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HTML

            
              <div class="target">Sass calculated matrix3d<span></span></div>
<div class="target2">Native transform<span></span></div>
!

CSS

            
              // Jump to the very bottom to see where _multiply is called~ :D

$pi: 3.14159265359;

@function _exp($base, $exp) {
  $value: 1;
  @if $exp > 0 {
    @for $i from 0 through ($exp - 1) {
      $value: $value * $base;
    }
  }
  @return $value;
}

@function _fact($val) {
  $value: 1;
  @if $val > 0 {
    @for $i from 1 through $val {
      $value: $value * $i;
    }
  }
  @return $value;
}

/* Taylor cos approximation series */
@function _sin($angle) {
  $angle: $angle / 180 * $pi;
  $sin: 0;
  @for $n from 0 through 10 {
    $sin: $sin + _exp(-1, $n) * _exp($angle, (2 * $n) + 1) / _fact(($n * 2) + 1);
  }
  @return $sin;
}

/* Sin tests */
/*
@debug "sin(0) " + _sin(0);
@debug "sin(90) " + _sin(90);
@debug "sin(180) " + _sin(180);
@debug "sin(270) " + _sin(270);
*/

/* Taylor cos approximation series */
@function _cos($angle) {
  $angle: $angle / 180 * $pi;
  $cos: 0;
  @for $n from 0 through 10 {
    $cos: $cos + _exp(-1, $n) * _exp($angle, 2 * $n) / _fact($n * 2);
  }
  @return $cos;
}

/* Cos tests */
/*
@debug "cos(0) " + _cos(0);
@debug "cos(90) " + _cos(90);
@debug "cos(180) " + _cos(180);
@debug "cos(270) " + _cos(270);
*/

@function _tan($angle) {
  $angle: $angle / 180 * $pi;
  $tan: _sin($angle) / _cos($angle);
  @return $tan;
}

