Method of simulating deformable object using geometrically motivated model

1. A computer-implemented method of simulating a deformation of a deformable object, the method comprising:

defining an original shape based on a non-deformed state of a deformable object, wherein the original shape comprises a plurality of original data points;

defining an actual shape corresponding to a deformed state of the deformable object, wherein the actual shape comprises a plurality of actual data points;

defining a goal shape corresponding to the non-deformed state of the deformable object such that the goal shape is a matched version of the original shape, wherein the goal shape comprises a plurality of goal data points;

matching the original shape comprising original data points to corresponding actual data points in the actual shape by rotating and translating the original shape of the deformable object; and

updating parameters of each actual data point according to a position of a corresponding goal data point in the goal shape by moving each of the plurality of actual data points corresponding to the deformed state toward a corresponding goal data point in the goal shape.

2. The computer-implemented method of claim 1 , wherein the updated parameters of each actual data point are used to simulate the deformation of the deformable object in a graphics simulation performed on a computing device.

3. The computer-implemented method of claim 1 , wherein the parameters comprise position and velocity.

4. The computer-implemented method of claim 3 , wherein the step of updating parameters of each actual data point comprises:

defining a velocity of the actual data point at a particular time based on a velocity of the actual data point at the particular time and a difference between a position of a corresponding goal point and a position of the actual data point at the particular time; and

defining a position of the actual data point at the particular time based on a position of the actual data point at the particular time and the velocity of the actual data point at the particular time.

5. A non-transitory computer-readable medium storing instructions that, when executed by a processor, cause the processor to simulate a deformation of a deformable object, by performing the steps of:

defining an original shape based on a non-deformed state of a deformable object, wherein the original shape comprises a plurality of original data points;

defining an actual shape corresponding to a deformed state of the deformable object, wherein the actual shape comprises a plurality of actual data points;

defining a goal shape corresponding to the non-deformed state of the deformable object such that the goal shape is a matched version of the original shape, wherein the goal shape comprises a plurality of goal data points;

matching the original shape comprising original data points to corresponding actual data points in the actual shape by rotating and translating the original shape of the deformable object; and

updating parameters of each actual data point according to a position of a corresponding goal data point in the goal shape by pulling moving each of the plurality of actual data points corresponding to the deformed state toward a corresponding goal data point in the goal shape.

6. The non-transitory computer-readable medium of claim 5 , wherein the updated parameters of each actual data point are used to simulate the deformation of the deformable object in a graphics simulation performed on a computing device.

7. The non-transitory computer-readable medium of claim 5 , wherein the parameters comprise position and velocity.

8. The non-transitory computer-readable medium of claim 7 , wherein the step of updating parameters of each actual data point comprises:

defining a velocity of the actual data point at a particular time based on a velocity of the actual data point at the particular time and a difference between a position of a corresponding goal point and a position of the actual data point at the particular time; and

defining a position of the actual data point at the particular time based on a position of the actual data point at the particular time and the velocity of the actual data point at the particular time.

9. A computer system, comprising:

a processor; and

a memory configured to store an application including instructions that, when executed by the processor, cause the processor to simulate a deformation of a deformable object, by performing the steps of:

defining an original shape based on a non-deformed state of a deformable object, wherein the original shape comprises a plurality of original data points;

defining an actual shape corresponding to a deformed state of the deformable object, wherein the actual shape comprises a plurality of actual data points;

defining a goal shape corresponding to the non-deformed state of the deformable object such that the goal shape is a matched version of the original shape, wherein the goal shape comprises a plurality of goal data points;

matching the original shape comprising original data points to corresponding actual data points in the actual shape by rotating and translating the original shape of the deformable object; and

updating parameters of each actual data point according to a position of a corresponding goal data point in the goal shape by moving each of the plurality of actual data points corresponding to the deformed state toward a corresponding goal data point in the goal shape.

10. The computer system of claim 9 , wherein the updated parameters of each actual data point are used to simulate the deformation of the deformable object in a graphics simulation performed on a computing device.

11. The computer system of claim 9 , wherein the parameters comprise position and velocity.

12. The computer system of claim 11 , wherein the step of updating parameters of each actual data point comprises:

defining a velocity of the actual data point at a particular time based on a velocity of the actual data point at the particular time and a difference between a position of a corresponding goal point and a position of the actual data point at the particular time; and

defining a position of the actual data point at the particular time based on a position of the actual data point at the particular time and the velocity of the actual data point at the particular time.

13. The computer-implemented method of claim 1 , wherein the amount of rotation and translation is determined by minimizing distance between goal data points in the goal shape and corresponding actual data points in the actual shape.

14. The computer-implemented method of claim 13 , wherein the rotation and translation are chosen to minimize a weighted least square distance between corresponding data points in the goal shape and the actual shape.

15. The non-transitory computer-readable medium of claim 5 , wherein the amount of rotation and translation is determined by minimizing distance between goal data points in the goal shape and corresponding actual data points in the actual shape.

16. The non-transitory computer-readable medium of claim 15 , wherein the rotation and translation are chosen to minimize a weighted least square distance between corresponding data points in the goal shape and the actual shape.

17. The computer system of claim 9 , wherein the amount of rotation and translation is determined by minimizing distance between goal data points in the goal shape and corresponding actual data points in the actual shape.

18. The computer system of claim 17 , wherein the rotation and translation are chosen to minimize a weighted least square distance between corresponding data points in the goal shape and the actual shape.