├── .gitignore
├── LICENSE
├── README.md
├── TODO
├── build.sh
├── build
    ├── trimesh.js
    └── trimesh.js.min
├── client.js
├── index.js
├── package.json
├── src
    ├── conway.js
    ├── distance.js
    ├── heap.js
    ├── loop_subdivision.js
    ├── marchingcubes.js
    ├── marchingtetrahedra.js
    ├── normals.js
    ├── obj.js
    ├── repair.js
    ├── shapes.js
    ├── surfacenets.js
    └── topology.js
└── tests
    ├── all.js
    ├── isosurface.js
    ├── metric.js
    ├── normals.js
    ├── repair.js
    ├── subdivision.js
    └── topology.js


/.gitignore:
--------------------------------------------------------------------------------
 1 | lib-cov
 2 | *.seed
 3 | *.log
 4 | *.csv
 5 | *.dat
 6 | *.out
 7 | *.pid
 8 | *.gz
 9 | 
10 | pids
11 | logs
12 | results
13 | 
14 | node_modules
15 | npm-debug.log


--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
 1 | 
 2 | The MIT License (MIT)
 3 | 
 4 | Copyright (c) 2013 Mikola Lysenko
 5 | 
 6 | Permission is hereby granted, free of charge, to any person obtaining a copy
 7 | of this software and associated documentation files (the "Software"), to deal
 8 | in the Software without restriction, including without limitation the rights
 9 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
10 | copies of the Software, and to permit persons to whom the Software is
11 | furnished to do so, subject to the following conditions:
12 | 
13 | The above copyright notice and this permission notice shall be included in
14 | all copies or substantial portions of the Software.
15 | 
16 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
17 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
18 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
19 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
20 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
21 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
22 | THE SOFTWARE.
23 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
  1 | # trimesh.js
  2 | 
  3 | (DEPRECATED WARNING:  I am currently in the process of splitting the functionality in trimesh.js up into smaller libraries.  This is still an ongoing process.)
  4 | 
  5 | ... is an ever expanding collection of algorithms for processing triangulated meshes in Javascript.
  6 | 
  7 | ## Server side (node.js)
  8 | 
  9 | First, install the library using npm:
 10 | 
 11 |     npm install trimesh
 12 |     
 13 | Then include the library in your project like usual:
 14 | 
 15 |     var trimesh = require('trimesh');
 16 | 
 17 | 
 18 | ## Client side
 19 | 
 20 | First download the script from the following URL:
 21 | 
 22 | https://raw.github.com/mikolalysenko/TrimeshJS/master/build/trimesh.js.min
 23 | 
 24 | Add a reference to the script in your header:
 25 | 
 26 |     <script src="trimesh.min.js"></script>
 27 |     
 28 | Which will create an object called `trimesh` in the global namespace that contains the API.
 29 | 
 30 | ## Getting Test Data
 31 | 
 32 | If you want to get some mesh data to mess around with and the built in shape generators are not enough for you, you can also take a look at the stuff stored in the sister MeshData npm module:
 33 | 
 34 | https://github.com/mikolalysenko/MeshData
 35 | 
 36 | 
 37 | # General Philosophal and Religious Discussion
 38 | 
 39 | Working with meshes is hard -- and yet it has to be done if we are to compute on surfaces. The situation is not helped by the enormous confusion of data structures for optimizing spatial and topological queries on meshes. Picking a single representation, like a winged edge, half edge or cell tuple complex brings with it many tradeoffs and introduces enormous complexity into algorithms which operate on these meshes. These choices cause implementations of mesh based algorithms to rapidly diverge, resulting in an enormous proliferation and duplication of effort. Clearly this situation is unacceptable from the stand point of interoperability and coder sanity.  The core philosophy of trimesh.js is a reaction to this offensive mess and can be summed up in the following central thesis:
 40 | 
 41 | > ** Meshes do not need their own data structure. **
 42 | 
 43 | To avoid falling into the trap of overengineering that seems to sidetrack other mesh libraries, trimesh.js adopts a "Just the facts, ma'am" personality, with each method taking only enough data to answer the necessary basic queries required to implement the described functionality. Guided by these ideals, trimesh.js departs radically from other mesh libraries in the following ways:
 44 | 
 45 | * No in place updates or side effects.
 46 | * No 'cute' accessors for member components (eg. x/y/z values of a 3D vector).  If an array will suffice to store the data, use an array.  Don't make a new object type.
 47 | * Along the same lines, store multiple vertex attributes in separate arrays.  This allows for more efficient iteration, since properties which are not needed are not stored.
 48 | * Spatial/topological indices (like grids/winged edge data) are maintained separately from mesh data.  If an index is needed, either build it from scratch or if possible reuse an existing index.
 49 | 
 50 | The advantage to this more functional style of mesh computation is that many algorithms can be written in a very straightforward manner.  However, it is not without consequences.  Most severely, because in place updates are not supported, this library may not suitable for large scale interactive mesh processing.  (Of course for those sort of problems you should probably not be using javascript anyway and should look for a way to engineer some sort of streaming solution...)  The other more serious problem is that because indices are not maintained, it may be necessary to rebuild certain indices that could have been computed more efficiently by merging or amortized over mesh operations.  However, it again my opinion that this tradeoff may be worthwhile, since most index calculations scale roughly linearly or log-linearly with the size of the mesh and so asymptotically the added cost is typically at most an extra log factor.  
 51 | 
 52 | Removing custom vertex/vector types may also offend some, however I find the x/y/z notation quite tedious and error prone, (as does Carmack, who after documenting his various programming mistakes found that x/y/z notation was the most frequent source of his errors).  Using numerical indices makes it much easier to write per component operations in a generic way.
 53 | 
 54 | 
 55 | # API
 56 | 
 57 | Trimesh.JS is just a big bag of functions.  Like any library of numerical recipes, many of these functions take a large number of arguments, some of which are optional.  Since javascript does not support features like named arguments, these methods are all called by passing in a dictionary (or object) containing all the parameters.  For example, to call a method which computes the stars of a mesh you would do the following:
 58 | 
 59 |     var stars = trimesh.vertex_stars({ faces: [ [0, 1, 2], [1, 2, 3] ], vertex_count: 4 });
 60 | 
 61 | Since certain parameters are used frequently, we use the following conventions:
 62 | 
 63 | * `faces` is always an array of triples representing the indices of each face in the mesh.
 64 | * `positions` is an array of length 3 arrays representing the position of each vertex.
 65 | * `stars` is an array of vertex stars, which can be precomputed using the `vertex_stars` function.
 66 | 
 67 | 
 68 | ## Topology
 69 | 
 70 | ### `edges`
 71 | 
 72 | Finds all edges in a mesh.
 73 | 
 74 | #### Parameters:
 75 | * `faces`:  The mesh topology
 76 | 
 77 | #### Returns:
 78 | A dictionary mapping pairs of vertex indices to lists of incident faces.
 79 | 
 80 | #### Running time: `O(faces.length)`
 81 | 
 82 | ### `vertex_stars`
 83 | 
 84 | Computes the set of incident faces for each vertex
 85 | 
 86 | #### Parameters:
 87 | * `faces`: The mesh topology
 88 | * `vertex_count`: (Optional) The number of vertices in the mesh.  If not present, is computed from `faces`.
 89 | 
 90 | #### Returns:
 91 | An array of length `vertex_count`, containing for each vertex an array of all faces incident to it.
 92 | 
 93 | #### Running time: `O(faces.length + vertex_count)`
 94 | 
 95 | 
 96 | 
 97 | ## Mesh Repair and Validation
 98 | 
 99 | ### `fuse_vertices`
100 | 
101 | Welds nearby vertices together, removing small cracks and sliver faces within a mesh.
102 | 
103 | #### Parameters:
104 | 
105 | * `positions`: Vertex positions
106 | * `faces`: Mesh faces
107 | * `tolerance`: Distance within which vertices must be welded
108 | 
109 | #### Returns:
110 | 
111 | * `positions`: The updated fused positions
112 | * `faces`: Fused face topology
113 | 
114 | #### Running time: `O(positions.length + faces.length)`
115 | 
116 | 
117 | ## Implicit Function Modeling
118 | 
119 | Trimesh.JS has 3 different methods for converting implicit functions into triangulated meshes.  They each take the same arguments and produce similar results.  For more information about the differences, see the following post: http://0fps.wordpress.com/2012/07/12/smooth-voxel-terrain-part-2/
120 | 
121 | 
122 | ### `marching_cubes`, `marching_tetrahedra`, `surface_nets`
123 | 
124 | #### Parameters:
125 | 
126 | * `potential` : A function f(x,y,z) that represents the potential function.  (<0 for in, >0 for out)
127 | * `resolution` : A triple [nx,ny,nz] representing the resolution of the isosurface
128 | * `bounds`:  (Optional) A pair of ranges [[x0,y0,z0], [x1,y1,z1]] representing the bounds for the volume.
129 | 
130 | #### Returns:
131 | 
132 | * `positions`: The positions of the vertices on the isosurface
133 | * `faces`: The faces of the isosurface
134 | 
135 | #### Running time: Makes `O(nx * ny * nz)` calls to `potential()`.
136 | 
137 | 
138 | 
139 | ## Differential Geometry
140 | 
141 | ### `vertex_normals`
142 | 
143 | #### Parameters:
144 | 
145 | * `positions`
146 | * `faces`
147 | * `stars` (Optional)
148 | 
149 | #### Returns:
150 | 
151 | An array representing an estimate for the normals of the mesh computed using cotangent weights.
152 | 
153 | #### Running time: `O( |stars| )`
154 | 
155 | ### `face_normals`
156 | 
157 | #### Parameters:
158 | 
159 | * `positions`
160 | * `faces`
161 | 
162 | #### Returns:
163 | 
164 | An array of normals for each face
165 | 
166 | #### Running time: `O( number of faces )`
167 | 
168 | ### `geodesic_distance`
169 | 
170 | #### Parameters:
171 | 
172 | * `initial_vertex`
173 | * `positions`
174 | * `faces`
175 | * `max_distance` (Optional)
176 | * `stars` (Optional)
177 | 
178 | #### Returns:
179 | 
180 | Hash map of distance to point
181 | 
182 | #### Running Time: Worse than `O( number of vertices^2 )`  (bad)
183 | 
184 | #### Notes:
185 | 
186 | The current implementation of this method is bad.
187 | 
188 | ## Subdivision Surfaces
189 | 
190 | ### `loop_subdivision`
191 | 
192 | Evaluates one iteration of Loop's algorithm
193 | 
194 | #### Parameters:
195 | 
196 | * `positions`
197 | * `faces`
198 | * `stars` (Optional)
199 | 
200 | #### Returns:
201 | 
202 | * `positions`
203 | * `faces`
204 | 
205 | 
206 | 
207 | # Acknowledgements
208 | 
209 | 
210 | 
211 | 
212 | 
213 | 


--------------------------------------------------------------------------------
/TODO:
--------------------------------------------------------------------------------
 1 | Huge list of stuff to do:
 2 | 
 3 | Mesh repair:
 4 |   Check manifoldness
 5 |   Fix orientation
 6 | 
 7 | Custom tolerances?
 8 | 
 9 | Subdivision surfaces:
10 |   Loop
11 |   sqrt(3)
12 | 
13 | Surface simplification
14 | 
15 | Differential stuff:
16 |   Tangent space calculations
17 |   Exponential maps
18 |   Parallel transport
19 | 
20 | Metrics:
21 |   Minkowski functionals
22 | 
23 | Geometry queries:  
24 |   Closest feature
25 |   Distance to point
26 |   Point membership test
27 | 
28 | Finite element:
29 |   Stiffness matrix assembly
30 |   Laplacian eigen functions
31 | 
32 | Solid modeling:
33 |   Booleans
34 |   Minkowski sums
35 |   
36 | Interoperability:
37 |   parsers/exporters for different STL, VRML, etc.
38 | 
39 | ...and probably much more
40 | 
41 | 


--------------------------------------------------------------------------------
/build.sh:
--------------------------------------------------------------------------------
1 | #!/bin/sh
2 | mkdir build
3 | ./node_modules/browserify/bin/cmd.js ./client.js -o ./build/trimesh.js
4 | ./node_modules/uglify-js/bin/uglifyjs < ./build/trimesh.js > ./build/trimesh.js.min
5 | 
6 | 


