add cloth.js file

1 files changed, 285 insertions, 0 deletions

diff --git a/Scripts/cloth.js b/Scripts/cloth.js
new file mode 100644
index 0000000..e84facc
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+++ b/Scripts/cloth.js
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+/**

+ *  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.set(a.x, a.y, a.z);

+  let v2 = new THREE.Vector3();

+  v2.set(b.x, b.y, b.z);

+

+  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 of 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;

+  }

+}

+

+/**

+ * 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 = [];

+

+  

+  /**

+   * 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 = [];

+

+    /**

+     * 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 * stepWidth, height - y * 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)));

+        newFace.springs.push(new Spring(vertices, getVertexIndex(x, y), getVertexIndex(x, y + 1)));

+        newFace.springs.push(new Spring(vertices, getVertexIndex(x, y), getVertexIndex(x + 1, y + 1)));

+        newFace.springs.push(new Spring(vertices, getVertexIndex(x + 1, y), getVertexIndex(x, y + 1)));

+        newFace.springs.push(new Spring(vertices, getVertexIndex(x + 1, y), getVertexIndex(x + 1, y + 1)));

+        newFace.springs.push(new Spring(vertices, getVertexIndex(x, y + 1), getVertexIndex(x + 1, y + 1)));

+        

+        faces.push(newFace);

+      }

+    }

+

+    /**

+     * call createExplicit

+     * with generated vertices and faces

+     */

+    this.createExplicit(vertices, faces);

+  }

+

+  /**

+   * 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 of Vector3} vertices 

+   * @param {Array of Face} faces 

+   */

+  createExplicit(vertices, faces) {

+    /**

+     * Copy vertices and initialize vertex weights to 0

+     */

+    for (let i in vertices) {

+      this.geometry.vertices.push(vertices[i]);

+      this.vertexWeights.push(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;

+

+      /**

+       * 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();

+  }

+

+  /**

+   * 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);

+    }

+  }

+}
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