Interpolation error minimization for data reduction

• US 20030025712A1
• Filed: 08/06/2002
• Published: 02/06/2003
• Est. Priority Date: 08/06/2001
• Status: Active Grant

• Current Assignee: William E. Corr
• Original Assignee: William E. Corr
• Inventors: Corr, William E.
• Granted Patent: US 7,072,812 B2
• Time in Patent Office: Days
• US Class Current: 345/606
• CPC Class Codes: G06F 17/17 Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method G06F17/18 takes precedence ; interpolation for numerical control G05B19/18
• CPC Class Codes: G06F 30/33 Design verification, e.g. functional simulation or model checking
• CPC Class Codes: G06F 30/367 Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods

Abstract

Systems and methods are provided for reducing a set of data points into a subset of best fit data points. According to one aspect, a method of adjusting a series of N data points into best fit data points for a set of sample data points that form a data source is provided. According to this method, M segments are identified, wherein M equals N−1. Each segment has endpoints defined by adjacent subset data points. An iterative process is performed that includes determining a linear interpolation error for each of the M segments, selecting a target segment (S_TARGET) from the segments, and reducing the interpolation error for S_TARGET by moving one endpoint of S_TARGET by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET. Other methods and systems are provided herein.

Claims

1. A method of adjusting a series of N subset data points into best fit data points for a series of sample data points that form a data source, comprising:

identifying M segments having endpoints defined by adjacent subset data points, wherein M equals N−

1; and

performing an iterative process, including;

determining a linear interpolation error for each of the M segments;

selecting a target segment (S_TARGET) from the segments; and

reducing the interpolation error for S_TARGET by moving one endpoint of S_TARGET by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET.

2. The method of claim 1, wherein determining a linear interpolation error for each of the M segments includes quantifying a distance between the segment and the data source.

3. The method of claim 1, wherein selecting a S_TARGET from the segments includes identifying a segment that has the largest interpolation error.

4. The method of claim 1, wherein reducing the interpolation error for S_TARGET includes:

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST.

5. The method of claim 1, wherein reducing the interpolation error includes:

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 to shorten S_TARGET and lengthen S_2ND; and

upon determining that ES_2ND is larger than ES_1ST, moving P_S to shorten S_TARGET and lengthen S_1ST.

6. A method of adjusting a series of N data points into best fit data points for a series of sample data points that form a data source, comprising:

identifying M segments having endpoints defined by adjacent subset data points, wherein M equals N−

1; and

performing an iterative process, including;

determining a linear interpolation error for each of the M segments;

selecting a target segment (S_TARGET) from the segments;

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P_S+1) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST.

7. The method of claim 6, wherein determining a linear interpolation error for each of the M segments includes quantifying a distance between the segment and the data source.

8. The method of claim 6, wherein selecting a target segment (S_TARGET) from the segments includes identifying a segment that has the largest interpolation error.

9. The method of claim 6, wherein:

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST.

10. A method of adjusting a series of N subset data points into best fit data points for a series of sample data points that form a data source, comprising:

identifying M segments having endpoints defined by adjacent subset data points, wherein M equals N−

1; and

performing an iterative process, including;

determining a linear interpolation error for each of the M segments;

selecting a target segment (S_TARGET) from the segments; and

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST.

11. The method of claim 10, wherein determining a linear interpolation error for each of the M segments includes quantifying a distance between the segment and the data source.

12. The method of claim 10, wherein selecting a target segment (S_TARGET) from the segments includes identifying a segment that has the largest interpolation error.

13. The method of claim 10, wherein:

upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST.

14. A method of adjusting a series of N subset data points into best fit data points for a series of sample data points that form a data source, comprising:

identifying M segments having endpoints defined by adjacent subset data points, wherein M equals N−

1; and

performing an iterative process, including;

determining a linear interpolation error for each of the M segments;

selecting a target segment (S_TARGET) from the segments;

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND;

upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST,

upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST.

15. The method of claim 14, wherein determining a linear interpolation error for each of the M segments includes quantifying a distance between the segment and the data source.

16. The method of claim 14, wherein selecting a S_TARGET from the segments includes identifying a segment that has the largest interpolation error.

17. A method of reducing linear interpolation error for a data subset that contains a series of data points from a data source, comprising:

identifying a target segment (S_TARGET) having endpoints defined by a first data point (P_S) and a second data point (P_S+1);

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_1ST.

18. The method of claim 17, wherein identifying a S_TARGET includes identifying a segment that has endpoints defined by two adjacent data points and that has the largest interpolation error.

19. The method of claim 17, further comprising:

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_1ST.

20. The method of claim 19, further comprising:

determining whether a moved data point is P_S or P_S+1;

determining whether the moved data point is oscillating between positions for successive iterations; and

upon determining that the moved data point is oscillating between positions, identifying a new target segment that has the next largest linear interpolation error.

