diff options
Diffstat (limited to 'Scripts/_cloth.js')
| -rw-r--r-- | Scripts/_cloth.js | 621 |
1 files changed, 621 insertions, 0 deletions
diff --git a/Scripts/_cloth.js b/Scripts/_cloth.js new file mode 100644 index 0000000..546f7d3 --- /dev/null +++ b/Scripts/_cloth.js @@ -0,0 +1,621 @@ +/**
+ * Convenience Function for calculating the distance between two vectors
+ * because THREE JS Vector functions mutate variables
+ * @param {Vector3} a - Vector A
+ * @param {Vector3} b - Vector B
+ */
+function vectorLength(a, b) {
+ let v1 = new THREE.Vector3();
+ v1.copy(a);
+ let v2 = new THREE.Vector3();
+ v2.copy(b);
+
+ return v1.sub(v2).length();
+}
+
+/**
+ * Class representing a quad face
+ * Each face consists of two triangular mesh faces
+ * containts four indices for determining vertices
+ * and six springs, one between each of the vertices
+ */
+export class Face {
+ a;
+ b;
+ c;
+ d;
+
+ springs = [];
+
+ constructor(a, b, c, d) {
+ this.a = a;
+ this.b = b;
+ this.c = c;
+ this.d = d;
+ }
+}
+
+/**
+ * Class representing a single spring
+ * has a current and resting length
+ * and indices to the two connected vertices
+ */
+export class Spring {
+ restLength;
+ currentLength;
+ index1;
+ index2;
+
+
+ /**
+ * set vertex indices
+ * and calculate inital length based on the
+ * vertex positions
+ * @param {Array<Vector3>} vertices
+ * @param {number} index1
+ * @param {number} index2
+ */
+ constructor(vertices, index1, index2) {
+ this.index1 = index1;
+ this.index2 = index2;
+
+ let length = vectorLength(vertices[index1], vertices[index2]);
+ this.restLength = length;
+ this.currentLength = length;
+ }
+
+ getDirection(vertices) {
+ let direction = new THREE.Vector3();
+ direction.copy(vertices[this.index1]);
+
+ direction.sub(vertices[this.index2]);
+ direction.divideScalar(vectorLength(vertices[this.index1], vertices[this.index2]));
+
+ return direction;
+ }
+
+ update(vertices) {
+ let length = vectorLength(vertices[this.index1], vertices[this.index2]);
+ this.currentLength = length;
+ }
+}
+
+/**
+ * Class representing a single piece of cloth
+ * contains THREE JS geometry,
+ * logically represented by an array of adjacent faces
+ * and vertex weights which are accessed by the same
+ * indices as the vertices in the Mesh
+ */
+export class Cloth {
+ VertexWeight = 1;
+
+ geometry = new THREE.Geometry();
+
+ faces = [];
+
+ vertexWeights = [];
+
+ vertexRigidness = [];
+
+ fixedPoints = [];
+
+ externalForces = [];
+ windForce = 50;
+
+ windFactor = new THREE.Vector3(0, 0, 0);
+
+ /**
+ * creates a rectangular piece of cloth
+ * takes the size of the cloth
+ * and the number of vertices it should be composed of
+ * @param {number} width - width of the cloth
+ * @param {number} height - height of the cloth
+ * @param {number} numPointsWidth - number of vertices in horizontal direction
+ * @param {number} numPointsHeight - number of vertices in vertical direction
+ */
+ createBasic(width, height, numPointsWidth, numPointsHeight) {
+ /** resulting vertices and faces */
+ let vertices = [];
+ let faces = [];
+
+ this.width = width;
+ this.height = height;
+ this.numPointsWidth = numPointsWidth;
+ this.numPointsHeight = numPointsHeight;
+
+ /**
+ * 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 Vector3 to "vertices"
+ */
+ for (let y = 0; y < numPointsHeight; y++) {
+ for (let x = 0; x < numPointsWidth; x++) {
+ vertices.push(
+ new THREE.Vector3((x - ((numPointsWidth-1)/2)) * stepWidth, height - (y + ((numPointsHeight-1)/2)) * stepHeight, 0)
+ );
+ }
+ }
+
+ /**
+ * 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
+ */
+ function getVertexIndex(x, y) {
