Using device orientation with 3D transforms
===========================================

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This article provides tips on how to use device orientation information in tandem with CSS 3D transforms.

Using orientation to rotate an element
--------------------------------------

The easiest way to convert orientation data to a 3D transform is basically to use the `alpha`, `gamma`, and `beta` values as `rotateZ`, `rotateX` and `rotateY` values.

It is important to keep in mind, however, that the Device Orientation coordinate system is different from the CSS coordinate system. Namely, the former is right-handed and its Y axis is positive upwards, while the latter is a left-handed coordinate system whose Y axis is positive to the bottom. Furthermore, the Device Orientation angle rotations should always be done in a Z - X' - Y'' order that does not match the order of some CSS Transforms. These are some of the practical consequences of these differences:

* The order of angle rotations matters, so make sure the alpha, beta and gamma rotations are applied in this order.
* The `rotate3d()` CSS transformation, and the `DOMMatrixReadOnly.rotate()` and `DOMMatrix.rotateSelf()` functions apply angle rotations in a Z - Y' - X'' order, so it is not possible to apply the alpha, beta and gamma rotations in the right order with a single call to any of them. Instead, you should rotate each axis individually in the correct order.
* Due to the differences in coordinate systems outlined above, when looking towards the origin rotations are applied clockwise around in CSS and counter-clockwise in the Device Orientation spec. This means alpha and beta need to be inverted (the rotations around Z and X), because they point to different directions in the two coordinate systems. However, gamma (the rotation around Y) should be kept as is.
 Here is a code snippet to sum it up:

```js
const elem = document.getElementById("view3d");

window.addEventListener("deviceorientation", (e) => {
  elem.style.transform = `rotateZ(${-e.alpha}deg) rotateX(${-e.beta}deg) rotateY(${
 e.gamma
 }deg)`;
});
```

Convert from `rotate3d()` angles to `deviceorientation` angles
--------------------------------------------------------------

Should you ever need to convert a rotate3d axis-angle to orientation Euler angles, used by `deviceorientation`, you can use the following algorithm:


```js
// convert a rotate3d axis-angle to deviceorientation angles
function orient(aa) {
  const x = aa.x,
    y = aa.y,
    z = aa.z,
    a = aa.a,
    c = Math.cos(aa.a),
    s = Math.sin(aa.a),
    t = 1 - c,
    // axis-angle to rotation matrix
    rm00 = c + x \* x \* t,
    rm10 = z \* s + y \* x \* t,
    rm20 = -y \* s + z \* x \* t,
    rm01 = -z \* s + x \* y \* t,
    rm11 = c + y \* y \* t,
    rm21 = x \* s + z \* y \* t,
    rm02 = y \* s + x \* z \* t,
    rm12 = -x \* s + y \* z \* t,
    rm22 = c + z \* z \* t,
    TO\_DEG = 180 / Math.PI,
    ea = [],
    n = Math.hypot(rm22, rm20);

  // rotation matrix to Euler angles
  ea[1] = Math.atan2(-rm21, n);

  if (n > 0.001) {
    ea[0] = Math.atan2(rm01, rm11);
    ea[2] = Math.atan2(rm20, rm22);
  } else {
    ea[0] = 0;
    ea[2] = (rm21 > 0 ? 1 : -1) \* Math.atan2(-rm10, rm00);
  }

  return {
    alpha: -ea[0] \* TO\_DEG - 180,
    beta: -ea[1] \* TO\_DEG,
    gamma: ea[2] \* TO\_DEG,
  };
}
```

See also
--------

* Using CSS transforms
* Detecting device orientation