21. The method of claim 20, wherein determining whether the moved data point is oscillating between positions includes:

recording the moved data point, the direction of motion for the moved data point, and the resulting interpolation error for the target segment (ES_TARGET);

determining whether the moved data points are the same point for successive iterations;

upon determining that the last data points moved are the same point, determining whether the last two movements of the same data point are in opposite directions; and

upon determining that the last two movements of the same data point are in opposite directions,

declaring that the moved data point is oscillating between positions, and

selecting the data point position that results in the smallest sum of a first ES_TARGET for a first S_TARGET and a second ES_TARGET for a second S_TARGET that is adjacent to the first S_TARGET and follows the first S_TARGET in a successive iteration.

22. The method of claim 17, wherein the source data is a series of sample points, and wherein moving P_S+1 includes decrementing P_S+1 along the series of source data sample points by at least one source data sample point, and moving P_S includes incrementing P_S along the series of source data sample points by at least one source data sample point.

23. The method of claim 22, wherein the at least one source data sample point is a programmable interval.

24. The method of claim 22, wherein the at least one source data sample point is one source data sample point.

25. The method of claim 17, wherein moving P_S+1 includes moving an X value for P_S+1 (X(P_S+1)) by a predetermined Δ

X and moving P_S includes moving an X value for P_S (X(P_S)) by the predetermined Δ

X.

26. The method of claim 25, wherein the predetermined Δ

X is programmable.

27. The method of claim 17, wherein moving P_S+1 includes moving a Y value for P_S+1 (Y(P_S+1)) by a predetermined Δ

Y and moving P_S includes moving a Y value for P_S (Y(P_S)) by the predetermined Δ

Y.

28. The method of claim 27, wherein the predetermined Δ

Y is programmable.

29. A method of reducing linear interpolation error for a data subset that contains a series of data points from a source data, comprising:

identifying a target segment (S_TARGET) having endpoints defined by a first data point (P_S) and a second data point (P_S+1);

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_1ST

30. The method of claim 29, wherein identifying a S_TARGET includes identifying a segment that has endpoints defined by two adjacent data points that has the largest interpolation error.

31. The method of claim 29, further comprising:

upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_1ST.

32. The method of claim 31, further comprising:

determining whether a moved data point is P_S or P_S+1;

determining whether the moved data point is oscillating between positions for successive iterations; and

upon determining that the moved data point is oscillating between positions for successive iterations, identifying a new target segment that has the next largest linear interpolation error.

33. The method of claim 32, wherein determining whether the moved data point is oscillating between positions for successive iterations includes:

recording the moved data point, the direction of motion for the moved data point, and the resulting interpolation error for the target segment (ES_TARGET);

determining whether the moved data points are the same point for successive iterations;

upon determining that the moved data points are the same point for successive iterations, determining whether the last two movements of the same data point are in opposite directions; and

upon determining that the last two movements of the same data point are in opposite directions,

declaring that the moved data point is oscillating between positions, and

selecting the data point position that results in the smallest sum of a first ES_TARGET for a first S_TARGET and a second ES_TARGET for a second S_TARGET that is adjacent to the first S_TARGET and follows the first S_TARGET in a successive iteration.

34. The method of claim 29, wherein the source data is a series of sample points, and wherein moving P_S+1 includes decrementing P_S+1 along the series of sample points by at least one sample point, and moving P_S includes incrementing P_S along the series of sample points by at least one sample point.

35. The method of claim 34, wherein the at least one sample point is a programmable interval.

36. The method of claim 34, wherein the at least one sample point is one sample point.

37. The method of claim 29, wherein moving P_S+1 includes moving an X value for P_S+1 (X(P_S+1)) by a predetermined Δ

X and moving P_S includes moving an X value for P_S (X(P_S)) by the predetermined Δ

X.

38. The method of claim 37, wherein the predetermined Δ

X is programmable.

39. The method of claim 29, wherein moving P_S+1 includes moving a Y value for P_S+1 (Y(P_S+1)) by a predetermined Δ

Y and moving P_S includes moving a Y value for P_S (Y(P_S)) by the predetermined Δ

Y.

40. The method of claim 37, wherein the predetermined Δ

Y is programmable.

41. A method of reducing linear interpolation error for a data subset that contains a series of data points from a source data, comprising:

identifying a target segment (S_TARGET) having endpoints defined by a first data point (P_S) and a second data point (P_S+1);

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_2ND;

upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_1ST;

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_1ST.

42. The method of claim 41, wherein identifying a S_TARGET includes identifying a segment that has endpoints defined by two adjacent data points and that has the largest interpolation error.

43. The method of claim 42, further comprising:

determining whether a moved data point is P_S or P_S+1;

determining whether the moved data point is oscillating between positions for successive iterations; and

upon determining that the moved data point is oscillating between positions for successive iterations, identifying a new target segment that has the next largest linear interpolation error.

