--- /dev/null
+/**\r
+ * Convenience Function for calculating the distance between two vectors\r
+ * because THREE JS Vector functions mutate variables\r
+ * @param {Vector3} a - Vector A\r
+ * @param {Vector3} b - Vector B\r
+ */\r
+function vectorLength(a, b) {\r
+ let v1 = new THREE.Vector3();\r
+ v1.copy(a);\r
+ let v2 = new THREE.Vector3();\r
+ v2.copy(b);\r
+\r
+ return v1.sub(v2).length();\r
+}\r
+\r
+/**\r
+ * Class representing a quad face\r
+ * Each face consists of two triangular mesh faces\r
+ * containts four indices for determining vertices\r
+ * and six springs, one between each of the vertices\r
+ */\r
+export class Face {\r
+ a;\r
+ b;\r
+ c;\r
+ d;\r
+\r
+ springs = [];\r
+\r
+ constructor(a, b, c, d) {\r
+ this.a = a;\r
+ this.b = b;\r
+ this.c = c;\r
+ this.d = d;\r
+ }\r
+}\r
+\r
+/**\r
+ * Class representing a single spring\r
+ * has a current and resting length\r
+ * and indices to the two connected vertices\r
+ */\r
+export class Spring {\r
+ restLength;\r
+ currentLength;\r
+ index1;\r
+ index2;\r
+\r
+\r
+ /**\r
+ * set vertex indices\r
+ * and calculate inital length based on the\r
+ * vertex positions\r
+ * @param {Array<Vector3>} vertices \r
+ * @param {number} index1 \r
+ * @param {number} index2 \r
+ */\r
+ constructor(vertices, index1, index2) {\r
+ this.index1 = index1;\r
+ this.index2 = index2;\r
+\r
+ let length = vectorLength(vertices[index1], vertices[index2]);\r
+ this.restLength = length;\r
+ this.currentLength = length;\r
+ }\r
+\r
+ getDirection(vertices) {\r
+ let direction = new THREE.Vector3();\r
+ direction.copy(vertices[this.index1]);\r
+\r
+ direction.sub(vertices[this.index2]);\r
+ direction.divideScalar(vectorLength(vertices[this.index1], vertices[this.index2]));\r
+\r
+ return direction;\r
+ }\r
+\r
+ update(vertices) {\r
+ let length = vectorLength(vertices[this.index1], vertices[this.index2]);\r
+ this.currentLength = length;\r
+ }\r
+}\r
+\r
+/**\r
+ * Class representing a single piece of cloth\r
+ * contains THREE JS geometry,\r
+ * logically represented by an array of adjacent faces\r
+ * and vertex weights which are accessed by the same\r
+ * indices as the vertices in the Mesh\r
+ */\r
+export class Cloth {\r
+ VertexWeight = 1;\r
+\r
+ geometry = new THREE.Geometry();\r
+\r
+ faces = [];\r
+\r
+ vertexWeights = [];\r
+\r
+ vertexRigidness = [];\r
+\r
+ fixedPoints = [];\r
+\r
+ externalForces = [];\r
+ windForce = 50;\r
+\r
+ windFactor = new THREE.Vector3(0, 0, 0);\r
+\r
+ /**\r
+ * creates a rectangular piece of cloth\r
+ * takes the size of the cloth\r
+ * and the number of vertices it should be composed of\r
+ * @param {number} width - width of the cloth\r
+ * @param {number} height - height of the cloth\r
+ * @param {number} numPointsWidth - number of vertices in horizontal direction\r
+ * @param {number} numPointsHeight - number of vertices in vertical direction\r
+ */\r
+ createBasic(width, height, numPointsWidth, numPointsHeight) {\r
+ /** resulting vertices and faces */\r
+ let vertices = [];\r
+ let faces = [];\r
+\r
+ this.width = width;\r
+ this.height = height;\r
+ this.numPointsWidth = numPointsWidth;\r
+ this.numPointsHeight = numPointsHeight;\r
+\r
+ /**\r
+ * distance between two vertices horizontally/vertically\r
