# Qt Quick 3D - Volumetric Rendering Example

```// Copyright (C) 2023 The Qt Company Ltd.
import QtQuick
import QtQuick3D

// The rotation math is based on the paper
// ARCBALL:
// A User Interface for Specifying Three-Dimensional Orientation Using a Mouse
// by Ken Shoemake, 1992
Item {
id: root
visible: false

required property Node controlledObject
property vector3d lastPos: Qt.vector3d(0, 0, 0)
property bool moving: false

// From Shoemake 1992:
// pt.x <- (screen.x - center.x)/radius;
// pt.y <- (screen.y - center.y)/radius;
// r <- pt.x*pt.x + pt.y*pt.y;
// IF r > 1.0
//   THEN s <- 1.0/Sqrt[r];
//     pt.x <- s*pt.x;
//     pt.y <- s*pt.y;
//     pt.z <- 0.0;
//   ELSE pt.z <- Sqrt[1.0 - r] ;
function pos2DToPos3D(posNDC) {
var pt = Qt.vector3d(posNDC.x, posNDC.y, 0)
let r = posNDC.x * posNDC.x + posNDC.y * posNDC.y
if (r > 1.0) {
let s = 1.0 / Math.sqrt(r)
pt.x = s * pt.x
pt.y = s * pt.y
pt.z = 0.0
} else {
pt.z = Math.sqrt(1.0 - r)
}

return pt
}

function mousePressed(posNDC) {
lastPos = pos2DToPos3D(posNDC)
moving = true
}

function mouseReleased(posNDC) {
moving = false
}

function mouseMoved(posNDC) {
if (!moving)
return

let currentPos = pos2DToPos3D(posNDC)

// From Shoemake 1992:
// [q.x, q.y, q.z] <- V3_Cross[pO, p1];
// q.w <- V3_Dot[pO, p1];
// qnow <- QuatMul[q, qstart];
let p0 = lastPos
let p1 = currentPos
let p0p1 = p0.crossProduct(p1)
let q = Qt.quaternion(p0.dotProduct(p1), p0p1.x, p0p1.y, p0p1.z)
let qnow = q.times(controlledObject.rotation)
controlledObject.rotation = qnow
lastPos = currentPos
}
}```