44. The method of claim 41, wherein the source data is a series of sample points, and wherein moving P_S+1 includes decrementing P_S+1 along the series of source data sample points by at least one source data sample point, and moving P_S includes incrementing P_S along the series of source data sample points by at least one source data sample point.

45. The method of claim 41, wherein moving P_S+1 includes moving an X value for P_S+1 (X(P_S+1)) by a predetermined Δ

X and moving P_S includes moving an X value for P_S (X(P_S)) by the predetermined Δ

X.

46. The method of claim 41, wherein moving P_S+1 includes moving a Y value for P_S+1 (Y(P_S+1)) by a predetermined Δ

Y and moving P_S includes moving a Y value for P_S (Y(P_S)) by the predetermined Δ

Y.

47. A method of reducing linear interpolation error for a data subset that contains a plurality of data points from source data, wherein the data points from the source data are sequenced from left to right, the method comprising:

identifying a target segment (S_TARGET) having endpoints defined by a left data point (P_L) and a right data point (P_R);

determining whether there is a left segment (S_LEFT) with respect to S_TARGET having endpoints defined by a left data point (P_L−

1) and a right data point (P_L);

determining whether there is a right segment (S_RIGHT) with respect to S_TARGET having endpoints defined by a left data point (P_R) and a right data point (P_R+1);

upon determining that there is no S_LEFT, shortening S_TARGET by moving P_R left by an increment corresponding to at least one data point in the series of data points;

upon determining that there is no S_RIGHT, shortening S_TARGET by moving P_L right by an increment corresponding to at least one data point in the series of data points;

upon determining that there is a S_LEFT and a S_RIGHT, determining whether an interpolation error for S_LEFT (ES_LEFT) or an interpolation error for S_RIGHT (ES_RIGHT) is larger;

upon determining that ES_LEFT is larger than ES_RIGHT, moving P_R left by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_RIGHT; and

upon determining that ES_RIGHT is larger than ES_LEFT, moving P_L right by an increment corresponding to at least one data point in the series of data points to shorten S_TARGET and lengthen S_LEFT.

48. The method of claim 47, wherein identifying a S_TARGET includes identifying a segment that has endpoints defined by two adjacent data points and that has the largest interpolation error.

49. The method of claim 48, further comprising:

determining whether a moved data point is P_L or P_R;

determining whether the moved data point is oscillating between positions for successive iterations; and

upon determining that the moved data point is oscillating between positions for successive iterations, identifying a new target segment that has the next largest linear interpolation error.

50. The method of claim 49, wherein determining whether the moved data point is oscillating between positions includes:

recording the moved data point, the direction of motion for the moved data point, and the resulting interpolation error for the target segment (ES_TARGET);

determining whether the moved data points are the same point for successive iterations;

upon determining that the moved data points are the same point for successive iterations, determining whether the last two movements of the same data point are in opposite directions; and

upon determining that the last two movements of the same data point are in opposite directions,

declaring that the moved data point is oscillating between positions, and

selecting the data point position that results in the smallest sum of a first ES_TARGET for a first S_TARGET and a second ES_TARGET for a second S_TARGET that is adjacent to the first S_TARGET and follows the first S_TARGET in a successive iteration.

51. The method of claim 47, wherein the source data is a series of sample points, and wherein moving P_S+1 includes decrementing P_S+1 along the series of sample points by at least one sample point, and moving P_S includes incrementing P_S along the series of sample points by at least one sample point.

52. The method of claim 47, wherein moving P_R left includes decrementing X(P_R) by a predetermined Δ

X and moving P_L right includes incrementing X(P_L) by the predetermined Δ

X.

53. A method of selecting best fit data points for a series of sample data points that form source data, comprising:

seeding a series of N data points on the source data; and

performing an iterative process, including;

determining linear interpolation errors between the N data points and the source data for M segments that are capable of being formed between adjacent data points, wherein M equals N−

1;

sorting the M segments based on linear interpolation error size;

identifying a target segment (S_TARGET) from the M segments; and

reducing the linear interpolation error for S_TARGET by moving one endpoint of S_TARGET by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET.

54. The method of claim 53, wherein seeding a series of N data points on the source data includes:

identifying a number N corresponding to a number of data points in a data subset; and

dividing an axis range of the source data into M segments.

55. The method of claim 54, wherein dividing an axis range of the source data into M segments includes dividing an axis range of the source data into M segments of equal length.

56. The method of claim 53, wherein determining linear interpolation errors between the N data points and the source data for M segments that are capable of being formed between adjacent data points includes:

identifying a first endpoint and a second endpoint for each of the M segments;

identifying incremental values extending from the first endpoint and to the second endpoint for each of the M segments;

quantifying a difference between the interpolated data and the source data for each of the incremental values; and

identifying the linear interpolation error (ES) for each of the M segments by selecting the largest difference obtained for the incremental values.