+ return y * numPointsWidth + x;
+ }
+
+ /**
+ * generate faces based on 4 vertices
+ * and 6 springs each
+ */
+ for (let y = 0; y < numPointsHeight - 1; y++) {
+ for (let x = 0; x < numPointsWidth - 1; x++) {
+ let newFace = new Face(
+ getVertexIndex(x, y),
+ getVertexIndex(x, y + 1),
+ getVertexIndex(x + 1, y),
+ getVertexIndex(x + 1, y + 1),
+ );
+
+ newFace.springs.push(new Spring(vertices, getVertexIndex(x, y), getVertexIndex(x + 1, y))); // oben
+ newFace.springs.push(new Spring(vertices, getVertexIndex(x, y), getVertexIndex(x, y + 1))); // links
+ newFace.springs.push(new Spring(vertices, getVertexIndex(x, y), getVertexIndex(x + 1, y + 1))); // oben links -> unten rechts diagonal
+ newFace.springs.push(new Spring(vertices, getVertexIndex(x + 1, y), getVertexIndex(x, y + 1))); // oben rechts -> unten links diagonal
+ newFace.springs.push(new Spring(vertices, getVertexIndex(x + 1, y), getVertexIndex(x + 1, y + 1))); // rechts
+ newFace.springs.push(new Spring(vertices, getVertexIndex(x, y + 1), getVertexIndex(x + 1, y + 1))); // unten
+
+ faces.push(newFace);
+ }
+ }
+
+ /**
+ * call createExplicit
+ * with generated vertices and faces
+ */
+ this.createExplicit(vertices, faces);
+
+ /**
+ * hand cloth from left and right upper corners
+ */
+ this.fixedPoints.push(getVertexIndex(0, 0));
+ this.fixedPoints.push(getVertexIndex(0, 19));
+ }
+
+ /**
+ * Generate THREE JS Geometry
+ * (list of vertices and list of indices representing triangles)
+ * and calculate the weight of each face and split it between
+ * surrounding vertices
+ * @param {Array<Vector3>} vertices
+ * @param {Array<Face>} faces
+ */
+ createExplicit(vertices, faces) {
+
+ /**
+ * Copy vertices and initialize vertex weights to 0
+ */
+ for (let i in vertices) {
+ this.geometry.vertices.push(vertices[i].clone());
+ this.previousPositions.push(vertices[i].clone());
+ // this.geometry.vertices.push(vertices[i]);
+ // this.previousPositions.push(vertices[i]);
+ this.vertexWeights.push(0);
+ this.vertexRigidness.push(false);
+ this.externalForces.push(new THREE.Vector3(0,0,0));
+ }
+ /**
+ * copy faces,
+ * generate two triangles per face,
+ * calculate weight of face as its area
+ * and split between the 4 vertices
+ */
+ for (let i in faces) {
+ let face = faces[i];
+
+ /** copy faces to class member */
+ this.faces.push(face);
+
+ /** generate triangles */
+ this.geometry.faces.push(new THREE.Face3(
+ face.a, face.b, face.c
+ ));
+ this.geometry.faces.push(new THREE.Face3(
+ face.c, face.b, face.d
+ ));
+
+ /**
+ * calculate area of face as combined area of
+ * its two composing triangles
+ */
+ let xLength = vectorLength(this.geometry.vertices[face.b], this.geometry.vertices[face.a]);
+ let yLength = vectorLength(this.geometry.vertices[face.c], this.geometry.vertices[face.a]);
+ let weight = xLength * yLength / 2;
+
+ xLength = vectorLength(this.geometry.vertices[face.b], this.geometry.vertices[face.d]);
+ yLength = vectorLength(this.geometry.vertices[face.c], this.geometry.vertices[face.d]);
+ weight += xLength * yLength / 2;
+
+ weight *= 10;
+
+ /**
+ * split weight equally between four surrounding vertices
+ */
+ this.vertexWeights[face.a] += weight / 4;
+ this.vertexWeights[face.b] += weight / 4;
+ this.vertexWeights[face.c] += weight / 4;
+ this.vertexWeights[face.d] += weight / 4;
+ }
+
+ /**
+ * let THREE JS compute bounding sphere around generated mesh
+ * needed for View Frustum Culling internally
+ */
+ this.geometry.computeBoundingSphere();
+ this.geometry.computeFaceNormals();
+ this.geometry.computeVertexNormals();
+ }
+
+ /**
+ * generate a debug mesh for visualizing
+ * vertices and springs of the cloth