--------------------------------------------------------------------------------
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t=e.potential,n=e.resolution,r=[],i=[],s=0,o=new Array(8),c=new Array(12),h=[0,0,0];for(h[2]=0;h[2]<n[2]-1;++h[2],s+=n[0])for(h[1]=0;h[1]<n[1]-1;++h[1],++s)for(h[0]=0;h[0]<n[0]-1;++h[0],++s){var p=0;for(var d=0;d<8;++d){var v=f[d],m=t(h[0]+v[0],h[1]+v[1],h[2]+v[2]);o[d]=m,p|=m>0?1<<d:0}var g=u[p];if(g===0)continue;for(var d=0;d<12;++d){if((g&1<<d)===0)continue;c[d]=r.length;var y=[0,0,0],b=l[d],w=f[b[0]],E=f[b[1]],S=o[b[0]],x=o[b[1]],T=S-x,N=0;Math.abs(T)>1e-6&&(N=S/T);for(var C=0;C<3;++C)y[C]=h[C]+w[C]+N*(E[C]-w[C]);r.push(y)}var k=a[p];for(var d=0;d<k.length;d+=3)i.push([c[k[d]],c[k[d+1]],c[k[d+2]]])}return{positions:r,faces:i}}}),e.define("/src/marchingtetrahedra.js",function(e,t,n,r,i,s,o){var u=[[0,0,0],[1,0,0],[1,1,0],[0,1,0],[0,0,1],[1,0,1],[1,1,1],[0,1,1]],a=[[0,2,3,7],[0,6,2,7],[0,4,6,7],[0,6,1,2],[0,1,6,4],[5,6,1,4]];n.marching_tetrahedra=function(e){function c(e,t){var n=o[e],i=o[t],s=u[e],a=u[t],f=[l[0],l[1],l[2]],c=n-i;Math.abs(c)>1e-6&&(c=n/c);for(var h=0;h<3;++h)f[h]+=s[h]+c*(a[h]-s[h]);return r.push(f),r.length-1}var t=e.potential,n=e.resolution,r=[],i=[],s=0,o=new Float32Array(8),f=new Int32Array(12),l=[0,0,0];for(l[2]=0;l[2]<n[2]-1;++l[2],s+=n[0])for(l[1]=0;l[1]<n[1]-1;++l[1],++s)for(l[0]=0;l[0]<n[0]-1;++l[0],++s){for(var h=0;h<8;++h){var p=u[h];o[h]=t(l[0]+p[0],l[1]+p[1],l[2]+p[2])}for(var h=0;h<a.length;++h){var d=a[h],v=0;o[d[0]]<0&&(v|=1),o[d[1]]<0&&(v|=2),o[d[2]]<0&&(v|=4),o[d[3]]<0&&(v|=8);switch(v){case 0:case 15:break;case 14:i.push([c(d[0],d[1]),c(d[0],d[3]),c(d[0],d[2])]);break;case 1:i.push([c(d[0],d[1]),c(d[0],d[2]),c(d[0],d[3])]);break;case 13:i.push([c(d[1],d[0]),c(d[1],d[2]),c(d[1],d[3])]);break;case 2:i.push([c(d[1],d[0]),c(d[1],d[3]),c(d[1],d[2])]);break;case 12:i.push([c(d[1],d[2]),c(d[1],d[3]),c(d[0],d[3]),c(d[0],d[2])]);break;case 3:i.push([c(d[1],d[2]),c(d[0],d[2]),c(d[0],d[3]),c(d[1],d[3])]);break;case 4:i.push([c(d[2],d[0]),c(d[2],d[1]),c(d[2],d[3])]);break;case 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--------------------------------------------------------------------------------
/client.js:
--------------------------------------------------------------------------------
1 | window.trimesh = require('./index.js');
2 | 


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/index.js:
--------------------------------------------------------------------------------
 1 | //Topology functions
 2 | var topology = require('./src/topology.js');
 3 | exports.vertex_stars = topology.vertex_stars;
 4 | exports.edges        = topology.edges;
 5 | 
 6 | //Mesh repair
 7 | var repair = require('./src/repair.js');
 8 | exports.fuse_vertices = repair.fuse_vertices;
 9 | 
10 | //Isosurface functions
11 | exports.marching_cubes = require('./src/marchingcubes.js').marching_cubes;
12 | exports.marching_tetrahedra = require('./src/marchingtetrahedra.js').marching_tetrahedra;
13 | exports.surface_nets = require('./src/surfacenets.js').surface_nets;
14 | 
15 | //Surface normal estimation
16 | var normals = require('./src/normals.js');
17 | exports.vertex_normals = normals.vertex_normals;
18 | exports.face_normals = normals.face_normals;
19 | 
20 | //Surface distance
21 | exports.geodesic_distance = require('./src/distance.js').geodesic_distance;
22 | 
23 | //Test shapes
24 | var shapes = require('./src/shapes.js');
25 | exports.grid_mesh = shapes.grid_mesh;
26 | exports.cube_mesh = shapes.cube_mesh;
27 | exports.sphere_mesh = shapes.sphere_mesh;
28 | 
29 | //Subdivisions
30 | exports.loop_subdivision = require('./src/loop_subdivision.js').loop_subdivision;
31 | 


--------------------------------------------------------------------------------
/package.json:
--------------------------------------------------------------------------------
 1 | {
 2 |   "name": "trimesh",
 3 |   "version": "0.0.8",
 4 |   "description": "Tools for processing triangulated meshes in Javascript",
 5 |   "main": "index.js",
 6 |   "author": {
 7 |     "name": "Mikola Lysenko",
 8 |     "email": "mikolalysenko@gmail.com",
 9 |     "url": "http://0fps.net"
10 |   },
11 |   "license": "MIT",
12 |   "keywords": [
13 |     "mesh",
14 |     "surface",
15 |     "triangle",
16 |     "3d"
17 |   ],
18 |   "dependencies": {
19 |   },
20 |   "devDependencies": {
21 |     "vows": "0.6.x",
22 |     "browserify": "1.16.x",
23 |     "uglify-js": "1.3.3"
24 |   },
25 |   "engine": "node >= 0.8"
26 | }
27 | 


--------------------------------------------------------------------------------
/src/conway.js:
--------------------------------------------------------------------------------
 1 | //Platonic solids (not triangulated)
 2 | 
 3 | 
 4 | var cube = {},
 5 |     tetrahedron = {},
 6 |     icosahedron = {};
 7 | 
 8 | function reflect(params) {
 9 |   var positions = params.positions;
10 |   var faces = params.faces;
11 |   
12 |   var npositions = new Array(positions.length);
13 |   var nfaces = new Array(faces.length);
14 |   
15 |   for(var i=0; i<positions.length; ++i) {
16 |     var p = positions[i];
17 |     var np = new Array(3);
18 |     for(var j=0; j<3; ++j) {
19 |       np[j] = -p[j];
20 |     }
21 |     npositions[i] = np;
22 |   }
23 |   
24 |   for(var i=0; )
25 | 
26 | }
27 | 
28 | function dual(params) {
29 | }
30 | 
31 | function ambo(params) {
32 | }
33 | 
34 | function chamfer() {
35 | }
36 | 
37 | function propellor() {
38 | }
39 | 


--------------------------------------------------------------------------------
/src/distance.js:
--------------------------------------------------------------------------------
  1 | var assert = require('assert');
  2 | var BinaryHeap = require('./heap.js').BinaryHeap;
  3 | var vertex_stars = require('./topology.js').vertex_stars;
  4 | 
  5 | var EPSILON   = 1e-6;
  6 | 
  7 | //Computes quadratic distance to point c
  8 | function quadratic_distance(a, b, c, dpa, dpb, orientation) {
  9 |   
 10 |   var ab = new Array(3);
 11 |   var ac = new Array(3);
 12 |   var dab2 = 0.0;
 13 |   for(var i=0; i<3; ++i) {
 14 |     ab[i] = b[i] - a[i];
 15 |     dab2 += ab[i] * ab[i];
 16 |     ac[i] = c[i] - a[i];
 17 |   }
 18 |   if(dab2 < EPSILON) {
 19 |     return 1e30;
 20 |   }
 21 |   
 22 |   //Transform c into triangle coordinate system
 23 |   var dab = Math.sqrt(dab2);
 24 |   var s = 1.0 / dab;
 25 |   var c0 = 0.0;
 26 |   for(var i=0; i<3; ++i) {
 27 |     ab[i] *= s;
 28 |     c0 += ab[i] * ac[i];
 29 |   }
 30 |   var c1 = 0.0;  
 31 |   for(var i=0; i<3; ++i) {
 32 |     c1 += Math.pow(ac[i] - c0 * ab[i], 2);
 33 |   }
 34 |   c1 = Math.sqrt(c1);
 35 |   
 36 |   //Compute center of distance field
 37 |   var dpa2 = dpa*dpa;
 38 |   var dpb2 = dpb*dpb;
 39 |   var p0 = (dpa2 - dpb2 + dab2) / (2.0 * dab);
 40 |   var p1 = dpa2 - p0*p0;
 41 |   if(p1 < 0.0) {
 42 |     return 1e30;
 43 |   }
 44 |   p1 = Math.sqrt(p1);
 45 |   if(orientation < 0) {
 46 |     p1 *= -1;
 47 |   }
 48 |   
 49 |   //Compute new distance bound
 50 |   var d = Math.sqrt(Math.pow(c0 - p0, 2) + Math.pow(c1 - p1, 2));
 51 |   
 52 |   //Return min
 53 |   return d;
 54 |   
 55 | }
 56 | 
 57 | function Pair(d,v) {
 58 |   this.d = d;
 59 |   this.v = v;
 60 | }
 61 | 
 62 | 
 63 | function dijkstra(p, stars, faces, positions, max_distance) {
 64 |   var to_visit  = new BinaryHeap(new Function("a", "return a.d;"));
 65 |   var distances = {};
 66 |   to_visit.push(new Pair(0, p));
 67 |   
 68 |   var center = positions[p];
 69 |   var msquared = max_distance * max_distance;
 70 |   
 71 |   while(to_visit.size() > 0) {
 72 |     var node = to_visit.pop();
 73 |     if(node.v in distances) {
 74 |       continue;
 75 |     }
 76 |     
 77 |     var d = node.d;
 78 |     var v = node.v;
 79 |     distances[v] = d;
 80 |     
 81 |     var a     = positions[v];
 82 |     var nbhd  = stars[v];
 83 |     
 84 |     for(var i=0; i<nbhd.length; ++i) {
 85 |       var f = faces[nbhd[i]];
 86 |       for(var j=0; j<f.length; ++j) {
 87 |         var u = f[j];
 88 |         if((u === v) || (u in distances)) {
 89 |           continue;
 90 |         }
 91 |         var b = positions[u];
 92 |         
 93 |         var dist = 0.0, ldist = 0.0;
 94 |         for(var k=0; k<3; ++k) {
 95 |           dist += Math.pow(a[k] - b[k], 2);
 96 |           ldist += Math.pow(center[k] - b[k], 2)
 97 |         }
 98 |         
 99 |         //NOTE: This is not quite correct, since we only have an upper bound on dist, not a lower bound...
100 |         if(ldist <= msquared) {
101 |           to_visit.push(new Pair(Math.sqrt(dist) + d,u));
102 |         }
103 |       }
104 |     }
105 |   }
106 |   return distances;
107 | }
108 | 
109 | function refine_distances(p, distances, positions, stars, faces, max_distance, tolerance) {
110 |   //Unpack distances into an array for easier processing
111 |   function compare_func(a, b) {
112 |     return distances[a] - distances[b];
113 |   }
114 |   
115 |   //Next, we do several passes to refine the initial bound on the distance until we get something that approaches the true distance to p
116 |   var stabilized = false;
117 |   while(!stabilized) {
118 |     stabilized = true;
119 | 
120 |     //First, sort vertices by distance
121 |     var vertices = [];
122 |     for(var v in distances) {
123 |       vertices.push(v);
124 |     }
125 |     vertices.sort(compare_func);
126 |     
127 |       //Next, walk over vertices in order of distance
128 |       for(var mm=0; mm<vertices.length; ++mm) {
129 |       var v     = vertices[mm];
130 |       if(distances[v] > max_distance) {
131 |         break;
132 |       }
133 |       
134 |       //Iterate over all faces incident to v
135 |       var nbhd  = stars[v];
136 |       
137 |       for(var nn=0; nn<nbhd.length; ++nn) {
138 |       
139 |         //Make a copy of the face
140 |         var face = faces[nbhd[nn]].slice(0);
141 |         face.sort(compare_func);
142 |         
143 |         if(Math.abs(distances[face[1]] - distances[face[2]]) < 1e-6) {
144 |           continue;
145 |         }
146 |         
147 |         //Compute new distance estimate for farthest point
148 |         var n_distance = quadratic_distance(
149 |             positions[face[0]],
150 |             positions[face[1]],
151 |             positions[face[2]],
152 |             distances[face[0]],
153 |             distances[face[1]],
154 |             -1);
155 |         if(n_distance > max_distance) {
156 |           continue;
157 |         }
158 |         
159 |         var o_distance = distances[face[2]];
160 |         
161 |         //Update distance
162 |         if(n_distance < o_distance && Math.abs(n_distance - o_distance) > tolerance) {
163 |           distances[face[2]] = Math.min(o_distance, n_distance);
164 |           stabilized = false;
165 |         }
166 |       }
167 |     }
168 |   }
169 | }
170 | 
171 | 
172 | //Computes a distances to a vertex p
173 | function geodesic_distance(args) {
174 | 
175 |   var positions   = args.positions;
176 |   var faces       = args.faces;
177 |   var p           = args.initial_vertex;
178 |   var stars       = args.stars 
179 |                   || vertex_stars({ vertex_count: positions.length, faces: faces });
180 |   var max_distance = args.max_distance 
181 |                   || Number.POSITIVE_INFINITY;
182 |   var tolerance   = args.tolerance || 1e-4;
183 | 
184 |   //First, run Dijkstra's algorithm to get an initial bound on the distance from each vertex
185 |   // to the base point just using edge lengths
186 |   var distances = dijkstra(p, stars, faces, positions, max_distance);
187 |   
188 |   //Then refine distances to acceptable threshold
189 |   refine_distances(p, distances, positions, stars, faces, max_distance, tolerance);
190 |   
191 |   return distances;
192 | }
193 | 
194 | exports.quadratic_distance = quadratic_distance;
195 | exports.geodesic_distance = geodesic_distance;
196 | 


