b-spline/test/index.js

B-spline interpolation

var interpolate = require('../index');
var tvalues = [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0];
var degree = 2;

/**
 * epsilon-based numerical equivalence for two points
 */
function equivalent(found, target, e) {
  e = e || 0.001;
  return !found.some(function(v,idx) {
    return Math.abs(v-target[idx]) > e;
  });
}

/**
 * verify that a particular full curve description matches the result of interpolate()
 */
function verify(description, tvalues, points, expected, degree, knots, weights) {
  degree = degree || 2;
  var errors = [];
  tvalues.map(function(t) {
    return interpolate(t, degree, points, knots, weights);
  }).forEach(function(v,idx) {
    var t = expected[idx];
    if (!equivalent(v, t)) {
      errors.push([
        'Sample',
        idx,
        'did not yield the expected result.',
        v,
        'not equal to',
        t
      ].join(' '));
    }
  });
  console.log(description + ": " + (errors.length>0 ? 'failed' : 'passed'));
  if (errors.length > 0) { 
    console.error(errors);
    process.exit(1);
  }
}

// test uniform curve
var points = [
  [-1.0,  0.0],
  [-0.5,  0.5],
  [ 0.5, -0.5],
  [ 1.0,  0.0]
];
var expected = [
  [ -0.75,  0.25 ],
  [ -0.64,  0.32 ],
  [ -0.51,  0.33 ],
  [ -0.36,  0.28 ],
  [ -0.19,  0.17 ],
  [  0   ,  0    ],
  [  0.19, -0.17 ],
  [  0.36, -0.28 ],
  [  0.51, -0.33 ],
  [  0.64, -0.32 ],
  [  0.75, -0.25 ]
];
verify("uniform b-spline test", tvalues, points, expected);


// test non-uniform curve
var knots = [0, 0, 0, 1, 2, 2, 2];
expected = [
  [ -1  ,  0    ],
  [ -0.8,  0.16 ],
  [ -0.6,  0.24 ],
  [ -0.4,  0.24 ],
  [ -0.2,  0.16 ],
  [  0  ,  0    ],
  [  0.2, -0.16 ],
  [  0.4, -0.24 ],
  [  0.6, -0.24 ],
  [  0.8, -0.16 ],
  [  1  ,  0    ]
];
verify("non-uniform b-spline test", tvalues, points, expected, degree, knots);


// test closed non-uniform curvce
points = [
  [-1.0,  0.0],
  [-0.5,  0.5],
  [ 0.5, -0.5],
  [ 1.0,  0.0],
  // ...
  [-1.0,  0.0],
  [-0.5,  0.5],
  [ 0.5, -0.5]
];
knots = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9];
expected = [
  [ -0.75  ,  0.25   ],
  [ -0.4375,  0.3125 ],
  [  0     ,  0      ],
  [  0.4375, -0.3125 ],
  [  0.75  , -0.25   ],
  [  0.6875, -0.0625 ],
  [  0     ,  0      ],
  [ -0.6875,  0.0625 ],
  [ -0.75  ,  0.25   ],
  [ -0.4375,  0.3125 ],
  [  0     ,  0      ]
];
verify("closed non-uniform b-spline test", tvalues, points, expected, degree, knots);


// test non-uniform rational curve
points = [
  [ 0.0, -0.5],
  [-0.5, -0.5],
  [-0.5,  0.0],
  [-0.5,  0.5],
  [ 0.0,  0.5],
  [ 0.5,  0.5],
  [ 0.5,  0.0],
  [ 0.5, -0.5],
  // duplicated first point
  [ 0.0, -0.5]
]
knots = [0, 0, 0, 1/4, 1/4, 1/2, 1/2, 3/4, 3/4, 1, 1, 1];
var w = Math.pow(0.5, 0.5);
var weights = [1, w, 1, w, 1, w, 1, w, 1];
expected = [
  [  0     , -0.5    ],
  [ -0.29  , -0.4069 ],
  [ -0.4779, -0.1469 ],
  [ -0.4779,  0.1469 ],
  [ -0.29  ,  0.4069 ],
  [  0     ,  0.5    ],
  [  0.29  ,  0.4069 ],
  [  0.4779,  0.1469 ],
  [  0.4779, -0.1469 ],
  [  0.29  , -0.4069 ],
  [  0     , -0.5    ]
];
verify("non-uniform rational b-spline test", tvalues, points, expected, degree, knots, weights);

// test non-uniform rational curve with boosted weights
var boosted = 4 * w;
var weights = [1, boosted, 1, boosted, 1, boosted, 1, boosted, 1];
expected = [
  [  0     , -0.5    ],
  [ -0.4041, -0.4574 ],
  [ -0.4874, -0.2981 ],
  [ -0.4874,  0.2981 ],
  [ -0.4041,  0.4574 ],
  [       0,  0.5    ],
  [  0.4041,  0.4574 ],
  [  0.4874,  0.2981 ],
  [  0.4874, -0.2981 ],
  [  0.4041, -0.4574 ],
  [       0, -0.5    ]
];

verify("weight-boosted non-uniform rational b-spline test", tvalues, points, expected, degree, knots, weights);