+ * and add it to scene for rendering
+ * @param {Scene} scene - Scene to add Debug Mesh to
+ */
+ createDebugMesh(scene) {
+ /**
+ * helper function to generate a single line
+ * between two Vertices with a given color
+ * @param {Vector3} from
+ * @param {Vector3} to
+ * @param {number} color
+ */
+ function addLine(from, to, color) {
+ let geometry = new THREE.Geometry();
+ geometry.vertices.push(from);
+ geometry.vertices.push(to);
+ let material = new THREE.LineBasicMaterial({ color: color, linewidth: 10 });
+ let line = new THREE.Line(geometry, material);
+ line.renderOrder = 1;
+ scene.add(line);
+ }
+ /**
+ * helper function to generate a small sphere
+ * at a given Vertex Position with color
+ * @param {Vector3} point
+ * @param {number} color
+ */
+ function addPoint(point, color) {
+ const geometry = new THREE.SphereGeometry(0.05, 32, 32);
+ const material = new THREE.MeshBasicMaterial({ color: color });
+ const sphere = new THREE.Mesh(geometry, material);
+ sphere.position.set(point.x, point.y, point.z);
+ scene.add(sphere);
+ }
+
+ let lineColor = 0x000000;
+ let pointColor = 0xff00000;
+
+ /**
+ * generate one line for each of the 6 springs
+ * and one point for each of the 4 vertices
+ * for all of the faces
+ */
+ for (let i in this.faces) {
+ let face = this.faces[i];
+ addLine(this.geometry.vertices[face.a], this.geometry.vertices[face.b], lineColor);
+ addLine(this.geometry.vertices[face.a], this.geometry.vertices[face.c], lineColor);
+ addLine(this.geometry.vertices[face.a], this.geometry.vertices[face.d], lineColor);
+ addLine(this.geometry.vertices[face.b], this.geometry.vertices[face.c], lineColor);
+ addLine(this.geometry.vertices[face.b], this.geometry.vertices[face.d], lineColor);
+ addLine(this.geometry.vertices[face.c], this.geometry.vertices[face.d], lineColor);
+
+ addPoint(this.geometry.vertices[face.a], pointColor);
+ addPoint(this.geometry.vertices[face.b], pointColor);
+ addPoint(this.geometry.vertices[face.c], pointColor);
+ addPoint(this.geometry.vertices[face.d], pointColor);
+ }
+ }
+
+ previousPositions = [];
+ time = 0;
+ /**
+ *
+ * @param {number} dt time in seconds since last frame
+ */
+ simulate(dt) {
+ for (let i in this.geometry.vertices) {
+ let acceleration = this.getAcceleration(i, dt);
+
+ //acceleration.clampLength(0, 10);
+
+ if (Math.abs(acceleration.length()) <= 10e-4) {
+ acceleration.set(0, 0, 0);
+ }
+
+ let currentPosition = this.verlet(this.geometry.vertices[i].clone(), this.previousPositions[i].clone(), acceleration, dt);
+ //let currentPosition = this.euler(this.geometry.vertices[i], acceleration, dt);
+
+ this.previousPositions[i].copy(this.geometry.vertices[i]);
+ this.geometry.vertices[i].copy(currentPosition);
+ }
+
+ this.checkIntersect();
+
+ this.time += dt;
+
+ for (let face of this.faces) {
+ for (let spring of face.springs) {
+ spring.update(this.geometry.vertices);
+ }
+ }
+
+ /**
+ * let THREE JS compute bounding sphere around generated mesh
+ * needed for View Frustum Culling internally
+ */
+
+ this.geometry.verticesNeedUpdate = true;
+ this.geometry.elementsNeedUpdate = true;
+ this.geometry.computeBoundingSphere();
+ this.geometry.computeFaceNormals();
+ this.geometry.computeVertexNormals();
+
+ }
+
+checkIntersect() {
+ let npw = this.numPointsWidth;
+ function getX(i, ) { return i % npw; }
+ function getY(i) { return Math.floor(i / npw); }
+ for (let i in this.geometry.vertices) {
+ for (let j in this.geometry.vertices) {
+ this.vertexRigidness[i] = false;
+ this.vertexRigidness[j] = false;
+ if (i == j || (Math.abs(getX(i) - getX(j)) == 1 && Math.abs(getY(i) - getY(j)) == 1))
