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单词 Point-Quadratic Distance
释义

Point-Quadratic Distance

Find the minimum distance between a point in the plane and a quadratic Plane Curve

(1)

The square of the distance is
 
 (2)

Minimizing the distance squared is the equivalent to minimizing the distance (since and have minima at thesame point), so take
(3)


(4)


(5)

Minimizing the distance therefore requires solution of a Cubic Equation.

See also Point-Point Distance--1-D, Point-Point Distance--2-D, Point-Point Distance--3-D
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更新时间:2025/5/23 7:10:08