getClickPosition : Model -> Mouse.Position -> Vec3
getClickPosition model pos =
    let
        x =
            toFloat pos.x

        y =
            toFloat pos.y

        normalizedPosition =
            ( (x * 2) / 1000 - 1, (1 - y / 1000 * 2) )

        homogeneousClipCoordinates =
            Vec4.vec4
                (Tuple.first normalizedPosition)
                (Tuple.second normalizedPosition)
                -1
                1

        invertedViewMatrix =
            Mat4.inverseOrthonormal (camera model)

        invertedProjectionMatrix =
            Maybe.withDefault Mat4.identity (Mat4.inverse perspective)

        vec4CameraCoordinates =
            mulVector invertedProjectionMatrix homogeneousClipCoordinates

        direction =
            Vec4.vec4 (Vec4.getX vec4CameraCoordinates) (Vec4.getY vec4CameraCoordinates) -1 0

        vec4WorldCoordinates =
            mulVector invertedViewMatrix direction

        vec3WorldCoordinates =
            vec3 (Vec4.getX vec4WorldCoordinates) (Vec4.getY vec4WorldCoordinates) (Vec4.getZ vec4WorldCoordinates)

        normalizedVec3WorldCoordinates =
            Vec3.normalize vec3WorldCoordinates

        origin =
            model.cameraPos

        scaledDirection =
            Vec3.scale 20 normalizedVec3WorldCoordinates

        destination =
            Vec3.add origin scaledDirection
    in
        destination