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ConvexPolyhedrons and Compound Shapes

Video Lecture

ConvexPolyhedrons and Compound Shapes ConvexPolyhedrons and Compound Shapes ConvexPolyhedrons and Compound Shapes ConvexPolyhedrons and Compound Shapes

Description

In this video I will demonstrate several different methods of creating collision boundaries, also sometimes called collision meshes, using various ConvexPolyhedrons and Compound Shapes. I will also compare the performance and differences between them.

When positioning the parts of a compound shape, you can use a 3d graphics tool to help estimate the positioning. It is is important to know though, that if you use Blender, then be aware that Blender, by default, uses a different coordinate system. In Blender, Z is UP, and the Y axis is used for Near/Far and it is also negative compared to Threejs. So you will need to swap around the coordinates for Y and Z and negate the new Z.

To position an object from the perspective of a default Threejs camera looking down the Z axis, with UP axis [0,1,0], see table for conversion.

Axis Threejs Blender
Up/Down Y / -Y Z / -Z
Left/Right -X / X -X / X
Near/Far Z / -Z -Y / Y

Eg, If the 3D coordinates in Blender are [1,2,3], then in Threejs, the equivalent is [1,3,-2]

Start Scripts

./src/server/server.ts

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import express from "express"
import path from "path"
import http from "http"

const port: number = 3000

class App {
    private server: http.Server
    private port: number

    constructor(port: number) {
        this.port = port
        const app = express()
        app.use(express.static(path.join(__dirname, '../client')))
        app.use('/build/three.module.js', express.static(path.join(__dirname, '../../node_modules/three/build/three.module.js')))
        app.use('/jsm/controls/OrbitControls', express.static(path.join(__dirname, '../../node_modules/three/examples/jsm/controls/OrbitControls.js')))
        app.use('/jsm/libs/stats.module', express.static(path.join(__dirname, '../../node_modules/three/examples/jsm/libs/stats.module.js')))
        app.use('/jsm/libs/dat.gui.module', express.static(path.join(__dirname, '../../node_modules/three/examples/jsm/libs/dat.gui.module.js')))
        app.use('/jsm/loaders/OBJLoader', express.static(path.join(__dirname, '../../node_modules/three/examples/jsm/loaders/OBJLoader.js')))
        app.use('/cannon/cannon.min', express.static(path.join(__dirname, '../../node_modules/cannon/build/cannon.js')))

        this.server = new http.Server(app);
    }

    public Start() {
        this.server.listen(this.port, () => {
            console.log( `Server listening on port ${this.port}.` )
        })
    }
}

new App(port).Start()

./src/client/client.ts

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import * as THREE from '/build/three.module.js'
import { OrbitControls } from '/jsm/controls/OrbitControls'
import Stats from '/jsm/libs/stats.module'
import { GUI } from '/jsm/libs/dat.gui.module'
import '/cannon/cannon.min'
import CannonDebugRenderer from './utils/cannonDebugRenderer.js'
import CannonUtils from './utils/cannonUtils.js'
import { OBJLoader } from '/jsm/loaders/OBJLoader'

const scene: THREE.Scene = new THREE.Scene()
const axesHelper = new THREE.AxesHelper(5)
scene.add(axesHelper)

var light1 = new THREE.SpotLight();
light1.position.set(2.5, 5, 5)
light1.angle = Math.PI / 4
light1.penumbra = 0.5
light1.castShadow = true;
light1.shadow.mapSize.width = 1024;
light1.shadow.mapSize.height = 1024;
light1.shadow.camera.near = 0.5;
light1.shadow.camera.far = 20
scene.add(light1);

var light2 = new THREE.SpotLight();
light2.position.set(-2.5, 5, 5)
light2.angle = Math.PI / 4
light2.penumbra = 0.5
light2.castShadow = true;
light2.shadow.mapSize.width = 1024;
light2.shadow.mapSize.height = 1024;
light2.shadow.camera.near = 0.5;
light2.shadow.camera.far = 20
scene.add(light2);

const camera: THREE.PerspectiveCamera = new THREE.PerspectiveCamera(75, window.innerWidth / window.innerHeight, 0.1, 1000)

const renderer: THREE.WebGLRenderer = new THREE.WebGLRenderer()
renderer.setSize(window.innerWidth, window.innerHeight)
renderer.shadowMap.enabled = true
renderer.shadowMap.type = THREE.PCFSoftShadowMap
document.body.appendChild(renderer.domElement)

