# Value interpolation

These are the most general interpolators, suitable for most values.

## interpolate(*a*, *b*)

Examples · Source · Returns an interpolator between the two arbitrary values *a* and *b*.

`d3.interpolate("red", "blue")(0.5) // "rgb(128, 0, 128)"`

The interpolator implementation is based on the type of the end value *b*, using the following algorithm:

- If
*b*is null, undefined or a boolean, use the constant*b*. - If
*b*is a number, use interpolateNumber. - If
*b*is a color or a string coercible to a color, use interpolateRgb. - If
*b*is a date, use interpolateDate. - If
*b*is a string, use interpolateString. - If
*b*is a typed array of numbers, use interpolateNumberArray. - If
*b*is a generic array, use interpolateArray. - If
*b*is coercible to a number, use interpolateNumber. - Use interpolateObject.

Based on the chosen interpolator, *a* is coerced to the suitable corresponding type.

## interpolateNumber(*a*, *b*)

Examples · Source · Returns an interpolator between the two numbers *a* and *b*.

`d3.interpolateNumber(20, 620)(0.8) // 500`

The returned interpolator is equivalent to:

```
function interpolator(t) {
return a * (1 - t) + b * t;
}
```

CAUTION

Avoid interpolating to or from the number zero when the interpolator is used to generate a string. When very small values are stringified, they may be converted to scientific notation, which is an invalid attribute or style property value in older browsers. For example, the number `0.0000001`

is converted to the string `"1e-7"`

. This is particularly noticeable with interpolating opacity. To avoid scientific notation, start or end the transition at 1e-6: the smallest value that is not stringified in scientific notation.

## interpolateRound(*a*, *b*)

Examples · Source · Returns an interpolator between the two numbers *a* and *b*.

`d3.interpolateNumber(20, 620)(0.821) // 513`

The interpolator is similar to interpolateNumber except it will round the resulting value to the nearest integer.

## interpolateString(*a*, *b*)

Examples · Source · Returns an interpolator between the two strings *a* and *b*.

`d3.interpolateString("20px", "32px")(0.5) // "26px"`

The string interpolator finds numbers embedded in *a* and *b*, where each number is of the form understood by JavaScript. A few examples of numbers that will be detected within a string: `-1`

, `42`

, `3.14159`

, and `6.0221413e+23`

.

For each number embedded in *b*, the interpolator will attempt to find a corresponding number in *a*. If a corresponding number is found, a numeric interpolator is created using interpolateNumber. The remaining parts of the string *b* are used as a template: the static parts of the string *b* remain constant for the interpolation, with the interpolated numeric values embedded in the template.

For example, if *a* is `"300 12px sans-serif"`

, and *b* is `"500 36px Comic-Sans"`

, two embedded numbers are found. The remaining static parts (of string *b*) are a space between the two numbers (`" "`

), and the suffix (`"px Comic-Sans"`

). The result of the interpolator at *t* = 0.5 is `"400 24px Comic-Sans"`

.

## interpolateDate(*a*, *b*)

Examples · Source · Returns an interpolator between the two dates *a* and *b*.

`d3.interpolateDate(new Date("2014-01-01"), new Date("2024-01-01"))(0.5) // 2019-01-01`

CAUTION

**No defensive copy** of the returned date is created; the same Date instance is returned for every evaluation of the interpolator. No copy is made for performance reasons, as interpolators are often part of the inner loop of animated transitions.

## interpolateArray(*a*, *b*)

Examples · Source · Returns an interpolator between the two arrays *a* and *b*.

`d3.interpolateArray([0, 0, 0], [1, 2, 3])(0.5) // [0.5, 1, 1.5]`

If *b* is a typed array (e.g., Float64Array), interpolateNumberArray is called instead.

Internally, an array template is created that is the same length as *b*. For each element in *b*, if there exists a corresponding element in *a*, a generic interpolator is created for the two elements using interpolate. If there is no such element, the static value from *b* is used in the template. Then, for the given parameter *t*, the template’s embedded interpolators are evaluated. The updated array template is then returned.

For example, if *a* is the array `[0, 1]`

and *b* is the array `[1, 10, 100]`

, then the result of the interpolator for *t* = 0.5 is the array `[0.5, 5.5, 100]`

.

CAUTION

**No defensive copy** of the template array is created; modifications of the returned array may adversely affect subsequent evaluation of the interpolator. No copy is made for performance reasons; interpolators are often part of the inner loop of animated transitions.

## interpolateNumberArray(*a*, *b*)

Examples · Source · Returns an interpolator between the two arrays of numbers *a* and *b*.

