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折射包絡線


折射包絡線是一條曲線,它是從給定鏡面形狀的指定點(或產生平行光線的無限遠點)發出的光線的包絡。光線發出的點稱為輻射點。折射包絡線是垂足曲線漸屈線(Lawrence 1972,第 60 頁)。

下表列出了某些常見曲線的折射包絡線,省略了為四葉線列出的不正確的折射包絡線(Lawrence 1972,第 207 頁)。


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阿特澤瑪螺線, 焦散, 折射焦散線

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參考文獻

Borovikov, V. A. and Kinber, B. Y. Geometrical Theory of Diffraction. London: Institute of Electrical Engineering, 1994.Bruce, J. W.; Giblin; P. G.; and Gibson, C. G. Amer. Math. Monthly 88, 651, 1981.Bruce, J. W.; Giblin, P. G.; and Gibson, C. G. Topology 21, 179, 1982.Bruce, J. W.; Giblin, P. G.; and Gibson, C. G. Proc. Symposia Pure Math. 40/1, 179, 1983.Cornbleet, S. Microwave and Geometrical Optics. London: Academic Press, 1994.Ehlers, J. and Newman, E. T. J. Math. Phys. 41, 3344, 2000.Georgiou, C.; Hasanis, T.; Koutroufiotis, D. Geom. Dedicata 28, 153, 1988.Giblin, P. J. and Kingston, J. G. Quart. J. Math Oxford 37, 17, 1986.Hairer, E. and Wanner, G. Analysis by Its History. New York: Springer-Verlag, 1996.Hartman, P. and Valentine, F. A. Duke Math. J. 26, 373, 1959.Knill, O. Elem. Math. 53, 89, 1998.Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 60 and 207, 1972.Loe, B. L. and Beagley, N. Coll. Math. J. 28, 277, 1997.Porteous, I. R. Geometric Differentiation for the Intelligence of Curves and Surfaces. Cambridge, England: Cambridge University Press, 1994.Poston, T. and Stewart, I. Catastrophe Theory and Its Application. London: Pitman, 1978.Schupp, H. and Dabrock, H. Höhere Kurven. Mannheim, Germany: BI, 1995.Trott, M. The Mathematica GuideBook for Graphics. New York: Springer-Verlag, pp. 9-11, 2004. http://www.mathematicaguidebooks.org/.

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折射包絡線

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Weisstein, Eric W. “折射包絡線。” 來自 Web 資源。 https://mathworld.tw/Catacaustic.html

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