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A method to calculate tangent vector of a given polyline curve

IP.com Disclosure Number: IPCOM000013912D
Original Publication Date: 2000-Nov-01
Included in the Prior Art Database: 2003-Jun-19
Document File: 2 page(s) / 80K

Publishing Venue

IBM

Abstract

Disclosed is a method to calculate a tangent vector at any point in a given polyline curve. Fig.1 shows a given polyline curve and a tangent vector at point. tangent vector Fig. 1 given polyline curve and tangent vector To calculate tangent vectors of given polyline, polyline can be converted to smooth parametric curve. In this method, there are 2 processes to calculate tangent vectors.

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A method to calculate tangent vector of a given polyline curve

   Disclosed is a method to calculate a tangent vector at any point in a given polyline curve. Fig.1 shows a given polyline curve and a tangent vector at point.

tangent vector

 Fig. 1 given polyline curve and tangent vector To calculate tangent vectors of given polyline, polyline can be converted to smooth parametric curve.

In this method, there are 2 processes to calculate tangent vectors.
(i) Calculating temporary tangent vectors using neighboring points.
(ii) Adjusting tangent vectors using other points weighted by distance. Fig.2 shows how to calculate a temporary tangent vector.

temporary tangent vector

circum scribed circle

polyline

 Fig.2 calculation of a temporary tangent vector A temporary tangent vector is calculated as a tangent vector of a circumscribed circle of a triangle consists of a given point and its neighboring 2 points. If a circumscribed circle can not be made, temporary tangent vector would be the vector directed to neighboring point. Then temporary tangent vectors are adjusted to minimize noise or local error.

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P0

C0

P0P1 P1

C0

C0'

P0C0 = P0C0' = P1C0'

R otation

 Fig.3 Adjustment of tangent vector To adjust tangent vector, this process uses normal vectors. Normal vectors can be calculated by rotating tangent vectors by 90 degree. Fig.3 shows how to adjust a normal vector.
(a) Calculating intersection of 2 normal vect...