# Curves

A **curve** defines how to turn a discrete representation of a line as a sequence of points [[*x₀*, *y₀*], [*x₁*, *y₁*], [*x₂*, *y₂*], …] into a continuous path; *i.e.*, how to interpolate between points. Curves are used by the line, area, and link marks, and are implemented by d3-shape.

```
Plot.plot({
marks: [
Plot.lineY(numbers, {curve: "catmull-rom"}),
Plot.dotY(numbers, {x: (d, i) => i})
]
})
```

The supported curve options are:

**curve**- the curve method, either a string or a function**tension**- the curve tension (for fine-tuning)

The following named curve methods are supported:

*basis*- a cubic basis spline (repeating the end points)*basis-open*- an open cubic basis spline*basis-closed*- a closed cubic basis spline*bump-x*- a Bézier curve with horizontal tangents*bump-y*- a Bézier curve with vertical tangents*bundle*- a straightened cubic basis spline (suitable for lines only, not areas)*cardinal*- a cubic cardinal spline (with one-sided differences at the ends)*cardinal-open*- an open cubic cardinal spline*cardinal-closed*- an closed cubic cardinal spline*catmull-rom*- a cubic Catmull–Rom spline (with one-sided differences at the ends)*catmull-rom-open*- an open cubic Catmull–Rom spline*catmull-rom-closed*- a closed cubic Catmull–Rom spline*linear*- a piecewise linear curve (*i.e.*, straight line segments)*linear-closed*- a closed piecewise linear curve (*i.e.*, straight line segments)*monotone-x*- a cubic spline that preserves monotonicity in*x**monotone-y*- a cubic spline that preserves monotonicity in*y**natural*- a natural cubic spline*step*- a piecewise constant function where*y*changes at the midpoint of*x**step-after*- a piecewise constant function where*y*changes after*x**step-before*- a piecewise constant function where*x*changes after*y**auto*- like*linear*, but use the (possibly spherical) projection, if any ^0.6.1

If **curve** is a function, it will be invoked with a given *context* in the same fashion as a D3 curve factory. The *auto* curve is only available for the line mark and link mark and is typically used in conjunction with a spherical projection to interpolate along geodesics.

The tension option only has an effect on bundle, cardinal and Catmull–Rom splines (*bundle*, *cardinal*, *cardinal-open*, *cardinal-closed*, *catmull-rom*, *catmull-rom-open*, and *catmull-rom-closed*). For bundle splines, it corresponds to beta; for cardinal splines, tension; for Catmull–Rom splines, alpha.