+ * divide by the number of points minus one\r
+ * because there are (n - 1) lines between n vertices\r
+ */\r
+ let stepWidth = width / (numPointsWidth - 1);\r
+ let stepHeight = height / (numPointsHeight - 1);\r
+\r
+ /**\r
+ * iterate over the number of vertices in x/y axis\r
+ * and add a new Vector3 to "vertices"\r
+ */\r
+ for (let y = 0; y < numPointsHeight; y++) {\r
+ for (let x = 0; x < numPointsWidth; x++) {\r
+ vertices.push(\r
+ new THREE.Vector3((x - ((numPointsWidth-1)/2)) * stepWidth, height - (y + ((numPointsHeight-1)/2)) * stepHeight, 0)\r
+ );\r
+ }\r
+ }\r
+\r
+ /**\r
+ * helper function to calculate index of vertex\r
+ * in "vertices" array based on its x and y positions\r
+ * in the mesh\r
+ * @param {number} x - x index of vertex\r
+ * @param {number} y - y index of vertex\r
+ */\r
+ function getVertexIndex(x, y) {\r
+ return y * numPointsWidth + x;\r
+ }\r
+\r
+ /**\r
+ * generate faces based on 4 vertices\r
+ * and 6 springs each\r
+ */\r
+ for (let y = 0; y < numPointsHeight - 1; y++) {\r
+ for (let x = 0; x < numPointsWidth - 1; x++) {\r
+ let newFace = new Face(\r
+ getVertexIndex(x, y),\r
+ getVertexIndex(x, y + 1),\r
+ getVertexIndex(x + 1, y),\r
+ getVertexIndex(x + 1, y + 1),\r
+ );\r
+\r
+ newFace.springs.push(new Spring(vertices, getVertexIndex(x, y), getVertexIndex(x + 1, y))); // oben\r
+ newFace.springs.push(new Spring(vertices, getVertexIndex(x, y), getVertexIndex(x, y + 1))); // links\r
+ newFace.springs.push(new Spring(vertices, getVertexIndex(x, y), getVertexIndex(x + 1, y + 1))); // oben links -> unten rechts diagonal\r
+ newFace.springs.push(new Spring(vertices, getVertexIndex(x + 1, y), getVertexIndex(x, y + 1))); // oben rechts -> unten links diagonal\r
+ newFace.springs.push(new Spring(vertices, getVertexIndex(x + 1, y), getVertexIndex(x + 1, y + 1))); // rechts\r
+ newFace.springs.push(new Spring(vertices, getVertexIndex(x, y + 1), getVertexIndex(x + 1, y + 1))); // unten\r
+\r
+ faces.push(newFace);\r
+ }\r
+ }\r
+\r
+ /**\r
+ * call createExplicit\r
+ * with generated vertices and faces\r
+ */\r
+ this.createExplicit(vertices, faces);\r
+\r
+ /**\r
+ * hand cloth from left and right upper corners\r
+ */\r
+ this.fixedPoints.push(getVertexIndex(0, 0));\r
+ this.fixedPoints.push(getVertexIndex(0, 19));\r
+ }\r
+\r
+ /**\r
+ * Generate THREE JS Geometry\r
+ * (list of vertices and list of indices representing triangles)\r
+ * and calculate the weight of each face and split it between\r
+ * surrounding vertices\r
+ * @param {Array<Vector3>} vertices \r
+ * @param {Array<Face>} faces \r
+ */\r
+ createExplicit(vertices, faces) {\r
+\r
+ /**\r
+ * Copy vertices and initialize vertex weights to 0\r
+ */\r
+ for (let i in vertices) {\r
+ this.geometry.vertices.push(vertices[i].clone());\r
+ this.previousPositions.push(vertices[i].clone());\r
+ // this.geometry.vertices.push(vertices[i]);\r
+ // this.previousPositions.push(vertices[i]);\r
+ this.vertexWeights.push(0);\r
+ this.vertexRigidness.push(false);\r
+ this.externalForces.push(new THREE.Vector3(0,0,0));\r
+ }\r
+ /**\r
+ * copy faces,\r
+ * generate two triangles per face,\r
+ * calculate weight of face as its area\r
+ * and split between the 4 vertices\r
+ */\r
+ for (let i in faces) {\r
+ let face = faces[i];\r
+\r