--------------------------------------------------------------------------------
/src/heap.js:
--------------------------------------------------------------------------------
  1 | // Binary Heap
  2 | // By: Marjin Haverbeke
  3 | // Web: http://eloquentjavascript.net/appendix2.html
  4 | 
  5 | function BinaryHeap(scoreFunction){
  6 |   this.content = [];
  7 |   this.scoreFunction = scoreFunction;
  8 | }
  9 | 
 10 | BinaryHeap.prototype = {
 11 |   push: function(element) {
 12 |     // Add the new element to the end of the array.
 13 |     this.content.push(element);
 14 |     // Allow it to bubble up.
 15 |     this.bubbleUp(this.content.length - 1);
 16 |   },
 17 | 
 18 |   pop: function() {
 19 |     // Store the first element so we can return it later.
 20 |     var result = this.content[0];
 21 |     // Get the element at the end of the array.
 22 |     var end = this.content.pop();
 23 |     // If there are any elements left, put the end element at the
 24 |     // start, and let it sink down.
 25 |     if (this.content.length > 0) {
 26 |       this.content[0] = end;
 27 |       this.sinkDown(0);
 28 |     }
 29 |     return result;
 30 |   },
 31 | 
 32 |   remove: function(node) {
 33 |     var len = this.content.length;
 34 |     // To remove a value, we must search through the array to find
 35 |     // it.
 36 |     for (var i = 0; i < len; i++) {
 37 |       if (this.content[i] == node) {
 38 |         // When it is found, the process seen in 'pop' is repeated
 39 |         // to fill up the hole.
 40 |         var end = this.content.pop();
 41 |         if (i != len - 1) {
 42 |           this.content[i] = end;
 43 |           if (this.scoreFunction(end) < this.scoreFunction(node))
 44 |             this.bubbleUp(i);
 45 |           else
 46 |             this.sinkDown(i);
 47 |         }
 48 |         return;
 49 |       }
 50 |     }
 51 |   },
 52 | 
 53 |   size: function() {
 54 |     return this.content.length;
 55 |   },
 56 | 
 57 |   bubbleUp: function(n) {
 58 |     // Fetch the element that has to be moved.
 59 |     var element = this.content[n];
 60 |     // When at 0, an element can not go up any further.
 61 |     while (n > 0) {
 62 |       // Compute the parent element's index, and fetch it.
 63 |       var parentN = Math.floor((n + 1) / 2) - 1,
 64 |           parent = this.content[parentN];
 65 |       // Swap the elements if the parent is greater.
 66 |       if (this.scoreFunction(element) < this.scoreFunction(parent)) {
 67 |         this.content[parentN] = element;
 68 |         this.content[n] = parent;
 69 |         // Update 'n' to continue at the new position.
 70 |         n = parentN;
 71 |       }
 72 |       // Found a parent that is less, no need to move it further.
 73 |       else {
 74 |         break;
 75 |       }
 76 |     }
 77 |   },
 78 | 
 79 |   sinkDown: function(n) {
 80 |     // Look up the target element and its score.
 81 |     var length = this.content.length,
 82 |         element = this.content[n],
 83 |         elemScore = this.scoreFunction(element);
 84 | 
 85 |     while(true) {
 86 |       // Compute the indices of the child elements.
 87 |       var child2N = (n + 1) * 2, child1N = child2N - 1;
 88 |       // This is used to store the new position of the element,
 89 |       // if any.
 90 |       var swap = null;
 91 |       // If the first child exists (is inside the array)...
 92 |       if (child1N < length) {
 93 |         // Look it up and compute its score.
 94 |         var child1 = this.content[child1N],
 95 |             child1Score = this.scoreFunction(child1);
 96 |         // If the score is less than our element's, we need to swap.
 97 |         if (child1Score < elemScore)
 98 |           swap = child1N;
 99 |       }
100 |       // Do the same checks for the other child.
101 |       if (child2N < length) {
102 |         var child2 = this.content[child2N],
103 |             child2Score = this.scoreFunction(child2);
104 |         if (child2Score < (swap == null ? elemScore : child1Score))
105 |           swap = child2N;
106 |       }
107 | 
108 |       // If the element needs to be moved, swap it, and continue.
109 |       if (swap != null) {
110 |         this.content[n] = this.content[swap];
111 |         this.content[swap] = element;
112 |         n = swap;
113 |       }
114 |       // Otherwise, we are done.
115 |       else {
116 |         break;
117 |       }
118 |     }
119 |   }
120 | };
121 | 
122 | 
123 | if(typeof(exports) !== "undefined") {
124 |   exports.BinaryHeap = BinaryHeap;
125 | }
126 | 
127 | 


--------------------------------------------------------------------------------
/src/loop_subdivision.js:
--------------------------------------------------------------------------------
  1 | var topology = require('./topology.js');
  2 | 
  3 | function opposite(u, v, f) {
  4 |   for(var i=0; i<3; ++i) {
  5 |     if(f[i] !== u && f[i] !== v) {
  6 |       return f[i];
  7 |     }
  8 |   }
  9 |   return 0;
 10 | }
 11 | 
 12 | //A super inefficient implementation of Loop's algorithm
 13 | exports.loop_subdivision = function(args) {
 14 |   var positions   = args.positions;
 15 |   var faces       = args.faces;
 16 |   var edges       = args.edges || topology.edges({faces: faces});
 17 |   var stars       = args.stars || topology.vertex_stars({ vertex_count: positions.length, faces: faces });
 18 |   var npositions  = [];
 19 |   var nfaces      = [];
 20 |   var e_indices   = {};
 21 |   var v_indices   = new Array(positions.length);  
 22 |   
 23 |   var e_verts = new Array(3);
 24 |   var v_verts = new Array(3);
 25 |   
 26 |   for(var f=0; f<faces.length; ++f) {
 27 |     var face = faces[f];
 28 |     
 29 |     for(var d=0; d<3; ++d) {
 30 |       var v = face[d];
 31 |       var u = face[(d+1)%3];
 32 |       var e = [u,v];
 33 |       e.sort();
 34 |       
 35 |       if(e in e_indices) {
 36 |         e_verts[d] = e_indices[e];
 37 |       } else {
 38 |         //Compute edge-vertex
 39 |         var wing = edges[e];
 40 |         var v0 = positions[u];
 41 |         var v1 = positions[v];
 42 |         var vertex = new Array(3);
 43 |         
 44 |         if(wing.length === 2) {
 45 |           var v2 = positions[opposite(u, v, faces[wing[0]])];
 46 |           var v3 = positions[opposite(u, v, faces[wing[1]])];
 47 |           
 48 |           for(var i=0; i<3; ++i) {
 49 |             vertex[i] = (3.0 * (v0[i] + v1[i]) + v2[i] + v3[i]) / 8.0;
 50 |           }
 51 |         } else {
 52 |           for(var i=0; i<3; ++i) {
 53 |             vertex[i] = 0.5 * (v0[i] + v1[i]);
 54 |           }
 55 |         }
 56 |         
 57 |         //Store vertex and continue
 58 |         e_indices[e] = e_verts[d] = npositions.length;
 59 |         npositions.push(vertex);
 60 |       }
 61 |       
 62 |       if(v in v_indices) {
 63 |         v_verts[d] = v_indices[v];
 64 |       } else {
 65 |         //Compute vertex-vertex weight
 66 |         
 67 |         //First, extract vertex neighborhood (slow and stupid here)
 68 |         var star = stars[v];
 69 |         var nbhd = [v];
 70 |         for(var i=0; i<star.length; ++i) {
 71 |           var tri = faces[star[i]];
 72 |           for(var j=0; j<3; ++j) {
 73 |             if(nbhd.indexOf(tri[j]) !== -1) {
 74 |               nbhd.push(tri[j]);
 75 |             }
 76 |           }
 77 |         }
 78 |         
 79 |         //Next, compute weights
 80 |         var beta = (star.length === 3 ? 3.0/16.0 : 3.0/(8.0*star.length) );
 81 |         var center_weight = 1.0 - star.length * beta;
 82 |         
 83 |         //Finally sum up weights
 84 |         var pos  = positions[v];
 85 |         var vertex = new Array(3);
 86 |         for(var i=0; i<3; ++i) {
 87 |           vertex[i] = center_weight * pos[i];
 88 |         }
 89 |         for(var i=1; i<nbhd.length; ++i) {
 90 |           var p = positions[nbhd[i]];
 91 |           for(var j=0; j<3; ++j) {
 92 |             vertex[j] += beta * p[j];
 93 |           }
 94 |         }
 95 | 
 96 |         //Store result and continue        
 97 |         v_verts[d] = v_indices[v] = npositions.length;
 98 |         npositions.push(vertex);
 99 |       }
100 |     }
101 |     
102 |     //Add subdivided faces
103 |     nfaces.push([v_verts[0], e_verts[0], e_verts[2]]);
104 |     nfaces.push([e_verts[0], e_verts[1], e_verts[2]]);
105 |     nfaces.push([e_verts[0], v_verts[1], e_verts[1]]);
106 |     nfaces.push([e_verts[1], v_verts[2], e_verts[2]]);
107 |   }
108 |   
109 |   return { positions: npositions, faces: nfaces };
110 | };
111 | 


