Window coordinates to camera angles?

Question

So I want to use quaternions and angles to control my camera using my mouse.

I accumulate the vertical/horizontal angles like this:

void Camera::RotateCamera(const float offsetHorizontalAngle, const float offsetVerticalAngle)
{
    mHorizontalAngle += offsetHorizontalAngle;
    mHorizontalAngle = std::fmod(mHorizontalAngle, 360.0f);

    mVerticalAngle += offsetVerticalAngle;
    mVerticalAngle = std::fmod(mVerticalAngle, 360.0f);
}

and compute my orientation like this:

Mat4 Camera::Orientation() const
{
    Quaternion rotation;
    rotation = glm::angleAxis(mVerticalAngle, Vec3(1.0f, 0.0f, 0.0f));
    rotation = rotation * glm::angleAxis(mHorizontalAngle, Vec3(0.0f, 1.0f, 0.0f));

    return glm::toMat4(rotation);
}

and the forward vector, which I need for glm::lookAt, like this:

Vec3 Camera::Forward() const
{
    return Vec3(glm::inverse(Orientation()) * Vec4(0.0f, 0.0f, -1.0f, 0.0f));
}

I think that should do the trick, but I do not know how in my example game to get actual angles? All I have is the current and previous mouse location in window coordinates.. how can I get proper angles from that?

EDIT: on a second thought.. my "RotateCamera()" cant be right; I am experiencing rubber-banding effect due to the angles reseting after reaching 360 deegres... so how do I accumulate angles properly? I can just sum them up endlessly

Answer 1

Take a cross section of the viewing frustum (the blue circle is your mouse position):

• Theta is half of your FOV
• p is your projection plane distance (don't worry - it will cancel out)

From simple ratios it is clear that:

But from simple trignometry

So ...

Just calculate the angle psi for each of your mouse positions and subtract to get the difference.

A similar formula can be found for the vertical angle:

Where A is your aspect ratio (width / height)