Dear Forum,

Hoping someone can help me with a little trig and geometry

In the attached pic the grey rectangle has been rotated by @ degrees, the red dotted box is then constructed around it to exactly enclose it.

given the dimensions of the bounding box and the angle of rotation, I want to calucate the size of the original rectangle (and hence its coordinates)

i.e. given w, h and @, what are x, y (and therby a, b, c, d)?

sin @ = c / x = b / y = S

cos @ = a / x = d / y = C

tan @ = c / a = b / d = T

w = a + b

y = c + d

=>

w = xC + yS

x = (w - yS) / C

h = xS + yC

x = (h - yC) / S

=>

(w - yS) / C = (h - yC) / S

S(w - yS) = C(h-yC)

Sw - ySS = Ch - yCC

Sw - Ch = ySS - yCC

Sw - Ch = y(SS - CC)

y = (Sw - Ch) / (SS - CC)

The problem is that at @=45, SS-CC is 0!

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)

Thank you!