+ continue;
+ let posI = this.geometry.vertices[i];
+ let posJ = this.geometry.vertices[j];
+ let dist = posI.distanceTo(posJ);
+ const collisionDistance = Math.min(this.width / this.numPointsWidth, this.height / this.numPointsHeight);
+ if (dist < collisionDistance) {
+ this.vertexRigidness[i] = true;
+ this.vertexRigidness[j] = true;
+ let diff = this.geometry.vertices[i].clone().sub(this.geometry.vertices[j]).normalize().multiplyScalar((collisionDistance - dist) * 1.001 / 2);
+ if (!(this.fixedPoints.includes(i) || this.fixedPoints.includes(j))) {
+ this.geometry.vertices[i].add(diff);
+ this.geometry.vertices[j].sub(diff);
+ }
+ }
+ }
+ }
+}
+
+/**
+ * Equation of motion for each vertex which represents the acceleration
+ * @param {number} vertexIndex The index of the current vertex whose acceleration should be calculated
+ * @param {number} dt The time passed since last frame
+ */
+getAcceleration(vertexIndex, dt) {
+ if (this.fixedPoints.includes(parseInt(vertexIndex)) ||
+ this.vertexRigidness[vertexIndex]) {
+ return new THREE.Vector3(0, 0, 0);
+ }
+
+ let externalForce = this.externalForces[vertexIndex];
+ let vertex = this.geometry.vertices[vertexIndex];//.add(externalForce);
+
+ // Mass of vertex
+ let M = this.vertexWeights[vertexIndex];
+ // constant gravity
+ let g = new THREE.Vector3(0, -9.8, 0);
+ // stiffness
+ let k = 1000;
+
+ // Wind vector
+ let fWind = new THREE.Vector3(
+ this.windFactor.x * (Math.sin(vertex.x * vertex.y * this.time)+1),
+ this.windFactor.y * Math.cos(vertex.z * this.time),
+ this.windFactor.z * Math.sin(Math.cos(5 * vertex.x * vertex.y * vertex.z))
+ );
+ //console.log(fWind);
+
+ /**
+ * constant determined by the properties of the surrounding fluids (air)
+ * achievement of cloth effects through try out
+ * */
+ let a = 0.1;
+
+ let velocity = new THREE.Vector3(
+ (this.previousPositions[vertexIndex].x - vertex.x) / dt,
+ (this.previousPositions[vertexIndex].y - vertex.y) / dt,
+ (this.previousPositions[vertexIndex].z - vertex.z) / dt
+ );
+
+ //console.log(velocity, vertex, this.previousPositions[vertexIndex]);
+
+ let fAirResistance = velocity.multiply(velocity).multiplyScalar(-a);
+
+ let springSum = new THREE.Vector3(0, 0, 0);
+
+ // Get the bounding springs and add them to the needed springs
+ // TODO: optimize
+
+ const numPointsX = this.numPointsWidth;
+ const numPointsY = this.numPointsHeight;
+ const numFacesX = numPointsX - 1;
+ const numFacesY = numPointsY - 1;
+
+ function getFaceIndex(x, y) {
+ return y * numFacesX + x;
+ }
+
+ let indexX = vertexIndex % numPointsX;
+ let indexY = Math.floor(vertexIndex / numPointsX);
+
+ let springs = [];
+
+ // 0 oben
+ // 1 links
+ // 2 oben links -> unten rechts diagonal
+ // 3 oben rechts -> unten links diagonal
+ // 4 rechts
+ // 5 unten
+
+ let ul = indexX > 0 && indexY < numPointsY - 1;
+ let ur = indexX < numPointsX - 1 && indexY < numPointsY - 1;
+ let ol = indexX > 0 && indexY > 0;
+ let or = indexX < numPointsX - 1 && indexY > 0;
+
+ if (ul) {
+ let faceUL = this.faces[getFaceIndex(indexX - 1, indexY)];
+ springs.push(faceUL.springs[3]);
+ if (!ol)
+ springs.push(faceUL.springs[0]);
+ springs.push(faceUL.springs[4]);
+ }
+ if (ur) {
+ let faceUR = this.faces[getFaceIndex(indexX, indexY)];
+ springs.push(faceUR.springs[2]);
+ if (!or)
+ springs.push(faceUR.springs[0]);
+ if (!ul)
+ springs.push(faceUR.springs[1]);
+ }
+ if (ol) {
+ let faceOL = this.faces[getFaceIndex(indexX - 1, indexY - 1)];
+ springs.push(faceOL.springs[2]);
+ springs.push(faceOL.springs[4]);
+ springs.push(faceOL.springs[5]);
+ }
+ if (or) {
+ let faceOR = this.faces[getFaceIndex(indexX , indexY - 1)];