`d3.interpolateNumberArray([0, 1], Float64Array.of(1, 3))(0.5) // [0.5, 2]`

Internally, an array template is created that is the same type and length as *b*. For each element in *b*, if there exists a corresponding element in *a*, the values are directly interpolated in the array template. If there is no such element, the static value from *b* is copied. The updated array template is then returned.

CAUTION

**No defensive copy** is made of the template array and the arguments *a* and *b*; modifications of these arrays may affect subsequent evaluation of the interpolator.

## interpolateObject(*a*, *b*)

Examples · Source · Returns an interpolator between the two objects *a* and *b*.

`d3.interpolateObject({x: 0, y: 1}, {x: 1, y: 10, z: 100})(0.5) // {x: 0.5, y: 5.5, z: 100}`

Internally, an object template is created that has the same properties as *b*. For each property in *b*, if there exists a corresponding property in *a*, a generic interpolator is created for the two elements using interpolate. If there is no such property, the static value from *b* is used in the template. Then, for the given parameter *t*, the template's embedded interpolators are evaluated and the updated object template is then returned.

For example, if *a* is the object `{x: 0, y: 1}`

and *b* is the object `{x: 1, y: 10, z: 100}`

, the result of the interpolator for *t* = 0.5 is the object `{x: 0.5, y: 5.5, z: 100}`

.

Object interpolation is particularly useful for *dataspace interpolation*, where data is interpolated rather than attribute values. For example, you can interpolate an object which describes an arc in a pie chart, and then use arc to compute the new SVG path data.

CAUTION

**No defensive copy** of the template object is created; modifications of the returned object may adversely affect subsequent evaluation of the interpolator. No copy is made for performance reasons; interpolators are often part of the inner loop of animated transitions.

## interpolateBasis(*values*)

Examples · Source · Returns a uniform nonrational B-spline interpolator through the specified array of *values*, which must be numbers.

`d3.interpolateBasis([0, 0.1, 0.4, 1])(0.5) // 0.2604166666666667`

Implicit control points are generated such that the interpolator returns *values*[0] at *t* = 0 and *values*[*values*.length - 1] at *t* = 1. See also curveBasis and interpolateRgbBasis.

## interpolateBasisClosed(*values*)

Examples · Source · Returns a uniform nonrational B-spline interpolator through the specified array of *values*, which must be numbers.

`d3.interpolateBasisClosed([0, 0.1, 0.4, 1])(0.5) // 0.45`

The control points are implicitly repeated such that the resulting one-dimensional spline has cyclical C² continuity when repeated around *t* in [0,1]. See also curveBasisClosed and interpolateRgbBasisClosed.

## interpolateDiscrete(*values*)

Examples · Source · Returns a discrete interpolator for the given array of *values*.

`d3.interpolateDiscrete(["red", "blue", "green"])(0.5) // "blue"`

The returned interpolator maps *t* in [0, 1 / *n*) to *values*[0], *t* in [1 / *n*, 2 / *n*) to *values*[1], and so on, where *n* = *values*.length. In effect, this is a lightweight quantize scale with a fixed domain of [0, 1].

## quantize(*interpolator*, *n*)

Examples · Source · Returns *n* uniformly-spaced samples from the specified *interpolator*, where *n* is an integer greater than one.

`d3.quantize(d3.interpolate("red", "blue"), 4) // ["rgb(255, 0, 0)", "rgb(170, 0, 85)", "rgb(85, 0, 170)", "rgb(0, 0, 255)"]`

The first sample is always at *t* = 0, and the last sample is always at *t* = 1. This can be useful in generating a fixed number of samples from a given interpolator, such as to derive the range of a quantize scale from a continuous interpolator.

CAUTION

This method will not work with interpolators that do not return defensive copies of their output, such as interpolateArray, interpolateDate and interpolateObject. For those interpolators, you must wrap the interpolator and create a copy for each returned value.

## piecewise(*interpolate*, *values*)

Examples · Source · Returns a piecewise interpolator, composing interpolators for each adjacent pair of *values*.

`d3.piecewise(d3.interpolateRgb.gamma(2.2), ["red", "green", "blue"])`

If *interpolate* is not specified, defaults to interpolate.

`d3.piecewise(["red", "green", "blue"])`

The returned interpolator maps *t* in [0, 1 / (*n* - 1)] to *interpolate*(*values*[0], *values*[1]), *t* in [1 / (*n* - 1), 2 / (*n* - 1)] to *interpolate*(*values*[1], *values*[2]), and so on, where *n* = *values*.length. In effect, this is a lightweight linear scale.