--------------------------------------------------------------------------------
/src/marchingcubes.js:
--------------------------------------------------------------------------------
  1 | /**
  2 |  * Javascript Marching Cubes
  3 |  *
  4 |  * Based on Paul Bourke's classic implementation:
  5 |  *    http://local.wasp.uwa.edu.au/~pbourke/geometry/polygonise/
  6 |  *
  7 |  * JS port by Mikola Lysenko
  8 |  */
  9 | 
 10 | var edgeTable= new Uint32Array([
 11 |       0x0  , 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c,
 12 |       0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00,
 13 |       0x190, 0x99 , 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c,
 14 |       0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90,
 15 |       0x230, 0x339, 0x33 , 0x13a, 0x636, 0x73f, 0x435, 0x53c,
 16 |       0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30,
 17 |       0x3a0, 0x2a9, 0x1a3, 0xaa , 0x7a6, 0x6af, 0x5a5, 0x4ac,
 18 |       0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0,
 19 |       0x460, 0x569, 0x663, 0x76a, 0x66 , 0x16f, 0x265, 0x36c,
 20 |       0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
 21 |       0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0xff , 0x3f5, 0x2fc,
 22 |       0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
 23 |       0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x55 , 0x15c,
 24 |       0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950,
 25 |       0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0xcc ,
 26 |       0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0,
 27 |       0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc,
 28 |       0xcc , 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
 29 |       0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c,
 30 |       0x15c, 0x55 , 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
 31 |       0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc,
 32 |       0x2fc, 0x3f5, 0xff , 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
 33 |       0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c,
 34 |       0x36c, 0x265, 0x16f, 0x66 , 0x76a, 0x663, 0x569, 0x460,
 35 |       0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac,
 36 |       0x4ac, 0x5a5, 0x6af, 0x7a6, 0xaa , 0x1a3, 0x2a9, 0x3a0,
 37 |       0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c,
 38 |       0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x33 , 0x339, 0x230,
 39 |       0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c,
 40 |       0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x99 , 0x190,
 41 |       0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c,
 42 |       0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x0   ])
 43 |   , triTable = [
 44 |       [],
 45 |       [0, 8, 3],
 46 |       [0, 1, 9],
 47 |       [1, 8, 3, 9, 8, 1],
 48 |       [1, 2, 10],
 49 |       [0, 8, 3, 1, 2, 10],
 50 |       [9, 2, 10, 0, 2, 9],
 51 |       [2, 8, 3, 2, 10, 8, 10, 9, 8],
 52 |       [3, 11, 2],
 53 |       [0, 11, 2, 8, 11, 0],
 54 |       [1, 9, 0, 2, 3, 11],
 55 |       [1, 11, 2, 1, 9, 11, 9, 8, 11],
 56 |       [3, 10, 1, 11, 10, 3],
 57 |       [0, 10, 1, 0, 8, 10, 8, 11, 10],
 58 |       [3, 9, 0, 3, 11, 9, 11, 10, 9],
 59 |       [9, 8, 10, 10, 8, 11],
 60 |       [4, 7, 8],
 61 |       [4, 3, 0, 7, 3, 4],
 62 |       [0, 1, 9, 8, 4, 7],
 63 |       [4, 1, 9, 4, 7, 1, 7, 3, 1],
 64 |       [1, 2, 10, 8, 4, 7],
 65 |       [3, 4, 7, 3, 0, 4, 1, 2, 10],
 66 |       [9, 2, 10, 9, 0, 2, 8, 4, 7],
 67 |       [2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4],
 68 |       [8, 4, 7, 3, 11, 2],
 69 |       [11, 4, 7, 11, 2, 4, 2, 0, 4],
 70 |       [9, 0, 1, 8, 4, 7, 2, 3, 11],
 71 |       [4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1],
 72 |       [3, 10, 1, 3, 11, 10, 7, 8, 4],
 73 |       [1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4],
 74 |       [4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3],
 75 |       [4, 7, 11, 4, 11, 9, 9, 11, 10],
 76 |       [9, 5, 4],
 77 |       [9, 5, 4, 0, 8, 3],
 78 |       [0, 5, 4, 1, 5, 0],
 79 |       [8, 5, 4, 8, 3, 5, 3, 1, 5],
 80 |       [1, 2, 10, 9, 5, 4],
 81 |       [3, 0, 8, 1, 2, 10, 4, 9, 5],
 82 |       [5, 2, 10, 5, 4, 2, 4, 0, 2],
 83 |       [2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8],
 84 |       [9, 5, 4, 2, 3, 11],
 85 |       [0, 11, 2, 0, 8, 11, 4, 9, 5],
 86 |       [0, 5, 4, 0, 1, 5, 2, 3, 11],
 87 |       [2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5],
 88 |       [10, 3, 11, 10, 1, 3, 9, 5, 4],
 89 |       [4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10],
 90 |       [5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3],
 91 |       [5, 4, 8, 5, 8, 10, 10, 8, 11],
 92 |       [9, 7, 8, 5, 7, 9],
 93 |       [9, 3, 0, 9, 5, 3, 5, 7, 3],
 94 |       [0, 7, 8, 0, 1, 7, 1, 5, 7],
 95 |       [1, 5, 3, 3, 5, 7],
 96 |       [9, 7, 8, 9, 5, 7, 10, 1, 2],
 97 |       [10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3],
 98 |       [8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2],
 99 |       [2, 10, 5, 2, 5, 3, 3, 5, 7],
100 |       [7, 9, 5, 7, 8, 9, 3, 11, 2],
101 |       [9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11],
102 |       [2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7],
103 |       [11, 2, 1, 11, 1, 7, 7, 1, 5],
104 |       [9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11],
105 |       [5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0],
106 |       [11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0],
107 |       [11, 10, 5, 7, 11, 5],
108 |       [10, 6, 5],
109 |       [0, 8, 3, 5, 10, 6],
110 |       [9, 0, 1, 5, 10, 6],
111 |       [1, 8, 3, 1, 9, 8, 5, 10, 6],
112 |       [1, 6, 5, 2, 6, 1],
113 |       [1, 6, 5, 1, 2, 6, 3, 0, 8],
114 |       [9, 6, 5, 9, 0, 6, 0, 2, 6],
115 |       [5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8],
116 |       [2, 3, 11, 10, 6, 5],
117 |       [11, 0, 8, 11, 2, 0, 10, 6, 5],
118 |       [0, 1, 9, 2, 3, 11, 5, 10, 6],
119 |       [5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11],
120 |       [6, 3, 11, 6, 5, 3, 5, 1, 3],
121 |       [0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6],
122 |       [3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9],
123 |       [6, 5, 9, 6, 9, 11, 11, 9, 8],
124 |       [5, 10, 6, 4, 7, 8],
125 |       [4, 3, 0, 4, 7, 3, 6, 5, 10],
126 |       [1, 9, 0, 5, 10, 6, 8, 4, 7],
127 |       [10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4],
128 |       [6, 1, 2, 6, 5, 1, 4, 7, 8],
129 |       [1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7],
130 |       [8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6],
131 |       [7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9],
132 |       [3, 11, 2, 7, 8, 4, 10, 6, 5],
133 |       [5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11],
134 |       [0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6],
135 |       [9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6],
136 |       [8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6],
137 |       [5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11],
138 |       [0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7],
139 |       [6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9],
140 |       [10, 4, 9, 6, 4, 10],
141 |       [4, 10, 6, 4, 9, 10, 0, 8, 3],
142 |       [10, 0, 1, 10, 6, 0, 6, 4, 0],
143 |       [8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10],
144 |       [1, 4, 9, 1, 2, 4, 2, 6, 4],
145 |       [3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4],
146 |       [0, 2, 4, 4, 2, 6],
147 |       [8, 3, 2, 8, 2, 4, 4, 2, 6],
148 |       [10, 4, 9, 10, 6, 4, 11, 2, 3],
149 |       [0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6],
150 |       [3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10],
151 |       [6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1],
152 |       [9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3],
153 |       [8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1],
154 |       [3, 11, 6, 3, 6, 0, 0, 6, 4],
155 |       [6, 4, 8, 11, 6, 8],
156 |       [7, 10, 6, 7, 8, 10, 8, 9, 10],
157 |       [0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10],
158 |       [10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0],
159 |       [10, 6, 7, 10, 7, 1, 1, 7, 3],
160 |       [1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7],
161 |       [2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9],
162 |       [7, 8, 0, 7, 0, 6, 6, 0, 2],
163 |       [7, 3, 2, 6, 7, 2],
164 |       [2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7],
165 |       [2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7],
166 |       [1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11],
167 |       [11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1],
168 |       [8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6],
169 |       [0, 9, 1, 11, 6, 7],
170 |       [7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0],
171 |       [7, 11, 6],
172 |       [7, 6, 11],
173 |       [3, 0, 8, 11, 7, 6],
174 |       [0, 1, 9, 11, 7, 6],
175 |       [8, 1, 9, 8, 3, 1, 11, 7, 6],
176 |       [10, 1, 2, 6, 11, 7],
177 |       [1, 2, 10, 3, 0, 8, 6, 11, 7],
178 |       [2, 9, 0, 2, 10, 9, 6, 11, 7],
179 |       [6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8],
180 |       [7, 2, 3, 6, 2, 7],
181 |       [7, 0, 8, 7, 6, 0, 6, 2, 0],
182 |       [2, 7, 6, 2, 3, 7, 0, 1, 9],
183 |       [1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6],
184 |       [10, 7, 6, 10, 1, 7, 1, 3, 7],
185 |       [10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8],
186 |       [0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7],
187 |       [7, 6, 10, 7, 10, 8, 8, 10, 9],
188 |       [6, 8, 4, 11, 8, 6],
189 |       [3, 6, 11, 3, 0, 6, 0, 4, 6],
190 |       [8, 6, 11, 8, 4, 6, 9, 0, 1],
191 |       [9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6],
192 |       [6, 8, 4, 6, 11, 8, 2, 10, 1],
193 |       [1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6],
194 |       [4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9],
195 |       [10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3],
196 |       [8, 2, 3, 8, 4, 2, 4, 6, 2],
197 |       [0, 4, 2, 4, 6, 2],
198 |       [1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8],
199 |       [1, 9, 4, 1, 4, 2, 2, 4, 6],
200 |       [8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1],
201 |       [10, 1, 0, 10, 0, 6, 6, 0, 4],
202 |       [4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3],
203 |       [10, 9, 4, 6, 10, 4],
204 |       [4, 9, 5, 7, 6, 11],
205 |       [0, 8, 3, 4, 9, 5, 11, 7, 6],
206 |       [5, 0, 1, 5, 4, 0, 7, 6, 11],
207 |       [11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5],
208 |       [9, 5, 4, 10, 1, 2, 7, 6, 11],
209 |       [6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5],
210 |       [7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2],
211 |       [3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6],
212 |       [7, 2, 3, 7, 6, 2, 5, 4, 9],
213 |       [9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7],
214 |       [3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0],
215 |       [6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8],
216 |       [9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7],
217 |       [1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4],
218 |       [4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10],
219 |       [7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10],
220 |       [6, 9, 5, 6, 11, 9, 11, 8, 9],
221 |       [3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5],
222 |       [0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11],
223 |       [6, 11, 3, 6, 3, 5, 5, 3, 1],
224 |       [1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6],
225 |       [0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10],
226 |       [11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5],
227 |       [6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3],
228 |       [5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2],
229 |       [9, 5, 6, 9, 6, 0, 0, 6, 2],
230 |       [1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8],
231 |       [1, 5, 6, 2, 1, 6],
232 |       [1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6],
233 |       [10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0],
234 |       [0, 3, 8, 5, 6, 10],
235 |       [10, 5, 6],
236 |       [11, 5, 10, 7, 5, 11],
237 |       [11, 5, 10, 11, 7, 5, 8, 3, 0],
238 |       [5, 11, 7, 5, 10, 11, 1, 9, 0],
239 |       [10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1],
240 |       [11, 1, 2, 11, 7, 1, 7, 5, 1],
241 |       [0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11],
242 |       [9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7],
243 |       [7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2],
244 |       [2, 5, 10, 2, 3, 5, 3, 7, 5],
245 |       [8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5],
246 |       [9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2],
247 |       [9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2],
248 |       [1, 3, 5, 3, 7, 5],
249 |       [0, 8, 7, 0, 7, 1, 1, 7, 5],
250 |       [9, 0, 3, 9, 3, 5, 5, 3, 7],
251 |       [9, 8, 7, 5, 9, 7],
252 |       [5, 8, 4, 5, 10, 8, 10, 11, 8],
253 |       [5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0],
254 |       [0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5],
255 |       [10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4],
256 |       [2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8],
257 |       [0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11],
258 |       [0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5],
259 |       [9, 4, 5, 2, 11, 3],
260 |       [2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4],
261 |       [5, 10, 2, 5, 2, 4, 4, 2, 0],
262 |       [3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9],
263 |       [5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2],
264 |       [8, 4, 5, 8, 5, 3, 3, 5, 1],
265 |       [0, 4, 5, 1, 0, 5],
266 |       [8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5],
267 |       [9, 4, 5],
268 |       [4, 11, 7, 4, 9, 11, 9, 10, 11],
269 |       [0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11],
270 |       [1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11],
271 |       [3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4],
272 |       [4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2],
273 |       [9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3],
274 |       [11, 7, 4, 11, 4, 2, 2, 4, 0],
275 |       [11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4],
276 |       [2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9],
277 |       [9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7],
278 |       [3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10],
279 |       [1, 10, 2, 8, 7, 4],
280 |       [4, 9, 1, 4, 1, 7, 7, 1, 3],
281 |       [4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1],
282 |       [4, 0, 3, 7, 4, 3],
283 |       [4, 8, 7],
284 |       [9, 10, 8, 10, 11, 8],
285 |       [3, 0, 9, 3, 9, 11, 11, 9, 10],
286 |       [0, 1, 10, 0, 10, 8, 8, 10, 11],
287 |       [3, 1, 10, 11, 3, 10],
288 |       [1, 2, 11, 1, 11, 9, 9, 11, 8],
289 |       [3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9],
290 |       [0, 2, 11, 8, 0, 11],
291 |       [3, 2, 11],
292 |       [2, 3, 8, 2, 8, 10, 10, 8, 9],
293 |       [9, 10, 2, 0, 9, 2],
294 |       [2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8],
295 |       [1, 10, 2],
296 |       [1, 3, 8, 9, 1, 8],
297 |       [0, 9, 1],
298 |       [0, 3, 8],
299 |       []]
300 |   , cubeVerts = [
301 |      [0,0,0]
302 |     ,[1,0,0]
303 |     ,[1,1,0]
304 |     ,[0,1,0]
305 |     ,[0,0,1]
306 |     ,[1,0,1]
307 |     ,[1,1,1]
308 |     ,[0,1,1]]
309 |   , edgeIndex = [ [0,1],[1,2],[2,3],[3,0],[4,5],[5,6],[6,7],[7,4],[0,4],[1,5],[2,6],[3,7] ];
310 | 
311 | 
312 | 
313 | exports.marching_cubes = function(args) {
314 |   var potential = args.potential;
315 |   var dims      = args.resolution;
316 |   var bounds    = args.bounds || [[0,0,0], dims];
317 |   var scale     = [0,0,0];
318 |   var shift     = [0,0,0];
319 |   for(var i=0; i<3; ++i) {
320 |     scale[i] = (bounds[1][i] - bounds[0][i]) / dims[i];
321 |     shift[i] = bounds[0][i];
322 |   }
323 | 
324 |   var vertices = []
325 |     , faces = []
326 |     , n = 0
327 |     , grid = new Array(8)
328 |     , edges = new Array(12)
329 |     , x = [0,0,0];
330 |   //March over the volume
331 |   for(x[2]=0; x[2]<dims[2]-1; ++x[2], n+=dims[0])
332 |   for(x[1]=0; x[1]<dims[1]-1; ++x[1], ++n)
333 |   for(x[0]=0; x[0]<dims[0]-1; ++x[0], ++n) {
334 |     //For each cell, compute cube mask
335 |     var cube_index = 0;
336 |     for(var i=0; i<8; ++i) {
337 |       var v = cubeVerts[i]
338 |         , s = potential(
339 |           scale[0]*(x[0]+v[0])+shift[0],
340 |           scale[1]*(x[1]+v[1])+shift[1],
341 |           scale[2]*(x[2]+v[2])+shift[2]);
342 |       grid[i] = s;
343 |       cube_index |= (s > 0) ? 1 << i : 0;
344 |     }
345 |     //Compute vertices
346 |     var edge_mask = edgeTable[cube_index];
347 |     if(edge_mask === 0) {
348 |       continue;
349 |     }
350 |     for(var i=0; i<12; ++i) {
351 |       if((edge_mask & (1<<i)) === 0) {
352 |         continue;
353 |       }
354 |       edges[i] = vertices.length;
355 |       var nv = [0,0,0]
356 |         , e = edgeIndex[i]
357 |         , p0 = cubeVerts[e[0]]
358 |         , p1 = cubeVerts[e[1]]
359 |         , a = grid[e[0]]
360 |         , b = grid[e[1]]
361 |         , d = a - b
362 |         , t = 0;
363 |       if(Math.abs(d) > 1e-6) {
364 |         t = a / d;
365 |       }
366 |       for(var j=0; j<3; ++j) {
367 |         nv[j] = scale[j] * ((x[j] + p0[j]) + t * (p1[j] - p0[j])) + shift[j];
368 |       }
369 |       vertices.push(nv);
370 |     }
371 |     //Add faces
372 |     var f = triTable[cube_index];
373 |     for(var i=0; i<f.length; i += 3) {
374 |       faces.push([edges[f[i]], edges[f[i+1]], edges[f[i+2]]]);
375 |     }
376 |   }
377 |   return { positions: vertices, faces: faces };
378 | };
379 | 
380 | 


