cube!

js/algebra.ts

@@ -0,0 +1,27 @@
+export type Vector = [number, number, number]
+
+export function compute_area(a: Vector, b: Vector, c:Vector) {
+    const [vx, vy, vz] = [b[0]-a[0], b[1]-a[1], b[2]-a[2]]
+    const [wx, wy, wz] = [c[0]-a[0], c[1]-a[1], c[2]-a[2]]
+    return 0.5*Math.sqrt((vy*wz-vz*wy)**2 + (vz*wx-vx*wz)**2 + (vx*wy-vy*wx)**2)
+}
+
+export function vector_diff(a: Vector, b: Vector): Vector {
+    return [a[0]-b[0], a[1]-b[1], a[2]-b[2]]
+}
+
+export function vector_sum(a: Vector, b: Vector): Vector {
+    return [a[0]+b[0], a[1]+b[1], a[2]+b[2]]
+}
+
+export function scale_vector(b: number, a: Vector): Vector {
+    return [a[0]*b, a[1]*b, a[2]*b]
+}
+
+export function number_product(a: Vector, b: Vector): number {
+    return a[0]*b[0] + a[1]*b[1] + a[2]*b[2]
+}
+
+export function squared_norm(a: Vector): number {
+    return number_product(a,a)
+}

js/examples.ts

@@ -0,0 +1,136 @@
+import Surf from './surf'
+
+const PI = Math.PI
+const cos = Math.cos
+const sin = Math.sin
+const sqrt = Math.sqrt
+
+export class Pringle extends Surf {
+    constructor(h:number=0.5,n:number=2) {
+        super()
+
+        this.addBorder(t => 
+            [  cos(t), 
+                sin(t), 
+                h*sin(n*t)], 2*PI)
+
+        this.addBorderVertex(0) // v0
+        this.addBorderVertex(2*PI/3) // v1
+        this.addBorderVertex(4*PI/3) // v2
+
+        this.addTriangle(0, 1, 2)
+    }
+
+    run() {
+        this.triangulate(1)
+        this.evolveMeanCurvature(0.05,20)
+        this.triangulate(0.5)
+        this.evolveMeanCurvature(0.05,20)
+    }
+}
+
+export class Catenoid extends Surf {
+    constructor(R:number=1, h:number=1) {
+        super()
+
+        this.addBorder(t => [R*cos(t), R*sin(t),0], 2*PI)
+        this.addBorder(t => [R*cos(t), R*sin(t),h], 2*PI)
+
+        this.addBorderVertex(0,0) // 0
+        this.addBorderVertex(2*PI/3, 0) // 1
+        this.addBorderVertex(4*PI/3, 0) // 2
+        this.addBorderVertex(0,1) // 3
+        this.addBorderVertex(2*PI/3, 1) // 4
+        this.addBorderVertex(4*PI/3, 1) // 5
+
+        this.addQuad(0,1,4,3)
+        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 {
+    constructor(simply_connected: boolean = true,sx: number = 1.0,sy: number = 1.0,sz: number = 1.0) {
+      super()
+
+      // 8 vertices cube 
+      const v000 = this.addVertex(0,0,0)
+      const v001 = this.addVertex(0,0,sz)
+      const v010 = this.addVertex(0,sy,0)
+      const v011 = this.addVertex(0,sy,sz)
+      const v100 = this.addVertex(sx,0,0)
+      const v101 = this.addVertex(sx,0,sz)
+      const v110 = this.addVertex(sx,sy,0)
+      const v111 = this.addVertex(sx,sy,sz)
+
+      // 4 vertices square (m=mid)
+      const vm00 = this.addVertex(0.5*sx,0.3*sy,0.3*sz)
+      const vm01 = this.addVertex(0.5*sx,0.3*sy,0.7*sz)
+      const vm10 = this.addVertex(0.5*sx,0.7*sy,0.3*sz)
+      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)
+
+      // fix border vertices
+      this.addBorderVertex(0,bx00,v000)
+      this.addBorderVertex(1,bx00,v100)
+      this.addBorderVertex(0,bx01,v001)
+      this.addBorderVertex(1,bx01,v101)
+      this.addBorderVertex(0,bx10,v010)
+      this.addBorderVertex(1,bx10,v110)
+      this.addBorderVertex(0,bx11,v011)
+      this.addBorderVertex(1,bx11,v111)
+      this.addBorderVertex(0,by00,v000)
+      this.addBorderVertex(1,by00,v010)
+      this.addBorderVertex(0,by01,v100)
+      this.addBorderVertex(1,by01,v110)
+      this.addBorderVertex(0,by10,v001)
+      this.addBorderVertex(1,by10,v011)
+      this.addBorderVertex(0,by11,v101)
+      this.addBorderVertex(1,by11,v111)
+      this.addBorderVertex(0,bz00,v000)
+      this.addBorderVertex(1,bz00,v001)
+      this.addBorderVertex(0,bz01,v010)
+      this.addBorderVertex(1,bz01,v011)
+      this.addBorderVertex(0,bz10,v100)
+      this.addBorderVertex(1,bz10,v101)
+      this.addBorderVertex(0,bz11,v110)
+      this.addBorderVertex(1,bz11,v111)
+
+      // facets 4+4+1 quads, 4 triangles
+      this.addQuad(v000,vm00,vm10,v010)
+      this.addQuad(v010,vm10,vm11,v011)
+      this.addQuad(v011,vm11,vm01,v001)
+      this.addQuad(v001,vm01,vm00,v000)
+      this.addQuad(vm00,v100,v110,vm10)
+      this.addQuad(vm10,v110,v111,vm11)
+      this.addQuad(vm11,v111,v101,vm01)
+      this.addQuad(vm01,v101,v100,vm00)
+      this.addTriangle(v000,v100,vm00)
+      this.addTriangle(v001,v101,vm01)
+      this.addTriangle(v010,v110,vm10)
+      this.addTriangle(v011,v111,vm11)
+      if (simply_connected)
+        this.addQuad(vm00,vm10,vm11,vm01)
+    }
+  }
+

js/main.ts

@@ -1,7 +1,7 @@
 import * as THREE from 'three'
 import {OrbitControls} from 'three/examples/jsm/controls/OrbitControls.js'
 
-import {Pringle,Catenoid} from './examples'
+import {Pringle,Catenoid,Cube} 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 Catenoid()
+const surf = new Cube()
 
 // Create a material
 const material = new THREE.MeshPhongMaterial();