helicoid!

paolini · Aug 12, 2024 · 4773fbf · 4773fbf
1 parent 7457ca0
commit 4773fbf
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Showing 3 changed files with 58 additions and 56 deletions.
diff --git a/js/examples.ts b/js/examples.ts
@@ -47,13 +47,6 @@ export class Catenoid extends Surf {
         this.addQuad(1,2,5,4)
         this.addQuad(2,0,3,5)
     }
-
-    run() {
-        this.triangulate(1)
-        this.evolveMeanCurvature(0.05,20)
-        this.triangulate(0.5)
-        this.evolveMeanCurvature(0.05,20)
-    }
 }
 
 export class Cube extends Surf {
@@ -77,18 +70,18 @@ export class Cube extends Surf {
       const vm11 = this.addVertex(0.5*sx,0.7*sy,0.7*sz)
 
       // 12 borders
-      const bx00 = this.addBorder(t => [t*sx, 0, 0], 0.0)
-      const bx01 = this.addBorder(t => [t*sx, 0,sz], 0.0)
-      const bx10 = this.addBorder(t => [t*sx,sy, 0], 0.0)
-      const bx11 = this.addBorder(t => [t*sx,sy,sz], 0.0)
-      const by00 = this.addBorder(t => [ 0,t*sy, 0], 0.0)
-      const by01 = this.addBorder(t => [sx,t*sy, 0], 0.0)
-      const by10 = this.addBorder(t => [ 0,t*sy,sz], 0.0)
-      const by11 = this.addBorder(t => [sx,t*sy,sz], 0.0)
-      const bz00 = this.addBorder(t => [ 0, 0,t*sz], 0.0)
-      const bz01 = this.addBorder(t => [ 0,sy,t*sz], 0.0)
-      const bz10 = this.addBorder(t => [sx, 0,t*sz], 0.0)
-      const bz11 = this.addBorder(t => [sx,sy,t*sz], 0.0)
+      const bx00 = this.addBorder(t => [t*sx, 0, 0], 1.0, false)
+      const bx01 = this.addBorder(t => [t*sx, 0,sz], 1.0, false)
+      const bx10 = this.addBorder(t => [t*sx,sy, 0], 1.0, false)
+      const bx11 = this.addBorder(t => [t*sx,sy,sz], 1.0, false)
+      const by00 = this.addBorder(t => [ 0,t*sy, 0], 1.0, false)
+      const by01 = this.addBorder(t => [sx,t*sy, 0], 1.0, false)
+      const by10 = this.addBorder(t => [ 0,t*sy,sz], 1.0, false)
+      const by11 = this.addBorder(t => [sx,t*sy,sz], 1.0, false)
+      const bz00 = this.addBorder(t => [ 0, 0,t*sz], 1.0, false)
+      const bz01 = this.addBorder(t => [ 0,sy,t*sz], 1.0, false)
+      const bz10 = this.addBorder(t => [sx, 0,t*sz], 1.0, false)
+      const bz11 = this.addBorder(t => [sx,sy,t*sz], 1.0, false)
 
       // fix border vertices
       this.addBorderVertex(0,bx00,v000)
@@ -133,4 +126,42 @@ export class Cube extends Surf {
         this.addQuad(vm00,vm10,vm11,vm01)
     }
   }
-
+
+export class Helicoid extends Surf {
+  constructor(R:number=1.0,r:number=0, h:number=1.0, N:number=2) {
+    super()
+
+    const PERIOD = 4.0
+    this.addBorder(t => {
+      if (t<2.0) {
+        if (t<1.0) { // t in [0,1]
+	        return [r+t*(R-r),0,-h]
+        } else { // t in [1,2]
+	        const a=N*2.0*PI*(t-1.0)
+	        return [R*cos(a),R*sin(a),(t-1.5)*2.0*h]
+        }
+      } else {
+        if (t<3.0) { // t in [2,3]
+	        const a=N*2.0*PI
+	        const s=(3.0-t)*(R-r)
+	        return [(r+s)*cos(a),(r+s)*sin(a),h]
+        } else { // t in [3,4]
+	        const a=N*2.0*PI*(4.0-t)
+	        return [r*cos(a),r*sin(a),(3.5-t)*2.0*h]
+        }
+      }
+    }, PERIOD)
+
+    this.addBorderVertex(0)
+    this.addBorderVertex(PERIOD/3)
+    this.addBorderVertex(2*PERIOD/3)
+    this.addTriangle(0,1,2)
+  }
+
+  run() {
+    for (let i=0; i<10; i++) {
+      this.triangulate()
+      this.evolveMeanCurvature(0.05,20)
+    }
+  }
+}
diff --git a/js/main.ts b/js/main.ts
@@ -1,7 +1,7 @@
 import * as THREE from 'three'
 import {OrbitControls} from 'three/examples/jsm/controls/OrbitControls.js'
 
