Confining a point in a rectangle

[mahadevan.swamy]

Hi,

This problem involves more of algebra and geometry. I rely on excel to
perform some calculations.

I have two parallel slopes (+'ive) and two slopes which is
perpendicular to these two slopes (-'ive). This design makes a
rectangle and I have a point (x,y). My objective is to come up with
conditions which will check whether a point is within this rectangle
or not and assign a value.

In my current design, I have two positive slopes A and B that are
parallel and have different y-intercepts (slope A at the bottom and
slope B and the top). I have two negative slopes C and D that are
perpendicular to A and B and also have different y-intercepts (slope D
at the bottom and slope C at the top) . This makes a rectangle.

The conditions that I have come up with is: m - slope and c -
intercept
A slope - y>ma(x)+ca
B slope - y<mb(x)+cb
C slope - y<mc(x)+cc
D slope - y>md(x)+cd

I have noticed that this conditon only works for 0 to 90 degrees. But
if i happen to shift my rectange to another angle beyond 90 degrees
and apply the same thing to 90-180, or 180-270 or 270-360 degrees, it
doesnt work. Can anyone suggest any solution to my logic. Thanks

 

[Guest]

In almost every computer solution dealing with such things, I've had to treat
the 4 cardinal points (0, 90, 180, 270) as unique exceptions and specifically
test for them. In some cases (depending on the application) when such an
angle was encountered, then an intentional error of some small fraction of a
degree can be introduced to prevent the failure. In some applications this
is acceptable, in others it is not.