+ /** copy faces to class member */\r
+ this.faces.push(face);\r
+\r
+ /** generate triangles */\r
+ this.geometry.faces.push(new THREE.Face3(\r
+ face.a, face.b, face.c\r
+ ));\r
+ this.geometry.faces.push(new THREE.Face3(\r
+ face.c, face.b, face.d\r
+ ));\r
+\r
+ /**\r
+ * calculate area of face as combined area of\r
+ * its two composing triangles\r
+ */\r
+ let xLength = vectorLength(this.geometry.vertices[face.b], this.geometry.vertices[face.a]);\r
+ let yLength = vectorLength(this.geometry.vertices[face.c], this.geometry.vertices[face.a]);\r
+ let weight = xLength * yLength / 2;\r
+\r
+ xLength = vectorLength(this.geometry.vertices[face.b], this.geometry.vertices[face.d]);\r
+ yLength = vectorLength(this.geometry.vertices[face.c], this.geometry.vertices[face.d]);\r
+ weight += xLength * yLength / 2;\r
+\r
+ weight *= 10;\r
+\r
+ /**\r
+ * split weight equally between four surrounding vertices\r
+ */\r
+ this.vertexWeights[face.a] += weight / 4;\r
+ this.vertexWeights[face.b] += weight / 4;\r
+ this.vertexWeights[face.c] += weight / 4;\r
+ this.vertexWeights[face.d] += weight / 4;\r
+ }\r
+\r
+ /**\r
+ * let THREE JS compute bounding sphere around generated mesh\r
+ * needed for View Frustum Culling internally\r
+ */\r
+ this.geometry.computeBoundingSphere();\r
+ this.geometry.computeFaceNormals();\r
+ this.geometry.computeVertexNormals();\r
+ }\r
+\r
+ /**\r
+ * generate a debug mesh for visualizing\r
+ * vertices and springs of the cloth\r
+ * and add it to scene for rendering\r
+ * @param {Scene} scene - Scene to add Debug Mesh to\r
+ */\r
+ createDebugMesh(scene) {\r
+ /**\r
+ * helper function to generate a single line\r
+ * between two Vertices with a given color\r
+ * @param {Vector3} from \r
+ * @param {Vector3} to \r
+ * @param {number} color \r
+ */\r
+ function addLine(from, to, color) {\r
+ let geometry = new THREE.Geometry();\r
+ geometry.vertices.push(from);\r
+ geometry.vertices.push(to);\r
+ let material = new THREE.LineBasicMaterial({ color: color, linewidth: 10 });\r
+ let line = new THREE.Line(geometry, material);\r
+ line.renderOrder = 1;\r
+ scene.add(line);\r
+ }\r
+ /**\r
+ * helper function to generate a small sphere\r
+ * at a given Vertex Position with color\r
+ * @param {Vector3} point \r
+ * @param {number} color \r
+ */\r
+ function addPoint(point, color) {\r
+ const geometry = new THREE.SphereGeometry(0.05, 32, 32);\r
+ const material = new THREE.MeshBasicMaterial({ color: color });\r
+ const sphere = new THREE.Mesh(geometry, material);\r
+ sphere.position.set(point.x, point.y, point.z);\r
+ scene.add(sphere);\r
+ }\r
+\r
+ let lineColor = 0x000000;\r
+ let pointColor = 0xff00000;\r
+\r
+ /**\r
+ * generate one line for each of the 6 springs\r
+ * and one point for each of the 4 vertices\r
+ * for all of the faces\r
+ */\r
+ for (let i in this.faces) {\r
+ let face = this.faces[i];\r
+ addLine(this.geometry.vertices[face.a], this.geometry.vertices[face.b], lineColor);\r
+ addLine(this.geometry.vertices[face.a], this.geometry.vertices[face.c], lineColor);\r
+ addLine(this.geometry.vertices[face.a], this.geometry.vertices[face.d], lineColor);\r
+ addLine(this.geometry.vertices[face.b], this.geometry.vertices[face.c], lineColor);\r
+ addLine(this.geometry.vertices[face.b], this.geometry.vertices[face.d], lineColor);\r
