場景套件平移二維平移到正確的三維只有水平

Question

我有一個更多的數學問題與3D編程，我希望你能幫助我！

我想創建一個3D等距角度的場景使用Scenekit。

此代碼創建我正視相機：

var cameraNode = SCNNode() 
cameraNode.camera = SCNCamera() 
cameraNode.name = "Camera" 
cameraNode.position = SCNVector3Make(-5.0, -5.0, 10.0) 
cameraNode.eulerAngles = SCNVector3Make(PI/3.0, 0.0, -PI/4.0) 
cameraNode.camera?.usesOrthographicProjection = true 
cameraNode.camera?.orthographicScale = 7.0 
scene.rootNode.addChildNode(cameraNode) 

現在我想用移動手勢移動相機，產生滾動的感覺。爲了實現這一點，相機不應該垂直移動，只能水平移動。屏幕上的觸摸位置和3D世界中未投影的位置在移動時應保持不變。

我想過計算二維平移到三維差異和忽略垂直分量。這段代碼實際上起作用並幾乎產生了期望的結果，但速度不正確。如果我搖攝，相機似乎加速並不能正確反應：

var previousTranslation = CGPointMake(0.0, 0.0) 

func pan(gesture: UIPanGestureRecognizer) 
{ 
    let view = self.view as SCNView 
    let translation = gesture.translationInView(view) 
    let location = gesture.locationInView(view) 

    let diffTrans = translation - previousTranslation 
    previousTranslation = translation 

    let cameraNode = scene.rootNode.childNodeWithName("Camera", recursively: false) 

    let worldPointTrans = view.unprojectPoint(SCNVector3Make(-Float(diffTrans.x), -Float(diffTrans.y), 0.0)) 
    let worldPoint0 = view.unprojectPoint(SCNVector3Make(0.0, 0.0, 0.0)) 

    var diff = worldPointTrans - worldPoint0 
    diff.x = diff.x/Float(cameraNode!.camera!.orthographicScale) 
    diff.y = diff.y/Float(cameraNode!.camera!.orthographicScale) 
    diff.z = 0 
    cameraNode?.position += diff 
} 

有誰知道計算屏幕轉換成水平的3D轉換，忽略了垂直軸的複雜的方法？

預先感謝您:)

編輯： 泛適用於水平翻譯了。但不適用於垂直，因爲我將z軸上的差異設置爲零。

Answer 1

我找到了我自己的解決方案。

我正在計算手勢開始位置（P1-P2）處的光線和轉換位置（Q1-Q2）處的光線。現在我有兩條光線，我讓兩者都與XY平面相交以接收點P0和Q0

P0和Q0的差異是未投影的平移。

這種技術也應該與非正交相機一起工作，但我還沒有測試。

在我看來，它的作品，但如果任何人都可以在數學上證實了這一假設，我會很高興讀到:)

下面是代碼：

var previousLocation = SCNVector3(x: 0, y: 0, z: 0) 

func pan(gesture: UIPanGestureRecognizer) 
{ 
    let view = self.view as SCNView 
    let translation = gesture.translationInView(view) 

    let location = gesture.locationInView(view) 
    let secLocation = location + translation 

    let P1 = view.unprojectPoint(SCNVector3(x: Float(location.x), y: Float(location.y), z: 0.0)) 
    let P2 = view.unprojectPoint(SCNVector3(x: Float(location.x), y: Float(location.y), z: 1.0)) 

    let Q1 = view.unprojectPoint(SCNVector3(x: Float(secLocation.x), y: Float(secLocation.y), z: 0.0)) 
    let Q2 = view.unprojectPoint(SCNVector3(x: Float(secLocation.x), y: Float(secLocation.y), z: 1.0)) 

    let t1 = -P1.z/(P2.z - P1.z) 
    let t2 = -Q1.z/(Q2.z - Q1.z) 

    let x1 = P1.x + t1 * (P2.x - P1.x) 
    let y1 = P1.y + t1 * (P2.y - P1.y) 

    let P0 = SCNVector3Make(x1, y1,0) 

    let x2 = Q1.x + t1 * (Q2.x - Q1.x) 
    let y2 = Q1.y + t1 * (Q2.y - Q1.y) 

    let Q0 = SCNVector3Make(x2, y2, 0) 

    var diffR = Q0 - P0 
    diffR *= -1 

    let cameraNode = view.scene!.rootNode.childNodeWithName("Camera", recursively: false) 

    switch gesture.state { 
    case .Began: 
     previousLocation = cameraNode!.position 
     break; 
    case .Changed: 
     cameraNode?.position = previousLocation + diffR 
     break; 
    default: 
     break; 
    } 
} 

Answer 2

我已經計算了等距平移的等式，代碼如下。

//camera pan ISOMETRIC logic 
func pan(gesture: UIPanGestureRecognizer) { 
    let view = self.sceneView as SCNView 
    let cameraNode = view.scene!.rootNode.childNode(withName: "Camera", recursively: false) 
    let translation = gesture.translation(in: view) 

    let constant: Float = 30.0 
    var translateX = Float(translation.y)*sin(.pi/4.0)/cos(.pi/3.0)-Float(translation.x)*cos(.pi/4.0) 
    var translateY = Float(translation.y)*cos(.pi/4.0)/cos(.pi/3.0)+Float(translation.x)*sin(.pi/4.0) 
    translateX = translateX/constant 
    translateY = translateY/constant 

    switch gesture.state { 
    case .began: 
     previousLocation = cameraNode!.position 
     break; 
    case .changed: 
     cameraNode?.position = SCNVector3Make((previousLocation.x + translateX), (previousLocation.y + translateY), (previousLocation.z)) 
     break; 
    default: 
     break; 
    } 
} 

爲了得到正確的縮放比例，您需要使用screenheight作爲orthographicScale的變量。我在這裏使用的縮放比例是30倍放大倍數，注意30也用於上面代碼中的常量。

let screenSize: CGRect = UIScreen.main.bounds 
    let screenHeight = screenSize.height 
    let cameraNode = SCNNode() 
    cameraNode.camera = SCNCamera() 
    cameraNode.name = "Camera" 
    let cameraDist = Float(20.0) 
    let cameraPosX = cameraDist*(-1.0)*cos(.pi/4.0)*cos(.pi/6.0) 
    let cameraPosY = cameraDist*(-1.0)*sin(.pi/4.0)*cos(.pi/6.0) 
    let cameraPosZ = cameraDist*sin(.pi/6) 
    cameraNode.position = SCNVector3Make(cameraPosX, cameraPosY, cameraPosZ) 
    cameraNode.eulerAngles = SCNVector3Make(.pi/3.0, 0.0, -.pi/4.0) 
    cameraNode.camera?.usesOrthographicProjection = true 
    cameraNode.camera?.orthographicScale = Double(screenHeight)/(2.0*30.0) //30x magnification constant. larger number = larger object 
    scene.rootNode.addChildNode(cameraNode)