57. The method of claim 56, wherein the source data is a series of data samples, and wherein identifying incremental values extending from the first endpoint and to the second endpoint for each of the M segments includes identifying incremental values that are an increment of at least one data sample.

58. The method of claim 56, wherein identifying incremental values extending from the first endpoint and to the second endpoint for each of the M segments includes identifying X axis incremental values, and wherein quantifying a difference between the interpolated data and the source data for each of the incremental values the data includes quantifying a difference in Y axis values for each of the X axis incremental values.

59. The method of claim 56, wherein identifying incremental values extending from the first endpoint and to the second endpoint for each of the M segments includes identifying Y axis incremental values, and wherein quantifying a difference between the interpolated data and the source data for each of the incremental values the data includes quantifying a difference in X axis values for each of the Y axis incremental values.

60. The method of claim 53, wherein determining linear interpolation errors between the N data points and the source data for M segments that are capable of being formed between adjacent data points includes the following for each segment S:

identifying a first endpoint P₁ and a second endpoint P₂ for segment S, wherein P₁ has an X value X(P₁) and a Y value Y(P₁), and P₂ has an X value X(P₂) and a Y value Y(P₂);

setting an increment variable (I) equal to X(P₁);

calculating a linear interpolation error value corresponding to the X value in the variable I that is equal to the absolute value of the Y value for the source data less the Y value for the segment (|Y(DATA)_I−

Y(SEG)_I|);

recording the I and the corresponding linear interpolation error value;

determining whether I equals X(P₂); and

upon determining that I does not equal X(P₂), incrementing I by a predetermined Δ

X and calculating a linear interpolation error value for the newly incremented I.

61. The method of claim 53, wherein determining linear interpolation errors between the N data points and the source data for M segments that are capable of being formed between adjacent data points includes the following for each segment S:

identifying a first endpoint P₁ and a second endpoint P₂ for segment S, wherein P₁ has an X value X(P₁) and a Y value Y(P₁), and P₂ has an X value X(P₂) and a Y value Y(P₂);

setting an increment variable (I) equal to Y(P₁);

calculating a linear interpolation error value corresponding to the Y value in the variable I that is equal to the absolute value of the X value for the source data less the X value for the segment (|X(DATA)_I−

X(SEG)_I|);

recording the I and the corresponding linear interpolation error value;

determining whether I equals Y(P₂); and

upon determining that I does not equal Y(P₂), incrementing I by a predetermined Δ

Y and calculating a linear interpolation error value for the newly incremented I.

62. The method of claim 53, wherein sorting the M segments based on linear interpolation error size includes sorting the M segments in order of decreasing interpolation error size from S_E(MAX) to S_E(MIN).

63. The method of claim 53, wherein identifying a target segment (S_TARGET) from the M segments includes identifying the segment with the largest linear interpolation error size as S_TARGET.

64. The method of claim 53, further comprising checking for termination, including:

calculating a total interpolation error for the source data;

determining whether the total interpolation error changes;

upon determining that the total interpolation error does not change, incrementing a counter;

determining whether the counter equals a termination value; and

upon determining that the counter equals a termination value, terminating the calculation process and extracting the data points.

65. A method of selecting best fit data points for a data subset of a sequence of sample data points that form source data, comprising:

seeding a series of N data points on the source data;

determining linear interpolation errors between the N data points and the source data for M segments that are capable of being formed between adjacent data points, wherein M equals N−

1;

sorting the M segments based on linear interpolation error size;

identifying a target segment (S_TARGET) from the M segments; and

reducing the linear interpolation error for S_TARGET, including;

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one data point in the sequence of sample data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one data point in the sequence of sample data points to shorten S_TARGET and lengthen S_1ST

66. The method of claim 65, wherein identifying a S_TARGET includes identifying a segment that has endpoints defined by two adjacent data points and that has the largest interpolation error.

67. The method of claim 65, further comprising:

upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one data point in the sequence of sample data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one data point in the sequence of sample data points to shorten S_TARGET and lengthen S_1ST.

68. The method of claim 67, further comprising:

determining whether a moved data point is P_S or P_S+1;

determining whether the moved data point is oscillating between positions for successive iterations; and

upon determining that the moved data point is oscillating between positions for successive iterations, identifying a new target segment that has the next largest linear interpolation error.

69. The method of claim 68, wherein determining whether the moved data point is oscillating between positions for successive iterations includes:

recording the moved data point, the direction of motion for the moved data point, and the resulting interpolation error for the target segment (ES_TARGET);

determining whether the moved data points are the same point for successive iterations;

upon determining that the moved data points are the same point for successive iterations, determining whether the last two movements of the same data point are in opposite directions; and

upon determining that the last two movements of the same data point are in opposite directions,

declaring that the moved data point is oscillating between positions, and

selecting the data point position that results in the smallest sum of a first ES_TARGET for a first S_TARGET and a second ES_TARGET for a second S_TARGET that is adjacent to the first S_TARGET and follows the first S_TARGET in a successive iteration.

