometric function at a relatively high speed; Using the calculated values, the source program is converted into an object program including a part for calculating a three-dimensional rotation matrix. (B) when the data is Euler angle data, convert the Euler angle data to quaternion data representing the same angular position before manufacturing an object program corresponding to the source program; The above source program is converted into an object program including a part for calculating a three-dimensional rotation matrix using addition / subtraction and multiplication with respect to the data of the quaternion obtained by the above. (C) when the data is quaternion data,
The source program is converted into an object program including a part for calculating a three-dimensional rotation matrix by using addition and subtraction and multiplication on the data of the element number. 10. A part for calculating a three-dimensional rotation matrix in the source program includes a call statement for calling a program routine for calculating a three-dimensional rotation matrix, and a part of the object program manufactured in the step (a). The part for calculating the three-dimensional rotation matrix includes a first object routine called by the above-mentioned call statement, and the first object routine uses the arithmetic unit to generate a plurality of trigonometric functions for the Euler angle data. Is a routine for calculating a three-dimensional rotation matrix using the calculated value, and calculating a three-dimensional rotation matrix in the object program manufactured in the step (b) or (c). The second part includes a second object routine called by the above call statement, and a second object 10. The program manufacturing method according to claim 9, wherein the routine is a routine for calculating a three-dimensional rotation matrix by using addition, subtraction, and multiplication on quaternion data. 11. An object program produced by a computer from an animation source program including Euler angle data representing a three-dimensional angular position of an object and a part for calculating a three-dimensional rotation matrix using the data. A program recording medium on which a program is recorded, wherein the program converts the Euler angle data into quaternion data representing the same angular position, and uses the obtained quaternion data as the source program. Then, the program is converted into an object program including a part for calculating a three-dimensional rotation matrix to produce an animation program. 12. A part for calculating a three-dimensional rotation matrix in the source program includes a call statement for calling a program routine for calculating a three-dimensional rotation matrix, and the conversion of the source program includes an object called by the call statement. 12. The program recording medium according to claim 11, further comprising a step of incorporating a routine as a part of the object program, wherein the object routine is a routine for calculating the three-dimensional rotation matrix by adding, subtracting, and multiplying quaternion data. 13. A computer which captures quaternion data representing a three-dimensional angular position of a three-dimensional object to be modeled by motion capture, and repeats the capturing by changing the angular position of the object. An animation source program including a part for calculating a three-dimensional rotation matrix using the quaternion data obtained by the capture is generated by an operator operation on a computer, and the above-described quaternion data is added and subtracted and multiplied by multiplication. A program recording medium in which a program for producing an animation program by converting the source program into a corresponding object program by a computer so as to include a part for calculating a three-dimensional rotation matrix is recorded. 14. A part for calculating a three-dimensional rotation matrix in the source program includes a call statement for calling a program routine for calculating a three-dimensional rotation matrix, and the conversion of the source program includes an object called by the call statement. 14. The program recording medium according to claim 13, further comprising a step of incorporating a routine as a part of the object program, wherein the object routine is a routine for calculating the three-dimensional rotation matrix by adding, subtracting, and multiplying quaternion data. 15. Data representing a three-dimensional angular position of the object;
A program for producing, by a computer, an object program for any one of a plurality of computers having different usable computing units from a source program for animation including a part for calculating a three-dimensional rotation matrix using the data. In the following two steps (a):
(B) is switched and executed. (A) when the data is Euler angle data, convert the Euler angle data into quaternion data representing the same angular position before manufacturing an object program corresponding to the source program; The source program is converted into an object program including a part for calculating a three-dimensional rotation matrix by using addition / subtraction and multiplication on the obtained quaternion data. (B) when the data is quaternion data,