+ springs.push(faceOR.springs[3]);
+ if (!ol)
+ springs.push(faceOR.springs[1]);
+ springs.push(faceOR.springs[5]);
+ }
+
+ for (let spring of springs) {
+ let springDirection = spring.getDirection(this.geometry.vertices);
+
+ if (spring.index1 == vertexIndex)
+ springDirection.multiplyScalar(-1);
+
+ springSum.add(springDirection.multiplyScalar(k * (spring.restLength - spring.currentLength)));
+ }
+
+ let result = new THREE.Vector3(1, 1, 1);
+ result.multiplyScalar(M).multiply(g).add(fWind).add(externalForce).add(fAirResistance).sub(springSum);
+
+ document.getElementById("Output").innerText = "SpringSum: " + Math.floor(springSum.y);
+
+ let threshold = 1;
+ let forceReduktion = 0.8;
+ if(Math.abs(externalForce.z) > threshold){
+ externalForce.z *= forceReduktion;
+ } else {
+ externalForce.z = 0;
+ }
+
+ if(Math.abs(externalForce.y) > threshold){
+ externalForce.y *= forceReduktion;
+ } else {
+ externalForce.y = 0;
+ }
+
+ if(Math.abs(externalForce.x) > threshold){
+ externalForce.x *= forceReduktion;
+ } else {
+ externalForce.x = 0;
+ }
+
+
+
+ return result;
+}
+
+/**
+ * The Verlet algorithm as an integrator
+ * to get the next position of a vertex
+ * @param {Vector3} currentPosition
+ * @param {Vector3} previousPosition
+ * @param {Vector3} acceleration
+ * @param {number} passedTime The delta time since last frame
+ */
+verlet(currentPosition, previousPosition, acceleration, passedTime) {
+ // verlet algorithm
+ // next position = 2 * current Position - previous position + acceleration * (passed time)^2
+ // acceleration (dv/dt) = F(net)
+ // Dependency for one vertex: gravity, fluids/air, springs
+ const DRAG = 0.97;
+ let nextPosition = new THREE.Vector3(
+ (currentPosition.x - previousPosition.x) * DRAG + currentPosition.x + acceleration.x * (passedTime * passedTime),
+ (currentPosition.y - previousPosition.y) * DRAG + currentPosition.y + acceleration.y * (passedTime * passedTime),
+ (currentPosition.z - previousPosition.z) * DRAG + currentPosition.z + acceleration.z * (passedTime * passedTime),
+ );
+
+ // let nextPosition = new THREE.Vector3(
+ // (2 * currentPosition.x) - previousPosition.x + acceleration.x * (passedTime * passedTime),
+ // (2 * currentPosition.y) - previousPosition.y + acceleration.y * (passedTime * passedTime),
+ // (2 * currentPosition.z) - previousPosition.z + acceleration.z * (passedTime * passedTime),
+ // );
+
+ return nextPosition;
+}
+
+euler(currentPosition, acceleration, passedTime) {
+ let nextPosition = new THREE.Vector3(
+ currentPosition.x + acceleration.x * passedTime,
+ currentPosition.y + acceleration.y * passedTime,
+ currentPosition.z + acceleration.z * passedTime,
+ );
+
+ return nextPosition;
+}
+
+wind(intersects) {
+ let intersect = intersects[0];
+ this.externalForces[intersect.face.a].z -= this.windForce;
+ this.externalForces[intersect.face.b].z -= this.windForce;
+ this.externalForces[intersect.face.c].z -= this.windForce;
+}
+
+mousePressed = false;
+mouseMoved = false;
+intersects;
+
+mousePress(intersects){
+ this.mousePressed = true;
+ this.intersects = intersects;
+
+}
+
+mouseMove(mousePos){
+ this.mouseMoved = true;
+ if(this.mousePressed){
+ let intersect = this.intersects[0];
+ this.externalForces[intersect.face.a].add(mousePos.clone().sub(this.geometry.vertices[intersect.face.a]).multiplyScalar(90));
+ /*
+ this.geometry.vertices[intersect.face.a].x = mousePos.x;
+ this.geometry.vertices[intersect.face.a].y = mousePos.y;
+ this.geometry.vertices[intersect.face.a].z = mousePos.z;
+ */
+ }
+}
+
+mouseRelease(){
+ this.mousePressed = false;
+}
+
+}
+
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