70. The method of claim 65, wherein the source data is a series of sample points, and moving P_S+1 includes decrementing P_S+1 along the series of sample points by at least one sample point, and moving P_S includes incrementing P_S along the series of sample points by at least one sample point.

71. The method of claim 65, wherein moving P_S+1 includes moving an X value for P_S+1 (X(P_S+1)) by a predetermined Δ

X and moving P_S includes moving an X value for P_S (X(P_S)) by the predetermined Δ

X.

72. The method of claim 65, wherein moving P_S+1 includes moving a Y value for P_S+1 (Y(P_S+1)) by a predetermined Δ

Y and moving P_S includes moving a Y value for P_S (Y(P_S)) by the predetermined Δ

Y.

73. A method of selecting best fit data points from a sequence of sample data points that form source data, comprising:

seeding a series of N data points on the source data;

determining linear interpolation errors between the N data points and the source data for M segments that are capable of being formed between adjacent data points, wherein M equals N−

1;

sorting the M segments based on linear interpolation error size;

identifying a target segment (S_TARGET) from the M segments; and

reducing the linear interpolation error for S_TARGET, including;

determining whether there is a left segment (S_LEFT) with respect to S_TARGET having endpoints defined by a left data point (P_L−

1) and a right data point (P_L);

determining whether there is a right segment (S_RIGHT) with respect to S_TARGET having endpoints defined by a left data point (P_R) and a right data point (P_R+1);

upon determining that there is no S_LEFT, shortening S_TARGET by moving P_R left by an increment corresponding to at least one data point in the sequence of sample data points;

upon determining that there is no S_RIGHT, shortening S_TARGET by moving P_L right by an increment corresponding to at least one data point in the sequence of sample data points;

upon determining that there is a S_LEFT and a S_RIGHT, determining whether an interpolation error for S_LEFT (ES_LEFT) or an interpolation error for S_RIGHT (ES_RIGHT) is larger;

upon determining that ES_LEFT is larger than ES_RIGHT, moving P_R left by an increment corresponding to at least one data point in the sequence of sample data points to shorten S_TARGET and lengthen S_RIGHT; and

upon determining that ES_RIGHT is larger than ES_LEFT, moving P_L right by an increment corresponding to at least one data point in the sequence of sample data points to shorten S_TARGET and lengthen S_LEFT.

74. The method of claim 73, wherein identifying a S_TARGET includes identifying a segment that has endpoints defined by two adjacent data points and that has the largest interpolation error.

75. The method of claim 74, further comprising:

determining whether a moved data point is P_L or P_R;

determining whether the moved data point is oscillating between positions for successive iterations; and

upon determining that the moved data point is oscillating between positions for successive iterations, identifying a new target segment that has the next largest linear interpolation error.

76. The method of claim 75, wherein determining whether the moved data point is oscillating between positions includes:

recording the moved data point, the direction of motion for the moved data point, and the resulting interpolation error for the target segment (ES_TARGET);

determining whether the moved data points are the same point for successive iterations;

upon determining that the moved data points are the same point for successive iterations, determining whether the last two movements of the same data point are in opposite directions; and

upon determining that the last two movements of the same data point are in opposite directions,

declaring that the moved data point is oscillating between positions, and

selecting the data point position that results in the smallest sum of a first ES_TARGET for a first S_TARGET and a second ES_TARGET for a second S_TARGET that is adjacent to the first S_TARGET and follows the first S_TARGET in a successive iteration.

77. The method of claim 73, wherein moving P_R left includes moving X(P_R) by a predetermined Δ

X and moving P_L right includes moving X(P_L) by the predetermined Δ

X.

78. A method of reducing a series of characterization data points from a characterization source data into a data subset for a model table by selecting best fit data points to reduce the linear interpolation error in a simulation model, comprising:

seeding a series of N data points on the characterization source data;

identifying M segments having endpoints defined by adjacent data points, wherein M equals N−

1;

determining a linear interpolation error for each of the M segments;

selecting a target segment (S_TARGET) from the segments; and

reducing the interpolation error for S_TARGET by moving one endpoint of S_TARGET by an increment corresponding to at least one data point in the series of characterization data points to shorten S_TARGET.

79. The method of claim 78, wherein determining a linear interpolation error for each of the M segments includes quantifying a distance between the segment and the data source.

80. The method of claim 78, wherein selecting a S_TARGET from the segments includes identifying a segment that has the largest interpolation error.

