FOV-based camera clipping in 3D

camera_clip.cpp

bool is_point_in_fov(const ls::draw::Camera& cam, math::vec3 point, const float fovReduction = 1.f) {
    // Get the local camera's absolute position and direction in world-space
    const math::vec3&& eyePos   = cam.get_abs_position();
    const math::vec3&& eyeDir   = math::normalize(cam.get_eye_direction());
    
    // translate the input point using a model-view matrix (no projection
    // matrix should be used).
    const math::mat4&& mvMat    = modelMatrix * cam.get_view_matrix();
    const math::vec4&& temp     = math::vec4{-point[0], -point[1],-point[2], 0.f} * mvMat;
    
    // Move the translated point into the camera's local space
    point                       = {temp[0], temp[1], temp[2]};
    point                       = math::normalize(eyePos - point);
    
    // Get the cosine of the angle at which the point is oriented from the
    // camera's view direction
    const float angleToPoint    = math::dot(point, eyeDir) * cam.get_fov();
    const float angleOfView     = std::cos(cam.get_fov()) / fovReduction;
    
    /* FOV is in radians, pointAngle is from -1 to 1. FOV defines the angle of
     * a cone by which objects can be clipped within. Through extensive
     * testing, it appears the difference in units between these two values
     * doesn't matter :D
     * 
     * A variable, fovReduction, has been provided to help grow or shrink the
     * FOV to account for the camera's viewport dimensions not fitting
     * perfectly within the clipping cone.
     *         ______
     *       /clipping\
     *      /__________\
     *     || viewport ||
     *     ||__________||
     *      \   cone   /
     *       \ ______ /
     */
    return angleToPoint >= angleOfView;
}

Updated with a more accurate way to clip points out of a camera's FOV while taking into account multiple resolutions/aspect ratios.