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Line Line Intersections Explanation .... | Reply
Nice article - one of the clearest explanations i have seen so far - there is one thing im not sure of ...

In the Line-Line Intersection part....

for 2 points on a straight line
(x1, y1) (x2, y2)
if
Ax + By = C
then
A = y2 - y1
B = x1 - x2
C = A*x1 + B *y1
could you expand on how this is derived / why it works ?

thanks

Jim
Re: Line Line Intersections Explanation .... (response to post by jimbarritt) | Reply
We know
A.x1 + B.y1 = C and A.x2 + B.y2 = C
so combining these gives
A.x1 + B.y1 = A.x2 + B.y2
=> A(x1 - x2) = B(y2 - y1)
The thing to remember is that A, B and C can all be scaled by a constant as much as we like - i.e. if {A, B, C} represent the line, so does {2A, 2B, 2C} - so we just have to find a solution to the above equation. One solution happens to be
A = y2 - y1 and B = x1 - x2
You can then work out C by putting those values into one of the original equations (the example you give uses the first one).
Re: Line Line Intersections Explanation .... (response to post by sql_lall) | Reply
thats a cool trick

So one solution to
A.c = B.d
is
d.c = c.d
nice.

thanks for your help and quick answer!
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