81. The method of claim 78, wherein reducing the interpolation error for S_TARGET includes:

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is no S_1ST, moving P_S+1 to shorten S_TARGET and lengthen S_2ND by an increment corresponding to at least one data point in the series of characterization data points; and

upon determining that there is no S_2ND, moving P_S to shorten S_TARGET and lengthen S_1ST by an increment corresponding to at least one data point in the series of characterization data points.

82. The method of claim 78, wherein reducing the interpolation error for S_TARGET includes:

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one data point in the series of characterization data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one data point in the series of characterization data points to shorten S_TARGET and lengthen S_1ST.

83. A method of reducing a series of characterization data points from a characterization source data into a data subset for a model table by selecting best fit data points to reduce the linear interpolation error in a simulation model, comprising:

seeding a series of N data points on the characterization source data;

identifying M segments having endpoints defined by adjacent subset data points, wherein M equals n−

1; and

performing an iterative process, including;

determining a linear interpolation error for each of the M segments;

selecting a target segment (S_TARGET) from the segments;

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 to shorten S_TARGET and lengthen S_2ND by an increment corresponding to at least one data point in the series of characterization data points; and

upon determining that ES_2ND is larger than ES_1ST, moving P_S to shorten S_TARGET and lengthen S_1ST by an increment corresponding to at least one data point in the series of characterization data points.

84. The method of claim 83, wherein determining a linear interpolation error for each of the M segments includes quantifying a distance between the segment and the data source.

85. The method of claim 83, wherein selecting a S_TARGET from the segments includes identifying a segment that has the largest interpolation error.

86. A method of reducing a series of characterization data points from characterization source data into a data subset for a model table by selecting best fit data points to reduce the linear interpolation error in a simulation model, comprising:

seeding a series of N data points on the characterization source data;

performing an iterative process to identify best fit data points, including;

determining linear interpolation errors between the N data points and the source data for M segments that are capable of being formed between adjacent data points, wherein M equals N−

1;

sorting the M segments based on linear interpolation error size;

identifying a target segment (S_TARGET) from the M segments; and

reducing the linear interpolation error for S_TARGET, including;

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 to shorten S_TARGET and lengthen S_2ND by an increment corresponding to at least one data point in the series of characterization data points; and

upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one data point in the series of characterization data points to shorten S_TARGET and lengthen S_1ST,

extracting the best fit data points upon completion of the iterative process; and

incorporating the best fit data points as the data subset for the simulation model table.

87. The method of claim 86, wherein identifying a S_TARGET includes identifying a segment that has endpoints defined by two adjacent data points and that has the largest interpolation error.

88. The method of claim 86, further comprising:

upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one data point in the series of characterization data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one data point in the series of characterization data points to shorten S_TARGET and lengthen S_1ST

89. A method of forming simulation model tables, comprising:

retrieving source data from cell libraries, the source data including a series of sample data points;

compressing the source data into subsets of best fit data points, including;

identifying M segments having endpoints defined by adjacent subset data points, wherein M equals N−

1; and

performing an iterative process, including;

determining a linear interpolation error for each of the M segments;

selecting a target segment (S_TARGET) from the segments; and

reducing the interpolation error for S_TARGET by moving one endpoint of S_TARGET by an increment of at least one sample point in the series of sample data points to shorten S_TARGET; and

incorporating the subsets into simulation model tables.

90. The method of claim 89, wherein determining a linear interpolation error for each of the M segments includes quantifying a distance between the segment and the data source.

91. The method of claim 89, wherein selecting a S_TARGET from the segments includes identifying a segment that has the largest interpolation error.

92. The method of claim 89, wherein reducing the interpolation error for S_TARGET includes:

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST.

93. The method of claim 89, wherein reducing the interpolation error includes:

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (E_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST.

94. A method of forming simulation model tables, comprising:

retrieving source data from cell libraries, the source data including a series of sample data points;

compressing the source data into subsets of best fit data points, including;

identifying M segments having endpoints defined by adjacent subset data points, wherein M equals N−

1; and

performing an iterative process, including;

determining a linear interpolation error for each of the M segments;

selecting a target segment (S_TARGET) from the segments;

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST; and

incorporating the subsets in to simulation model tables.

95. The method of claim 94, wherein determining a linear interpolation error for each of the M segments includes quantifying a distance between the segment and the data source.

96. The method of claim 94, wherein selecting a S_TARGET from the segments includes identifying a segment that has the largest interpolation error.

97. The method of claim 94, wherein:

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 to shorten S_TARGET and lengthen S_2ND; and

upon determining that ES_2ND is larger than ES_1ST, moving P_S to shorten S_TARGET and lengthen S_1ST.

98. A method of forming simulation model tables, comprising:

retrieving source data from cell libraries, the source data including a series of sample data points;

compressing the source data into subsets of best fit data points, including;

identifying M segments having endpoints defined by adjacent subset data points, wherein M equals N−

1; and

performing an iterative process, including;

determining a linear interpolation error for each of the M segments;

selecting a target segment (S_TARGET) from the segments; and

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST; and

incorporating the subsets in to simulation model tables.

