Methods and apparatuses for producing smooth representations of input motion in time and space
The present invention provides a method that comprises accepting a plurality of positional data with corresponding times of the motion, determining one or more continuous positional functions that together represent an approximation of path of the positional data, and determining, for each positional function, one or more time functions that together represent an approximation of the times for the positional data corresponding to the positional functions. The present invention provides an apparatus that comprises an input device and a computer system configured to accept the motion signals generated by the input device, determine one or more continuous positional functions that together represent an approximation of the path of the positional data, and determine, for each positional function, one or more time functions that together represent an approximation of the times for the positional data corresponding to the positional functions.
1. A method for determining a smooth representation of a motion of an input device, comprising:
receiving a plurality of positional data for an audio source at a processor, each positional data having associated time data;
determining with the processor one or more continuous positional functions that output an approximation of the positional data; and
determining with the processor one or more time functions that output an approximation of the associated time data.
2. The method of claim 1 , further comprising:
dividing the positional data into two or more subsets using the processor; and
determining one or more continuous positional functions for each of the subsets using the processor, wherein the continuous positional functions output an approximation of each of the subsets.
3. The method of claim 2 wherein dividing the positional data into two or more subsets using the processor comprises:
determining a derivative of the continuous positional function for the plurality of position data; and
dividing the positional data where the derivative of the continuous positional function for the plurality of position data for a first point is approximately equal to the derivative of the continuous positional function for the plurality of position data for an adjacent point to the first point.
4. The method of claim 1 , wherein determining with the processor one or more time functions that output an approximation of the associated time data comprises calculating one or more parametric transforms of the corresponding positional data for the positional functions using the processor.
5. The method of claim 4 , wherein each of the time functions maps the parametric transforms of the positional data for the corresponding positional functions and corresponding times within a range specified by a start time and an end time.
6. The method of claim 1 , wherein the positional data is a representation of one or more a position, a motion and an orientation of the input device.
7. The method of claim 1 , wherein the time associated with the positional data comprises a time corresponding to the input device at an associated position.
8. The method of claim 1 further comprising generating the positional data and the associated time data using the input device.
9. The method of claim 8 wherein generating the positional data and the associated time data using the input device comprises generating a series of positional data values, each positional data point having an associated time data value.
10. An apparatus for determining a smooth representation of a motion, comprising:
an input device, configured to generate a series of positional data values for an audio source, each positional data value having associated time data values;
a computer system, configured to:
receive the series of positional data values and associated time data values;
determine one or more continuous positional functions that generate an approximation of the positional data values; and
determine, for each positional function, one or more time functions that generate an approximation of the associated time data values for the positional data values.
11. The apparatus of claim 10 , wherein the computer system is further configured to:
divide the series of positional data values into two or more subsets; and
determine one or more continuous positional functions for each of the subsets, wherein the continuous positional functions generate an approximation of the positional data values of the associated subset.
12. The apparatus of claim 10 , wherein the computer system is further configured to calculating one or more parametric transforms of the corresponding positional data values for the continuous positional functions.
13. The apparatus of claim 12 , wherein each of the time functions maps the parametric transforms of the positional data for the corresponding positional functions and corresponding time data values within a range specified by a start time and an end time.
14. The apparatus of claim 10 , wherein the positional data values comprise one or more of a position, a motion and an orientation of the input device.
15. The apparatus of claim 10 , wherein the time data values correspond to the input device at an associated position.
16. The apparatus of claim 11 wherein dividing the positional data into two or more subsets comprises:
determining a derivative of the continuous positional function for the plurality of position data; and
dividing the positional data where the derivative of the continuous positional function for the plurality of position data for a first point is approximately equal to the derivative of the continuous positional function for the plurality of position data for an adjacent point to the first point.
17. A method for determining a smooth representation of a motion of an input device, comprising:
receiving a plurality of positional data for an audio source at a processor, each positional data having associated time data;
determining with the processor one or more continuous positional functions that output an approximation of the positional data; and
determining with the processor one or more time functions that output an approximation of the associated time data, wherein the positional data is a representation of one or more a position, a motion and an orientation of the input device and wherein the time associated with the positional data comprises a time corresponding to the input device at an associated position.
18. The method of claim 17 , further comprising:
dividing the positional data into two or more subsets using the processor; and
determining one or more continuous positional functions for each of the subsets using the processor, wherein the continuous positional functions output an approximation of each of the subsets.
19. The method of claim 17 , wherein determining with the processor one or more time functions that output an approximation of the associated time data comprises calculating one or more parametric transforms of the corresponding positional data for the positional functions using the processor.
20. The method of claim 17 further comprising generating the positional data and the associated time data using the input device.