const controls = new OrbitControls(camera, renderer.domElement)
controls.screenSpacePanning = true

const world = new CANNON.World()
world.gravity.set(0, -9.82, 0)
//world.broadphase = new CANNON.NaiveBroadphase() //
//world.solver.iterations = 10
//world.allowSleep = true

const normalMaterial: THREE.MeshNormalMaterial = new THREE.MeshNormalMaterial()
const phongMaterial: THREE.MeshPhongMaterial = new THREE.MeshPhongMaterial()

let monkeyMeshes: THREE.Object3D[] = new Array()
let monkeyBodies: CANNON.Body[] = new Array()
let monkeyLoaded: Boolean = false

const objLoader: OBJLoader = new OBJLoader();
objLoader.load(
    'models/monkey.obj',
    //'models/monkeyPhysics.obj',
    (object) => {
        //scene.add(object)

        const monkeyMesh = object.children[0];
        (monkeyMesh as THREE.Mesh).material = normalMaterial

        // let monkeyMesh: THREE.Object3D
        // let monkeyCollisionMesh: THREE.Object3D
        // object.traverse(function (child) {
        //     console.log(child.name)
        //     if (child.name === "Suzanne") {
        //         monkeyMesh = child;
        //         (monkeyMesh as THREE.Mesh).material = normalMaterial
        //     } else if (child.name.startsWith("physics")) {
        //         monkeyCollisionMesh = child;
        //     }
        // })

        for (let i = 0; i < 10; i++) {
            const monkeyMeshClone = monkeyMesh.clone()
            monkeyMeshClone.position.x = Math.floor(Math.random() * 10) - 5
            monkeyMeshClone.position.z = Math.floor(Math.random() * 10) - 5
            monkeyMeshClone.position.y = 5 + i
            scene.add(monkeyMeshClone)
            monkeyMeshes.push(monkeyMeshClone)

            const monkeyShape = CannonUtils.CreateTrimesh((monkeyMesh as THREE.Mesh).geometry)
            //const monkeyShape = CannonUtils.CreateConvexPolyhedron(new THREE.IcosahedronGeometry(1))
            //const monkeyShape = CannonUtils.CreateConvexPolyhedron((monkeyMesh as THREE.Mesh).geometry)
            //const monkeyShape = CannonUtils.CreateConvexPolyhedron((monkeyCollisionMesh as THREE.Mesh).geometry)
            const monkeyBody = new CANNON.Body({ mass: 1 });
            monkeyBody.addShape(monkeyShape)
            // monkeyBody.addShape(new CANNON.Sphere(.8), new CANNON.Vec3(0, .2, 0))// head,
            // monkeyBody.addShape(new CANNON.Sphere(.05), new CANNON.Vec3(0, -.97, 0.46))// chin,
            // monkeyBody.addShape(new CANNON.Sphere(.05), new CANNON.Vec3(-1.36, .29, -0.5)) //left ear
            // monkeyBody.addShape(new CANNON.Sphere(.05), new CANNON.Vec3(1.36, .29, -0.5)) //right ear
            // monkeyBody.addShape(new CANNON.Sphere(.05), new CANNON.Vec3(0, .56, -0.85)) //head top
            // monkeyBody.addShape(new CANNON.Sphere(.05), new CANNON.Vec3(0, .98, -0.07)) //forehead top
            monkeyBody.position.x = monkeyMeshClone.position.x
            monkeyBody.position.y = monkeyMeshClone.position.y
            monkeyBody.position.z = monkeyMeshClone.position.z
            world.addBody(monkeyBody)
            monkeyBodies.push(monkeyBody)
        }

        monkeyLoaded = true
    },
    (xhr) => {
        console.log((xhr.loaded / xhr.total * 100) + '% loaded');
    },
    (error) => {
        console.log('An error happened');
    }
);


const planeGeometry: THREE.PlaneGeometry = new THREE.PlaneGeometry(25, 25)
const planeMesh: THREE.Mesh = new THREE.Mesh(planeGeometry, phongMaterial)
planeMesh.rotateX(-Math.PI / 2)
planeMesh.receiveShadow = true;
scene.add(planeMesh)
const planeShape = new CANNON.Plane()
const planeBody = new CANNON.Body({ mass: 0 })
planeBody.addShape(planeShape)
planeBody.quaternion.setFromAxisAngle(new CANNON.Vec3(1, 0, 0), -Math.PI / 2)
world.addBody(planeBody)

