├── .gitignore
├── LICENSE
├── README.md
├── index.js
└── package.json


/.gitignore:
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1 | test*
2 | 


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/LICENSE:
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 1 | The MIT License (MIT)
 2 | 
 3 | Copyright (c) 2015 Thibaut Séguy <thibaut.seguy@gmail.com>
 4 | 
 5 | Permission is hereby granted, free of charge, to any person obtaining a copy
 6 | of this software and associated documentation files (the "Software"), to deal
 7 | in the Software without restriction, including without limitation the rights
 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 | 
12 | The above copyright notice and this permission notice shall be included in
13 | all copies or substantial portions of the Software.
14 | 
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
21 | THE SOFTWARE.


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/README.md:
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 1 | cubic-hermite-spline
 2 | ====================
 3 | ### Cubic Hermite spline interpolation
 4 | 
 5 | [Cubic Hermite spline](http://en.wikipedia.org/wiki/Cubic_Hermite_spline) interpolation of points / tangents in any dimension with optional derivative computation. The interpolator can also take a knot-like vector as an optional parameter, which may be useful to enforce time at control points when used for position / velocity interpolation.
 6 | 
 7 | 
 8 | Install
 9 | -------
10 | 
11 | ```bash
12 | $ npm install cubic-hermite-spline
13 | ```
14 | 
15 | Example
16 | -------
17 | 
18 | Basic usage
19 | 
20 | ```javascript
21 | var hermite = require('cubic-hermite-spline');
22 | 
23 | var points = [
24 |   [-1, 0],
25 |   [ 0, 0],
26 |   [ 1, 0]
27 | ];
28 | 
29 | var tangents = [
30 |   [1, 1],
31 |   [0, 1],
32 |   [1, 1]
33 | ];
34 | 
35 | for(var t=0; t<1; t+=0.01) {
36 |   var point = hermite(t, points, tangents);
37 |   var tangent = hermite(t, points, tangents, null, true);
38 | }
39 | ```
40 | 
41 | <img src="http://i.imgur.com/vqyUHxF.png" />
42 | 
43 | 
44 | With a knot vector
45 | 
46 | ```javascript
47 | var hermite = require('cubic-hermite-spline');
48 | 
49 | var points = [
50 |   [-1, 0],
51 |   [ 0, 0],
52 |   [ 1, 0]
53 | ];
54 | 
55 | var tangents = [
56 |   [1, 1],
57 |   [0, 1],
58 |   [1, 1]
59 | ];
60 | 
61 | var knots = [
62 |   0, 1.5, 2
63 | ];
64 | 
65 | for(var t=0; t<1; t+=0.01) {
66 |   var point = hermite(t, points, tangents);
67 |   var tangent = hermite(t, points, tangents, knots, true);
68 | }
69 | ```
70 | 
71 | <img src="http://i.imgur.com/v5FRZNT.png" />
72 | 
73 | 
74 | Usage
75 | -----
76 | 
77 | ### `hermite(t, points, tangents[, knots, derivative, result])`
78 | 
79 | Computes the interpolation at `t` for the provided set of points and tangents, and optional knots.
80 | 
81 | * `t` position along the curve: in the [0, 1] range for regular use, and [0, last-knot-value] when using knots
82 | * `points` vectors to interpolate
83 | * `tangents` tangents at provided points
84 | * `knots` enforced values of `t` at provided points
85 | * `derivative` if true return the tangeant at `t` instead of the position
86 | * `result` preallocated array in which the result will be stored (to avoid garbage collection)
87 | 
88 | **Returns** the interpolated vector
89 | 


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/index.js:
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 1 | 
 2 | 
 3 | function interpolate(t, points, tangents, knots, derivative, result) {
 4 | 
 5 |   var n = points.length;    // number or points / tangents / knots
 6 |   var d = points[0].length; // vector dimensionality
 7 |   var v = result || new Array(d); // destination vector
 8 | 
 9 |   if(knots) {
10 |     // find knot interval for t
11 |     for(var i=0; i<n-1; i++) {
12 |       if(t >= knots[i] && t <= knots[i+1]) {
13 |         break;
14 |       }
15 |     }
16 | 
17 |     if(i === n-1) throw new Error('out of bounds');
18 | 
19 |     var i0 = i;
20 |     var i1 = i + 1;
21 |     var k0 = knots[i0];
22 |     var k1 = knots[i1];
23 |     var scale = k1 - k0;
24 | 
25 |     t = (t - k0) / scale;
26 | 
27 |   } else {
28 | 
29 |     var t = t * (n - 1); // rescale t to [0, n-1]
30 |     var i0 = t|0;        // truncate
31 |     var i1 = i0 + 1;
32 | 
33 |     if(i0 > n-1) throw new Error('out of bounds');
34 |     if(i0 === n-1) i1 = i0;
35 | 
36 |     var scale = i1 - i0;
37 | 
38 |     t = (t - i0) / scale;
39 |   }
40 | 
41 |   if(derivative) {
42 |     var t2 = t * t;
43 |     var h00 = 6 * t2 - 6 * t;
44 |     var h10 = 3 * t2 - 4 * t + 1;
45 |     var h01 = - 6 * t2 + 6 * t;
46 |     var h11 = 3 * t2 - 2 * t;
47 |   } else {
48 |     var t2 = t * t;
49 |     var it = 1 - t;
50 |     var it2 = it * it;
51 |     var tt = 2 * t;
52 |     var h00 = (1 + tt) * it2;
53 |     var h10 = t * it2;
54 |     var h01 = t2 * (3 - tt);
55 |     var h11 = t2 * (t - 1);
56 |   }
57 | 
58 |   for(var i=0; i<d; i++) {
59 |     v[i] = h00 * points[i0][i] + 
60 |            h10 * tangents[i0][i] * scale +
61 |            h01 * points[i1][i] +
62 |            h11 * tangents[i1][i] * scale;
63 |   }
64 | 
65 |   return v;
66 | }
67 | 
68 | 
69 | module.exports = interpolate;


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/package.json:
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 1 | {
 2 |   "name": "cubic-hermite-spline",
 3 |   "version": "1.0.1",
 4 |   "description": "Cubic Hermite spline interpolation",
 5 |   "main": "index.js",
 6 |   "scripts": {
 7 |     "test": "echo \"Error: no test specified\" && exit 1"
 8 |   },
 9 |   "author": "thibauts",
10 |   "license": "MIT",
11 |   "repository": {
12 |     "type": "git",
13 |     "url": "git://github.com/thibauts/cubic-hermite-spline.git"
14 |   },
15 |   "keywords": [
16 |     "cubic",
17 |     "hermite",
18 |     "spline",
19 |     "interpolation"
20 |   ]
21 | }
22 | 


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