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can you help me with an algorithm that determines if a given...

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Question by sait_pietro
Submitted on 12/8/2003
Related FAQ: sci.math FAQ: How to compute Pi?
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can you help me with an algorithm that determines if a given line (p1,p2) intetrcepts a circle (center,radius)


Answer by okp
Submitted on 3/25/2004
Rating: Not yet rated Rate this answer: Vote
Lets P1=(x1,y1)
     P2=(x2,y2)
center=(x0,y0)
radius=r
The line (p1,p2) intercepts the circle (x0,y0,r)
iff
(  (x1-x2)*(y1-y0)-(y1-y2)*(x1-x0)  )^2  <  (  (x1-x2)^2+(y1-y2)^2  ) * r^2
or in a compact form
   dx=x1-x2    cx=x1-x0
   dy=y1-y2    cy=y1-y0
  ( dx*cy-dy*cx )^2  <  ( dx^2+dy^2 ) * r^2

It can be probed to steps if
1.- Translation the origin to the center of the circle.
2.- write the line in normal form
    x*Cos(a)+y*Sin(a)=d
if the distance of the line to the new origin (now the center) is less/equal to the radius then the line intercepts/is tangent to the circle.

 

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