Position based energy minimizing function

A method comprising:

• at a processor:
• controlling a virtual manipulator based on input data received from an input system, the virtual manipulator being configured to manipulate a virtual object in a virtual environment;
• determining an initial state of a system that includes at least an initial state of the virtual manipulator and an initial state of the virtual object;
• detecting at least one contact point between a portion of the virtual manipulator and the virtual object;
• determining one or more positional quantities for the initial state of the system;
• detecting a subsequent state of the virtual manipulator;
• determining one or more positional quantities for a subsequent state of the system that includes the subsequent state of the virtual manipulator;
• calculating a subsequent state for the virtual object that minimizes a set of energies or residuals defined in terms of the one or more positional quantities determined for the initial state of the system and the one or more positional quantities determined for the subsequent state of the system using a position-based energy minimizing function;
• and
• moving the virtual object to the calculated subsequent state;
• wherein the initial state and the subsequent state of the virtual object include three-dimensional positions and orientations of the virtual object in the virtual environment, and wherein the initial state and the subsequent state of the virtual manipulator include respective three-dimensional positions and orientations of the portion of the virtual manipulator in the virtual environment.

A head computed display device comprising:

• a near-eye display;
• a camera system configured to capture images of a user's hand;
• and
• a processor configured to:
• track a position of the user's hand based on the captured images received from the camera system;
• control a virtual manipulator based on the tracked position of the user's hand, the virtual manipulator being configured to manipulate a virtual object in a virtual environment;
• determine an initial state of a system that includes at least an initial state of the virtual manipulator and an initial state of the virtual object;
• detect at least one contact point between a portion of the virtual manipulator and the virtual object;
• determine one or more positional quantities for the initial state of the system;
• detect a subsequent state of the virtual manipulator;
• determine one or more positional quantities for a subsequent state of the system that includes the subsequent state of the virtual manipulator;
• calculate a subsequent state for the virtual object that minimizes a set of energies or residuals defined in terms of the one or more positional quantities determined for the initial state of the system and the one or more positional quantities determined for the subsequent state of the system using a position-based energy minimizing function;
• move the virtual object to the calculated subsequent state and
• display the subsequent state of the system in the virtual environment via the near-eye display;
• wherein the initial state and the subsequent state of the virtual object include three-dimensional positions and orientations of the virtual object in the virtual environment, and wherein the initial state and the subsequent state of the virtual manipulator include respective three-dimensional positions and orientations of the portion of the virtual manipulator in the virtual environment.

A computer system comprising:

• an input system;
• and
• a processor configured to:
• control a virtual manipulator based on input data received from the input system, the virtual manipulator being configured to manipulate a virtual object in a virtual environment;
• determine an initial state of a system that includes at least an initial state of the virtual manipulator and an initial state of the virtual object;
• detect at least one contact point between a portion of the virtual manipulator and the virtual object;
• determine one or more positional quantities for the initial state of the system;
• detect a subsequent state of the virtual manipulator;
• determine one or more positional quantities for a subsequent state of the system that includes the subsequent state of the virtual manipulator;
• calculate a subsequent state for the virtual object that minimizes a set of energies or residuals defined in terms of the one or more positional quantities determined for the initial state of the system and the one or more positional quantities determined for the subsequent state of the system using a position-based energy minimizing function;
• and
• move the virtual object to the calculated subsequent state;
• wherein the portion of the virtual manipulator includes at least a first articulable portion and a second articulable portion;
• and
• wherein the processor is further configured to detect at least two contact points including a first contact point between the first articulable portion and the virtual object and a second contact point between the second articulable portion and the virtual object.