Computer graphics processing and selective visual display system – Computer graphics processing – Graphic manipulation
Reexamination Certificate
2001-08-23
2004-07-06
Luu, Matthew (Department: 2672)
Computer graphics processing and selective visual display system
Computer graphics processing
Graphic manipulation
C345S643000, C345S645000, C345S648000, C345S427000, C345S647000
Reexamination Certificate
active
06760040
ABSTRACT:
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is based upon and claims the benefit of priorities from the prior Japanese Patent Applications No. 2000-254065 filed on Aug. 24, 2000 and No. 2001-247430 filed on Aug. 16, 2001, the entire contents of both of which are incorporated herein by reference.
BACKGROUND OF THE INVENTION
The present invention relates to a technology for expressing an object using computer graphics, etc., and more specifically, to an image processing technology for transforming coordinates of shape specific points which specify the shape of a graphic that represents an object, so as to express the behavior of the object such as motion and deformation.
Recent years have seen significant advances in the computer-graphics-related technology and the results of various computer-simulated events are now visually expressed through a display. For example, conducting a simulation on an object created by means of CAD (Computer Aided Design) and expressing the simulation result visually through computer graphics to check the behavior of the object such as motion and deformation constitutes an important step in design and development of a product.
Motion of an object, motion of a rigid body in particular, is expressed using the following transformation matrix (Equation 1). This transformation matrix is intended to transform coordinate values of a shape specific point P (X, Y, Z) for specifying the shape of a rigid body using a 4×4 transformation matrix and determine a transformed shape specific point P′(X′, Y′, z′). In this Specification, a “shape specific point” refers to a point for specifying the shape of an object such as a vertex.
(
X
′
Y
′
Z
′
1
)
=
(
R
00
R
01
R
02
R
03
R
10
R
11
R
12
R
13
R
20
R
21
R
22
R
23
0
0
0
1
)
(
X
Y
Z
1
)
[
Equation
1
]
Of the above transformation matrix, the 3×3 matrix section with the 1st to 3rd rows and the 1st to 3rd columns represents a rotational displacement, while the 1×3 matrix section with the 4th column represents a translation. Since the 3×3 matrix section with the 1st to 3rd rows and the 1st to 3rd columns is a matrix that represents a rotational displacement, it satisfies the condition of the following Equation 2:
R
=
(
R
00
R
01
R
02
R
10
R
11
R
12
R
20
R
21
R
22
)
R
-
1
=
t
R
det
R
=
1
[
Equation
2
]
Motion of a rigid body is expressed by computing the above-described transformation matrix for all shape specific points of the graphic that represents the object. In the case of a rigid body, a positional relationship such as a distance between a plurality of shape specific points of one object does not change. Therefore, it is also possible to determine coordinate values of other shape specific points from the positional relationship with the shape specific point P′ determined by the Equation 1.
Here, since an object is represented by a three-dimensional graphic, the transformation matrix is set to be a 4×4 matrix. However, when an object is represented by a two-dimensional graphic, a similar transformation can be performed using a 3×3matrix. In this case, Equation 2 is changed so as to hold for a 2×2 matrix with elements R
00
, R
01
, R
10
and R
11
.
On the other hand, if the object is an elastic body, its motion is expressed by regarding the object as a model with a plurality of shape specific points for specifying the shape of a graphic that represents the object, mutually connected via a virtual spring. The elastic body is expressed by solving an equation of motion of a force of the spring acting on each shape specific point.
For example, in the case of a model with a shape specific point P connected to three neighboring shape specific points via three springs, suppose when the shape specific point P is regarded as a starting point, position vectors of the three neighboring shape specific points at time t are v
0
(t), v
1
(t) and v
2
(t), spring constants are k
0
, k
1
and k
2
and natural lengths of the springs are L
0, L
1
and L
2
. Then, a force F(t) that acts on the shape specific point P is expressed by the following Equation 3:
F
(
t
)
=
k
0
(
&LeftBracketingBar;
v
0
(
t
)
&RightBracketingBar;
-
L
0
)
*
v
0
(
t
)
&LeftBracketingBar;
v
0
(
t
)
&RightBracketingBar;
+
k
1
(
&LeftBracketingBar;
v
1
(
t
)
&RightBracketingBar;
-
L
1
)
*
v
1
(
t
)
&LeftBracketingBar;
v
1
(
t
)
&RightBracketingBar;
+
k
2
(
&LeftBracketingBar;
v
2
(
t
)
&RightBracketingBar;
-
L
2
)
*
v
2
(
t
)
&LeftBracketingBar;
v
2
(
t
)
&RightBracketingBar;
[
Equation
3
]
Suppose the shape specific point P is a mass point, the mass of the shape specific point P is M, the damping coefficient of vibration of spring is D, and the coordinate value of the shape specific point P at time t is P(t)=(x(t), y(t), z(t)). Then, the equation of motion of the shape specific point P is expressed by the following Equation 4:
M
ⅆ
2
ⅆ
t
2
P
(
t
)
=
F
(
t
)
-
D
ⅆ
ⅆ
t
P
(
t
)
[
Equation
4
]
Solving this equation of motion allows the coordinate value P(t) of the shape specific point P at time t to be calculated. The elastic body is expressed by applying the above-described computation to all shape specific points of the graphic that represents the elastic body.
Such a coordinate transformation for expressing an elastic body requires computations of Equation 3 and Equation 4 to be carried out for all shape specific points that specify the shape of the graphic that expresses the elastic body. The load on the image processing apparatus that carries out such computations becomes enormous as the amount of computation is enormous. For this reason, in the case where it is necessary to display an elastic body in real time in a video game, etc., a high performance image processing apparatus is required. This is because if the performance of the image processing apparatus is low, its computation processing will not catch up with the motion of the elastic body, which causes the motion of the elastic body to appear unnatural.
However, high performance image processing apparatuses tend to be costly and cannot be used for apparatuses, such as home video game machines, which require high cost performance. Thus, there is a demand for a technology capable of expressing the behavior of an object in a quasi-natural manner while suppressing the load on the apparatus to a minimum.
SUMMARY OF THE INVENTION
Therefore, it is an object of the present invention to provide an image processing technology capable of expressing the behavior of an object such as displacement and deformation naturally while suppressing the load on the apparatus to a minimum.
According to one aspect of the present invention, there is provided an image processing method executed in an apparatus for transforming coordinates of shape specific points that specify a shape of a graphic representing an object so as to generate graphics data representing a behavior of the object, the method comprising the steps of: setting a transformation matrix having elements each of which is expressed by a function having time as a variable, the function converging to a corresponding element of a matrix that represents a behavior of the object when the object is assumed to be a rigid body; and transforming the coordinates of the shape specific points using the transformation matrix and generating the graphics data based on the coordinates obtained.
Conventionally, expressing the motion of an elastic body requires equations of motion to be solved for all shape specific points that specify the shape of the elastic
Chung Daniel
Lerner David Littenberg Krumholz & Mentlik LLP
Luu Matthew
Sony Computer Entertainment Inc.
LandOfFree
Image processing method, image processing apparatus,... does not yet have a rating. At this time, there are no reviews or comments for this patent.
If you have personal experience with Image processing method, image processing apparatus,..., we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Image processing method, image processing apparatus,... will most certainly appreciate the feedback.
Profile ID: LFUS-PAI-O-3219305