Unskewed child not aligning

Question

Note: This question is about a problem with output, and not about creation of any shape.

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I recently created a shape :

Answer 1

The behaviour of the "unskewed" child is normal, it is the way skew works. In order to understand this, I am going to simplify the question to :

why isn't skewX(40deg) the same as skewX(20deg) skewX(20deg)?

div {
    width: 100px; height: 100px;
    position:absolute;
    top:20px; left:20px;
    transform-origin: 0 0;
}
.d1 {
    transform: skewX(40deg);
    background: red;
    opacity:0.7;
}
.d2 {
    transform: skewX(20deg) skewX(20deg);
    background: blue;
    opacity:0.7;
}
/** FOR THE DEMO **/
body {background: url('http://i.stack.imgur.com/GySvQ.png');background-size: 10px;}
.m {text-align:right;padding-top:105px;}
.m1{width:83px;color:red;border-right:1px solid red;}
.m2 {width:72px;color:blue;border-right:1px solid blue;}
p{margin:0 0 5px 150px;color:red;}
.b{color:blue;}

x = 83

x = 72
skewX(40deg)
skewX(20deg) skewX(20deg)

Note: for the sake of explanation I will be using a 100*100 square div and the transform origin is set on the top left corner of this div. Like in the above code snippet.

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To understand the difference between the two transformations, we need to explore the way the CSS skew() function works. The specs say :

A 2D skew transformation along the X axis with the parameter alpha is equivalent to the matrix:

So this means we can calculate the coordinates of each point of a 2D X skewed element like this :

| 1 tan(α) | . | x |
| 0   1    |   | y |

• α is the X skewed angle
• x/y the coordinates of the point before transformation

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For skewX(40deg)

α = tan(40deg) ~= 0.83

| 1  0.83 | . | 0   |   | 83  |
| 0  1    |   | 100 | = | 100 |

The new coordinates are x = 83 as seen in the code snippet example.

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For skewX(20deg) skewX(20deg)

α = tan(20deg) ~= 0.36

first skew :

| 1  0.36 | . | 0   |   | 36  |
| 0  1    |   | 100 | = | 100 |

Second skew :

| 1  0.36 | . | 36  |   | 72  |
| 0  1    |   | 100 | = | 100 |

The new coordinates are x = 72 as seen in the code snippet.

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Conclusion

Both transformations don't give the same result. So skewY(20deg) skewY(-40deg) isn't the same transformation as skewY(-20deg) and the two top corners of the red and green elements can't align as :

tan(20deg) != tan(40deg)/2 

References :

• The CSS3 matrix() Transform for the Mathematically Challenged
• CSS transform skew: math unveiled
• CSS Transforms Module Level 1