99. The method of claim 98, wherein determining a linear interpolation error for each of the M segments includes quantifying a distance between the segment and the data source.

100. The method of claim 98, wherein selecting a target segment (S_TARGET) from the segments includes identifying a segment that has the largest interpolation error.

101. The method of claim 98, wherein:

upon determining that there is no S_1ST, moving P_S+1 to shorten S_TARGET and lengthen S_2ND; and

upon determining that there is no S_2ND, moving P_S to shorten S_TARGET and lengthen S_1ST.

102. A method of forming simulation model tables, comprising:

retrieving source data from cell libraries, the source data including a series of sample data points;

compressing the source data into subsets of best fit data points, including;

identifying M segments having endpoints defined by adjacent subset data points, wherein M equals N−

1; and

performing an iterative process, including;

determining a linear interpolation error for each of the M segments;

selecting a target segment (S_TARGET) from the segments;

determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND;

upon determining that ES₂ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST;

upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST.

103. The method of claim 102, wherein determining a linear interpolation error for each of the M segments includes quantifying a distance between the segment and the data source.

104. The method of claim 102, wherein selecting a S_TARGET from the segments includes identifying a segment that has the largest interpolation error.

105. A method of designing a circuit, comprising:

providing libraries of source data, the source data including a series of sample data points;

compressing the libraries into subsets of best fit data points for simulation model tables, including;

retrieving source data from cell libraries;

compressing the source data into subsets of best fit data points, including;

identifying M segments having endpoints defined by adjacent subset data points, wherein M equals N−

1; and

performing an iterative process that includes determining a linear interpolation error for each of the M segments, selecting a target segment (S_TARGET) from the segments; and

reducing the interpolation error for S_TARGET by an increment corresponding to at least one sample data point in the series of sample data points; and

incorporating subsets into simulation model tables; and

designing high level circuit using the simulation model tables.

106. The method of claim 105, further comprising fabricating a physical circuit upon completing the design of the high level circuit.

107. The method of claim 105, wherein providing libraries of source data includes:

simulating electronics at device and cell levels to collect simulation results; and

converting simulation results into libraries of source data.

108. The method of claim 105, wherein designing high level circuits using the simulation models includes:

building higher level circuit using model tables;

simulating the higher level circuit;

determining whether the circuit requires a design modification; and

upon determining that the circuit requires a design modification, modifying the circuit and simulating the modified circuit.

109. A system, comprising:

a processor;

computer readable medium coupled to the processor, wherein the computer readable medium is encoded with a computer program for reducing linear interpolation error between a series of data points in a data subset and source data, the source data including a series of sample data points, wherein the computer readable medium includes;

programming code for identifying a target segment (S_TARGET) having endpoints defined by a first data point (P_S) and a right data point (P_S+1);

programming code for determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

programming code for determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

programming code for, upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

programming code for, upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

programming code for, upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST.

110. The system of claim 109, wherein programming code for identifying a S_TARGET includes programming code for identifying a segment that has endpoints defined by two adjacent data points and that has the largest interpolation error.

111. The system of claim 109, further comprising:

programming code for, upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

programming code for, upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST.

112. The system of claim 111, further comprising:

programming code for determining whether a moved data point is P_S or P_S+1;

programming code for determining whether the move data point is oscillating between positions for successive iterations; and

programming code for, upon determining that the moved data point is oscillating between positions for successive iterations, identifying a new target segment that has the next largest linear interpolation error.

113. The system of claim 112, wherein programming code for determining whether the moved data point is oscillating between positions includes:

programming code for recording the moved data point, the direction of motion for the moved data point, and the resulting interpolation error for the target segment (ES_TARGET);

programming code for determining whether the moved data points are the same point for successive iterations;

programming code for, upon determining that the moved data points are the same point for successive iterations, determining whether the last two movements of the same data point are in opposite directions; and

programming code for, upon determining that the last two movements of the same data point are in opposite directions,

declaring that the moved data point is oscillating between positions, and

selecting the data point position that results in the smallest sum of a first ES_TARGET for a first S_TARGET and a second ES_TARGET for a second S_TARGET that is adjacent to the first S_TARGET and follows the first S_TARGET in successive iterations, combination of ES_TARGET for the successive adjacent target segments.

114. The system of claim 109, wherein moving P_S+1 includes decrementing P_S+1 along the series of source data sample points by at least one sample point, and moving P_S includes incrementing P_S along the series of source data sample points by at least one sample point.

115. The system of claim 109, wherein moving P_S+1 includes moving an X value for P_S+1 (X(P_S+1)) by a predetermined Δ

X and moving P_S includes moving an X value for P_S (X(P_S)) by the predetermined Δ

X.

