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b-spline

b-spline

B-spline interpolation

B-spline interpolation of control points of any dimensionality using de Boor's algorithm.

The interpolator can take an optional weight vector, making the resulting curve a Non-Uniform Rational B-Spline (NURBS) curve if you wish so.

The knot vector is optional too, and when not provided an unclamped uniform knot vector will be generated internally.

Install

$ npm install b-spline

Examples

Unclamped knot vector

var bspline = require('b-spline');
 
var points = [
  [-1.0,  0.0],
  [-0.5,  0.5],
  [ 0.5, -0.5],
  [ 1.0,  0.0]
];
 
var degree = 2;
 
// As we don't provide a knot vector, one will be generated  
// internally and have the following form : 
// 
// var knots = [0, 1, 2, 3, 4, 5, 6]; 
// 
// Knot vectors must have `number of points + degree + 1` knots. 
// Here we have 4 points and the degree is 2, so the knot vector  
// length will be 7. 
// 
// This knot vector is called "uniform" as the knots are all spaced uniformly, 
// ie. the knot spans are all equal (here 1). 
 
for(var t=0; t<1; t+=0.01) {
  var point = bspline(t, degree, points);
}

Clamped knot vector

var bspline = require('b-spline');
 
var points = [
  [-1.0,  0.0],
  [-0.5,  0.5],
  [ 0.5, -0.5],
  [ 1.0,  0.0]
];
 
var degree = 2;
 
// B-splines with clamped knot vectors pass through  
// the two end control points. 
// 
// A clamped knot vector must have `degree + 1` equal knots  
// at both its beginning and end. 
 
var knots = [
  0, 0, 0, 1, 2, 2, 2
];
 
for(var t=0; t<1; t+=0.01) {
  var point = bspline(t, degree, points, knots);
}

Closed curves

var bspline = require('b-spline');
 
// Closed curves are built by repeating the `degree + 1` first  
// control points at the end of the curve 
 
var 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]
];
 
var degree = 2;
 
// and using an unclamped knot vector 
 
var knots = [
  0, 1, 2, 3, 4, 5, 6, 7, 8, 9
];
 
for(var t=0; t<1; t+=0.01) {
  var point = bspline(t, degree, points, knots);
}

Non-uniform rational

var bspline = require('b-spline');
 
var 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],
  [ 0.0, -0.5]  // P0 
]
 
// Here the curve is called non-uniform as the knots  
// are not equally spaced 
 
var knots = [
  0, 0, 0, 1/4, 1/4, 1/2, 1/2, 3/4, 3/4, 1, 1, 1
];
 
var w = Math.pow(2, 0.5) / 2;
 
// and rational as its control points have varying weights 
 
var weights = [
  1, w, 1, w, 1, w, 1, w, 1
]
 
var degree = 2;
 
for(var t=0; t<1; t+=0.01) {
  var point = bspline(t, degree, points, knots, weights);
}

Usage

bspline(t, degree, points[, knots, weights])

  • t position along the curve in the [0, 1] range
  • degree degree of the curve. Must be less than or equal to the number of control points minus 1. 1 is linear, 2 is quadratic, 3 is cubic, and so on.
  • points control points that will be interpolated. Can be vectors of any dimensionality ([x, y], [x, y, z], ...)
  • knots optional knot vector. Allow to modulate the control points interpolation spans on t. Must be a non-decreasing sequence of number of points + degree + 1 length values.
  • weights optional control points weights. Must be the same length as the control point array.