For a point in an irregular polygon, what is the most efficient way to select the edge closest to the point?

Question

Given an irregular polygon and a point inside that polygon, how do you determine which edge in a polygon is closest to a point?

I probably have to run this calculation for a large set of points in the polygon (for example, 50-200 points).

Answer 1

• Calculate the nearest point on the line tangent to each edge of the polygon.
• Calculate the nearest point on each line segment (the edge of the polygon) to the point in question.
• Calculate the distance from the nearest point on each line segment to the point in question.
• . .

- (O (n)).

:

, .

• p1 = {x1, y1}.
• p2 = {x2, y2}.
• p3 = {x3,y3}.
• u - p1 p2, , p1 p2, p1+u(p2-p1)= p3 ( p3 , p1 p2).
• u = ((x3 - x1)(x2 - x1)+(y3 - y1)(y2 - y1)) / ((x2 - x1)^2 + (y2 - y1)^2)
• , p3 , p1 p2, pu = {xu, yu}
• xu = x1 + u (x2 - x1)
• yu = y1 + u (y2- y1)
• , , pu = {xu, yu}
• (.. p1s p2s)

( ) .

pu , 0 <= u <= 1. . , pu, p1, p2, and u, , :

• Let pc = {xc, yc} .
• IF u<0 THEN pc = p1
• ELSE IF u>1 THEN pc = p2
• ELSE pc = pu

.

• p3 pc= `sqrt ((x3 - xc) ^ 2 + (y3 - yc) ^ 2)

. .

• , . .

, , :

....

Answer 2

: , ? , . ? ? , ?

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Answer 3

Put this message in SO for inspiration, the distance from a point within the polygon to the edge of the polygon, or is this the shortest distance between a point and a line segment