US5140236A
Expired / Lapsed
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Spline interpolation method
Assignee: Fanuc Corp
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Filing: 1989-09-29
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Granted: 1992-08-18
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Expires: 2009-09-29
Abstract
Abstract A spline interpolation method of subjecting given points to interpolation by using a cubic spline curve is provided. A first-derivative vector is derived from a preset number of points including a starting point (P 1 ), and a cubic equation between the starting point and a next point is derived based on the coordinate values of the preset points including the starting point (P 1 ) and the extreme point condition of the starting point (P 1 ), to derive a spline curve between the starting point (P 1 ) and a point (P 2 ) next to the starting point (P 1 ). Next, the first-derivative vector at P 2 and a new next point are used instead of the starting point (P 1 ), to derive a cubic curve between P 2 and P 3 . In this way, a cubic equation between points is sequentially derived to obtain a cubic spline curve, and as a result, a spline curve posing no practical problems can be obtained without previously receiving all of the sequential points, while sequentially receiving the sequential points in a forward direction.
Inventors
- 👤 Hideaki Kawamura
- 👤 Takao Sasaki
- 👤 Toshiaki Otsuki
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-10-27 14:49
CPC Classifications
G; G05; G05B; G05B19/00; G05B19/02; G05B19/18; G05B19/41; G05B19/4103; G05B2219/00; G05B2219/30; G05B2219/34; G05B2219/34145
Claims Analysis
Total Claims: 10
Claim 1
Independent Claim
140 words
A spline interpolation method for performing machining according to sequentially created cubic spline curves by subjecting given points to interpolation using the cubic spline curves, comprising the steps of: deriving a first-derivative vector from a preset number of points including a starting point; deriving a first cubic equation between said starting point and a next point based on coordinate values of the preset number of points including said starting point, an extreme point condition of said starting point and said first-derivative vector, to derive a first cubic spline curve between said starting point and a point next to said starting point; using a new point instead of said starting point and sequentially deriving a second cubic equation between points, to thereby derive a second cubic spline curve; and performing machining in accordance with the first and second cubic spline curves.
Claim 2
Dependent Claim
140 words
A spline interpolation method for performing machining according to sequentially created cubic spline curves by subjecting given points to interpolation using the cubic spline curves, comprising the steps of: deriving a first-derivative vector from a preset number of points including a starting point; deriving a first cubic equation between said starting point and a next point based on coordinate values of the preset number of points including said starting point, an extreme point condition of said starting point and said first-derivative vector, to derive a first cubic spline curve between said starting point and a point next to said starting point; using a new point instead of said starting point and sequentially deriving a second cubic equation between points, to thereby derive a second cubic spline curve; and performing machining in accordance with the first and second cubic spline curves.
Claim 3
Dependent Claim
38 words
A spline interpolation method according to claim 1, wherein the cubic spline curve is subjected to interpolation in said extreme point condition in which second-derivative vectors at said starting point and an end point are set at 0.
Claim 4
Dependent Claim
45 words
A spline interpolation method according to claim 1, wherein the cubic spline curve is subjected to interpolation in said extreme point condition in which the first-derivative vector at the starting point is given and a second-derivative vector at an end point is set at 0.
Claim 5
Dependent Claim
29 words
A spline interpolation method according to claim 1, characterized in that the cubic spline curve near an end point is derived by using auxiliary points after the end point.
Claim 6
Dependent Claim
141 words
A spline interpolation method for performing machining according to sequentially created cubic spline curves by subjecting given points to interpolation using the cubic spline curves, comprising the steps of: deriving a first-derivative vector from a preset number of points including a starting point; deriving a first cubic equation between said starting point and a next point including said starting point, an extreme point condition of said starting point and said first-derivative vector, to derive a first spline curve between said starting point and a point next to said starting point; using a new point instead of said starting point and sequentially deriving a second cubic equation between points, to thereby derive a second cubic spline curve; distributing interpolation pulses in accordance with the cubic spline curves; driving servo motors with the interpolation pulses; and performing machining along the cubic spline curve.
Claim 7
Dependent Claim
141 words
A spline interpolation method for performing machining according to sequentially created cubic spline curves by subjecting given points to interpolation using the cubic spline curves, comprising the steps of: deriving a first-derivative vector from a preset number of points including a starting point; deriving a first cubic equation between said starting point and a next point including said starting point, an extreme point condition of said starting point and said first-derivative vector, to derive a first spline curve between said starting point and a point next to said starting point; using a new point instead of said starting point and sequentially deriving a second cubic equation between points, to thereby derive a second cubic spline curve; distributing interpolation pulses in accordance with the cubic spline curves; driving servo motors with the interpolation pulses; and performing machining along the cubic spline curve.
Claim 8
Dependent Claim
38 words
A spline interpolation method according to claim 5, wherein the cubic spline curve is subjected to interpolation ins aid extreme point condition in which second-derivative vectors at said starting point and an end point are set at 0.
Claim 9
Dependent Claim
45 words
A spline interpolation method according to claim 5, wherein the cubic spline curve is subjected to interpolation in said extreme point condition in which the first-derivative vector at the starting point is given and a second-derivative vector at an end point is set at 0.
Claim 10
Dependent Claim
29 words
A spline interpolation method according to claim 5, characterized in that the cubic spline curve near an end point is derived by using auxiliary points after the end point.
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USPTO Annuity & Maintenance Windows
| Annuity Stage | Window Opens | Payment Deadline | Surcharge Period Until | Estimated Fee | Status |
|---|---|---|---|---|---|
| 3.5 Years (Year 4) | 1995-08-18 | 1996-02-17 | 1996-08-18 | $2000.00 | Window Closed / Lapsed |
| 7.5 Years (Year 8) | 1999-08-18 | 2000-02-17 | 2000-08-18 | $3760.00 | Window Closed / Lapsed |
| 11.5 Years (Year 12) | 2003-08-18 | 2004-02-17 | 2004-08-18 | $7700.00 | Window Closed / Lapsed |