So I've trying to find an alternative method of representing this equation.
plotting y against @ for 0-90 degrees, gives the graph in graph.png - which shows a nice smooth curve but with the asymptotic problem at 45 degrees.
Would be quite happy with an equivalent but alternate solution which works well for say, angles < 30 and > 60. (which is what i'm expecting, i.e. some equation dividing by sin or cos, given the /0 at 0 or 90degrees)
April 22nd 2008, 09:14 AM
Your work is excellent!
If , both rectangles are squares . . . and all bets are off. . . Your derived formulas are not needed and do not apply.
April 22nd 2008, 09:58 AM
Hi, thanks for 1st reply!
For solving this in the general case (using a computer) I've obviously got to avoid the case where @=45, but I really also need to be careful with angles close to 45 because all the maths goes screwy with those tiny divisors! An input angle of 45.0001 is quite possible and will give a divisor of 3.5e-5, obviously the dividend also becomes unusable.
What I would really like is a quick test along the lines of:
if angle < 40 or angle > 50:
y = (Sw - Ch) / (SS - CC)
y = ...
April 22nd 2008, 01:21 PM
Your answer isn't quite right - the original rectangle maintains its dimensions no matter what the angle is, so at 45 degrees w = h, but x != y.