根据其转换矩阵获取UIImageView的旋转和大小 [英] obtaining the rotation and size of a UIImageView based on its transformation matrices

问题描述

如果我有一个矩形UIImageView的原始变换矩阵并且该图像被缩放和旋转，并且到最后我可以读取该相同视图的最终变换矩阵，我如何计算缩放和旋转图像的数量？ / p>

我想这些矩阵不知何故包含这两个信息。问题是如何提取它...

任何线索？

感谢您的帮助。

解决方案

一点矩阵代数和三角函数可以帮助你解决这个问题。

我们将继续生成可缩放和旋转的矩阵，然后使用它来分析如何分析提取比例因子和旋转。

A缩放矩阵按比例缩放Sx（在X轴上）和Sy（在Y轴上）如下所示：

 ⎡Sx 0⎤$ b $b⎣0Sy⎦
  

顺时针旋转R弧度的矩阵看起来像这样：

 ⎡cos（R）sin（R）⎤
⎣-sin（R）cos（R）⎦ 
  

使用标准矩阵乘法，组合缩放和旋转矩阵将如下所示：

 ⎡Sx.cos（R）Sx.sin（R）⎤
⎣-Sy.sin（R）Sy.cos（R ）⎦
  

请注意，线性变换还可能包括剪切或其他变换，但我会假设这个问题只发生了旋转和缩放（如果剪切变换在矩阵中，则会得到不一致的结果跟随代数;但是同样的方法可以用来确定分析解决方案。）

A CGAffineTransform 有四个成员a，b，c，d，对应到二维矩阵：

 ⎡ab⎤$ b $b⎣cd⎦
  

现在我们要从这个矩阵中提取Sx，Sy和R的值。我们可以在这里使用一个简单的三角函数：

  tan（A）= sin（A）/ cos（A）
  

我们可以在矩阵的第一行使用它来得出结论：

  tan（R）= Sx.sin（R）/ Sx.cos（R）= b / a因此R = atan（b / a）
  

现在我们知道R，我们可以使用主对角线提取比例因子：

  a = Sx.cos（R）因此Sx = a / cos（R）
d = Sy.cos（R）因此Sy = d / cos（R）
  

所以你现在知道Sx，Sy和R.

If I have the original transform matrix of a rectangular UIImageView and this image is scaled and rotated and by the end I can read the final transform matrix of this same view, how can I calculate how much the image scaled and rotated?

I suppose that somehow these matrix contain these two informations. The problem is how to extract it...

any clues?

thanks for any help.

解决方案

A little bit of matrix algebra and trigonometric identities can help you solve this.

We'll work forward to generate a matrix that scales and rotates, and then use that to figure out how to extract the scale factors and rotations analytically.

A scaling matrix to scale by Sx (in the X axis) and Sy (in the Y axis) looks like this:

⎡Sx  0 ⎤
⎣0   Sy⎦

A matrix to rotate clockwise by R radians looks like this:

⎡cos(R)   sin(R)⎤
⎣-sin(R)  cos(R)⎦

Using standard matrix multiplication, the combined scaling and rotation matrix will look like this:

⎡Sx.cos(R)   Sx.sin(R)⎤
⎣-Sy.sin(R)  Sy.cos(R)⎦

Note that linear transformations could also include shearing or other transformations, but I'll assume for this question that only rotation and scaling have occurred (if a shear transform is in the matrix, you will get inconsistent results from following the algebra here; but the same approach can be used to determine an analytical solution).

A CGAffineTransform has four members a, b, c, d, corresponding to the 2-dimensional matrix:

⎡a  b⎤
⎣c  d⎦

Now we want to extract from this matrix the values of Sx, Sy, and R. We can use a simple trigonometric identity here:

tan(A) = sin(A) / cos(A)

We can use this with the first row of the matrix to conclude that:

tan(R) = Sx.sin(R) / Sx.cos(R) = b / a    and therefore    R = atan(b / a)

And now we know R, we can extract the scale factors by using the main diagonal:

a = Sx.cos(R)    and therefore    Sx = a / cos(R)
d = Sy.cos(R)    and therefore    Sy = d / cos(R)

So you now know Sx, Sy, and R.

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