Align a camera to a rectangle

Question

We are trying to align our camera in order to see as closest as possible a rectangle(a face of a parallelepiped since we are in 3D). The aspect ratio of the viewport considered here and the rectangle to align do not match.

What we do:

In our scene is this rectangle. The camera is position in front of it. Here is the configuration of the camera:

projection = Matrix.CreatePerspectiveFieldOfView(
    Fov, AspectRatio, NearPlane, FarPlane
);

view = Matrix.CreateLookAt(Position, Target, this.Up);

float Fov = PI/4;

float AspectRatio = device.Viewport.AspectRatio;

Vector3 Target is set to the center of the rectangle.

Vector3 Position is the value we are looking for.

And then to initialize the camera: oat width = (float)GraphicsDevice.Viewport.Width; float height = (float)GraphicsDevice.Viewport.Height;

float dist = (width / 2) + (height / 2);

float alpha = 0;
float beta = 0;
float gamma = 0;

alpha = (float)Math.Sqrt(Math.Pow(width / 2, 2) + Math.Pow(height / 2, 2));
beta = height / ((float)Math.Cos(MathHelper.ToRadians(70.3f)) * 2);
gamma = (float)Math.Sqrt(beta * beta - alpha * alpha);


position = new Vector3(width / 2, -height / 2, gamma);
target = new Vector3(width / 2, -height / 2, dist / 2);

camera = new Camera(GraphicsDevice.Viewport)
{
    Position = position,
    Target = target,
    Near = 1f,
    Far = 10000f
};

(VS solution)

One more precision: to create the view, we are using Matrix.CreateLookAt and for the projection Matrix.CreatePerspectiveFieldOfView. We are not sure if these are the perfect choices either but sounds like it.

What we get:

After some basic trigonometry we got a camera Position which works when the Height > Width. As:

But it does not when the Width > Height:

Do you...

...have any idea what are we doing wrong? Do you have any other or better way to achieve this?

Answer 1

Finding the height of the pyramid does not work. Just use the Tan and since the Fov = PI/4 the code should look like this:

float tanGamma = (height / 2) * ((float)Math.Tan(MathHelper.ToRadians(67.5f)));