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#1 2007-08-19 21:29:30

kskan2005
Member
Registered: 2007-08-19
Posts: 2

Help: Co-ordinates

y

10|                  A .______________. B
09|                   /                         /
08|                  /                       /
07|    E1.        /       E2.          /
06|              /                     /
05|             /                   /               E3.
04|            /                 /
03|          /                / 
02|        /           __ /. C
01|    D./ __ -----               
00|_____________________________  x
      1   2   3   4   5   6   7   8   9   10                                                               


Please help me.
I need a formula or algorithm that can calculate whether each point E1, E2 or E3 is within the coverage area of 4 coordinates A, B, C & D like above. Result suppose is:
  E1- Not
  E2- Yes
  E3- Not

Please help.

Thanks

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#2 2007-08-19 21:34:52

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

Re: Help: Co-ordinates

make a set of inequalities that have to be true:

so for example, the top line (AB) will be y < 10, any point inside the shape, must have y < 10.
then for the AD line, find the line equation y = mx + c, and the inequality will be y < mx + c for that line
then for the BC line, it will be y > mx + c, for line DC, y > mx + c.

then you will have 4 inequalities that if all true, tell you the point is inside the shape.


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The End Of All Things To Come.

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#3 2007-08-20 13:27:17

kskan2005
Member
Registered: 2007-08-19
Posts: 2

Re: Help: Co-ordinates

I am newbie. Can you show the example below to me, i wish to have step by step.
Question giving 4 points(cannot use any graft to support), which is (1,1), (2,3), (5,5),(8,6), then request to proof that (2,2) is in the area. How?

First step, we will get 4 line equations:
1. y=2x-1
2. y=0.6667x+1.6667
3. y=0.3333x+3.3333
4. y=0.7143x+0.2857

Second step?

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