3D Geometry projecting a point in space to an image given FOV and angles

I'm attempting to project a 3D point in Cartesian space onto an image, so it is shown as a circle at the location on the image it would be seen if a certain camera was looking at it.

Knows: The camera has horizontal field of view, vertical FOV, azimuth and elevation. It is located at (0,0,0) although being able to change this would be good. The image has a certain size. The point in space has a know X, Y, Z location.

I'm using the very good C++ library MathGeoLib

In my attempt, changing azimuth or elevation does not work, but the projection seems to work ok if rotation is ignored.

Does anyone have experience with this kind of problem?

Frustum MyClass::GetCameraFrustrum()
{
  Frustum frustrum;
  frustrum.SetPerspective(DegToRad(_horizontal_field_of_view), DegToRad(_vertical_filed_of_view));
  // Looking straight down the z axis
  frustrum.SetFront(vec(0, 0, 1));
  frustrum.SetUp(vec(0, 1, 0));
  frustrum.SetPos(vec(0,0,0));
  frustrum.SetKind(FrustumSpaceGL, FrustumRightHanded);

  frustrum.SetViewPlaneDistances(1, 2000);
  float3x3 rotate_around_x = float3x3::RotateX(DegToRad(_angle_azimuth));
  frustrum.Transform(rotate_around_x);

  float3x3 rotate_around_y = float3x3::RotateY(DegToRad(_angle_elevation));
  frustrum.Transform(rotate_around_y);
  return frustrum;
}

void MyClass::Test()
{
  cv::Mat image = cv::Mat::zeros(2000, 2000, CV_8UC1);
  Frustum camera_frustrum = GetCameraFrustrum();
  vec projection = camera_frustrum.Project(_position_of_object);

  cv::Point2d location_on_image(projection.x * image.cols, projection.y * image.rows);

  LOG_DEBUG << location_on_image;
  cv::circle(image, location_on_image, 5, cv::Scalar(255, 0, 0), 3, cv::LINE_AA);
}