116. The system of claim 109, wherein moving P_S+1 includes moving a Y value for P_S+1 (Y(P_S+1)) by a predetermined Δ

Y and moving P_S includes moving a Y value for P_S (Y(P_S)) by the predetermined Δ

Y.

117. A cell characterization system, comprising:

a processor;

computer readable medium coupled to the processor, wherein the computer readable medium is encoded with a computer program for extracting best fit data points from a cell characterization source data for modeling of a cell using linear interpolation, the source data including a series of sample data points, wherein the computer readable medium includes;

programming code for seeding a series of N data points on the characterization source data;

programming code for performing an iterative process to identify best fit data points, including;

programming code for determining linear interpolation errors between the N data points and the source data for M segments that are capable of being formed between adjacent data points, wherein M equals N−

1;

programming code for sorting the M segments based on linear interpolation error size;

programming code for identifying a target segment (S_TARGET) from the M segments; and

programming code for reducing the linear interpolation error for S_TARGET, including;

programming code for determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

programming code for determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

programming code for, upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

programming code for, upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

programming code for, upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST;

programming code for extracting the best fit data points upon completion of the iterative process; and

programming code for incorporating the best fit data points as the data subset for the simulation model table.

118. The system of claim 117, wherein the programming code for determining a linear interpolation error for each of the M segments includes programming code for quantifying a distance between the segment and the data source.

119. The system of claim 117, wherein the programming code for identifying a S_TARGET includes programming code for identifying a segment that has the largest interpolation error.

120. A cell characterization system, comprising:

a processor;

computer readable medium coupled to the processor, including;

a first memory storage for storing cell characterization source data that includes a series of sample data points;

a second memory storage for storing a data subset for a simulation model table; and

a third memory storage for storing a program for extracting best fit data points from a cell characterization source data for modeling of a cell using linear interpolation, wherein the memory storage includes;

programming code for seeding a series of N data points on the cell characterization source data;

programming code for identifying M segments having endpoints defined by adjacent data points, wherein M equals N−

1;

programming code for determining a linear interpolation error for each of the M segments;

programming code for selecting a target segment (S_TARGET) from the segments; and

programming code for reducing the interpolation error for S_TARGET by moving one endpoint of S_TARGET by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET.

121. The system of claim 120, wherein the programming code for determining a linear interpolation error for each of the M segments includes programming code for quantifying a distance between the segment and the data source.

122. The system of claim 120, wherein the programming code for selecting a S_TARGET includes programming code for identifying a segment that has the largest interpolation error.

123. The method of claim 120, wherein the programming code for reducing the interpolation error for S_TARGET includes:

programming code for determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

programming code for determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

programming code for, upon determining that there is no S_1ST, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

programming code for, upon determining that there is no S_2ND, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST.

124. A cell characterization system, comprising:

a processor;

computer readable medium coupled to the processor, including;

a first memory storage for storing cell characterization source data that includes a series of sample data points;

a second memory storage for storing a data subset for a simulation model table; and

a third memory storage for storing a program for extracting best fit data points from a cell characterization data source for modeling of a cell using linear interpolation, wherein the memory storage includes;

programming code for seeding a series of N data points on the characterization source data;

programming code for performing an iterative process to identify best fit data points, including;

programming code for determining linear interpolation errors between the N data points and the source data for M segments that are capable of being formed between adjacent data points, wherein M equals N−

1;

programming code for sorting the M segments based on linear interpolation error size;

programming code for identifying a target segment (S_TARGET) from the M segments; and

programming code for reducing the linear interpolation error for S_TARGET, including;

programming code for determining whether there is a first adjacent segment (S_1ST) having a common endpoint with S_TARGET such that S_1ST has endpoints defined by a first data point (P<sub>S−

1</sub>) and a second data point (P_S);

programming code for determining whether there is a second adjacent segment (S_2ND) having a common endpoint with S_TARGET such that S_2ND has endpoints defined by a first data point (P_S+1) and a second data point (P_S+2);

programming code for, upon determining that there is a S_1ST and a S_2ND, determining whether an interpolation error for S_1ST (ES_1ST) or an interpolation error for S_2ND (ES_2ND) is larger;

programming code for, upon determining that ES_1ST is larger than ES_2ND, moving P_S+1 by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_2ND; and

programming code for, upon determining that ES_2ND is larger than ES_1ST, moving P_S by an increment corresponding to at least one sample data point in the series of sample data points to shorten S_TARGET and lengthen S_1ST;

programming code for extracting the best fit data points upon completion of the iterative process; and

programming code for incorporating the best fit data points as the data subset for the simulation model table.

125. The system of claim 124, wherein the programming code for determining a linear interpolation error for each of the M segments includes programming code for quantifying a distance between the segment and the data source.

126. The system of claim 124, wherein the programming code for identifying a S_TARGET includes programming code for identifying a segment that has the largest interpolation error.