--------------------------------------------------------------------------------
/src/marchingtetrahedra.js:
--------------------------------------------------------------------------------
  1 | /**
  2 |  * Marching Tetrahedra in Javascript
  3 |  *
  4 |  * Based on Paul Bourke's implementation
  5 |  *  http://local.wasp.uwa.edu.au/~pbourke/geometry/polygonise/
  6 |  *
  7 |  * (Several bug fixes were made to deal with oriented faces)
  8 |  *
  9 |  * Javascript port by Mikola Lysenko
 10 |  */
 11 | var cube_vertices = [
 12 |         [0,0,0]
 13 |       , [1,0,0]
 14 |       , [1,1,0]
 15 |       , [0,1,0]
 16 |       , [0,0,1]
 17 |       , [1,0,1]
 18 |       , [1,1,1]
 19 |       , [0,1,1] ]
 20 |   , tetra_list = [
 21 |         [0,2,3,7]
 22 |       , [0,6,2,7]
 23 |       , [0,4,6,7]
 24 |       , [0,6,1,2]
 25 |       , [0,1,6,4]
 26 |       , [5,6,1,4] ];
 27 | 
 28 | exports.marching_tetrahedra = function(args) {
 29 | 
 30 |   var potential = args.potential;
 31 |   var dims      = args.resolution;
 32 |   var bounds    = args.bounds || [[0,0,0], dims];
 33 |   var scale     = [0,0,0];
 34 |   var shift     = [0,0,0];
 35 |   for(var i=0; i<3; ++i) {
 36 |     scale[i] = (bounds[1][i] - bounds[0][i]) / dims[i];
 37 |     shift[i] = bounds[0][i];
 38 |   }
 39 |    
 40 |    var vertices = []
 41 |     , faces = []
 42 |     , n = 0
 43 |     , grid = new Float32Array(8)
 44 |     , edges = new Int32Array(12)
 45 |     , x = [0,0,0];
 46 |     
 47 |   function interp(i0, i1) {
 48 |     var g0 = grid[i0]
 49 |       , g1 = grid[i1]
 50 |       , p0 = cube_vertices[i0]
 51 |       , p1 = cube_vertices[i1]
 52 |       , v  = [x[0], x[1], x[2]]
 53 |       , t = g0 - g1;
 54 |     if(Math.abs(t) > 1e-6) {
 55 |       t = g0 / t;
 56 |     }
 57 |     for(var i=0; i<3; ++i) {
 58 |       v[i] = scale[i] * (v[i] + p0[i] + t * (p1[i] - p0[i])) + shift[i];
 59 |     }
 60 |     vertices.push(v);
 61 |     return vertices.length - 1;
 62 |   }
 63 |   
 64 |   //March over the volume
 65 |   for(x[2]=0; x[2]<dims[2]-1; ++x[2], n+=dims[0])
 66 |   for(x[1]=0; x[1]<dims[1]-1; ++x[1], ++n)
 67 |   for(x[0]=0; x[0]<dims[0]-1; ++x[0], ++n) {
 68 |     //Read in cube  
 69 |     for(var i=0; i<8; ++i) {
 70 |       var cube_vert = cube_vertices[i];
 71 |       grid[i] = potential(
 72 |         scale[0]*(x[0]+cube_vert[0])+shift[0],
 73 |         scale[1]*(x[1]+cube_vert[1])+shift[1],
 74 |         scale[2]*(x[2]+cube_vert[2])+shift[2]);
 75 |     }
 76 |     for(var i=0; i<tetra_list.length; ++i) {
 77 |       var T = tetra_list[i]
 78 |         , triindex = 0;
 79 |       if (grid[T[0]] < 0) triindex |= 1;
 80 |       if (grid[T[1]] < 0) triindex |= 2;
 81 |       if (grid[T[2]] < 0) triindex |= 4;
 82 |       if (grid[T[3]] < 0) triindex |= 8;
 83 |       
 84 |       //Handle each case
 85 |       switch (triindex) {
 86 |         case 0x00:
 87 |         case 0x0F:
 88 |         break;
 89 |         case 0x0E:
 90 |           faces.push([ 
 91 |               interp(T[0], T[1])
 92 |             , interp(T[0], T[3]) 
 93 |             , interp(T[0], T[2]) ]);
 94 |         break;
 95 |         case 0x01:
 96 |           faces.push([ 
 97 |               interp(T[0], T[1])
 98 |             , interp(T[0], T[2])
 99 |             , interp(T[0], T[3])  ]);
100 |         break;
101 |         case 0x0D:
102 |           faces.push([ 
103 |               interp(T[1], T[0])
104 |             , interp(T[1], T[2]) 
105 |             , interp(T[1], T[3]) ]);
106 |         break;
107 |         case 0x02:
108 |           faces.push([ 
109 |               interp(T[1], T[0])
110 |             , interp(T[1], T[3])
111 |             , interp(T[1], T[2]) ]);
112 |         break;
113 |         case 0x0C:
114 |           faces.push([ 
115 |                 interp(T[1], T[2])
116 |               , interp(T[1], T[3])
117 |               , interp(T[0], T[3])
118 |               , interp(T[0], T[2]) ]);
119 |         break;
120 |         case 0x03:
121 |           faces.push([ 
122 |                 interp(T[1], T[2])
123 |               , interp(T[0], T[2])
124 |               , interp(T[0], T[3])
125 |               , interp(T[1], T[3]) ]);
126 |         break;
127 |         case 0x04:
128 |           faces.push([ 
129 |                 interp(T[2], T[0])
130 |               , interp(T[2], T[1])
131 |               , interp(T[2], T[3]) ]);
132 |         break;
133 |         case 0x0B:
134 |           faces.push([ 
135 |                 interp(T[2], T[0])
136 |               , interp(T[2], T[3]) 
137 |               , interp(T[2], T[1]) ]);
138 |         break;
139 |         case 0x05:
140 |           faces.push([ 
141 |                 interp(T[0], T[1])
142 |               , interp(T[1], T[2])
143 |               , interp(T[2], T[3])
144 |               , interp(T[0], T[3]) ]);
145 |         break;
146 |         case 0x0A:
147 |           faces.push([ 
148 |                 interp(T[0], T[1])
149 |               , interp(T[0], T[3])
150 |               , interp(T[2], T[3])
151 |               , interp(T[1], T[2]) ]);
152 |         break;
153 |         case 0x06:
154 |           faces.push([ 
155 |                 interp(T[2], T[3])
156 |               , interp(T[0], T[2])
157 |               , interp(T[0], T[1])
158 |               , interp(T[1], T[3]) ]);
159 |         break;
160 |         case 0x09:
161 |           faces.push([ 
162 |                 interp(T[2], T[3])
163 |               , interp(T[1], T[3])
164 |               , interp(T[0], T[1])
165 |               , interp(T[0], T[2]) ]);
166 |         break;
167 |         case 0x07:
168 |           faces.push([ 
169 |                 interp(T[3], T[0])
170 |               , interp(T[3], T[1])
171 |               , interp(T[3], T[2]) ]);
172 |         break;
173 |         case 0x08:
174 |           faces.push([ 
175 |                 interp(T[3], T[0])
176 |               , interp(T[3], T[2])
177 |               , interp(T[3], T[1]) ]);
178 |         break;
179 |       }
180 |     }
181 |   }
182 |   
183 |   return { positions: vertices, faces: faces };
184 | }
185 | 
186 | 