The above source program is converted into an object program including a part for calculating a three-dimensional rotation matrix by using addition and subtraction and multiplication on the data of the element number. 16. A part for calculating a three-dimensional rotation matrix in the source program includes a call statement for calling a program routine for calculating a three-dimensional rotation matrix, wherein the part is manufactured in the step (a) or (b). The part for calculating the three-dimensional rotation matrix in the object program includes an object routine called by the above call statement, and the object routine calculates the three-dimensional rotation matrix using addition, subtraction, and multiplication on quaternion data. 16. The program recording medium according to claim 15, wherein the program recording medium is a routine for performing a program. 17. An operation unit which can be used from an animation source program including Euler angle data representing a three-dimensional angular position of an object and including a part for calculating a three-dimensional rotation matrix using the data. A recording medium recording a program for manufacturing an object program for any one of a plurality of different computers by a computer, wherein the program switches and executes the following two steps (a) and (b). (A) Using a calculator capable of calculating the value of the trigonometric function at a relatively high speed, calculating the values of the plurality of trigonometric functions for the data of the Euler angles, and further using the calculated values,
The above source program is converted into an object program including a part for calculating a three-dimensional rotation matrix. (B) Before manufacturing the object program corresponding to the source program, the Euler angle data is converted into quaternion data representing the same angular position, and the quaternion data obtained by the conversion is converted. The source program is converted into an object program including a part for calculating a three-dimensional rotation matrix using addition and subtraction and multiplication. 18. A part for calculating a three-dimensional rotation matrix in the source program includes a call statement for calling a program routine for calculating a three-dimensional rotation matrix, and includes a call statement in the object program manufactured in the step (a). The part for calculating the three-dimensional rotation matrix includes a first object routine called by the above-mentioned call statement, and the first object routine uses the arithmetic unit to generate a plurality of trigonometric functions for the Euler angle data. Is a routine for calculating a three-dimensional rotation matrix using the calculated value, and a part for calculating the three-dimensional rotation matrix in the object program manufactured in the step (b) is: Including a second object routine called in the above call statement, the second object routine 18. The program recording medium according to claim 17, wherein the routine is a routine for calculating a three-dimensional rotation matrix using addition / subtraction and multiplication on quaternion data. 19. An animation source program including data representing a three-dimensional angular position of an object and including a part for calculating a three-dimensional rotation matrix using the data, wherein a plurality of usable arithmetic units differ from each other. A program recording medium recording a program for manufacturing an object program for any one of the computers by a computer, wherein the program includes the following three steps (a):
(B) Switch and execute (c). (A) When the data is Euler angle data, a plurality of trigonometric function values with respect to the Euler angle data are calculated using an arithmetic unit capable of calculating the trigonometric function value at a relatively high speed as an object program. Then, using the calculated values, the source program is converted into a part including a part for calculating a three-dimensional rotation matrix. (B) when the data is Euler angle data, convert the Euler angle data into quaternion data representing the same angular position before manufacturing an object program corresponding to the source program; The source program is converted into an object program including a part for calculating a three-dimensional rotation matrix by using addition / subtraction and multiplication on the obtained quaternion data. (C) when the data is quaternion data,
The above source program is converted into an object program including a part for calculating a three-dimensional rotation matrix by using addition and subtraction and multiplication on the data of the element number. 20. A part for calculating a three-dimensional rotation matrix in the source program includes a call statement for calling a program routine for calculating a three-dimensional rotation matrix, and a part of the object program manufactured in the step (a) includes: The part for calculating the three-dimensional rotation matrix includes a first object routine called by the above-mentioned call statement, and the first object routine uses the arithmetic unit to generate a plurality of trigonometric functions for the Euler angle data. Is a routine for calculating a three-dimensional rotation matrix using the calculated value, and calculating a three-dimensional rotation matrix in the object program manufactured in the step (b) or (c). The second object routine includes a second object routine called by the above call statement, and the second object routine 20. The program recording medium according to claim 19, wherein the ctroutine is a routine for calculating a three-dimensional rotation matrix using addition, subtraction, and multiplication on quaternion data.