Currently I'm writing an augmented reality app and I have some problems to get the objects on my screen. It's very frustrating for me that I'm not able to transform gps-points to the correspending screen-points on my android device. I've read many articles and many other posts on stackoverflow (I've already asked similar questions) but I still need your help.
I did the perspective projection which is explained in wikipedia.
What do I have to do with the result of the perspective projection to get the resulting screenpoint?
The Wikipedia article also confused me when I read it some time ago. Here is my attempt to explain it differently:
Let's simplify the situation. We have:
... and we want:
A schema for the X-screen-coordinates:
E is the position of our "eye" in this configuration, which I chose as origin to simplify.
The focal length f can be estimated knowing that:
tan(α) = (w/2) / f(1)
You can see on the picture that the triangles ECD and EBM are similar, so using the Side-Splitter Theorem, we get:
MB / CD = EM / EC<=>
X / x = f / z(2)
With both (1) and (2), we now have:
X = (x / z) * ( (w / 2) / tan(α) )
If we go back to the notation used in the Wikipedia article, our equation is equivalent to:
b_x = (d_x / d_z) * r_z
You can notice we are missing the multiplication by
s_x / r_x. This is because in our case, the "display size" and the "recording surface" are the same, so
s_x / r_x = 1.
Note: Same reasoning for Y.
tan(α) = 1. That's why this term doesn't appear in many implementations.
If you want to preserve the ratio of the elements you display, keep f constant for both X and Y, ie instead of calculating:
X = (x / z) * ( (w / 2) / tan(α) )and
Y = (y / z) * ( (h / 2) / tan(α) )
X = (x / z) * ( (min(w,h) / 2) / tan(α) )and
Y = (y / z) * ( (min(w,h) / 2) / tan(α) )
Note: when I said that "the "display size" and the "recording surface" are the same", that wasn't quite true, and the min operation is here to compensate this approximation, adapting the square surface r to the potentially-rectangular surface s.
Note 2: Instead of using min(w,h) / 2, Appunta uses
screenRatio= (getWidth()+getHeight())/2as you noticed. Both solutions preserve the elements ratio. The focal, and thus the angle of view, will simply be a bit different, depending on the screen's own ratio. You can actually use any function you want to define f.
As you may have noticed on the picture above, the screen coordinates are here defined between [-w/2 ; w/2] for X and [-h/2 ; h/2] for Y, but you probably want [0 ; w] and [0 ; h] instead.
X += w/2 and
Y += h/2 - Problem solved.
I hope this will answer your questions. I'll stay near if it needs editions.