--------------------------------------------------------------------------------
/src/normals.js:
--------------------------------------------------------------------------------
  1 | var EPSILON = 1e-6;
  2 | 
  3 | //Estimate the vertex normals of a mesh
  4 | exports.vertex_normals = function(args) {
  5 |   
  6 |   var positions = args.positions;
  7 |   var faces     = args.faces;
  8 |   var N         = positions.length;
  9 |   var normals   = new Array(N);
 10 |   
 11 |   //Initialize normal array
 12 |   for(var i=0; i<N; ++i) {
 13 |     normals[i] = [0.0, 0.0, 0.0];
 14 |   }
 15 |   
 16 |   //Walk over all the faces and add per-vertex contribution to normal weights
 17 |   for(var i=0; i<faces.length; ++i) {
 18 |     var f = faces[i];
 19 |     var p = 0;
 20 |     var c = f[f.length-1];
 21 |     var n = f[0];
 22 |     for(var j=0; j<f.length; ++j) {
 23 |     
 24 |       //Shift indices back
 25 |       p = c;
 26 |       c = n;
 27 |       n = f[(j+1) % f.length];
 28 |     
 29 |       var v0 = positions[p];
 30 |       var v1 = positions[c];
 31 |       var v2 = positions[n];
 32 |       
 33 |       //Compute arc lengths
 34 |       var d01 = new Array(3);
 35 |       var m01 = 0.0;
 36 |       var d21 = new Array(3);
 37 |       var m21 = 0.0;
 38 |       for(var k=0; k<3; ++k) {
 39 |         d01[k] = v0[k]  - v1[k];
 40 |         m01   += d01[k] * d01[k];
 41 |         d21[k] = v2[k]  - v1[k];
 42 |         m21   += d21[k] * d21[k];
 43 |       }
 44 | 
 45 |       //Accumulate values in normal
 46 |       if(m01 * m21 > EPSILON) {
 47 |         var norm = normals[c];
 48 |         var w = 1.0 / Math.sqrt(m01 * m21);
 49 |         for(var k=0; k<3; ++k) {
 50 |           var u = (k+1)%3;
 51 |           var v = (k+2)%3;
 52 |           norm[k] += w * (d21[u] * d01[v] - d21[v] * d01[u]);
 53 |         }
 54 |       }
 55 |     }
 56 |   }
 57 |   
 58 |   //Scale all normals to unit length
 59 |   for(var i=0; i<N; ++i) {
 60 |     var norm = normals[i];
 61 |     var m = 0.0;
 62 |     for(var k=0; k<3; ++k) {
 63 |       m += norm[k] * norm[k];
 64 |     }
 65 |     if(m > EPSILON) {
 66 |       var w = 1.0 / Math.sqrt(m);
 67 |       for(var k=0; k<3; ++k) {
 68 |         norm[k] *= w;
 69 |       }
 70 |     } else {
 71 |       for(var k=0; k<3; ++k) {
 72 |         norm[k] = 0.0;
 73 |       }
 74 |     }
 75 |   }
 76 | 
 77 |   //Return the resulting set of patches
 78 |   return normals;
 79 | }
 80 | 
 81 | //Compute face normals of a mesh
 82 | exports.face_normals = function(args) {
 83 |   var positions = args.positions;
 84 |   var faces     = args.faces;
 85 |   var N         = faces.length;
 86 |   var normals   = new Array(N);
 87 |   
 88 |   for(var i=0; i<N; ++i) {
 89 |     var f = faces[i];
 90 |     var pos = new Array(3);
 91 |     for(var j=0; j<3; ++j) {
 92 |       pos[j] = positions[f[j]];
 93 |     }
 94 |     
 95 |     var d01 = new Array(3);
 96 |     var d21 = new Array(3);
 97 |     for(var j=0; j<3; ++j) {
 98 |       d01[j] = pos[1][j] - pos[0][j];
 99 |       d21[j] = pos[2][j] - pos[0][j];
100 |     }
101 |     
102 |     var n = new Array(3);
103 |     var l = 0.0;
104 |     for(var j=0; j<3; ++j) {
105 |       var u = (j+1)%3;
106 |       var v = (j+2)%3;
107 |       n[j] = d01[u] * d21[v] - d01[v] * d21[u];
108 |       l += n[j] * n[j];
109 |     }
110 |     if(l > EPSILON) {
111 |       l = 1.0 / Math.sqrt(l);
112 |     } else {
113 |       l = 0.0;
114 |     }
115 |     for(var j=0; j<3; ++j) {
116 |       n[j] *= l;
117 |     }
118 |     normals[i] = n;
119 |   }
120 |   return normals;
121 | }
122 | 
123 | 
124 | 


--------------------------------------------------------------------------------
/src/obj.js:
--------------------------------------------------------------------------------
 1 | exports.parse_obj = function(obj) {
 2 |   var lines = obj.split("\n");
 3 |   
 4 |   var positions           = [];
 5 |   var texture_coordinates = [];
 6 |   var normals             = [];
 7 |   var parameters          = [];
 8 |   var faces               = [];
 9 |   var materials           = {};
10 |   for(var i=0; i<lines.length; ++i) {
11 |     var toks = lines[i].split(" ");
12 |     if(toks[0] === '#') {
13 |       continue;
14 |     } else if(toks[0] === 'v') {
15 |       positions.push([parseFloat(toks[1]), parseFloat(toks[2]), parseFloat(toks[3])]);
16 |     } else if(toks[0] === 'vt') {
17 |       //Add texture coordinate
18 |     } else if(toks[0] === 'vn') {
19 |       //Add normal
20 |     } else if(toks[0] === 'vp') {
21 |       //Add free parameter
22 |     } else if(toks[0] === 'f') {
23 |       //Add face
24 |     } else {
25 |       //Ignore field
26 |     }
27 |   }
28 |   
29 |   //Return all of the 
30 |   
31 | }
32 | 
33 | exports.export_obj = function(args) {
34 | }
35 | 


--------------------------------------------------------------------------------
/src/repair.js:
--------------------------------------------------------------------------------
 1 | "use strict";
 2 | 
 3 | //Fuses vertices in a mesh to remove cracks
 4 | function fuse_vertices(args) {  
 5 |   
 6 |   //Unpack arguments
 7 |   var positions   = args.positions;
 8 |   var faces       = args.faces;
 9 |   var tol         = args.tolerance || 1e-6;
10 |   
11 |   //First, fuse vertices together
12 |   var grid        = {};
13 |   var n_positions = [];
14 |   var n_index     = new Array(positions.length);
15 |   for(var i=0; i<positions.length; ++i) {
16 | 
17 |     var p = positions[i];
18 |     var r = new Array(3);
19 |     for(var j=0; j<3; ++j) {
20 |       r[j] = Math.floor(p[j] / tol);
21 |     }
22 |     
23 |     if(r in grid) {
24 |       n_index[i] = grid[r];
25 |     } else {
26 |       var idx = n_positions.length;
27 |       grid[r] = idx;
28 |       n_index[i] = idx;
29 |       n_positions.push(p.slice(0));
30 |     }
31 |   }
32 |   
33 |   
34 |   //Then fix up faces
35 |   var n_faces = [];
36 |   for(var i=0; i<faces.length; ++i) {
37 |     var face = faces[i].slice(0);
38 |     var skip = false;
39 |     for(var j=0; j<face.length; ++j) {
40 |       face[j] = n_index[face[j]];
41 |       for(var k=0; k<j; ++k) {
42 |         if(face[j] === face[k]) {
43 |           skip = true;
44 |         }
45 |       }
46 |     }
47 |     
48 |     if(!skip) {
49 |       n_faces.push(face);
50 |     }
51 |   }
52 |   
53 |   //Return resulting mesh
54 |   return { positions: n_positions, faces: n_faces };
55 | };
56 | 
57 | //Triangulates a collection of convex polyhedra (needed for non-triangular meshes)
58 | function triangulate(faces) {
59 |   var result = [];
60 |   for(var i=0; i<faces.length; ++i) {
61 |     var f = faces[i];
62 |     for(var j=2; j<f.length; ++j) {
63 |       result.push([f[0], f[j-1], f[j]]);
64 |     }
65 |   }
66 |   return result;
67 | }
68 | 
69 | exports.fuse_vertices = fuse_vertices;
70 | 


--------------------------------------------------------------------------------
/src/shapes.js:
--------------------------------------------------------------------------------
  1 | "use strict";
  2 | var repair = require('./repair.js');
  3 | 
  4 | //Creates a grid mesh
  5 | function grid_mesh(args) {
  6 |   var nx = args.width   || 10;
  7 |   var ny = args.height  || 10;
  8 | 
  9 |   var positions = new Array((nx+1) * (ny+1));
 10 |   for(var j=0; j<=ny; ++j) {
 11 |     for(var i=0; i<=nx; ++i) {
 12 |       positions[i + (nx+1)*j] = [i, j, 0];
 13 |     }
 14 |   }
 15 |   
 16 |   function p(x,y) { return x + (nx+1)*y; };
 17 |   
 18 |   var faces     = [];
 19 |   for(var j=0; j<ny; ++j) {
 20 |     for(var i=0; i<nx; ++i) {
 21 |       faces.push([ p(i,j), p(i+1, j), p(i, j+1) ]);
 22 |       faces.push([ p(i+1,j), p(i+1,j+1), p(i,j+1) ]);
 23 |     }
 24 |   }
 25 | 
 26 |   return {positions: positions, faces: faces};
 27 | }
 28 | 
 29 | //Creates a cubical mesh
 30 | // resolution is an integer representing number of subdivisions per linear dimension
 31 | // scale is a 3d vector representing the scale of the cube
 32 | function cube_mesh(args) {
 33 | 
 34 |   var resolution = args.resolution || 10;
 35 |   var scale      = typeof(args.scale) === "number" ? [args.scale, args.scale, args.scale] : (args.scale || [1.0, 1.0, 1.0]);
 36 | 
 37 |   var radius = resolution >> 1;
 38 |   var side_len = 2*radius + 1;
 39 |   function p(x,y,s) { 
 40 |     return x + side_len * (y + side_len * s); 
 41 |   }
 42 |   
 43 |   var positions = new Array(6 * side_len * side_len);
 44 |   var faces = [];  
 45 |   
 46 |   for(var d=0; d<3; ++d) {
 47 |     var u = (d+1)%3;
 48 |     var v = (d+2)%3;
 49 |     
 50 |     for(var s=0; s<2; ++s) {
 51 |       var f = 2*d + s;
 52 |       var x = new Array(3);
 53 |       
 54 |       x[u] = -radius;
 55 |       x[v] = -radius;
 56 |       x[d] = (1 - 2*s) * radius;
 57 |     
 58 |       for(var j=0; j<side_len; ++j, ++x[v]) {
 59 |         x[u] = -radius;
 60 |         for(var i=0; i<side_len; ++i, ++x[u]) {
 61 |           var pos = new Array(3);
 62 |           for(var k=0; k<3; ++k) {
 63 |             pos[k] = x[k] * scale[k] / radius;
 64 |           }
 65 |         
 66 |           positions[p(i, j, f)] = pos;
 67 |           
 68 |           if(i < side_len-1 && j < side_len-1) {
 69 |             if(s) {
 70 |               faces.push([ p(i,j,f), p(i,j+1,f), p(i+1,j,f) ]);
 71 |               faces.push([ p(i+1,j,f), p(i,j+1,f), p(i+1,j+1,f) ]);          
 72 |             } else {
 73 |               faces.push([ p(i,j,f), p(i+1,j,f), p(i,j+1,f) ]);
 74 |               faces.push([ p(i,j+1,f), p(i+1,j,f), p(i+1,j+1,f) ]);
 75 |             }
 76 |           }
 77 |         }
 78 |       }
 79 |     }
 80 |   }
 81 | 
 82 |   //Glue 6 faces together and return
 83 |   var tol = 0.5 * Math.min(scale[0], Math.min(scale[1], scale[2])) / radius;
 84 |   return repair.fuse_vertices({positions: positions, faces: faces}, tol);
 85 | };
 86 | 
 87 | 
 88 | //Creates a spherical mesh
 89 | //  resolution is an integer representing number of (vertices/6)^(1/2)
 90 | //  radius is the radius of the sphere
 91 | function sphere_mesh(args) {
 92 |   var resolution = args.resolution || 10;
 93 |   var radius     = args.radius || 1.0;
 94 | 
 95 |   var base = cube_mesh({ resolution: resolution });
 96 |   
 97 |   for(var i=0; i<base.positions.length; ++i) {
 98 |     var p = base.positions[i];
 99 |     var l = 0.0;
100 |     for(var j=0; j<3; ++j) {
101 |       l += p[j] * p[j];
102 |     }
103 |     l = radius / Math.sqrt(l);
104 |     for(var j=0; j<3; ++j) {
105 |       p[j] *= l;
106 |     }
107 |   }
108 |   
109 |   return base;
110 | }
111 | 
112 | 
113 | exports.grid_mesh = grid_mesh;
114 | exports.cube_mesh = cube_mesh;
115 | exports.sphere_mesh = sphere_mesh;
116 | 