camera.position.y = 4
camera.position.z = 4
controls.target.y = 2

window.addEventListener('resize', onWindowResize, false)
function onWindowResize() {
    camera.aspect = window.innerWidth / window.innerHeight
    camera.updateProjectionMatrix()
    renderer.setSize(window.innerWidth, window.innerHeight)
    render()
}

const stats = Stats()
document.body.appendChild(stats.dom)

const gui = new GUI()
const physicsFolder = gui.addFolder("Physics")
physicsFolder.add(world.gravity, "x", -10.0, 10.0, 0.1)
physicsFolder.add(world.gravity, "y", -10.0, 10.0, 0.1)
physicsFolder.add(world.gravity, "z", -10.0, 10.0, 0.1)
physicsFolder.open()

const clock: THREE.Clock = new THREE.Clock()

const cannonDebugRenderer = new CannonDebugRenderer(scene, world)

var animate = function () {
    requestAnimationFrame(animate)

    controls.update()

    let delta = clock.getDelta()
    if (delta > .1) delta = .1
    world.step(delta)
    cannonDebugRenderer.update()

    // Copy coordinates from Cannon.js to Three.js
    if (monkeyLoaded) {
        monkeyMeshes.forEach((m, i) => {
            m.position.set(monkeyBodies[i].position.x, monkeyBodies[i].position.y, monkeyBodies[i].position.z);
            m.quaternion.set(monkeyBodies[i].quaternion.x, monkeyBodies[i].quaternion.y, monkeyBodies[i].quaternion.z, monkeyBodies[i].quaternion.w);
        })
    }

    render()

    stats.update()
};

function render() {
    renderer.render(scene, camera)
}
animate();

./src/client/utils/cannonUtils.ts

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import * as THREE from '/build/three.module.js'

class CannonUtils {

    constructor() { }

    public static CreateTrimesh(geometry: THREE.BufferGeometry): CANNON.Trimesh {
        const vertices: number[] = <number[]>geometry.attributes.position.array
        const indices: number[] = Object.keys(vertices).map(Number);
        return new CANNON.Trimesh(vertices, indices);
    }

    public static CreateConvexPolyhedron(geometry: THREE.BufferGeometry): CANNON.ConvexPolyhedron {
        const position = geometry.attributes.position;
        const normal = geometry.attributes.normal;
        let vertices: THREE.Vector3[] = []
        for (let i = 0; i < position.count; i++) {
            vertices.push(new THREE.Vector3().fromBufferAttribute(position, i));
        }
        const faces: THREE.Face3[] = []
        for (let i = 0; i < position.count; i += 3) {
            const vertexNormals = (normal === undefined) ? [] : [
                new THREE.Vector3().fromBufferAttribute(normal, i),
                new THREE.Vector3().fromBufferAttribute(normal, i + 1),
                new THREE.Vector3().fromBufferAttribute(normal, i + 2)
            ];
            const face = new THREE.Face3(i, i + 1, i + 2, vertexNormals, []);
            faces.push(face);
        }

        const verticesMap: { [key: string]: number } = {}
        const points: CANNON.Vec3[] = []
        const changes: number[] = [];
        for (let i = 0, il = vertices.length; i < il; i++) {
            const v = vertices[i];
            const key = Math.round(v.x * 100) + '_' + Math.round(v.y * 100) + '_' + Math.round(v.z * 100);
            if (verticesMap[key] === undefined) {
                verticesMap[key] = i;
                points.push(new CANNON.Vec3(vertices[i].x, vertices[i].y, vertices[i].z));
                changes[i] = points.length - 1;
            } else {
                changes[i] = changes[verticesMap[key]];
            }
        }

        const faceIdsToRemove = [];
        for (let i = 0, il = faces.length; i < il; i++) {
            const face = faces[i];
            face.a = changes[face.a];
            face.b = changes[face.b];
            face.c = changes[face.c];
            const indices = [face.a, face.b, face.c];
            for (let n = 0; n < 3; n++) {
                if (indices[n] === indices[(n + 1) % 3]) {
                    faceIdsToRemove.push(i);
                    break;
                }
            }
        }

        for (let i = faceIdsToRemove.length - 1; i >= 0; i--) {
            const idx = faceIdsToRemove[i];
            faces.splice(idx, 1);
        }

        const cannonFaces: number[][] = faces.map(function (f) {
            return [f.a, f.b, f.c]
        })

        return new CANNON.ConvexPolyhedron(points, cannonFaces);
    }

    public static offsetCenterOfMass(body: CANNON.Body, centreOfMass: CANNON.Vec3) {
        body.shapeOffsets.forEach(function (offset) {
            centreOfMass.vadd(offset, centreOfMass)
        })
        centreOfMass.scale(1 / body.shapes.length, centreOfMass)
        body.shapeOffsets.forEach(function (offset) {
            offset.vsub(centreOfMass, offset)
        })
        const worldCenterOfMass = new CANNON.Vec3()
        body.vectorToWorldFrame(centreOfMass, worldCenterOfMass)
        body.position.vadd(worldCenterOfMass, body.position)
    }
}

export default CannonUtils;

