const DAMPING = 0.03; const DRAG = 1 - DAMPING; const MASS = 0.1; const GRAVITY = new THREE.Vector3(0, -9.81 * MASS, 0); const K = 1; const MAX_STRETCH = 1.5; const options = { wind: true, }; class Spring { constructor(p1, p2, restDist) { this.p1 = p1; this.p2 = p2; this.restDist = restDist; } satisfy() { /** calculate current spring length */ const diff = this.p2.position.clone().sub(this.p1.position); const currentDist = diff.length(); if (currentDist == 0) return; if (currentDist <= this.restDist) return; //const correction = diff.multiplyScalar(1 - (this.restDist / currentDist)); /** calculate necessary correction length and direction */ const correction = diff.multiplyScalar((currentDist - this.restDist) / currentDist); correction.multiplyScalar(K); const correctionHalf = correction.multiplyScalar(0.5); let p1movable = this.p1.movable && this.p1.movableTmp; let p2movable = this.p2.movable && this.p2.movableTmp; /** apply correction if masses aren't fixed */ /** divide correction if both are movable */ if (p1movable && p2movable) { this.p1.position.add(correctionHalf); this.p2.position.sub(correctionHalf); } else if (! p1movable && p2movable) { this.p2.position.sub(correction); } else if (p1movable && ! p2movable) { this.p1.position.add(correction); } } } class Mass { movableTmp = true; movable = true; constructor(x, y, z, mass) { this.position = new THREE.Vector3(x, y, z); this.previous = new THREE.Vector3(x, y, z); this.acceleration = new THREE.Vector3(0, 0, 0); this.mass = mass; } addForce(force) { this.acceleration.add( force.clone().multiplyScalar(1/this.mass) ); } verlet(dt) { // verlet algorithm // next position = 2 * current Position - previous position + acceleration * (passed time)^2 // acceleration (dv/dt) = F(net) /** calculate velocity */ const nextPosition = this.position.clone().sub(this.previous); /** apply drag */ nextPosition.multiplyScalar(DRAG); /** add to current position and add acceleration */ nextPosition.add(this.position); nextPosition.add(this.acceleration.multiplyScalar(dt*dt)); if (this.movable && this.movableTmp) { this.previous = this.position; this.position = nextPosition; } /** reset for next frame */ this.acceleration.set(0, 0, 0); } } class Cloth { constructor(width, height, numPointsWidth, numPointsHeight) { this.width = width; this.height = height; this.numPointsWidth = numPointsWidth; this.numPointsHeight = numPointsHeight; this.windFactor = new THREE.Vector3(3, 2, 2); /** * distance between two vertices horizontally/vertically * divide by the number of points minus one * because there are (n - 1) lines between n vertices */ let stepWidth = width / (numPointsWidth - 1); let stepHeight = height / (numPointsHeight - 1); /** * iterate over the number of vertices in x/y axis * and add a new Particle to "masses" */ this.masses = []; for (let y = 0; y < numPointsHeight; y++) { for (let x = 0; x < numPointsWidth; x++) { this.masses.push( new Mass( (x - ((numPointsWidth-1)/2)) * stepWidth, height - (y + ((numPointsHeight-1)/2)) * stepHeight, 0, MASS) ); } } /** attach cloth to flag pole */ const n = 3; for (let i = 0; i < numPointsHeight; i++) this.masses[this.getVertexIndex(0, i)].movable = false; const REST_DIST_X = width / (numPointsWidth-1); const REST_DIST_Y = height / (numPointsHeight-1); /** * generate springs (constraints) */ this.springs = []; for (let y = 0; y < numPointsHeight; y++) { for (let x = 0; x < numPointsWidth; x++) { if (x < numPointsWidth-1) { this.springs.push(new Spring( this.masses[this.getVertexIndex(x, y)], this.masses[this.getVertexIndex(x+1, y)], REST_DIST_X )); } if (y < numPointsHeight-1) { this.springs.push(new Spring( this.masses[this.getVertexIndex(x, y)], this.masses[this.getVertexIndex(x, y+1)], REST_DIST_Y )); } } } } generateGeometry() { const geometry = new THREE.BufferGeometry(); const vertices = []; const indices = []; const uvs = []; /** create one vertex and one uv coordinate per mass */ for (let i in this.masses) { let particle = this.masses[i]; vertices.push( particle.position.x, particle.position.y, particle.position.z); uvs.push( this.getX(i) / (this.numPointsWidth-1), 1 - (this.getY(i) / (this.numPointsHeight-1)) ); } /** * generate