/* Stupid sass matrix multiplication bahahahahahahaa.... XD */
@function _multiply($m1, $m2) {
  $m1_j1: nth($m1, 1);
  $m1_j2: nth($m1, 2);
  $m1_j3: nth($m1, 3);
  $m1_j4: nth($m1, 4);
  $m2_j1: nth($m2, 1);
  $m2_j2: nth($m2, 2);
  $m2_j3: nth($m2, 3);
  $m2_j4: nth($m2, 4);
  $m1_i1_j1: nth($m1_j1, 1);
  $m1_i2_j1: nth($m1_j1, 2);
  $m1_i3_j1: nth($m1_j1, 3);
  $m1_i4_j1: nth($m1_j1, 4);
  $m1_i1_j2: nth($m1_j2, 1);
  $m1_i2_j2: nth($m1_j2, 2);
  $m1_i3_j2: nth($m1_j2, 3);
  $m1_i4_j2: nth($m1_j2, 4);
  $m1_i1_j3: nth($m1_j3, 1);
  $m1_i2_j3: nth($m1_j3, 2);
  $m1_i3_j3: nth($m1_j3, 3);
  $m1_i4_j3: nth($m1_j3, 4);
  $m1_i1_j4: nth($m1_j4, 1);
  $m1_i2_j4: nth($m1_j4, 2);
  $m1_i3_j4: nth($m1_j4, 3);
  $m1_i4_j4: nth($m1_j4, 4);
  $m2_i1_j1: nth($m2_j1, 1);
  $m2_i2_j1: nth($m2_j1, 2);
  $m2_i3_j1: nth($m2_j1, 3);
  $m2_i4_j1: nth($m2_j1, 4);
  $m2_i1_j2: nth($m2_j2, 1);
  $m2_i2_j2: nth($m2_j2, 2);
  $m2_i3_j2: nth($m2_j2, 3);
  $m2_i4_j2: nth($m2_j2, 4);
  $m2_i1_j3: nth($m2_j3, 1);
  $m2_i2_j3: nth($m2_j3, 2);
  $m2_i3_j3: nth($m2_j3, 3);
  $m2_i4_j3: nth($m2_j3, 4);
  $m2_i1_j4: nth($m2_j4, 1);
  $m2_i2_j4: nth($m2_j4, 2);
  $m2_i3_j4: nth($m2_j4, 3);
  $m2_i4_j4: nth($m2_j4, 4);
  @return (
    (
      $m1_i1_j1 * $m2_i1_j1 + $m1_i2_j1 * $m2_i1_j2 + $m1_i3_j1 * $m2_i1_j3 + $m1_i4_j1 * $m2_i1_j4,
      $m1_i1_j1 * $m2_i2_j1 + $m1_i2_j1 * $m2_i2_j2 + $m1_i3_j1 * $m2_i2_j3 + $m1_i4_j1 * $m2_i2_j4,
      $m1_i1_j1 * $m2_i3_j1 + $m1_i2_j1 * $m2_i3_j2 + $m1_i3_j1 * $m2_i3_j3 + $m1_i4_j1 * $m2_i3_j4,
      $m1_i1_j1 * $m2_i4_j1 + $m1_i2_j1 * $m2_i4_j2 + $m1_i3_j1 * $m2_i4_j3 + $m1_i4_j1 * $m2_i4_j4
    ),
    (
      $m1_i1_j2 * $m2_i1_j1 + $m1_i2_j2 * $m2_i1_j2 + $m1_i3_j2 * $m2_i1_j3 + $m1_i4_j2 * $m2_i1_j4,
      $m1_i1_j2 * $m2_i2_j1 + $m1_i2_j2 * $m2_i2_j2 + $m1_i3_j2 * $m2_i2_j3 + $m1_i4_j2 * $m2_i2_j4,
      $m1_i1_j2 * $m2_i3_j1 + $m1_i2_j2 * $m2_i3_j2 + $m1_i3_j2 * $m2_i3_j3 + $m1_i4_j2 * $m2_i3_j4,
      $m1_i1_j2 * $m2_i4_j1 + $m1_i2_j2 * $m2_i4_j2 + $m1_i3_j2 * $m2_i4_j3 + $m1_i4_j2 * $m2_i4_j4
    ),
    (
      $m1_i1_j3 * $m2_i1_j1 + $m1_i2_j3 * $m2_i1_j2 + $m1_i3_j3 * $m2_i1_j3 + $m1_i4_j3 * $m2_i1_j4,
      $m1_i1_j3 * $m2_i2_j1 + $m1_i2_j3 * $m2_i2_j2 + $m1_i3_j3 * $m2_i2_j3 + $m1_i4_j3 * $m2_i2_j4,
      $m1_i1_j3 * $m2_i3_j1 + $m1_i2_j3 * $m2_i3_j2 + $m1_i3_j3 * $m2_i3_j3 + $m1_i4_j3 * $m2_i3_j4,
      $m1_i1_j3 * $m2_i4_j1 + $m1_i2_j3 * $m2_i4_j2 + $m1_i3_j3 * $m2_i4_j3 + $m1_i4_j3 * $m2_i4_j4
    ),
    (
      $m1_i1_j4 * $m2_i1_j1 + $m1_i2_j4 * $m2_i1_j2 + $m1_i3_j4 * $m2_i1_j3 + $m1_i4_j4 * $m2_i1_j4,
      $m1_i1_j4 * $m2_i2_j1 + $m1_i2_j4 * $m2_i2_j2 + $m1_i3_j4 * $m2_i2_j3 + $m1_i4_j4 * $m2_i2_j4,
      $m1_i1_j4 * $m2_i3_j1 + $m1_i2_j4 * $m2_i3_j2 + $m1_i3_j4 * $m2_i3_j3 + $m1_i4_j4 * $m2_i3_j4,
      $m1_i1_j4 * $m2_i4_j1 + $m1_i2_j4 * $m2_i4_j2 + $m1_i3_j4 * $m2_i4_j3 + $m1_i4_j4 * $m2_i4_j4
    )
  );
}