Final Script

./src/client/client.ts

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import * as THREE from '/build/three.module.js'
import { OrbitControls } from '/jsm/controls/OrbitControls'
import Stats from '/jsm/libs/stats.module'
import { GUI } from '/jsm/libs/dat.gui.module'
import '/cannon/cannon.min'
import CannonDebugRenderer from './utils/cannonDebugRenderer.js'
import CannonUtils from './utils/cannonUtils.js'
import { OBJLoader } from '/jsm/loaders/OBJLoader'

const scene: THREE.Scene = new THREE.Scene()
const axesHelper = new THREE.AxesHelper(5)
scene.add(axesHelper)

var light1 = new THREE.SpotLight();
light1.position.set(2.5, 5, 5)
light1.angle = Math.PI / 4
light1.penumbra = 0.5
light1.castShadow = true;
light1.shadow.mapSize.width = 1024;
light1.shadow.mapSize.height = 1024;
light1.shadow.camera.near = 0.5;
light1.shadow.camera.far = 20
scene.add(light1);

var light2 = new THREE.SpotLight();
light2.position.set(-2.5, 5, 5)
light2.angle = Math.PI / 4
light2.penumbra = 0.5
light2.castShadow = true;
light2.shadow.mapSize.width = 1024;
light2.shadow.mapSize.height = 1024;
light2.shadow.camera.near = 0.5;
light2.shadow.camera.far = 20
scene.add(light2);

const camera: THREE.PerspectiveCamera = new THREE.PerspectiveCamera(75, window.innerWidth / window.innerHeight, 0.1, 1000)

const renderer: THREE.WebGLRenderer = new THREE.WebGLRenderer()
renderer.setSize(window.innerWidth, window.innerHeight)
renderer.shadowMap.enabled = true
renderer.shadowMap.type = THREE.PCFSoftShadowMap
document.body.appendChild(renderer.domElement)

const controls = new OrbitControls(camera, renderer.domElement)
controls.screenSpacePanning = true

const world = new CANNON.World()
world.gravity.set(0, -9.82, 0)
//world.broadphase = new CANNON.NaiveBroadphase() //
//world.solver.iterations = 10
//world.allowSleep = true

const normalMaterial: THREE.MeshNormalMaterial = new THREE.MeshNormalMaterial()
const phongMaterial: THREE.MeshPhongMaterial = new THREE.MeshPhongMaterial()

let monkeyMeshes: THREE.Object3D[] = new Array()
let monkeyBodies: CANNON.Body[] = new Array()
let monkeyLoaded: Boolean = false

const objLoader: OBJLoader = new OBJLoader();
objLoader.load(
    'models/monkey.obj',
    //'models/monkeyPhysics.obj',
    (object) => {
        //scene.add(object)

        const monkeyMesh = object.children[0];
        (monkeyMesh as THREE.Mesh).material = normalMaterial;
        (<THREE.MeshNormalMaterial>(<THREE.Mesh>monkeyMesh).material).flatShading = true

        // let monkeyMesh: THREE.Object3D
        // let monkeyCollisionMesh: THREE.Object3D
        // object.traverse(function (child) {
        //     console.log(child.name)
        //     if (child.name === "Suzanne") {
        //         monkeyMesh = child;
        //         (monkeyMesh as THREE.Mesh).material = normalMaterial
        //     } else if (child.name.startsWith("physics")) {
        //         monkeyCollisionMesh = child;
        //     }
        // })

        for (let i = 0; i < 200; i++) {
            const monkeyMeshClone = monkeyMesh.clone()
            monkeyMeshClone.position.x = Math.floor(Math.random() * 10) - 5
            monkeyMeshClone.position.z = Math.floor(Math.random() * 10) - 5
            monkeyMeshClone.position.y = 5 + i
            scene.add(monkeyMeshClone)
            monkeyMeshes.push(monkeyMeshClone)

