如何仅翻转变换矩阵的一个轴? [英] How to flip only one axis of transformation matrix?
问题描述
我有一个4x4的转换矩阵.但是，在尝试了变换之后，我注意到Y轴的移动和正相反.其余的是正确的.
我从其他API得到了这个矩阵，所以大概是坐标系的差异.那么，如何翻转转换矩阵的轴?
如果仅平移，我可以在Y平移上添加减号，但是我不知道只有一个轴的反向旋转，因为所有旋转都在同一3x3区域中表示.我认为可能会有某种方式甚至同时影响平移和旋转.(真正地翻转轴)
我很确定您要查找的操作是在更改坐标系的同时保持Z向上或Y向上.在这种情况下，请尝试将矩阵第二列(或行)的所有元素设置为相反的元素.
这个问题对于Math StackExchange会更好.首先，
给定一个从相同旋转顺序得出的矩阵，结果矩阵如下，其中alpha是X角，beta是Y角，gamma是Z角:
您可以从此矩阵得出每个轴角的各个分量.例如，您可以使用一些反三角函数从 -sin(beta)得出Y角.给定Beta，您可以从 cos(beta)sin(alpha)派生alpha.您也可以从 cos(beta)sin(gamma)导出伽马.请注意，矩阵中的相同数字可以表示多个值(例如 sin(0)= 0 和 sin(180)= 0 ).
现在您知道alpha，beta和gamma了，您可以反转beta并重新制作旋转矩阵.
使用四元数有一种更好的方法来完成此操作的可能性很大，但是您应该向Math StackExchange询问这类与语言无关的问题.
I have a 4x4 transformation matrix. However, after trying out the transformation I noticed that movement and rotation of the Y axis is going the opposite way. The rest is correct.
I got this matrix from some other API so probably it is the difference of coordinate system. So, how can I flip an axis of transformation matrix?
If only translation I can add minus sign on the Y translation, but I have no idea about opposite rotation of only one axis since all the rotation is being represented in the same 3x3 area. I thought there might be some way that even affect both translation and rotation at the same time. (truly flipping the axis)
Edit: I'm pretty sure the operation you're looking for is changing coordinate systems while maintaining Z-up or Y-up. In this case, try setting all the elements of the second column (or row) of your matrix to their inverse.
This question would be better for the Math StackExchange. First, a really helpful read on rotation matrices.
The first problem is the matter of rotation order. I will be assuming the XYZ rotation order. We know the rotation matrices for each axis is as follows:
Given a matrix derived from the same rotation order, the resulting matrix would be as follows, where alpha is the X angle, beta is the Y angle, and gamma is the Z angle:
You can derive the individual components of each axis angle from this matrix. For example, you can derive the Y angle from -sin(beta) using some inverse trig. Given beta, you can derive alpha from cos(beta)sin(alpha). You can also derive gamma from cos(beta)sin(gamma). Note that the same number in the matrix can represent multiple values (e.g. sin(0)=0 and sin(180)=0).
Now that you know alpha, beta, and gamma, you can reverse beta and remake the rotation matrix.
There's a good chance that there's a better way to do this using quaternions, but you should ask the Math StackExchange these kinds of language-agnostic questions.
这篇关于如何仅翻转变换矩阵的一个轴?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！
