bezier-spline

Creates splines from cubic bezier curves.

This module fits a spline to a set of knots. The curves used are cubic Bezier curves, and the spline is G2 continuous, as this is intended primarily for graphics. C2 continuous splines are a simplification, and may come as an option in future versions.

The theory behind the spline is not documented in the code, as it is too lengthy. Instead, the source code repository contains a .tex file in the theory directory that can be compiled to an explanatory document.

Install

$ npm install bezier-spline

Usage

To create a spline, pass in knots. For n knots, n-1 curves will be produced.

const BezierSpline = require('bezier-spline')

let spline = new BezierSpline([
    [1, 3],
    [0, 4],
    [5, 5]
])

You can access the control points of each curve with the curves property. Curves are array-like with 4 elements, which are control points.

let bezier0 = spline.curves[0]
bezier0[0]                // The first knot
bezier0[1]                // The first generated control point
bezier0[2]                // The second generated control point
bezier0[3]                // The second knot

console.log(bezier0[0])   // [ 1, 3 ]

These points can then be fed to an api that understands cubic Bezier curves.

A large part of the point of this module is to be able to locate points on the spline by coordinate. For example, if we want to find where the spline above passes through y = 3.14:

spline.getPoints(1, 3.14)
[ [ 0.8369150530498445, 3.1399999999999997 ] ]

Or where x = 0.5:

spline.getPoints(0, 0.5)
[ [ 0.4999999999999999, 3.438251607472109 ],
  [ 0.5000000000000002, 4.73728665361036 ] ]

Notably, the results are not exact. We're dealing with lots of floating point addition and inverting functions twice, so this is expected. These splines are not designed for precise mathematics.

Bezier Curves

Individual curves can be solved similarly if necessary. at plugs in a clamped t value to the cubic Bezier equation.

// Yeah, it's not a very curvy curve, but it makes the math easy
let curve = new BezierSpline.BezierCurve([
    [0, 0],
    [1, 1],
    [2, 2],
    [3, 3]
])

curve.at(0.5)
[ 1.5, 1.5 ]

And inversely, you can solve for the t values that correspond to particular values along an axis:

curve.solve(0, 1.5)
[ 0.5 ]