# 垂足曲线

${\displaystyle t\mapsto c(t)+{\langle c'(t),P-c(t)\rangle \over |c'(t)|^{2}}c'(t)}$

${\displaystyle X[x,y]={\frac {(xy'-yx')y'}{x'^{2}+y'^{2}}}}$

${\displaystyle Y[x,y]={\frac {(yx'-xy')x'}{x'^{2}+y'^{2}}}}$

## 参考文献

• Gray, A. "Pedal Curves." §5.8 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 117-125, 1997.
• Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 46-49 and 204, 1972.
• Lockwood, E. H. "Pedal Curves." Ch. 18 in A Book of Curves. Cambridge, England: Cambridge University Press, pp. 152-155, 1967.
• Yates, R. C. "Pedal Curves." A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 160-165, 1952.