-import {Pringle,Catenoid,Cube} from './examples'
+import {Pringle,Catenoid,Cube,Helicoid} from './examples'
 
 const scene = new THREE.Scene()
 const camera = new THREE.PerspectiveCamera(75, window.innerWidth/window.innerHeight, 0.1, 1000)
@@ -12,7 +12,7 @@ const renderer = new THREE.WebGLRenderer()
 renderer.setSize(window.innerWidth, window.innerHeight)
 document.body.appendChild(renderer.domElement)
 
-const surf = new Cube()
+const surf = new Helicoid()
 
 // Create a material
 const material = new THREE.MeshPhongMaterial();

diff --git a/js/surf.ts b/js/surf.ts
@@ -10,6 +10,7 @@ export default class Surf {
         f: (t:number)=>Vector,
         indices: [Index,number][]
         period: number,
+        closed: boolean
     })[]
 
     constructor() {
@@ -25,13 +26,10 @@ export default class Surf {
      * @param period period of parameter if curve is closed, 0 if it is open
      * @returns the index of the newly created border
      */
-    addBorder(f:((number)=>Vector), period: number = 1.0): Index {
+    addBorder(f:((number)=>Vector), period: number = 1.0, closed: boolean=true): Index {
         const borderIndex = this.borders.length
-        this.borders.push({
-            f: f,
-            indices: [],
-            period: period,
-        })
+        const indices = []
+        this.borders.push({f, indices, period, closed})
         return borderIndex
     }
 
@@ -236,7 +234,7 @@ export default class Surf {
                 const t = indices[i][1]
                 const tt = indices[ii][1]
                 let ttt = 0.5*(t+tt)
-                if (border.period && Math.abs(tt-t) > 0.5*border.period) {
+                if (border.closed && Math.abs(tt-t) > 0.5*border.period) {
                     ttt -= 0.5*border.period
                     if (ttt<0) ttt += border.period
                 }
@@ -253,33 +251,6 @@ export default class Surf {
         return false
     }
 
-    evolve() {
-        const N_TRIANGLES = this.indices.length / 3
-        const N_VERTICES = this.vertices.length / 3
-
-        function vertex(i) { return this.getVertex(i)}
-
-        for (let i=0; i<N_TRIANGLES; i++) {
-            const a = this.indices[3*i]
-            const b = this.indices[3*i+1]
-            const c = this.indices[3*i+2]
-            const area = compute_area(vertex(a), vertex(b), vertex(c))
-
-            /* WIP, see vertex.cc vertex::grad */
-            const v = vector_diff(vertex(b), vertex(a))
-            const w = vector_diff(vertex(c), vertex(a))
-
-
-            const grad: Vector = scale_vector(1/(2*area), 
-                vector_diff(scale_vector(number_product(v,w),vector_sum(v,w)), 
-                    vector_sum(
-                        scale_vector(squared_norm(v),w),
-                        scale_vector(squared_norm(w),v))))
-
-            /* WIP */
-        }
-    }
-
     printVertices() {
         const vertices = this.vertices
         for (let i=0; 3*i<vertices.length; i++) {