System and method for visualization of objects using energy minimization of customized potential functions

1. A method for positioning objects on a viewing area, the method comprising the steps of:

specifying a plurality of objects;

specifying a plurality of object pairs from the plurality of objects;

specifying a potential function for each one of the specified plurality of object pairs;

specifying a similarity value (s) for each one of the specified object pairs;

determining an energy (e) for each one of the potential functions;

solving for a minimum total energy (E) of the plurality of potential functions such that a distance (r) between objects in each of the specified object pairs is determined;

specifying a first constant (a) for each potential function;

specifying a second constant (b) for each potential function;

specifying a third constant (c) for each potential function;

wherein each one of the potential functions defining the energy (e) of each one of the specified object pairs is specified by

e ( r,s )= a/r+bsr 2 +cr

and wherein E is determined by summing the determined energies of each one of the specified object pairs; and

outputting the plurality of objects for display on a display device according to the determined distances.

2. The method of claim 1 , further comprising the step of preventing collision of the objects of a specified object pair by determining a value of the first constant of the potential function for that object pair.

3. The method of claim 1 , further comprising the step of keeping an object within the viewing area by determining a value of the third constant of the potential function for that object pair.

4. The method of claim 1 , further comprising the steps of:

specifying a new first constant for at least one of the potential functions; and

recomputing E based upon the change of e caused by the new first constant.

5. The method of claim 1 , further comprising the steps of:

specifying a new second constant for at least one of the potential functions; and

recomputing E based upon the change of e caused by the new second constant.

6. The method of claim 1 , further comprising the steps of:

specifying a new third constant for at least one of the potential functions; and

recomputing E based upon the change of e caused by the new third constant.

7. A system which positions objects on a viewing area, comprising:

a processing system configured to determine position of a plurality of objects;

a memory residing in the processing system; and

logic residing in the memory, the logic configured to perform:

receiving a specification of a plurality of objects;

receiving a specification of a plurality of object pairs from the plurality of objects;

receiving a specification of a potential function for each one of the specified object pairs;

receiving a specification of a similarity value (s) for each one of the specified object pairs;

determining an energy (e) for each one of the potential functions; and

solving for a minimum total energy (E) of the plurality of potential functions such that a distance (r) between objects in each of the specified object pairs is determined;

receiving the specification of a first constant (a) for each potential function;

receiving the specification of a second constant (b) for each potential function; and

receiving the specification of a third constant (c) for each potential function;

wherein each one of the potential functions defining the energy (e) of each one of the specified object pairs is specified by

e ( r,s )= a/r+bsr 2 +cr

and wherein E is determined by summing the determined energies of each one of the specified object pairs; and

wherein the processing system is configured to provide the plurality of objects for display on a display device according to the determined distances.

8. A system for positioning objects on a viewing area, comprising:

means for specifying a plurality of objects;

means for specifying a plurality of object pairs from the plurality of objects;

means for specifying a potential function for each one of the specified object pairs;

means for specifying a similarity value (s) for each one of the specified object pairs, wherein the similarity value (s) for each object pair represents relative similarity of the objects in the object pair;

means for determining an energy (e) for each one of the potential functions;

means for solving for the minimum total energy (E) of the plurality of potential functions such that a distance (r) between objects in each of the specified object pairs is determined, the total energy (E) being based on the determined energies;

means for specifying a first constant (a) for each potential function;

means for specifying a second constant (b) for each potential function;

means for specifying a third constant (c) for each potential function;

wherein each one of the potential functions defining the energy (e) of each one of the specified object pairs is specified by

e ( r,s )= a/r+bsr 2 +cr,

and wherein E is determined by summing the determined energies of each one of the specified object pairs; and

means for outputting the plurality of objects for display on a display device according to the determined distances.

9. The system of claim 8 , further comprising:

means for repositioning at least one of the objects such that a corresponding r is changed; and

means for recomputing E based upon the changed r.

10. The system of claim 8 , further comprising:

means for receiving a new similarity value for at least one of the specified object pairs; and

means for recomputing E based upon the new similarity value.