Direct interactive, constant-time curve apparatus and method

An apparatus for interactively feeding back to a user in real time a smoothed output signal in response to an input signal controlled directly by a user, the apparatus comprising:

• an input device operable by a user to sense movements by a user and to selectively provide input signals corresponding directly and interactively to the movements along a path;
• a processor connected to the input device to receive the input signals for logically operating on the input signals to provide process signals corresponding to a linearly transformable, nonlinear curve fitted to the input signals;
• a memory device operably connected to the processor for storing input data corresponding to the input signals and for storing output data corresponding to the process signals;
• and
• an output device connected to the processor for receiving output data and for interactively feeding back to a user in real time the smoothed output signals, the smoothed output signals being sensible by a user and corresponding to the output data.

A method for incrementally augmenting a path-defined curve in real time, the method comprising:

• moving a pointer associated with an input device;
• creating input data corresponding to locations along a path specified by a user moving the pointer therealong;
• creating in a processor, connected to the input device, process data corresponding to a linearly transformable curve fitted to the inut data;
• mapping the process data to building variable data representing a linear system corresponding to the linearly transformable curve;
• operating on the building variable data to create output data corresponding to the curve;
• feeding back to a user on an output device connected to the processor a first image of the curve;
• moving the pointer in response to the image;
• providing additional input data from the input device, the added input data corresponding to additional locations from additional movement of the pointer;
• linearly transforming the building variable data to create new building variable data for replacing the building variable data;
• and
• feeding back to a user, in real time, on the output device, a second image for replacing the first image.

An apparatus adapted to directly and interactively create a nonlinear curve, the apparatus comprising:

• an input device adapted to directly and interactively provide input signals corresponding to locations on a path;
• a processor adapted to receive the input signals, to provide output data corresponding to a first curve fitted to the locations, linearly transform the nonlinear curve to create a second nonlinear curve, and to provide output data corresponding to the second nonlinear curve;
• a memory device adapted to store the output data;
• and
• an output device adapted to interactively feed back the output signals corresponding to the second nonlinear curve.