+ addLine(this.geometry.vertices[face.c], this.geometry.vertices[face.d], lineColor);\r
+\r
+ addPoint(this.geometry.vertices[face.a], pointColor);\r
+ addPoint(this.geometry.vertices[face.b], pointColor);\r
+ addPoint(this.geometry.vertices[face.c], pointColor);\r
+ addPoint(this.geometry.vertices[face.d], pointColor);\r
+ }\r
+ }\r
+\r
+ previousPositions = [];\r
+ time = 0;\r
+ /**\r
+ * \r
+ * @param {number} dt time in seconds since last frame\r
+ */\r
+ simulate(dt) {\r
+ for (let i in this.geometry.vertices) {\r
+ let acceleration = this.getAcceleration(i, dt);\r
+\r
+ //acceleration.clampLength(0, 10);\r
+\r
+ if (Math.abs(acceleration.length()) <= 10e-4) {\r
+ acceleration.set(0, 0, 0);\r
+ }\r
+ \r
+ let currentPosition = this.verlet(this.geometry.vertices[i].clone(), this.previousPositions[i].clone(), acceleration, dt);\r
+ //let currentPosition = this.euler(this.geometry.vertices[i], acceleration, dt);\r
+ \r
+ this.previousPositions[i].copy(this.geometry.vertices[i]);\r
+ this.geometry.vertices[i].copy(currentPosition);\r
+ }\r
+ \r
+ this.checkIntersect();\r
+ \r
+ this.time += dt;\r
+\r
+ for (let face of this.faces) {\r
+ for (let spring of face.springs) {\r
+ spring.update(this.geometry.vertices);\r
+ }\r
+ }\r
+\r
+ /**\r
+ * let THREE JS compute bounding sphere around generated mesh\r
+ * needed for View Frustum Culling internally\r
+ */\r
+\r
+ this.geometry.verticesNeedUpdate = true;\r
+ this.geometry.elementsNeedUpdate = true;\r
+ this.geometry.computeBoundingSphere();\r
+ this.geometry.computeFaceNormals();\r
+ this.geometry.computeVertexNormals();\r
+\r
+ }\r
+\r
+checkIntersect() {\r
+ let npw = this.numPointsWidth;\r
+ function getX(i, ) { return i % npw; }\r
+ function getY(i) { return Math.floor(i / npw); }\r
+ for (let i in this.geometry.vertices) {\r
+ for (let j in this.geometry.vertices) {\r
+ this.vertexRigidness[i] = false;\r
+ this.vertexRigidness[j] = false;\r
+ if (i == j || (Math.abs(getX(i) - getX(j)) == 1 && Math.abs(getY(i) - getY(j)) == 1))\r
+ continue;\r
+ let posI = this.geometry.vertices[i];\r
+ let posJ = this.geometry.vertices[j];\r
+ let dist = posI.distanceTo(posJ);\r
+ const collisionDistance = Math.min(this.width / this.numPointsWidth, this.height / this.numPointsHeight);\r
+ if (dist < collisionDistance) {\r
+ this.vertexRigidness[i] = true;\r
+ this.vertexRigidness[j] = true;\r
+ let diff = this.geometry.vertices[i].clone().sub(this.geometry.vertices[j]).normalize().multiplyScalar((collisionDistance - dist) * 1.001 / 2);\r
+ if (!(this.fixedPoints.includes(i) || this.fixedPoints.includes(j))) {\r
+ this.geometry.vertices[i].add(diff);\r
+ this.geometry.vertices[j].sub(diff);\r
+ }\r
+ }\r
+ }\r
+ }\r
+}\r
+\r
+/**\r
+ * Equation of motion for each vertex which represents the acceleration \r
+ * @param {number} vertexIndex The index of the current vertex whose acceleration should be calculated\r
+ * @param {number} dt The time passed since last frame\r
+ */\r
+getAcceleration(vertexIndex, dt) {\r
+ if (this.fixedPoints.includes(parseInt(vertexIndex)) ||\r
+ this.vertexRigidness[vertexIndex]) {\r
+ return new THREE.Vector3(0, 0, 0);\r
+ }\r
+\r
+ let externalForce = this.externalForces[vertexIndex];\r
