How to cast a CMRotationMatrix from CoreMotion to be used by a SceneKit camera (or any SCNNode)

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英文:

How to cast a CMRotationMatrix from CoreMotion to be used by a SceneKit camera (or any SCNNode)

问题

我正在尝试使用CMHeadphoneMotionManager提供的attitude来指导SKSceneView内的摄像机。如果我没有弄错的话,它们使用不同的参考系统,因此直接初始化一个float4x4矩阵类似于这样在没有任何排列或更改的情况下将无法正常工作(CoreMotion和SceneKit之间的轴不匹配)。

为了提供一些背景信息,我可能是错的,因为我找不到确切的参考系统,不得不运行一些测试来找出。通过你的Airpods(或支持运动的耳机)提供的attitude所使用的坐标系统如下:正Y指向从你的鼻子前方,正Z指向逆着重力穿过头部向上,正X指向右边(在开始捕捉运动时选择的随机方向):How to cast a CMRotationMatrix from CoreMotion to be used by a SceneKit camera (or any SCNNode)

然而,SceneKit的参考坐标系统具有正Y指向上方,正Z指向后方(假设你是摄像机,它朝着负Z方向看)。X轴似乎是相同的:

How to cast a CMRotationMatrix from CoreMotion to be used by a SceneKit camera (or any SCNNode)

我的线性代数知识在这个水平上有些有限,尽管我已经尝试了几天,但我不知道如何将来自HeadphoneMotion的给定旋转矩阵转换为SceneKit摄像机的变换。这就是问题所在。(理想情况下,还需配合所需的列排列背后的概念,以了解如何完成这个转换)。

此外,我想避免在这个阶段使用eulerAnglesquaternions

英文:

I'm trying to use the attitude given by CMHeadphoneMotionManager to guide a camera inside a SKSceneView. If I'm not mistaken, they use difference reference systems, and so the direct initialisation of a float4x4 matrix like this one would not work without any permutation or change (axis do not match between CoreMotion and SceneKit).

To add some context, and I might well be wrong because I couldn't find the exact reference system, and had to run some tests to find out, the coordinate system used as reference by the attitude given by your Airpods (or motion-enabled headphones), goes like this, with positive Y pointing forward from your nose, positive Z pointing up against gravity through your head, and positive X pointing right (at a random direction picked when you start capturing motion): How to cast a CMRotationMatrix from CoreMotion to be used by a SceneKit camera (or any SCNNode)

However, the reference coordinate system for SceneKit have positive Y pointing upwards, and positive Z pointing backwards (assuming you are the camera, which looks towards negative Z). Axis X seems the be the same:

How to cast a CMRotationMatrix from CoreMotion to be used by a SceneKit camera (or any SCNNode)

My linear algebra knowledge at this level is sort of limited, and even though I've been trying for a few days, I don't know how to convert the given rotation matrix from HeadphoneMotion, to be used by the transform of a SceneKit camera. That would be the question. (Ideally, paired with the concepts behind the permutation of columns required, to learn how it's done.)

Also, I would like to avoid using eulerAngles or quaternions at this point.

答案1

得分: 0

在深入研究矩阵后,我提出了一个解决方案。不确定是否是正确的方法,也不确定背后的原因(如果有人知道并愿意详细解释,请随时)。基本上,假设我绘制的两个坐标系的方案是正确的(尤其是CoreMotion的那个),我们可以计算一个旋转矩阵 T,将两个系统分开;也就是说,一个矩阵将一个系统转换为另一个系统。

通过查看这些方案,我们知道SceneKit坐标系统与CoreMotion坐标系统相距90°(在X轴上),旋转矩阵T如下(用Swift表示,逐列):

let matrixT = simd_float4x4([
          simd_float4( 1.0, 0.0, 0.0, 0.0),
          simd_float4( 0.0, 0.0, 1.0, 0.0),
          simd_float4( 0.0, -1.0, 0.0, 0.0),
          simd_float4( 0.0, 0.0, 0.0, 1.0)
        ])

知道这一点,我们可以获得R',它只是目标坐标系统中的初始旋转矩阵R,方法如下(这是关键):

R' = T^-1 * R * T

在Swift中,可以这样表示:

let newRotation = matrixT.inverse * originalRotationMatrix * matrixT;

就像这样,新的旋转可以用作SceneKit相机中的变换,它可以正常工作。

英文:

After digging a bit more into matrices, I came up with a solution.
Not sure if it's the right way, and not sure of the reasoning behind it (If someone knows and want to elaborate, please feel free).

Basically, assuming the schemes I drew of both coordinates systems are correct (specially the CoreMotion one), we can calculate a rotation matrix T that separates both system; this is, one matrix that would turn one system into the other.

By looking at those schemes, we know the SceneKit coordinate system is 90º apart (on the axis X) from the CoreMotion coordinate system, and the rotation matrix T would be as follows (in swift, column by column):

let matrixT = simd_float4x4([
          simd_float4( 1.0, 0.0, 0.0, 0.0),
          simd_float4( 0.0, 0.0, 1.0, 0.0),
          simd_float4( 0.0, -1.0, 0.0, 0.0),
          simd_float4( 0.0, 0.0, 0.0, 1.0)
        ])

Knowing this, we can obtain R', which is just the initial rotation matrix R but in the target coordinate system, by doing this (and this is the key):

R' = T^-1 * R * T

Which in swift, would be:

let newRotation = matrixT.inverse * originalRotationMatrix * matrixT;

Just like that, the newRotation can be used as a transform in the SceneKit camera, and it works.

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  • 本文由 发表于 2023年2月16日 18:40:26
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