QUADRATIC APPROXIMATE OFFSET CURVES FOR QUADRATIC CURVE SEGMENTS
First Claim
Patent Images
1. A method for producing an offset curve, implemented using tangible and physical computing functionality, comprising:
- receiving data that describes an original control triangle, the original control triangle defining an original curve segment, the original curve segment, in turn, defining a portion of a parabola having an axis a;
constructing an original axis-symmetric control triangle based on the original control triangle, the original axis-symmetric control triangle being symmetric with respect to the axis a of the parabola;
constructing a new control triangle by adjusting positions of control points associated with the original axis-symmetric control triangle, the new control triangle also being symmetric with respect to the axis a of parabola, the new control triangle defining an approximate offset curve, and all points on the approximate offset curve being separated from all points on the original curve segment by at least a distance d; and
performing an application-specific action based on the approximate offset curve.
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Abstract
A system is described herein that produces at least one approximate offset curve that is separated by an original curve segment So by at least a distance d, thus defining a bounding region between the original curve segment So and the approximate offset curve. The original curve segment So and the approximate offset curve both have a quadratic form. In view of this quadratic form, the system can represent the approximate offset curve in an efficient manner (e.g., using three control points). Further, the system can perform calculations with respect to the approximate offset curve in an efficient manner.
11 Citations
20 Claims
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1. A method for producing an offset curve, implemented using tangible and physical computing functionality, comprising:
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receiving data that describes an original control triangle, the original control triangle defining an original curve segment, the original curve segment, in turn, defining a portion of a parabola having an axis a; constructing an original axis-symmetric control triangle based on the original control triangle, the original axis-symmetric control triangle being symmetric with respect to the axis a of the parabola; constructing a new control triangle by adjusting positions of control points associated with the original axis-symmetric control triangle, the new control triangle also being symmetric with respect to the axis a of parabola, the new control triangle defining an approximate offset curve, and all points on the approximate offset curve being separated from all points on the original curve segment by at least a distance d; and performing an application-specific action based on the approximate offset curve. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
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13. A system for producing and applying an offset curve, implemented using tangible and physical computing functionality, comprising:
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an offset curve determination module for; receiving data that describes an original control triangle, the original control triangle defining an original curve segment; and producing an approximate offset curve based on the original control triangle, all points on the approximate offset curve being separated from all points on the original curve segment by at least a distance d, the original curve segment and the approximate offset curve each representing quadratic curves; and an application module for performing an application-specific action based on the approximate offset curve. - View Dependent Claims (14, 15, 16, 17)
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18. A computer readable storage medium for storing computer readable instructions, the computer readable instructions providing an offset curve determination module when executed by one or more processing devices, the computer readable instructions comprising:
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logic configured to receive data that describes an original control triangle associated with control points p0, p1, and p2, the original control triangle defining an original curve segment So; logic configured to determine a line m which connects a midpoint of a line segment p0p2 to the control point p1; logic configured to draw a chord that is perpendicular to the line m which intersects an extended version of the original curve segment So twice, defining new control points q0 and q2; logic configured to extend tangent lines at the new control points q0 and q2, yielding a new control point q1 at an intersection of the tangent lines, the control points q0, q1, and q2 together describing an original axis-symmetric control triangle; and logic configured to displace the new control points (q0, q1, q2) in an inward or outward direction to produce new control points (q′
0, q′
1, q′
2), the new control points (q′
0, q′
1, q′
2) defining a new control triangle and an associated approximate offset curve. - View Dependent Claims (19, 20)
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Specification