+ let vertex = this.geometry.vertices[vertexIndex];//.add(externalForce);\r
+\r
+ // Mass of vertex\r
+ let M = this.vertexWeights[vertexIndex];\r
+ // constant gravity\r
+ let g = new THREE.Vector3(0, -9.8, 0);\r
+ // stiffness\r
+ let k = 1000;\r
+\r
+ // Wind vector\r
+ let fWind = new THREE.Vector3(\r
+ this.windFactor.x * (Math.sin(vertex.x * vertex.y * this.time)+1),\r
+ this.windFactor.y * Math.cos(vertex.z * this.time),\r
+ this.windFactor.z * Math.sin(Math.cos(5 * vertex.x * vertex.y * vertex.z))\r
+ );\r
+ //console.log(fWind);\r
+\r
+ /**\r
+ * constant determined by the properties of the surrounding fluids (air)\r
+ * achievement of cloth effects through try out\r
+ * */\r
+ let a = 0.1;\r
+ \r
+ let velocity = new THREE.Vector3(\r
+ (this.previousPositions[vertexIndex].x - vertex.x) / dt,\r
+ (this.previousPositions[vertexIndex].y - vertex.y) / dt,\r
+ (this.previousPositions[vertexIndex].z - vertex.z) / dt\r
+ );\r
+\r
+ //console.log(velocity, vertex, this.previousPositions[vertexIndex]);\r
+\r
+ let fAirResistance = velocity.multiply(velocity).multiplyScalar(-a);\r
+ \r
+ let springSum = new THREE.Vector3(0, 0, 0);\r
+\r
+ // Get the bounding springs and add them to the needed springs\r
+ // TODO: optimize\r
+\r
+ const numPointsX = this.numPointsWidth;\r
+ const numPointsY = this.numPointsHeight;\r
+ const numFacesX = numPointsX - 1;\r
+ const numFacesY = numPointsY - 1;\r
+\r
+ function getFaceIndex(x, y) {\r
+ return y * numFacesX + x;\r
+ }\r
+\r
+ let indexX = vertexIndex % numPointsX;\r
+ let indexY = Math.floor(vertexIndex / numPointsX);\r
+\r
+ let springs = [];\r
+\r
+ // 0 oben\r
+ // 1 links\r
+ // 2 oben links -> unten rechts diagonal\r
+ // 3 oben rechts -> unten links diagonal\r
+ // 4 rechts\r
+ // 5 unten\r
+\r
+ let ul = indexX > 0 && indexY < numPointsY - 1;\r
+ let ur = indexX < numPointsX - 1 && indexY < numPointsY - 1;\r
+ let ol = indexX > 0 && indexY > 0;\r
+ let or = indexX < numPointsX - 1 && indexY > 0;\r
+\r
+ if (ul) {\r
+ let faceUL = this.faces[getFaceIndex(indexX - 1, indexY)];\r
+ springs.push(faceUL.springs[3]);\r
+ if (!ol)\r
+ springs.push(faceUL.springs[0]);\r
+ springs.push(faceUL.springs[4]);\r
+ }\r
+ if (ur) {\r
+ let faceUR = this.faces[getFaceIndex(indexX, indexY)];\r
+ springs.push(faceUR.springs[2]);\r
+ if (!or)\r
+ springs.push(faceUR.springs[0]);\r
+ if (!ul)\r
+ springs.push(faceUR.springs[1]);\r
+ }\r
+ if (ol) {\r
+ let faceOL = this.faces[getFaceIndex(indexX - 1, indexY - 1)];\r
+ springs.push(faceOL.springs[2]);\r
+ springs.push(faceOL.springs[4]);\r
+ springs.push(faceOL.springs[5]);\r
+ }\r
+ if (or) {\r
+ let faceOR = this.faces[getFaceIndex(indexX , indexY - 1)];\r
+ springs.push(faceOR.springs[3]);\r
+ if (!ol)\r
+ springs.push(faceOR.springs[1]);\r
+ springs.push(faceOR.springs[5]);\r
+ }\r
+\r
+ for (let spring of springs) {\r
+ let springDirection = spring.getDirection(this.geometry.vertices);\r
+\r
+ if (spring.index1 == vertexIndex)\r
+ springDirection.multiplyScalar(-1);\r
+\r
+ springSum.add(springDirection.multiplyScalar(k * (spring.restLength - spring.currentLength)));\r
+ }\r
+ \r
+ let result = new THREE.Vector3(1, 1, 1);\r
+ result.multiplyScalar(M).multiply(g).add(fWind).add(externalForce).add(fAirResistance).sub(springSum);\r
+\r