faces based on 4 vertices * and 6 springs each */ for (let y = 0; y < this.numPointsHeight - 1; y++) { for (let x = 0; x < this.numPointsWidth - 1; x++) { indices.push( this.getVertexIndex(x, y), this.getVertexIndex(x+1, y), this.getVertexIndex(x+1, y+1) ); indices.push( this.getVertexIndex(x, y), this.getVertexIndex(x+1, y+1), this.getVertexIndex(x, y+1) ); } } /** set up geometry */ geometry.setIndex(indices); geometry.setAttribute('position', new THREE.Float32BufferAttribute(vertices, 3)); geometry.setAttribute('uv', new THREE.Float32BufferAttribute(uvs, 2)); geometry.computeBoundingSphere(); geometry.computeVertexNormals(); return geometry; } updateGeometry(geometry) { /** update vertex positions in place */ const positions = geometry.attributes.position.array; for (let i in this.masses) { let p = this.masses[i]; positions[i*3+0] = p.position.x; positions[i*3+1] = p.position.y; positions[i*3+2] = p.position.z; } /** update internally and recalculate bounding volume */ geometry.attributes.position.needsUpdate = true; geometry.computeBoundingSphere(); geometry.computeVertexNormals(); } simulate(dt) { let now = performance.now(); for (let mass of this.masses) { /** accumulate acceleration: * - wind * - gravity */ let vertex = mass.position; let fWind = new THREE.Vector3( this.windFactor.x * (Math.sin(vertex.x * vertex.y * now)+1), this.windFactor.y * Math.cos(vertex.z * now), this.windFactor.z * Math.sin(Math.cos(5 * vertex.x * vertex.y * vertex.z)) ); // normalize then multiply? if (options.wind) mass.addForce(fWind); // calculate wind with normal? mass.addForce(GRAVITY); /** integrate motion */ mass.verlet(dt); } /** run satisfy step */ for (let constraint of this.springs) { constraint.satisfy(); } /** prevent self-intersections */ this.intersect(); } intersect() { for (let i in this.masses) { for (let j in this.masses) { let p1 = this.masses[i]; let p2 = this.masses[j]; p1.movableTmp = true; p2.movableTmp = true; /** skip if i == j or if masses are adjacent */ if (i == j || (Math.abs(this.getX(i) - this.getX(j)) == 1 && Math.abs(this.getY(i) - this.getY(j)) == 1)) continue; /** calculate distance of points */ let dist = p1.position.distanceTo(p2.position); /** calculate minimal resting distance (largest distance that should not be fallen below) */ let collisionDistance = Math.min(this.width / this.numPointsWidth, this.height / this.numPointsHeight); // collisionDistance /= 2; /** calculate "sphere intersection" */ if (dist < collisionDistance) { // p1.movableTmp = false; // p2.movableTmp = false; /** vectors from p1 to p2 and the other way round */ let diffP2P1 = p1.position.clone().sub(p2.position).normalize(); diffP2P1.multiplyScalar((collisionDistance - dist) * 1.001 / 2); let diffP1P2 = diffP2P1.clone().multiplyScalar(-1); // let v1 = p1.position.clone().sub(p1.previous).normalize(); // let v2 = p2.position.clone().sub(p2.previous).normalize(); // let factor1 = (Math.PI - Math.acos(v1.dot(diffP2P1))) / Math.PI * 2; // let factor2 = (Math.PI - Math.acos(v2.dot(diffP1P2))) / Math.PI * 2; /** move masses apart */ if (p1.movable) p1.position.add(diffP2P1); //p1.position.add(diffP2P1.multiplyScalar(factor1)); if (p2.movable) p2.position.add(diffP1P2); //p2.position.add(diffP1P2.multiplyScalar(factor2)); } } } } blow(camPos, intersects) { let face = intersects[0].face; /** vector from cam to intersection (wind) */ let dir = intersects[0].point.clone().sub(camPos).multiplyScalar(100); /** apply to all vertices of affected face */ this.masses[face.a].addForce(dir); this.masses[face.b].addForce(dir); this.masses[face.c].addForce(dir); } drag(mousePosWorld, index) { /** calculate vector from vertex to cursor */ let dir = mousePosWorld.clone().sub(this.masses[index].position).multiplyScalar(200); /** apply to grabbed vertex */ this.masses[index].addForce(dir); } /** * helper function to calculate index of vertex * in "vertices" array based on its x and y positions * in the mesh * @param {number} x - x index of vertex * @param {number} y - y index of vertex */ getVertexIndex(x, y) { return y * this.numPointsWidth + x; } getX(i) { return i % this.numPointsWidth; } getY(i) { return Math.floor(i / this.numPointsWidth); } }