Image processing method, image processing apparatus, semiconductor device, computer program and recording medium

• US 6,760,040 B2
• Filed: 08/23/2001
• Issued: 07/06/2004
• Est. Priority Date: 08/24/2000
• Status: Expired due to Term

• Current Assignee: Dropbox, Inc.
• Original Assignee: Sony Computer Entertainment Incorporated (Sony Group Corp.)
• Inventors: Oka, Masaaki
• Primary Examiner(s): Luu, Matthew
• Assistant Examiner(s): CHUNG, DANIEL J
• Application Number:
  US09/935,879
• Publication Number:
  US 20020113804A1
• Time in Patent Office: 1,048 Days
• Field of Search: 345/644, 345/643, 345/645, 345/646, 345/427, 345/648, 345/649, 345/660, 345/647
• US Class Current: 345/644
• CPC Class Codes: G06T 13/20 3D [Three Dimensional] animation

Abstract

A technique for expressing an elastic body using computer graphics. The elastic body is expressed by transforming coordinates of shape specific points which specify the shape of an object using a transformation matrix. Each element of the transformation matrix is expressed by a function having time as a variable which converges to a corresponding element of a matrix that represents the motion of the object when the object is assumed to be a rigid body. By substituting a predetermined time into this function, a value of each element of the transformation matrix is determined. The shape of the object is determined based on the coordinate values of the shape specific points after coordinate transformation.

Claims

1. 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 said object, said method comprising the steps of:

setting a transformation matrix having elements each of which is expressed by a solution to the equation;

$M_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{{<br><br>}^2<br><br>\text{\hspace{1em}<br><br>}}{<br><br>t^2}<br><br>\text{\hspace{1em}<br><br>}<br><br>A_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t\right)=k_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(A_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t\right)-R_{\mathrm{ij}}\right)-D_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{<br><br>\text{\hspace{1em}<br><br>}}{<br><br>t}<br><br>\text{\hspace{1em}<br><br>}<br><br>A_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t\right)$

wherein

M_ij, k_ij, D_ij are constants defining physical characteristics of the object,

A_ij is a function that expresses an element at row i, column j of the transformation matrix,

R_ij is a value of an element at row i, column j of the matrix when the object is assumed to be a rigid body,

0<

i<

3,

0<

j<

3, and t is time; and

transforming the coordinates of said shape specific points said transformation matrix and generating said graphics data based on the coordinates obtained.

2. An image processing 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 said object, said apparatus comprising:

means for generating a transformation matrix having elements each of which is expressed by a solution to the equation;

$M_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{{<br><br>}^2<br><br>\text{\hspace{1em}<br><br>}}{<br><br>t^2}<br><br>\text{\hspace{1em}<br><br>}<br><br>A_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t\right)=k_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(A_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t\right)-R_{\mathrm{ij}}\right)-D_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{<br><br>\text{\hspace{1em}<br><br>}}{<br><br>t}<br><br>\text{\hspace{1em}<br><br>}<br><br>A_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t\right)$

wherein

M_ij, k_ij, D_ij are constants defining physical characteristics of the object,

A_ij is a function that expresses an element at row i, column j of the transformation matrix,

R_ij is a value of an element at row i, column j of the matrix when the object is assumed to be a rigid body,

0<

i<

3,

0<

j<

3, and t is time; and

means for transforming the coordinates of said shape specific points using said transformation matrix and generating said graphics data based on the coordinates obtained.

3. The image processing apparatus according to claim 2, further comprising recording means for recording constants that represent physical characteristics of said object, wherein said means for generating said transformation matrix is configured to set said equation for each element of said transformation matrix based on said constants.

4. A semiconductor device 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 said object, said semiconductor device comprising:

means for generating a transformation matrix having elements each of which is expressed by a solution to the equation;

$M_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{{<br><br>}^2<br><br>\text{\hspace{1em}<br><br>}}{<br><br>t^2}<br><br>\text{\hspace{1em}<br><br>}<br><br>A_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t\right)=k_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(A_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t\right)-R_{\mathrm{ij}}\right)-D_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{<br><br>\text{\hspace{1em}<br><br>}}{<br><br>t}<br><br>\text{\hspace{1em}<br><br>}<br><br>A_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t\right)$

wherein

M_ij, k_ij, D_ij are constants defining physical characteristics of the object,

A_ij, is a function that expresses an element at row i, column j of the transformation matrix,

R_ij is a value of an element at row i, column j of the matrix when the object is assumed to be a rigid body,

0<

i<

3,

0<

j<

3, and

t is time; and

means for transforming the coordinates of said shape specific points using said transformation matrix and generating said graphics data based on the coordinates obtained.

5. A recording medium recorded with a computer program for causing a computer to operate as an image processing 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 said object, said computer program causing the computer to execute a process comprising:

generating a transformation matrix having elements each of which is expressed by a solution to the equation;

$M_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{{<br><br>}^2<br><br>\text{\hspace{1em}<br><br>}}{<br><br>t^2}<br><br>\text{\hspace{1em}<br><br>}<br><br>A_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t\right)=k_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(A_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t\right)-R_{\mathrm{ij}}\right)-D_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{<br><br>\text{\hspace{1em}<br><br>}}{<br><br>t}<br><br>\text{\hspace{1em}<br><br>}<br><br>A_{\mathrm{ij}}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(t\right)$

wherein

M_ij, k_ij, D_ij are constants defining physical characteristics of the object, A_ij is a function that expresses an element at row i, column j of the transformation matrix, R_ij, is a value of an element at row i, column j of the matrix when the object is assumed to be a rigid body,

0<

i<

3,

0<

j<

3, and

t is time; and

transforming the coordinates of said shape specific points using said transformation matrix and generating said graphics data based on the coordinates obtained.