Databases
StackOverflow2013
Postsdbo
PO
 

Note that there are some explanatory texts on larger screens.

plurals
  1. PO
    primarykey
    data
    text
    <p>A little bit of matrix algebra and trigonometric identities can help you solve this.</p> <p>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.</p> <p>A scaling matrix to scale by Sx (in the X axis) and Sy (in the Y axis) looks like this:</p> <pre><code>⎡Sx 0 ⎤ ⎣0 Sy⎦ </code></pre> <p>A matrix to rotate clockwise by R radians looks like this:</p> <pre><code>⎡cos(R) sin(R)⎤ ⎣-sin(R) cos(R)⎦ </code></pre> <p>Using standard matrix multiplication, the combined scaling and rotation matrix will look like this:</p> <pre><code>⎡Sx.cos(R) Sx.sin(R)⎤ ⎣-Sy.sin(R) Sy.cos(R)⎦ </code></pre> <p>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).</p> <p>A <a href="http://developer.apple.com/iPhone/library/documentation/GraphicsImaging/Reference/CGAffineTransform/Reference/reference.html#//apple_ref/doc/uid/TP30000946-CH2g-C016165" rel="noreferrer">CGAffineTransform</a> has four members a, b, c, d, corresponding to the 2-dimensional matrix:</p> <pre><code>⎡a b⎤ ⎣c d⎦ </code></pre> <p>Now we want to extract from this matrix the values of Sx, Sy, and R. We can use a simple trigonometric identity here:</p> <pre><code>tan(A) = sin(A) / cos(A) </code></pre> <p>We can use this with the first row of the matrix to conclude that:</p> <pre><code>tan(R) = Sx.sin(R) / Sx.cos(R) = b / a and therefore R = atan(b / a) </code></pre> <p>And now we know R, we can extract the scale factors by using the main diagonal:</p> <pre><code>a = Sx.cos(R) and therefore Sx = a / cos(R) d = Sy.cos(R) and therefore Sy = d / cos(R) </code></pre> <p>So you now know Sx, Sy, and R.</p>
    singulars
    1. This table or related slice is empty.
    1. POobtaining the rotation and size of a UIImageView based on its transformation matrices
      singulars
      1. PTQuestion
    1. PTAnswer
    1. This table or related slice is empty.
    1. USadurdin
    plurals
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. POobtaining the rotation and size of a UIImageView based on its transformation matrices
      singulars
      1. PTQuestion
    1. This table or related slice is empty.
    1. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTUpMod
    2. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTUpMod
    3. VO
      singulars
      1. PO
      1. This table or related slice is empty.
      1. VTAcceptedByOriginator
    1. COthat's a good answer.
      singulars
      1. PO
      1. USDimitris
    2. COLooks like the scale can be negative. I'd recommend taking the absolute value of Sx and Sy.
      singulars
      1. PO
      1. USPaul Solt
    3. COA negative scale is perfectly valid; it inverts the axis. Sx = -1 would indicate that the image was flipped horizontally.
      singulars
      1. PO
      1. USadurdin
 

Querying!

 
Guidance
A row detail

Detail views are divided into sections. All the information in the data section comes from columns in the selected row. The other sections display data from other, related rows.

Related data can be related in a to-one or a to-many fashion. Captions of data related in a to-many fashion link to a list view showing a filtered view of the table.

Try moving around until you find a non-empty to-many entry and click on the label to get to one. You can move back to the root by clicking on the database name in the header.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload