Maintaining Aspect Ratio and Scale Independent of Window Size with freeglut - c++

Question

I've been wanting to experiment with platforming physics using freeglut, but before I would allow myself to start, I had an old problem to take care of.
You see, I want to write a reshape handler that not only maintains the scale and eliminates any distortion of the view, but also allows all of the onscreen shapes to maintain their size even while the window is too small to contain them (i.e. let them be clipped).
I've almost got all three parts solved, but when I scale my window, the circle I have drawn onto it scales just slightly. Otherwise, I got the clipping, and I have eliminated the distortion. Update: What I want to achieve is a program that maintains scale and aspect ratio independent of window size.
Here's my code:
void reshape(int nwidth,int nheight)
{
glViewport(0,0,nwidth,nheight);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
//here begins the code
double bound = 1.5;
double aspect = double(nwidth)/nheight;
//so far, I get the best results by normalizing the dimensions
double norm = sqrt(bound*bound+aspect*aspect);
double invnorm = sqrt(bound*bound+(1/aspect)*(1/aspect));
if(nwidth <= nheight)
glOrtho(-bound/invnorm,bound/invnorm,-bound/aspect/invnorm,bound/aspect/invnorm,-1,1);
else
glOrtho(-bound*aspect/norm,bound*aspect/norm,-bound/norm,bound/norm,-1,1);
//without setting the modelview matrix to the identity form,
//the circle becomes an oval, and does not clip when nheight > nwidth
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
}
Update: As per Mr. Coleman's suggestion, I've tried switching out single precision for double. The scaling issue has improved along the vertical axis, but whenever I drag the horizontal axis in either direction, the shape still scales by a noticeable amount. It's still the same shape throughout, but a visual inspection tells me that the shape is not the same size when the window is 150x300 as it is when the window is 600x800, regardless of which glOrtho is being executed.

Answer 1

I've got it. Here's how I changed my code:
//at the top of the source file, in global scope:
int init_width;//the initial width
int init_height;//the initial height
void reshape(int new_width, int new_height)
{
//moved the glViewport call further down (it was part of an earlier idea that didn't work out)
glMatrixMode(GL_PROJECTION);
glLoadIdentity();//these two lines are unchanged
double bound = 1.0; //I reduced the edge distance to make the shape larger in the window
double scaleX = double(new_width)/init_width;
double scaleY = double(new_height)/init_height;
glOrtho( -bound*scaleX/2, bound*scaleX/2, //these are halved in order to un-squash the shape
-bound*scaleY, bound*scaleY, -1,1 );
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
glViewport(0,0,new_width,new_height);
}
That is what my code looks like now. It maintains the scale and shape of what I have on screen, and allows it to go offscreen when the window is too small to contain the entire shape.