            //const monkeyShape = CannonUtils.CreateTrimesh((monkeyMesh as THREE.Mesh).geometry)
            //const monkeyShape = CannonUtils.CreateConvexPolyhedron(new THREE.IcosahedronGeometry(1))
            //const monkeyShape = CannonUtils.CreateConvexPolyhedron((monkeyMesh as THREE.Mesh).geometry)
            //const monkeyShape = CannonUtils.CreateConvexPolyhedron((monkeyCollisionMesh as THREE.Mesh).geometry)
            const monkeyBody = new CANNON.Body({ mass: 1 });
            //monkeyBody.addShape(monkeyShape)
            monkeyBody.addShape(new CANNON.Sphere(.8), new CANNON.Vec3(0, .2, 0))// head,
            monkeyBody.addShape(new CANNON.Sphere(.05), new CANNON.Vec3(0, -.97, 0.46))// chin,
            monkeyBody.addShape(new CANNON.Sphere(.05), new CANNON.Vec3(-1.36, .29, -0.5)) //left ear
            monkeyBody.addShape(new CANNON.Sphere(.05), new CANNON.Vec3(1.36, .29, -0.5)) //right ear
            // monkeyBody.addShape(new CANNON.Sphere(.05), new CANNON.Vec3(0, .56, -0.85)) //head top
            // monkeyBody.addShape(new CANNON.Sphere(.05), new CANNON.Vec3(0, .98, -0.07)) //forehead top
            monkeyBody.addShape(new CANNON.Sphere(.05), new CANNON.Vec3(-.32, .75, 0.73)) //left eyebrow top
            monkeyBody.position.x = monkeyMeshClone.position.x
            monkeyBody.position.y = monkeyMeshClone.position.y
            monkeyBody.position.z = monkeyMeshClone.position.z
            world.addBody(monkeyBody)
            monkeyBodies.push(monkeyBody)
        }

        monkeyLoaded = true
    },
    (xhr) => {
        console.log((xhr.loaded / xhr.total * 100) + '% loaded');
    },
    (error) => {
        console.log('An error happened');
    }
);


const planeGeometry: THREE.PlaneGeometry = new THREE.PlaneGeometry(25, 25)
const planeMesh: THREE.Mesh = new THREE.Mesh(planeGeometry, phongMaterial)
planeMesh.rotateX(-Math.PI / 2)
planeMesh.receiveShadow = true;
scene.add(planeMesh)
const planeShape = new CANNON.Plane()
const planeBody = new CANNON.Body({ mass: 0 })
planeBody.addShape(planeShape)
planeBody.quaternion.setFromAxisAngle(new CANNON.Vec3(1, 0, 0), -Math.PI / 2)
world.addBody(planeBody)

camera.position.y = 4
camera.position.z = 4
controls.target.y = 2

window.addEventListener('resize', onWindowResize, false)
function onWindowResize() {
    camera.aspect = window.innerWidth / window.innerHeight
    camera.updateProjectionMatrix()
    renderer.setSize(window.innerWidth, window.innerHeight)
    render()
}

const stats = Stats()
document.body.appendChild(stats.dom)

const gui = new GUI()
const physicsFolder = gui.addFolder("Physics")
physicsFolder.add(world.gravity, "x", -10.0, 10.0, 0.1)
physicsFolder.add(world.gravity, "y", -10.0, 10.0, 0.1)
physicsFolder.add(world.gravity, "z", -10.0, 10.0, 0.1)
physicsFolder.open()

const clock: THREE.Clock = new THREE.Clock()

const cannonDebugRenderer = new CannonDebugRenderer(scene, world)

var animate = function () {
    requestAnimationFrame(animate)

    controls.update()

    let delta = clock.getDelta()
    if (delta > .1) delta = .1
    world.step(delta)
    cannonDebugRenderer.update()

    // Copy coordinates from Cannon.js to Three.js
    if (monkeyLoaded) {
        monkeyMeshes.forEach((m, i) => {
            m.position.set(monkeyBodies[i].position.x, monkeyBodies[i].position.y, monkeyBodies[i].position.z);
            m.quaternion.set(monkeyBodies[i].quaternion.x, monkeyBodies[i].quaternion.y, monkeyBodies[i].quaternion.z, monkeyBodies[i].quaternion.w);
        })
    }

    render()

    stats.update()
};

function render() {
    renderer.render(scene, camera)
}
animate();