Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
2001-03-09
2009-10-27
Jones, Hugh (Department: 2128)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
C703S007000
Reexamination Certificate
active
07610182
ABSTRACT:
An image display system and method that use physical models to produce a realistic display of a scene are disclosed. The image display method involves operating a computer having a display screen, a memory and a processing unit for simulating the motion of objects and displaying the results on the display screen. The method includes the steps of storing in the memory position and velocity parameters which define an initial state of a model system having a plurality of bodies, storing in the memory parameters which define at least one constraint function constraining the motion of the bodies in the model system, and calculating in the processor the position and velocity parameters which define the state of the system after a predetermined time step based on rigid body dynamics, including carrying out a semi-implicit integration step subject to the constraints, to determine the velocity after the step, including determining the constraint forces that act to keep the system in compliance with the constraints by ensuring that the first derivative of the constraint function is zero.
REFERENCES:
Baraff; Coping with friction for non-penetrating rigid body simulation; Computer Graphics; 1991; pp. 31-40.
Mihai Anitescu, et al., “Time-Stepping for Three-Dimensional Rigid Body Dynamics,” Computer Methods in Applied Mechanics and Engineering, Jul. 20, 1999, Netherlands, vol. 177, No. 3-4, pp. 183-197, p. 184, last paragraph, p. 188, paragraph 3.
David E. Stewart, “Convergence of a Time-Stepping Scheme for Rigid-Body Dynamics and Resolution of Painleve's Program”, Archive for Rational Mechanics and Analysis, 1998, Germany, vol. 145, No. 3, pp. 215-260, p. 215, line 1—p. 217, last paragraph, p. 222, paragraph 3—p. 223, last paragraph.
Y.H. Chen, “Equations of Motion of Constrained Mechanical Systems: Given Force Depends on Constraint Force,” Mechatronics, Great Britain, Jun. 1999, vol. 9, No. 4, pp. 411-428.
Claude Lacoursiere
Smith Russell Leigh
Albert Philip H.
Electronic Arts Inc.
Jones Hugh
Townsend and Townsend / and Crew LLP
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