formular to calculate width/height (relative to parent) of container with translateZ inside of parent container with perspective

Question

What is the formular to calculate the widths/heights of child elements with translateZ inside of parent container with set perspective (keyword: &

Answer 1

You've already solved your problem. Your code does exactly what you need it to do, it's just a CSS layout issue now.

https://codepen.io/anon/pen/xLWGzp?editors=0100

Because of the perspective changes, if you hang everything off the x-axis center everything will begin to line up properly:

(I'm just adding in the code changes here, I've left everything else the same)

#projection
    perspective-origin: center top

.pro
    transform-origin: center top

Now everything's lining up better, but it's still a bit off - you can change the $width variable to anything other than 100% to see the problem (60% is a good one)

So the problem now is just due to the positioning of the elements, when you set position: absolute they're default positioned to the left, change the width and add scale and transform and you get this equal-width/not-equal-position, so center them by adding:

#projection
    position: relative

.pro
    left: 50%
    margin-left: $width * -.5

(info here as to why that works to center: https://css-tricks.com/quick-css-trick-how-to-center-an-object-exactly-in-the-center/)

So now jiggle $width around to double-check, I tested it from 20% up to 150% and it works fine.

Answer 2

I have changed the style slightly, to make things more visible.

The result seems ok for me. May be I am misunderstanding something?

html, body {
  height: 100%;
  overflow: hidden;
  width: 100%;
}

#projection {
  perspective: 1px;
  perspective-origin: 0 0;
  height: 50%;
  overflow: visible;
  width: 50%;
  margin-left: 50px;
  background-color: grey;
}

.pro {
  transform: scale(1) translate(0px, 0px) translateZ(0px);
  height: 50%;
  position: absolute;
  transform-origin: 0 0;
  transform-style: preserve-3d;
  width: 100%;
}

.pro--1 {
  transform: scale(4) translate(0px, 0px) translateZ(-3px);
  width: 110%;
}

.pro--2 {
  transform: scale(3) translate(0px, 120%) translateZ(-2px);
  width: 110%;
}

.pro--3 {
  transform: scale(2) translate(0px, 240%) translateZ(-1px);
  width: 110%;
}

.pro--1 {
  background: rgba(0, 0, 75, 0.5);
  color: blue;
  line-height: 1em;
  text-align: center;
}

.pro--2 {
  background: rgba(0, 75, 0, 0.5);
  color: green;
  line-height: 4em;
}

.pro--3 {
  background: rgba(75, 0, 0, 0.5);
  color: red;
  line-height: 7em;
}

<div id="projection">
  <div class="pro pro--1">pro--1</div>
  <div class="pro pro--2">pro--2</div>
  <div class="pro pro--3">pro--3</div>
</div>

Answer 3

The formular to calculate the widths/heights of child elements with translateZ inside of parent container with set perspective is:
$scale = 1 + (translateZ * -1) / perspective.

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Where to throw this formular at transform: scale( $scale ).
perspective is parents perspective value and translateZ is elements translateZ value as well. See snippet at the bottom or SASS mockup as you like.

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So actually the answer was given in the question!
While this is the correct answer to the asked question this didn't solve my specific problem at all so here is a follow-up-question.

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Credits: @Trolleymusic who at least opened my eyes somehow with his answer.

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CSS example:

/* formular: 1 + (translateZ * -1) / perspective */

#parent {
  perspective: 10px;
}

.child--1 { /* 1 + (-100 * -1) / 10 */
  transform: translateZ(-100px) scale( 11 );
}

.child--2 { /* 1 + (-200 * -1) / 10 */
  transform: translateZ(-200px) scale( 21 );
}

.child--3 { /* 1 + (1 * -1) / 10 */
  transform: translateZ(1px) scale( 0.9 );
}