--------------------------------------------------------------------------------
/src/surfacenets.js:
--------------------------------------------------------------------------------
  1 | /**
  2 |  * SurfaceNets in JavaScript
  3 |  *
  4 |  * Written by Mikola Lysenko (C) 2012
  5 |  *
  6 |  * MIT License
  7 |  *
  8 |  * Based on: S.F. Gibson, "Constrained Elastic Surface Nets". (1998) MERL Tech Report.
  9 |  */
 10 | "use strict";
 11 | 
 12 | //Precompute edge table, like Paul Bourke does.
 13 | // This saves a bit of time when computing the centroid of each boundary cell
 14 | var cube_edges = new Int32Array(24)
 15 |   , edge_table = new Int32Array(256);
 16 | (function() {
 17 | 
 18 |   //Initialize the cube_edges table
 19 |   // This is just the vertex number of each cube
 20 |   var k = 0;
 21 |   for(var i=0; i<8; ++i) {
 22 |     for(var j=1; j<=4; j<<=1) {
 23 |       var p = i^j;
 24 |       if(i <= p) {
 25 |         cube_edges[k++] = i;
 26 |         cube_edges[k++] = p;
 27 |       }
 28 |     }
 29 |   }
 30 | 
 31 |   //Initialize the intersection table.
 32 |   //  This is a 2^(cube configuration) ->  2^(edge configuration) map
 33 |   //  There is one entry for each possible cube configuration, and the output is a 12-bit vector enumerating all edges crossing the 0-level.
 34 |   for(var i=0; i<256; ++i) {
 35 |     var em = 0;
 36 |     for(var j=0; j<24; j+=2) {
 37 |       var a = !!(i & (1<<cube_edges[j]))
 38 |         , b = !!(i & (1<<cube_edges[j+1]));
 39 |       em |= a !== b ? (1 << (j >> 1)) : 0;
 40 |     }
 41 |     edge_table[i] = em;
 42 |   }
 43 | })();
 44 | 
 45 | //Internal buffer, this may get resized at run time
 46 | var buffer = new Array(4096);
 47 | (function() {
 48 |   for(var i=0; i<buffer.length; ++i) {
 49 |     buffer[i] = 0;
 50 |   }
 51 | })();
 52 | 
 53 | //Export function
 54 | exports.surface_nets = function(args) {
 55 | 
 56 |   var potential = args.potential;
 57 |   var dims      = args.resolution;
 58 |   var bounds    = args.bounds || [[0,0,0], dims];
 59 |   var scale     = [0,0,0];
 60 |   var shift     = [0,0,0];
 61 |   for(var i=0; i<3; ++i) {
 62 |     scale[i] = (bounds[1][i] - bounds[0][i]) / dims[i];
 63 |     shift[i] = bounds[0][i];
 64 |   }
 65 | 
 66 |   
 67 |   
 68 |   var vertices = []
 69 |     , faces = []
 70 |     , n = 0
 71 |     , x = [0, 0, 0]
 72 |     , R = [1, (dims[0]+1), (dims[0]+1)*(dims[0]+1)]
 73 |     , grid = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 74 |     , buf_no = 1;
 75 |   
 76 |    
 77 |   //Resize buffer if necessary 
 78 |   if(R[2] * 2 > buffer.length) {
 79 |     var ol = buffer.length;
 80 |     buffer.length = R[2] * 2;
 81 |     while(ol < buffer.length) {
 82 |       buffer[ol++] = 0;
 83 |     }
 84 |   }
 85 |   
 86 |   //March over the voxel grid
 87 |   for(x[2]=0; x[2]<dims[2]-1; ++x[2], n+=dims[0], buf_no ^= 1, R[2]=-R[2]) {
 88 |   
 89 |     //m is the pointer into the buffer we are going to use.  
 90 |     //This is slightly obtuse because javascript does not have good support for packed data structures, so we must use typed arrays :(
 91 |     //The contents of the buffer will be the indices of the vertices on the previous x/y slice of the volume
 92 |     var m = 1 + (dims[0]+1) * (1 + buf_no * (dims[1]+1));
 93 |     
 94 |     for(x[1]=0; x[1]<dims[1]-1; ++x[1], ++n, m+=2)
 95 |     for(x[0]=0; x[0]<dims[0]-1; ++x[0], ++n, ++m) {
 96 |     
 97 |       //Read in 8 field values around this vertex and store them in an array
 98 |       //Also calculate 8-bit mask, like in marching cubes, so we can speed up sign checks later
 99 |       var mask = 0, g = 0;
100 |       for(var k=0; k<2; ++k)
101 |       for(var j=0; j<2; ++j)      
102 |       for(var i=0; i<2; ++i, ++g) {
103 |         var p = potential(
104 |           scale[0]*(x[0]+i)+shift[0],
105 |           scale[1]*(x[1]+j)+shift[1],
106 |           scale[2]*(x[2]+k)+shift[2]);
107 |         grid[g] = p;
108 |         mask |= (p < 0) ? (1<<g) : 0;
109 |       }
110 |       
111 |       //Check for early termination if cell does not intersect boundary
112 |       if(mask === 0 || mask === 0xff) {
113 |         continue;
114 |       }
115 |       
116 |       //Sum up edge intersections
117 |       var edge_mask = edge_table[mask]
118 |         , v = [0.0,0.0,0.0]
119 |         , e_count = 0;
120 |         
121 |       //For every edge of the cube...
122 |       for(var i=0; i<12; ++i) {
123 |       
124 |         //Use edge mask to check if it is crossed
125 |         if(!(edge_mask & (1<<i))) {
126 |           continue;
127 |         }
128 |         
129 |         //If it did, increment number of edge crossings
130 |         ++e_count;
131 |         
132 |         //Now find the point of intersection
133 |         var e0 = cube_edges[ i<<1 ]       //Unpack vertices
134 |           , e1 = cube_edges[(i<<1)+1]
135 |           , g0 = grid[e0]                 //Unpack grid values
136 |           , g1 = grid[e1]
137 |           , t  = g0 - g1;                 //Compute point of intersection
138 |         if(Math.abs(t) > 1e-6) {
139 |           t = g0 / t;
140 |         } else {
141 |           continue;
142 |         }
143 |         
144 |         //Interpolate vertices and add up intersections (this can be done without multiplying)
145 |         for(var j=0, k=1; j<3; ++j, k<<=1) {
146 |           var a = e0 & k
147 |             , b = e1 & k;
148 |           if(a !== b) {
149 |             v[j] += a ? 1.0 - t : t;
150 |           } else {
151 |             v[j] += a ? 1.0 : 0;
152 |           }
153 |         }
154 |       }
155 |       
156 |       //Now we just average the edge intersections and add them to coordinate
157 |       var s = 1.0 / e_count;
158 |       for(var i=0; i<3; ++i) {
159 |         v[i] = scale[i] * (x[i] + s * v[i]) + shift[i];
160 |       }
161 |       
162 |       //Add vertex to buffer, store pointer to vertex index in buffer
163 |       buffer[m] = vertices.length;
164 |       vertices.push(v);
165 |       
166 |       //Now we need to add faces together, to do this we just loop over 3 basis components
167 |       for(var i=0; i<3; ++i) {
168 |         //The first three entries of the edge_mask count the crossings along the edge
169 |         if(!(edge_mask & (1<<i)) ) {
170 |           continue;
171 |         }
172 |         
173 |         // i = axes we are point along.  iu, iv = orthogonal axes
174 |         var iu = (i+1)%3
175 |           , iv = (i+2)%3;
176 |           
177 |         //If we are on a boundary, skip it
178 |         if(x[iu] === 0 || x[iv] === 0) {
179 |           continue;
180 |         }
181 |         
182 |         //Otherwise, look up adjacent edges in buffer
183 |         var du = R[iu]
184 |           , dv = R[iv];
185 |         
186 |         //Remember to flip orientation depending on the sign of the corner.
187 |         if(mask & 1) {
188 |           faces.push([buffer[m],    buffer[m-du],    buffer[m-dv]]);
189 |           faces.push([buffer[m-dv], buffer[m-du],    buffer[m-du-dv]]);
190 |         } else {
191 |           faces.push([buffer[m],    buffer[m-dv],    buffer[m-du]]);
192 |           faces.push([buffer[m-du], buffer[m-dv],    buffer[m-du-dv]]);
193 |         }
194 |       }
195 |     }
196 |   }
197 |   
198 |   //All done!  Return the result
199 |   return { positions: vertices, faces: faces };
200 | };
201 | 
202 | 
203 | 


--------------------------------------------------------------------------------
/src/topology.js:
--------------------------------------------------------------------------------
 1 | function vmax(faces) {
 2 |   var vc = 0;
 3 |   for(var i=0; i<faces.length; ++i) {
 4 |     var f = faces[i];
 5 |     for(var j=0; j<f.length; ++j) {
 6 |       vc = Math.max(vc, f[j]);
 7 |     }
 8 |   }
 9 |   return vc+1;
10 | }
11 | 
12 | /**
13 |  * Returns an array containing the set of all faces incident to each vertex in the mesh.
14 |  */
15 | exports.vertex_stars = function(args) {
16 |   var faces         = args.faces;
17 |   var vertex_count  = args.vertex_count || vmax(faces);
18 | 
19 |   var stars = new Array(vertex_count);
20 |   for(var i=0; i<stars.length; ++i) {
21 |     stars[i] = [];
22 |   }
23 |   
24 |   for(var i=0; i<faces.length; ++i) {  
25 |     var f = faces[i];
26 |     for(var j=0; j<f.length; ++j) {
27 |       stars[f[j]].push(i);
28 |     }
29 |   }
30 |   
31 |   return stars;
32 | };
33 | 
34 | // Compute all edges of a mesh
35 | exports.edges = function(args) {
36 |   var faces = args.faces;
37 |   var edges = { };
38 |   
39 |   for(var i=0; i<faces.length; ++i) {
40 |     var f = faces[i];
41 |     for(var j=0; j<f.length; ++j) {
42 |       var e = [ f[j], f[(j+1)%f.length] ];
43 |       e.sort();
44 |       if(e in edges) {
45 |         edges[e].push(i);
46 |       } else {
47 |         edges[e] = [i];
48 |       }
49 |     }
50 |   }
51 |   
52 |   return edges;
53 | }
54 | 
55 | 
56 | var edge_compare = new Function("a", "b", "return a[0] === b[0] ? a[1]-b[1] : a[0]-b[0];");
57 | 
58 | // Computes the 1-ring around each vertex
59 | exports.rings = function(args) {
60 |   var faces = args.faces;
61 |   var stars = args.stars || exports.vertex_stars(args);
62 |   var vertex_count = args.vertex_count || stars.length;
63 |   var rings = new Array(vertex_count);
64 |   
65 |   for(var i=0; i<vertex_count; ++i) {
66 |     var nbhd = stars[i];
67 |     var edges = [];
68 |     
69 |     for(var n=0; n<nbhd.length; ++n) {
70 |       var f = faces[nbhd[n]];
71 |       for(var j=0; j<f.length; ++j) {
72 |         var e = [f[j], f[(j+1)%3]];
73 |         e.sort();
74 |         edges.push(e);
75 |       }
76 |     }
77 |     
78 |     edges.sort(edge_compare);
79 |     
80 |     //Extract unique edges store in ring
81 |   }
82 | }
83 | 
84 | 


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/tests/all.js:
--------------------------------------------------------------------------------
1 | require('./topology.js');
2 | require('./repair.js');
3 | require('./normals.js');
4 | require('./metric.js');
5 | require('./isosurface.js');
6 | require('./subdivision.js');


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/tests/isosurface.js:
--------------------------------------------------------------------------------
 1 | var vows = require('vows');
 2 | var assert = require('assert');
 3 | var marching_cubes = require('../src/marchingcubes.js').marching_cubes;
 4 | var marching_tetrahedra = require('../src/marchingtetrahedra.js').marching_tetrahedra;
 5 | var surface_nets = require('../src/surfacenets.js').surface_nets;
 6 | 
 7 | var TOLERANCE = 1e-3;
 8 | 
 9 | 
10 | function sphere(x,y,z) {
11 |   return Math.sqrt(x*x + y*y + z*z) - 1.0;
12 | }
13 | 
14 | function validate_surface(mesh, potential) {
15 |   for(var i=0; i<mesh.positions.length; ++i) {
16 |     var p = mesh.positions[i];
17 |     var s = potential(p[0], p[1], p[2]);
18 |     assert.ok(Math.abs(s) < TOLERANCE, "Unacceptable error in isosurface");
19 |   }
20 | }
21 | 
22 | //These tests kind of suck, but
23 | vows.describe("isosurfaces").addBatch({
24 |   'sphere': {
25 |     
26 |     topic: {
27 |         potential:  sphere
28 |       , resolution: [64,64,64]
29 |       , bounds:     [[-1.5, -1.5, -1.5], [1.5,1.5,1.5]]
30 |     },
31 |     
32 |     'marching cubes': function(field) {
33 |       validate_surface(marching_cubes(field), field.potential);
34 |     },
35 |   
36 |     'marching tets': function(field) {
37 |       validate_surface(marching_tetrahedra(field), field.potential);
38 |     },
39 |     
40 |     'surface nets': function(field) {
41 |       validate_surface(surface_nets(field), field.potential);
42 |     }    
43 |   },
44 |   
45 | }).run();
46 | 
47 | 


