RealityKit_DirectionalLight_Question

My application calculates three distinct Meesus Double [x, y, z] Radian values to light a sphere in RealityKit with DirectionalLight. It is my understanding that I must use (simd_quatf) for each radian value to properly light the sphere in the view. The code correctly [orientates] the sphere with the combined (simd_quatf) DirectionalLight in the view, but the illumination (Z-axis) fails to properly illuminate the sphere with the expected result, compared to associated Meesus web page images. For the moment, I do not know how to correct the (Z-axis). Curious for a suggestion ... :]

//  Location values.
let theLatitude: Double = 51.13107260
let theLongitude: Double = -114.01127910
let currentDate: Date = Date()

struct TheCalculatedMoonPhaseTest_ContentView: View {
    var body: some View {
        VStack {
            if #available(macOS 15.0, *) {
                RealityView { content in
                    let moonSphere_Entity = Entity.createSphere(radius: 0.90, color: .black)
                    moonSphere.Entity.name = "MoonSphere"
                    moonSphere.Entity.position = SIMD3<Float>(x: 0, y: 0, z: 0)
                    content.add(moonSphere.Entity)
                    let sunLight_Entity = createDirectionalLight(latitude: theLatitude, longitude: theLongitude, date: currentDate)
                    content.add(sunLight_Entity)
                }   //  End of [RealityView]
            } else {
                // Earlier version required.
            }   //  End of [if #available(macOS 15.0, *)]
        }   //  End of [VStack]
        .background(Color.black)
    }   //  End of [var body: some View]
    
//  MARK: - 🟠🟠🟠🟠 [SET THE BACKGROUND COLOUR] 🟠🟠🟠🟠
    var backgroundColor: Color = Color.init(.black)

//  MARK: - 🟠🟠🟠🟠 [CREATE THE DIRECTIONAL LIGHT FOR THE SPHERE] 🟠🟠🟠🟠
    func createDirectionalLight(latitude: Double, longitude: Double, date: Date) -> Entity {
        let directionalLight = DirectionalLight()
        directionalLight.light.color = .white
        directionalLight.light.intensity = 1000000
        directionalLight.shadow = DirectionalLightComponent.Shadow()
        directionalLight.shadow?.maximumDistance = 5
        directionalLight.shadow?.depthBias = 1
        
//  MARK: 🟠🟠🟠🟠 Retrieve the [MEESUS MOON AGE VALUES] from the [CONSTANT FOLDER] 🟠🟠🟠🟠
        let theMeesusMoonAge_LunarAgeDaysValue = 25.90567592898601
        if theMeesusMoonAge_LunarAgeDaysValue >= 23.10 && theMeesusMoonAge_LunarAgeDaysValue < (29.530588853 - 1.00) {
            let someCalculatedX_WestEastRadian: Float = Float(1.00)
            // Identify the sphere’s DirectionalLight Tilt Angle (Y) radian value ::
            // Note :: The following Tilt Angle is corrected to [Zenith] with the [MeesusCalculatedTilt_Angle] minus the [MeesusCalculatedPar_Angle].
            let someCalculatedY_TiltAngleRadian: Float = Float(1.3396086)
            // Identify the sphere’s DirectionalLight Illumination (Z) radian Value ::
            // Note :: The Meesus calculated illumination fraction is converted to degrees, then converted to a radian value.
            let someCalculatedZ_IlluminationAngleRadian: Float = Float(0.45176168630244457)  //  <=== 14.3800% Illumination.
            //  Define rotation angles in radians for X, Y, and Z axes.
            let x_Radians = someCalculatedX_WestEastRadian
            let y_Radians = someCalculatedY_TiltAngleRadian
            let z_Radians = someCalculatedZ_IlluminationAngleRadian
            //  Identify and separate the quaternion [simd_quatf] for each Radian.
            let q_X = simd_quatf(angle: x_Radians, axis: SIMD3<Float>(1, 0, 0))
            let q_Y = simd_quatf(angle: y_Radians, axis: SIMD3<Float>(0, 1, 0))
            let q_Z = simd_quatf(angle: z_Radians, axis: SIMD3<Float>(0, 0, 1))
            //  Apply and combine the rotations, where order matters.
            let combinedRotation = q_Z * q_Y * q_X
            //  Identify the [Combined Rotation].
            //  The [MyMoonMeesus] :: [WANING CRESCENT] calculated [combinedRotation] :: simd_quatf(real: 0.73715997, imag: SIMD3<Float>(0.24427173, 0.61516714, -0.13599981)) ° Radians
            //  Normalize the [combinedRotation].
            let theNormalizesRotation = simd_normalize(combinedRotation)
            //  Identify the [Normalized Combined Rotation].
            //  The [MyMoonMeesus] :: [WANING CRESCENT] calculated [normalizedRotation] :: simd_quatf(real: 0.73715997, imag: SIMD3<Float>(0.24427173, 0.61516714, -0.13599981)) ° Radians
            //  Assume the [theNormalizesRotation] appears reversed.
            let theCorrectedRotation = theNormalizesRotation.inverse
            //  Identify the [Reversed Combined Rotation].
            //  The [MyMoonMeesus] :: [WANING CRESCENT] calculated [correctedRotation] :: simd_quatf(real: 0.73715997, imag: SIMD3<Float>(-0.24427173, -0.61516714, 0.13599981)) ° Radians
            //  Apply the [Corrected Rotation] to the entity.
            directionalLight.transform.rotation  *= theCorrectedRotation
            //  Add the [directionalLight] to the scene ::
            let anchor = AnchorEntity()
            anchor.addChild(directionalLight)
        }   //  End of [if theMeesusMoonAge_LunarAgeDaysValue >= 23.10 && theMeesusMoonAge_LunarAgeDaysValue < (29.530588853 - 1.00)]
        return directionalLight
    }   //  End of [func createDirectionalLight(latitude: Double, longitude: Double, date: Date) -> Entity]
}   //  End of [struct TheCalculatedMoonPhaseTest_ContentView: View]

//  MARK: 🟠🟠🟠🟠 [ENTITY HELPER EXTENSION] 🟠🟠🟠🟠
extension Entity {
    static func createSphere(radius: Float, color: NSColor) -> Entity {
        let mesh = MeshResource.generateSphere(radius: radius)
        var material = PhysicallyBasedMaterial()
        material.baseColor = .init(tint: color)
        let modelComponent = ModelComponent(mesh: mesh, materials: [material])
        let entity = Entity()
        entity.components.set(modelComponent)
        entity.components.set(Transform())
        return entity
    }   //  End of [static func createSphere(radius: Float, color: NSColor) -> Entity]
}   //  End of [extension Entity]

// Application Image :: Calgary

// Website Image :: timeanddate

// mooncalc.org