EP0393680A2
Expired / Lapsed
EP
⏱️ 0.0 years remaining
Method for fitting third-degree Bezier curves to series of data points
Assignee: Toshiba Corp
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Filing: 1990-04-19
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Granted: —
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Expires: 2010-04-19
Abstract
Abstract In curve fitting with respect to a series of data points representing a figure, control points Q1, Q2 are set for a parameter tx in accordance with a start point Q0, an end point Q3, and a passing point X, and gradients ϑ0, ϑ3, ϑx of the respective points. A gradient ϑ(tx) of a Bezier curve specified on the basis of the start and end points Q0, Q3 and the control points Q1, Q2 is obtained for the parameter tx. If the gradient ϑ(tx), the gradient ϑx and a predetermined reference gradient ϑref satisfy a relation of |ϑ(tx)-ϑx| < ϑref, the curve specified by the start and end points Q0, Q3 and the control points Q1, Q2 for the parameter tx is determined to be a Bezier curve passing the passing point X.
Inventors
- 👤 Keiichi C/O Intellectual Property Div. Yamada
Bibliographic Details
Application Number
—
Jurisdiction
EP
Data Source
google_patents
Last Synchronized
2026-11-09 00:27
CPC Classifications
G; G06; G06F; G06F17/00; G06F17/10; G06F17/17; G06T; G06T11/00; G06T11/20; G06T11/23
Claims Analysis
Total Claims: 8
Claim 1
Independent Claim
99 words
A method for fitting a third-degree Bezier curve to a series of data points, characterized by comprising the steps of: setting parameters representing a curve segment having a passing point; calculating two control parameters for representing the third-degree Bezier curve from the set parameters; calculating a gradient of the third-degree Bezier curve from the set parameters and the calculated two control parameters; comparing the calculated gradient with a gradient of the passing point; determining a fitting degree in accordance with a comparison result; and fitting the third-degree Bezier curve to the curve segment in accordance with a determination result.
Claim 2
Independent Claim
99 words
A method for fitting a third-degree Bezier curve to a series of data points, characterized by comprising the steps of: setting parameters representing a curve segment having a passing point; calculating two control parameters for representing the third-degree Bezier curve from the set parameters; calculating a gradient of the third-degree Bezier curve from the set parameters and the calculated two control parameters; comparing the calculated gradient with a gradient of the passing point; determining a fitting degree in accordance with a comparison result; and fitting the third-degree Bezier curve to the curve segment in accordance with a determination result.
Claim 3
Dependent Claim
29 words
The method according to claim 1, characterized in that the set parameters represent a start point, the passing point, an end point and respective gradients in the curve segment.
Claim 4
Dependent Claim
50 words
The method according to claim 1, characterized in that the determining step includes the step of obtaining the two control parameters as control parameters of the third-degree Bezier curve when a difference gradient between the calculated gradient and the gradient of the passing point is smaller than a desired gradient.
Claim 5
Independent Claim
193 words
A method for fitting a third-degree Bezier curve to a series of data points, characterized by comprising the steps of: setting parameters representing a curve segment having a plurality of passing points, the parameters including at least two couples of first control parameters for representing the third-degree Bezier curves; calculating at least two couples of second control parameters for representing the third-degree Bezier curves from the set parameters; calculating a plurality of gradients of the third-degree Bezier curves from the set parameters and the calculated second control parameters; comparing the calculated gradients with gradients of the passing points; determining a fitting degree for each passing point in accordance with a first comparison result; calculating at least two couples of distances between the first control parameters and the second control parameters for each passing point from the set parameters and the calculated second control parameters in accordance with a first determination result; comparing the calculated distances with a desired distance; determining a fitting degree for at least two passing points in accordance with a second comparison result; and fitting the third-degree Bezier curve to the curve segment in accordance with a second determination result.
Claim 6
Independent Claim
193 words
A method for fitting a third-degree Bezier curve to a series of data points, characterized by comprising the steps of: setting parameters representing a curve segment having a plurality of passing points, the parameters including at least two couples of first control parameters for representing the third-degree Bezier curves; calculating at least two couples of second control parameters for representing the third-degree Bezier curves from the set parameters; calculating a plurality of gradients of the third-degree Bezier curves from the set parameters and the calculated second control parameters; comparing the calculated gradients with gradients of the passing points; determining a fitting degree for each passing point in accordance with a first comparison result; calculating at least two couples of distances between the first control parameters and the second control parameters for each passing point from the set parameters and the calculated second control parameters in accordance with a first determination result; comparing the calculated distances with a desired distance; determining a fitting degree for at least two passing points in accordance with a second comparison result; and fitting the third-degree Bezier curve to the curve segment in accordance with a second determination result.
Claim 7
Dependent Claim
29 words
The method according to claim 4, characterized in that the set parameters represent a start point, the passing point, an end point and respective gradients in the curve segment.
Claim 8
Dependent Claim
58 words
The method according to claim 4, characterized in that the step of determining the fitting degree for at least two passing points includes the step of obtaining the second control parameters as control parameters of the third-degree Bezier curve for at least two passing points when a summation of the calculated distances is smaller than a desired distance.
References Cited (Backward Citations)
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