Systems and methods for representing complex n-curves for direct control of tool motion

A method for direct control of a mechanism through the use of higher-dimensional n-curves, comprising:

• providing an electronically-controlled mechanism;
• establishing electronic communication by a computer with the electronically-controlled mechanism;
• executing a controller on the computer to send mechanism commands to the electronically-controlled mechanism;
• and
• executing process control software to control the electronically-controlled mechanism, wherein the process control software uses a higher-dimensional n-curve to control the electronically-controlled mechanism, wherein the higher-dimensional n-curve comprises a representation of the variation of a plurality of parameters associated with the electronically-controlled mechanism, wherein the variation of the plurality of nanometers is expressed in terms of an extent parameter that defines a boundary of the curve, and wherein the process control software generates commands that are directly usable by the controller.

A system for controlling a mechanism through the use of higher-dimensional n-curves, comprising:

• an electronically controlled mechanism;
• a computer in electronic communication with the electronically-controlled mechanism,
• the computer comprising:
• a processor;
• memory in electronic communication with the processor;
• process control software to control the electronically-controlled mechanism,
• wherein the process control software uses a higher-dimensional n-curve to control the electronically-controlled mechanism, wherein the higher-dimensional n-curve comprises a representation of the variation of a plurality of parameters associated with the electronically-controlled mechanism, and wherein the variation of the plurality of parameters is expressed in terms of an extent parameter that defines a boundary of the curve.

A system for direct control of a mechanism through the use of higher-dimensional n-curves, comprising:

• an electronically controlled mechanism;
• a computer in electronic communication with the electronically-controlled mechanism,
• the computer comprising:
• a processor;
• memory in electronic communication with the processor;
• process control software to control the electronically-controlled mechanism,
• wherein the process control software uses a higher-dimensional n-curve to control the electronically-controlled mechanism, wherein the higher-dimensional n-curve comprises a representation of the variation of a plurality of parameters associated with the electronically-controlled mechanism, wherein the variation of the naturality of parameters is expressed in terms of an extent parameter that defines a boundary of the curve, and wherein the process control software generates commands that are directly usable by the controller.