/* Return a unity (no transform) matrix */
@function _unity() {
  @return (
    (1, 0, 0, 0),
    (0, 1, 0, 0),
    (0, 0, 1, 0),
    (0, 0, 0, 1)
  );
}

/* Convert a 4x4 matrix into a string */
@function _unify($matrix) {
  $rtn: '';
  @each $row in $matrix {
    @each $item in $row {
      @if $rtn == '' {
        $rtn: '' + $item;
      } @else {
        $rtn: $rtn + ', ' + $item;
      }
    }
  }
  @return unquote($rtn);
}

/* A scale matrix */
@function _scale($x, $y, $z) {
  @return (
    ($x, 0, 0, 0),
    (0, $y, 0, 0),
    (0, 0, $z, 0),
    (0, 0, 0, 1)
  );
}

/* Rotation matrix for x, y, z */
@function _rotateX($angle) {
  $angle: -$angle; // Match CSS transform
  @return (
    (1, 0, 0, 0),
    (0, _cos($angle), _sin(-$angle), 0),
    (0, _sin($angle), _cos( $angle), 0),
    (0, 0, 0, 1)
  );
}
@function _rotateY($angle) {
  $angle: -$angle; // Match CSS transform
  @return (
    (_cos($angle), 0, _sin($angle), 0),
    (0, 1, 0, 0),
    (_sin(-$angle), 0, _cos($angle), 0),
    (0, 0, 0, 1)
  );
}
@function _rotateZ($angle) {
  $angle: -$angle; // Match CSS transform
  @return (
    (_cos($angle), _sin(-$angle), 0, 0),
    (_sin($angle), _cos($angle), 0, 0),
    (0, 0, 1, 0),
    (0, 0, 0, 1)
  );
}

/* A translate matrix */
@function _translate($x, $y, $z) {
  @return (
    (1, 0, 0, 0),
    (0, 1, 0, 0),
    (0, 0, 1, 0),
    ($x, $y, $z, 1)
  );
}

$matrix3d: _unity();
$matrix3d: _multiply($matrix3d, _rotateX(20));
$matrix3d: _multiply($matrix3d, _rotateY(15));
$matrix3d: _multiply($matrix3d, _rotateZ(10));
$matrix3d: _multiply($matrix3d, _translate(50, 50, 0));
$matrix3d: _multiply($matrix3d, _scale(2, 2, 2));
$matrix3d: _unify($matrix3d);

body {
  div {
    position: absolute;
    display: inline-block;
    width: 100px;
    height: 100px;
    border: 1px solid #222;
    border-radius: 1px;
    padding: 10px;
    color: #333;
    font-family: arial;
    font-size: 10px;
    box-shadow: 10px 10px 5px #888888;
    span:after {
      clear:both;
      display: block;
      width: 100%;
      margin-top: 10px;
      font-weight: bold;
      font-size: 6px;
      color: #000;
    }
  }
}
.target {
  background: #7fff7f;
  transform: matrix3d($matrix3d);
  -webkit-transform: matrix3d($matrix3d);
  span:after {
    content: "transform: matrix3d(" + $matrix3d + ")";
  }
}

.target2 {
  background: #7f7fff;
  transform: scaleX(2) scaleY(2) scaleZ(2) translate3d(250px, 50px, 0) rotateZ(10deg) rotateY(15deg) rotateX(20deg);
  -webkit-transform:scaleX(2) scaleY(2) scaleZ(2) translate3d(250px, 50px, 0) rotateZ(10deg) rotateY(15deg) rotateX(20deg);
  span:after {
    content: "transform: scaleX(2) scaleY(2) scaleZ(2) translate3d(250px, 50px, 0) rotateZ(10deg) rotateY(15deg) rotateX(20deg)";
  }
}
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