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.
$ npm install bezier-spline
To create a spline, pass in knots. For
n-1 curves will be produced.
const BezierSpline =let spline =1 30 45 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 = splinecurves0bezier00 // The first knotbezier01 // The first generated control pointbezier02 // The second generated control pointbezier03 // The second knotconsole // [ 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:
x = 0.5:
spline04999999999999999 343825160747210905000000000000002 473728665361036
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.
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 easylet curve =0 01 12 23 3curve15 15
And inversely, you can solve for the
t values that correspond to particular values along an axis: