Method of simulating deformable object using geometrically motivated model

1. A computer-implemented method of modeling the deformation of a deformable object in a graphics simulation, the method comprising:

defining a goal shape related to the deformable object by transforming an original non-deformed shape related to the deformable object to a deformed shape related to the deformable object;

defining elastic forces associated with the deformation in proportion to distance between a first set of data points associated with the deformed shape and a second set of data points associated with the goal shape;

describing the deformation using an explicit integration scheme, comprising:

selecting a set of points x i 0 in an original shape of the deformable object and a corresponding set of points x i in the deformed shape; and

determining a rotation matrix R and translation vectors t and t 0 minimize the summation for all “i” of w i (R(x 0 i −t 0 )+t −x i ) 2 , where w i is the weight associated with each point in the set of points x i in the deformed shape; and

resolving the explicit integration scheme by pulling each point in the first set of points towards a corresponding point in the second set of points in the goal shape, wherein the first set of data points is used to model the deformation of the deformable object in the graphics simulation performed on a computing device.

2. The computer-implemented method of claim 1 , further comprising the step of, for each point in the set of points x i 0 in the original shape, defining a location for a corresponding point g i in the goal shape, where g i =R(x i 0 −x cm 0 )+x cm , where x cm 0 is a center of mass of the original shape and x cm is a center of mass of the deformed shape.

3. The computer-implemented method of claim 1 , further comprising the step of, for each point in the set of points x i 0 in the original shape, defining a location for a corresponding point g i in the goal shape as g i =Ã{tilde over (q)} i where à is a quadratic transformation matrix and {tilde over (q)} i is a vector containing linear, quadratic, and mixed terms.

4. A non-transitory computer-readable storage medium storing instructions that, when executed by a processor, cause the processor to model the deformation of a deformable object in a graphics simulation, by performing the steps of:

defining a goal shape related to the deformable object by transforming an original non-deformed shape related to the deformable object to a deformed shape related to the deformable object;

defining elastic forces associated with the deformation in proportion to distance between a first set of data points associated with the deformed shape and a second set of data points associated with the goal shape;

describing the deformation using an explicit integration scheme, comprising:

selecting a set of points x i 0 in an original shape of the deformable object and a corresponding set of points x i in the deformed shape; and

determining a rotation matrix R and translation vectors t and t 0 minimize the summation for all “i” of w i R(x 0 i −t 0 )+t −x i ) 2 , where w i is the weight associated with each point in the set of points x i in the deformed shape; and

resolving the explicit integration scheme by pulling each point in the first set of points towards a corresponding point in the second set of points in the goal shape, wherein the first set of data points is used to model the deformation of the deformable object in the graphics simulation performed on a computing device.

5. The computer-readable medium of claim 4 , further comprising the step of, for each point in the set of points x i 0 in the original shape, defining a location for a corresponding point g i in the goal shape, where g i =R(x i 0 −x cm 0 )+x cm , where x cm 0 is a center of mass of the original shape and x cm is a center of mass of the deformed shape.

6. The computer-readable medium of claim 4 , further comprising the step of, for each point in the set of points x i 0 in the original shape, defining a location for a corresponding point g i in the goal shape as g i =Ã{tilde over (q)} i where à is a quadratic transformation matrix and {tilde over (q)} i is a vector containing linear, quadratic, and mixed terms.

7. A computer system, comprising:

a processor; and

a memory configured to store instructions that, when executed by the processor, cause the processor to model the deformation of a deformable object in a graphics simulation, by performing the steps of:

defining a goal shape related to the deformable object by transforming an original non-deformed shape related to the deformable object to a deformed shape related to the deformable object;

defining elastic forces associated with the deformation in proportion to distances between a first set of data points associated with a deformed shape and a second set of data points associated with the goal shape;

describing the deformation using an explicit integration scheme, comprising:

selecting a set of points x i 0 in an original shape of the deformable object and a corresponding set of points x i in the deformed shape; and

determining a rotation matrix R and translation vectors t and t 0 minimize the summation for all “i” of w i (R(x 0 i −t 0 )+t −x i ) 2 , where w i is the weight associated with each point in the set of points x i in the deformed shape; and

resolving the explicit integration scheme by pulling each point in the first set of points towards a corresponding point in the second set of points in the goal shape, wherein the first set of data points is used to model the deformation of the deformable object in the graphics simulation performed on a computing device.

8. The computer system of claim 7 , further comprising the step of, for each point in the set of points x i 0 in the original shape, defining a location for a corresponding point g i in the goal shape, where g i =R(x i 0 −x cm 0 )+x cm , where x cm 0 is a center of mass of the original shape and x cm is a center of mass of the deformed shape.