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/tests/metric.js:
--------------------------------------------------------------------------------
  1 | var vows = require('vows');
  2 | var assert = require('assert');
  3 | var distance = require('../src/distance.js');
  4 | var shapes = require('../src/shapes.js');
  5 | 
  6 | 
  7 | vows.describe("distance.js").addBatch({
  8 |   'quadratic_distance' : {
  9 |     'testing quadratic distance' : function() {
 10 |     
 11 |       var qd = distance.quadratic_distance([1, 0, 0], [0, 1, 0], [1, 1, 0], 1, 1, -1);
 12 |       assert.ok(Math.abs(qd - Math.sqrt(2.0)) < 1e-6, "Invalid quadratic distance");
 13 |     },
 14 |     
 15 |     'testing planar distances' : function() {
 16 |     
 17 |       var points = new Array(4);
 18 |       for(var i=0; i<4; ++i) {
 19 |         points[i] = new Array(3);
 20 |       }
 21 |       
 22 |       var distances = new Array(4);
 23 |     
 24 |       for(var i=0; i<1000; ++i) {
 25 |         for(var j=0; j<4; ++j) {
 26 |           distances[j] = 0.0;
 27 |           for(var k=0; k<3; ++k) {
 28 |             if(k !== 2) {
 29 |               points[j][k] = 1000.0 * (Math.random() - 1.0);
 30 |             } else {
 31 |               points[j][k] = 0;
 32 |             }
 33 |             distances[j] += Math.pow(points[j][k] - points[0][k], 2);
 34 |           }
 35 |           distances[j] = Math.sqrt(distances[j]);
 36 |         }
 37 |         
 38 |         //Sort points
 39 |         for(var j=0; j<4; ++j) {
 40 |           for(var k=0; k<j; ++k) {
 41 |             if(distances[j] < distances[k]) {
 42 |               var t0 = points[j];
 43 |               points[j] = points[k];
 44 |               points[k] = t0;
 45 |               
 46 |               var t1 = distances[j];
 47 |               distances[j] = distances[k];
 48 |               distances[k] = t1;
 49 |             }
 50 |           }
 51 |         }
 52 |         
 53 |         var d0 = distance.quadratic_distance(points[1], points[2], points[3], distances[1], distances[2], -1);
 54 |         var d1 = distance.quadratic_distance(points[1], points[2], points[3], distances[1], distances[2], 1);
 55 | 
 56 |         
 57 |         assert.ok(Math.abs(d0 - distances[3]) < 1e-6 || Math.abs(d1 - distances[3]) < 1e-6, "Incorrect distances: " + d0 + "," + d1 + ".\nPoints="+JSON.stringify(points)+"\nDistances= "+distances);
 58 |       }
 59 |     
 60 |     }
 61 |   },
 62 |   
 63 |   '5x5 grid': {
 64 |     topic: shapes.grid_mesh(5, 5),
 65 |     
 66 |     'testing all pairwise grid distances':  function(mesh) {
 67 |     
 68 |       //Testing pairwise distances
 69 |       for(var j=0; j<mesh.positions.length; ++j) {
 70 |         var p = mesh.positions[j];
 71 |         var distances = distance.geodesic_distance({
 72 |           positions:mesh.positions,
 73 |           faces: mesh.faces,
 74 |           initial_vertex: j
 75 |         });
 76 |         for(var i=0; i<mesh.positions.length; ++i) {
 77 |           var q = mesh.positions[i];
 78 |           var d = 0.0;
 79 |           for(var k=0; k<3; ++k) {
 80 |             d += Math.pow(p[k] - q[k], 2);
 81 |           }
 82 |           d = Math.sqrt(d);
 83 |           
 84 |           assert.ok(Math.abs(distances[i] - d) < 1e-4, "Incorrect distance from " + j + "->" + i + ". Expected: " + d + ", got: " + distances[i]);
 85 |         }
 86 |       }      
 87 |     },
 88 |     
 89 |     //This still doesn't quite work...
 90 |     'sphere': {
 91 |       topic: shapes.sphere_mesh(10, 1.0),
 92 |       
 93 |       'testing sphere pairwise distances': function(sphere) {
 94 |       
 95 |         for(var i=0; i<100; ++i) {
 96 |           var p_idx = Math.floor(Math.random() * sphere.positions.length);
 97 |           var distances = distance.geodesic_distance({
 98 |             positions: sphere.positions,
 99 |             faces: sphere.faces, 
100 |             initial_vertex: p_idx, 
101 |             max_distance: Math.PI/4.0
102 |           });
103 |           var p = sphere.positions[p_idx];
104 |           
105 |           for(var j in distances) {
106 |             if(distances[j] > Math.PI/4) {
107 |               continue;
108 |             }
109 |           
110 |             var q = sphere.positions[j];
111 |             var angle = 0.0;
112 |             for(var k=0; k<3; ++k) {
113 |               angle += p[k] * q[k];
114 |             }
115 |             angle = Math.min(1.0, Math.max(-1.0, angle));
116 |             angle = Math.acos(angle);
117 |             
118 |             assert.ok(Math.abs(distances[j] - angle) < 0.2, "Incorrect distance from " + i + "->" + j + ". Expected: " + angle + ", got: " + distances[j]);
119 |           }
120 |         }
121 |       
122 |       }
123 |     },
124 |   },
125 | }).run();
126 | 
127 | 
128 | 


--------------------------------------------------------------------------------
/tests/normals.js:
--------------------------------------------------------------------------------
 1 | var vows = require('vows');
 2 | var assert = require('assert');
 3 | var normals = require('../src/normals.js');
 4 | var vertex_normals = normals.vertex_normals;
 5 | var face_normals = normals.face_normals;
 6 | var shapes = require('../src/shapes.js');
 7 | 
 8 | 
 9 | vows.describe("surface normals").addBatch({
10 |   'normals' : {
11 |     topic: shapes.sphere_mesh(20, 1.0),
12 |     
13 |     'testing vertex normals': function(sphere) {
14 |     
15 |       var normals = vertex_normals(sphere);
16 |       
17 |       for(var i=0; i<normals.length; ++i) {
18 |         var n = normals[i];
19 |         var p = sphere.positions[i];
20 |         
21 |         var d = 0.0;
22 |         for(var j=0; j<3; ++j) {
23 |           d += Math.pow(n[j] - p[j], 2);
24 |         }
25 |         d = Math.sqrt(d);
26 |         
27 |         assert.ok(d < 5e-2, "Incorrect normal: " + JSON.stringify(n) + " vs. " + JSON.stringify(p) + ", err = " + d);
28 |       }      
29 |     },
30 |     
31 |     
32 |     'testing face normals': function(sphere) {
33 |     
34 |       var normals = face_normals(sphere);
35 |       
36 |       //TODO: Test these
37 |     },
38 |   },
39 | }).run();
40 | 
41 | 
42 | 


--------------------------------------------------------------------------------
/tests/repair.js:
--------------------------------------------------------------------------------
 1 | var vows = require('vows');
 2 | var assert = require('assert');
 3 | var repair = require('../src/repair.js');
 4 | 
 5 | vows.describe("repair.js").addBatch({
 6 |   'fuse_vertices' : {
 7 |     topic: {
 8 |       positions: [ 
 9 |         [0, 0, 0],
10 |         [0, 1, 0],
11 |         [1, 0, 0],
12 |         [0, 1.00001, 0],
13 |         [1.001, 0, 0],
14 |         [1, 1, 0] ],
15 |       faces: [ [0, 1, 2], [3, 4, 5] ]
16 |     },
17 |     
18 |     'fusing at tol = 0.01': function(mesh) {
19 |       var fused = repair.fuse_vertices({ 
20 |             positions:mesh.positions
21 |           , faces:mesh.faces
22 |           , tolerance:0.01 
23 |         });
24 |       
25 |       assert.ok(fused.positions.length === 4);
26 |       assert.ok(fused.faces.length === 2);
27 |       
28 |       for(var i=0; i<fused.faces.length; ++i) {
29 |         var f = fused.faces[i];
30 |         for(var j=0; j<f.length; ++j) {
31 |           assert.ok(0 <= f[j] && f[j] < fused.positions.length, "vertex out of bounds: " + f);
32 |         }
33 |       }
34 |     },
35 |     
36 |     'fusing at tol = 0.0001': function(mesh) {
37 |       var fused = repair.fuse_vertices({ 
38 |             positions:mesh.positions
39 |           , faces:mesh.faces
40 |           , tolerance:0.0001 
41 |         });
42 |       
43 |       assert.ok(fused.positions.length === 5);
44 |       assert.ok(fused.faces.length === 2);
45 |       
46 |       for(var i=0; i<fused.faces.length; ++i) {
47 |         var f = fused.faces[i];
48 |         for(var j=0; j<f.length; ++j) {
49 |           assert.ok(0 <= f[j] && f[j] < fused.positions.length, "vertex out of bounds: " + f);
50 |         }
51 |       }
52 |     },
53 | 
54 |     'fusing at tol = 0.000001': function(mesh) {
55 |       var fused = repair.fuse_vertices({ 
56 |             positions:mesh.positions
57 |           , faces:mesh.faces
58 |           , tolerance:0.000001 
59 |         });
60 |       
61 |       assert.ok(fused.positions.length === 6);
62 |       assert.ok(fused.faces.length === 2);
63 |       
64 |       for(var i=0; i<fused.faces.length; ++i) {
65 |         var f = fused.faces[i];
66 |         for(var j=0; j<f.length; ++j) {
67 |           assert.ok(0 <= f[j] && f[j] < fused.positions.length, "vertex out of bounds: " + f);
68 |         }
69 |       }
70 |     },
71 |     
72 |     
73 |     'fusing at tol = 2.0': function(mesh) {
74 |       var fused = repair.fuse_vertices({ 
75 |             positions: mesh.positions
76 |           , faces: mesh.faces
77 |           , tolerance: 2.0
78 |         });
79 |               
80 |       assert.ok(fused.positions.length === 1);
81 |       assert.ok(fused.faces.length === 0);
82 |       
83 |       for(var i=0; i<fused.faces.length; ++i) {
84 |         var f = fused.faces[i];
85 |         for(var j=0; j<f.length; ++j) {
86 |           assert.ok(0 <= f[j] && f[j] < fused.positions.length, "vertex out of bounds: " + f);
87 |         }
88 |       }
89 |     },
90 |   }
91 | }).run();
92 | 
93 | 


--------------------------------------------------------------------------------
/tests/subdivision.js:
--------------------------------------------------------------------------------
 1 | var vows = require('vows');
 2 | var assert = require('assert');
 3 | var loop_subdivision = require('../src/loop_subdivision.js').loop_subdivision;
 4 | var shapes = require('../src/shapes.js');
 5 | 
 6 | 
 7 | vows.describe('subdivision.js').addBatch({
 8 |   'loop_subdivision' : {
 9 |     topic: shapes.grid_mesh(5,5),
10 |     'subdivide': function(mesh) {
11 |       var subdiv = loop_subdivision(mesh);
12 |       assert.ok(subdiv.faces.length === 4*mesh.faces.length);
13 |     },
14 |     
15 |     'triangle': function() {
16 |       var positions = [[1, 0, 0], [0, 1, 0], [0, 0, 1]];
17 |       var faces    = [[0,1,2]];
18 |       
19 |       var mesh = { positions: positions, faces: faces };
20 |       for(var i=0; i<2; ++i) {
21 |         mesh = loop_subdivision(mesh);
22 |         console.log(mesh);
23 |       }
24 |     }
25 |   }
26 | }).run();
27 | 


--------------------------------------------------------------------------------
/tests/topology.js:
--------------------------------------------------------------------------------
 1 | var vows = require('vows');
 2 | var assert = require('assert');
 3 | var topology = require('../src/topology.js');
 4 | var shapes = require('../src/shapes.js');
 5 | 
 6 | 
 7 | vows.describe("topology.js").addBatch({
 8 |   'vertex_stars' : {
 9 |     topic: shapes.grid_mesh(5, 5),
10 |     
11 |     'computing star' : function(mesh) {
12 |       var stars = topology.vertex_stars({
13 |             vertex_count: mesh.positions.length
14 |           , faces:        mesh.faces 
15 |         });
16 |       for(var i=0; i<stars.length; ++i) {
17 |         var s = stars[i];
18 |         for(var j=0; j<s.length; ++j) {
19 |           assert.ok(mesh.faces[s[j]].indexOf(i) >= 0, 'Invalid face in star #' + i + ", face=" + mesh.faces[s[j]] + ", star= " + stars[i]);
20 |         }
21 |       }
22 |     },
23 |   }
24 | }).run();
25 | 
26 | 
27 | 


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