Intersection of Spiral Curve with Circle
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Abstract
This study examines the problem of the intersection of a spiral curve with a circle, which especially occurs in the design of junctions. To achieve the requirements, an iterative method which has been programmed, is suggested with full mathematical formulas. Assessments of selected examples are made, and the results are tabulated. The intersection points are derived by starting first from a upper limit and second from a lower limit. If the same points are obtained when the iteration starts from both the upper and lower limits, the circle intersects the spiral at one point. If they are different points, the circle intersects the spiral at two points. However, if the iteration does not converge there are two cases for the problem: the circle either is tangent to the spiral or does not intersect it. In the tangent case, a method is suggested in order to find the tangent points at a sufficient precision.
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References
1.
“Forschungsgesellschaft für das StraBenwesen.” (1973). Richtlinien für die Anlage von LandstraBen. Teil II: Linienführung (RAL-L-V), Ausgabe, Germany (in German).
2.
Hubeny, K. (1980). “Die Klothoide, Formeln, Tafeln und Beispiele.”Mitt. d. geod., Institute der Techn. Univ. Graz., Folge 34, Graz, Germany (in German).
3.
Kasper, H., Schürba, W., and Lorenz, H. (1968). Die Klothoide als Trassierungselement . Ferd. Dümmlers Verlag, Bonn, Germany.
4.
McCormick, J. M., and Salvadori, M. G. (1984). Numerical methods with FORTRAN, G. Özmen, translator, The Publishing House of Technical Books, Istanbul, Turkey (in Turkish).
5.
Müller, G. (1984). Ingenieurgeodasie- Verkehrsbau- Grundlagen . VEB Verlag für Bauwesen, Berlin, Germany.
6.
Öztan, O., and Baykal, O. (1991). “Methods and recommendations for finding the intersection point of two clothoid curves.”Zeitschrift für Vermessungswesen. Stuttgart, Germany, Vol. 2, 74–84.
7.
Pipes, A. L., and Harvill, R. L. (1970). Applied mathematics for engineers and physicists . McGraw-Hill Book Co., New York, N.Y.
8.
Rothe, R. (1959). Höhere Mathematik; Teil II. B. G. Teubner Verlagsgeselschaft, Stuttgart, Germany.
9.
Schnadelbach, K. (1979). “Zur Berechnung von Elementen der Klothoide mittels rechtwinkliger Koordinaten.”Geodesy Schriftenreihe der TU Braunschweig, Germany, Vol. 1, 217–224.
10.
Schnadelbach, K. (1983). “Zur Berechnung von Schnittpunkten mit der Klothoide.”Zeitschrift für Vermessungswesen, Vol. 3, 112–118.
11.
Strubecker, K. (1967). Einführung in die Höhere Mathematik . Band II R. Oldenbourg Verlag, Munich, Germany.
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Copyright © 1995 American Society of Civil Engineers.
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Published online: Feb 1, 1995
Published in print: Feb 1995
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