three.js calculate STL file mesh volume

Question

I have to calculate the volume of an STL file, I successfully got the sizes of the model with

var box = new THREE.Box3().setFromObject( mesh );
var sizes = box.getSize();

but I just can't wrap my head around the concept of calculating it. I load the model with

var loader = new THREE.STLLoader();
loader.load(stlFileURL, function ( geometry ) {});

Can someone help me out and point me in the right direction? I'm doing it with javascript.

Answer 1

You can find it with the algorithm from my comment.

In the code snippet, the volume is computed without scaling.

Also, I've added a simple check that the algorithm calculates correctly by finding the volume of a hollow cylinder. As THREE.STLLoader() returns a non-indexed geometry, I've casted the geometry of the cylinder to non-indexed too.

Related forum topic

 var scene = new THREE.Scene(); var camera = new THREE.PerspectiveCamera(60, window.innerWidth / window.innerHeight, 0.01, 1000); camera.position.setScalar(20); var renderer = new THREE.WebGLRenderer(); renderer.setClearColor(0x404040); renderer.setSize(window.innerWidth, window.innerHeight); document.body.appendChild(renderer.domElement); var controls = new THREE.OrbitControls(camera, renderer.domElement); var loader = new THREE.STLLoader(); loader.load('https://threejs.org/examples/models/stl/binary/pr2_head_pan.stl', function(geometry) { var mesh = new THREE.Mesh(geometry, new THREE.MeshBasicMaterial({ color: 0xff00ff, wireframe: true })); mesh.rotation.set(-Math.PI / 2, 0, 0); mesh.scale.setScalar(100); scene.add(mesh); console.log("stl volume is " + getVolume(geometry)); }); // check with known volume: var hollowCylinderGeom = new THREE.LatheBufferGeometry([ new THREE.Vector2(1, 0), new THREE.Vector2(2, 0), new THREE.Vector2(2, 2), new THREE.Vector2(1, 2), new THREE.Vector2(1, 0) ], 90).toNonIndexed(); console.log("pre-computed volume of a hollow cylinder (PI * (R^2 - r^2) * h): " + Math.PI * (Math.pow(2, 2) - Math.pow(1, 2)) * 2); console.log("computed volume of a hollow cylinder: " + getVolume(hollowCylinderGeom)); function getVolume(geometry) { let position = geometry.attributes.position; let faces = position.count / 3; let sum = 0; let p1 = new THREE.Vector3(), p2 = new THREE.Vector3(), p3 = new THREE.Vector3(); for (let i = 0; i < faces; i++) { p1.fromBufferAttribute(position, i * 3 + 0); p2.fromBufferAttribute(position, i * 3 + 1); p3.fromBufferAttribute(position, i * 3 + 2); sum += signedVolumeOfTriangle(p1, p2, p3); } return sum; } function signedVolumeOfTriangle(p1, p2, p3) { return p1.dot(p2.cross(p3)) / 6.0; } renderer.setAnimationLoop(() => { renderer.render(scene, camera); });

 body { overflow: hidden; margin: 0; }

 <script src="https://threejs.org/build/three.min.js"></script> <script src="https://threejs.org/examples/js/loaders/STLLoader.js"></script> <script src="https://threejs.org/examples/js/controls/OrbitControls.js"></script>

Answer 2

I'm also looking for a solution to this, And didn't have any implementation so far.

But extending from the voxelization idea like @manthrax mentioned.

I think we can voxelized into the octree structure.

If the cube still intersects with multiple triangles then voxelized deeper octree.

Until we reached the level of a single triangle cut through,
Then we calculate the volume of the cube using this method:

https://math.stackexchange.com/questions/454583/volume-of-cube-section-above-intersection-with-plane

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After understood prisoner849's solution, This idea is no more valid compared to his solution.

Answer 3

This is a pretty tricky problem. One way is to decompose the object into a bunch of convex polyhedra and sum the volumes of those...

Another way is to voxelize it, and add up the voxels on the inside to get an estimate whos accuracy is limited by the resolution of your voxelization.

Edit: prisoner849 has a rad solution!