+ document.getElementById("Output").innerText = "SpringSum: " + Math.floor(springSum.y);\r
+\r
+ let threshold = 1;\r
+ let forceReduktion = 0.8;\r
+ if(Math.abs(externalForce.z) > threshold){\r
+ externalForce.z *= forceReduktion;\r
+ } else {\r
+ externalForce.z = 0;\r
+ }\r
+\r
+ if(Math.abs(externalForce.y) > threshold){\r
+ externalForce.y *= forceReduktion;\r
+ } else {\r
+ externalForce.y = 0;\r
+ }\r
+\r
+ if(Math.abs(externalForce.x) > threshold){\r
+ externalForce.x *= forceReduktion;\r
+ } else {\r
+ externalForce.x = 0;\r
+ }\r
+ \r
+ \r
+\r
+ return result;\r
+}\r
+\r
+/**\r
+ * The Verlet algorithm as an integrator \r
+ * to get the next position of a vertex \r
+ * @param {Vector3} currentPosition \r
+ * @param {Vector3} previousPosition \r
+ * @param {Vector3} acceleration \r
+ * @param {number} passedTime The delta time since last frame\r
+ */\r
+verlet(currentPosition, previousPosition, acceleration, passedTime) {\r
+ // verlet algorithm\r
+ // next position = 2 * current Position - previous position + acceleration * (passed time)^2\r
+ // acceleration (dv/dt) = F(net)\r
+ // Dependency for one vertex: gravity, fluids/air, springs\r
+ const DRAG = 0.97;\r
+ let nextPosition = new THREE.Vector3(\r
+ (currentPosition.x - previousPosition.x) * DRAG + currentPosition.x + acceleration.x * (passedTime * passedTime),\r
+ (currentPosition.y - previousPosition.y) * DRAG + currentPosition.y + acceleration.y * (passedTime * passedTime),\r
+ (currentPosition.z - previousPosition.z) * DRAG + currentPosition.z + acceleration.z * (passedTime * passedTime),\r
+ );\r
+\r
+ // let nextPosition = new THREE.Vector3(\r
+ // (2 * currentPosition.x) - previousPosition.x + acceleration.x * (passedTime * passedTime),\r
+ // (2 * currentPosition.y) - previousPosition.y + acceleration.y * (passedTime * passedTime),\r
+ // (2 * currentPosition.z) - previousPosition.z + acceleration.z * (passedTime * passedTime),\r
+ // );\r
+\r
+ return nextPosition;\r
+}\r
+\r
+euler(currentPosition, acceleration, passedTime) {\r
+ let nextPosition = new THREE.Vector3(\r
+ currentPosition.x + acceleration.x * passedTime,\r
+ currentPosition.y + acceleration.y * passedTime,\r
+ currentPosition.z + acceleration.z * passedTime,\r
+ );\r
+\r
+ return nextPosition;\r
+}\r
+\r
+wind(intersects) {\r
+ let intersect = intersects[0];\r
+ this.externalForces[intersect.face.a].z -= this.windForce;\r
+ this.externalForces[intersect.face.b].z -= this.windForce;\r
+ this.externalForces[intersect.face.c].z -= this.windForce;\r
+}\r
+\r
+mousePressed = false;\r
+mouseMoved = false;\r
+intersects;\r
+\r
+mousePress(intersects){\r
+ this.mousePressed = true;\r
+ this.intersects = intersects;\r
+\r
+}\r
+\r
+mouseMove(mousePos){\r
+ this.mouseMoved = true;\r
+ if(this.mousePressed){\r
+ let intersect = this.intersects[0];\r
+ this.externalForces[intersect.face.a].add(mousePos.clone().sub(this.geometry.vertices[intersect.face.a]).multiplyScalar(90));\r
+ /*\r
+ this.geometry.vertices[intersect.face.a].x = mousePos.x;\r
+ this.geometry.vertices[intersect.face.a].y = mousePos.y;\r
+ this.geometry.vertices[intersect.face.a].z = mousePos.z;\r
+ */ \r
+ }\r
+}\r
+\r
+mouseRelease(){\r
+ this.mousePressed = false;\r
+}\r
+\r
+}\r
+\r
projects / cloth_sim / blobdiff