---
title: "Phaser.Math.Interpolation"
docs: "Phaser v4.1.0"
url: https://phaser.io/oss/docs/api-documentation/namespace/math-interpolation
site: Phaser - https://phaser.io
---

> This page is about the open-source Phaser framework, for writing a game's code by hand. To make a game with AI, use Phaser AE (https://phaser.io/): the desk's tools work with Web MCP, and the CLI works with your own coding agent. See "For AI agents: Phaser AE" at the end of this page.

# Phaser.Math.Interpolation

Scope: 
static
> Source: [src/math/interpolation/index.js#L7](https://github.com/phaserjs/phaser/blob/v4.1.0/src/math/interpolation/index.js#L7)  


## Static functions

### Bezier

#### \<static> Bezier(v, k)


**Description:**

Performs a generalized Bezier interpolation over an arbitrary number of control points. The `v` array provides the control point values and `k` (0 to 1) determines the position along the curve. Unlike CubicBezierInterpolation which uses exactly 4 points, this supports any number.

**Parameters:**
| name | type | optional | description |
| ---- | ---- | -------- | ----------- |
| v | Array.\<number> | No | The input array of values to interpolate between. |
| k | number | No | The percentage of interpolation, between 0 and 1. |


**Returns:** number - The interpolated value.


> Source: [src/math/interpolation/BezierInterpolation.js#L9](https://github.com/phaserjs/phaser/blob/v4.1.0/src/math/interpolation/BezierInterpolation.js#L9)  
Since: 3.0.0


---

### CatmullRom

#### \<static> CatmullRom(v, k)


**Description:**

Performs a Catmull-Rom spline interpolation over an array of values, producing a smooth curve that passes through every control point. The `k` parameter (0 to 1) determines the position along the full curve.

If the first and last values in `v` are equal, the curve is treated as closed (looping), and the interpolation wraps around seamlessly. Otherwise, the curve is treated as open, and values of `k` outside the 0 to 1 range will extrapolate beyond the endpoints.

**Parameters:**
| name | type | optional | description |
| ---- | ---- | -------- | ----------- |
| v | Array.\<number> | No | The input array of control point values to interpolate between. |
| k | number | No | The percentage of interpolation, between 0 and 1. Values outside this range extrapolate on an open curve, or wrap on a closed curve. |


**Returns:** number - The interpolated value.


> Source: [src/math/interpolation/CatmullRomInterpolation.js#L9](https://github.com/phaserjs/phaser/blob/v4.1.0/src/math/interpolation/CatmullRomInterpolation.js#L9)  
Since: 3.0.0


---

### CubicBezier

#### \<static> CubicBezier(t, p0, p1, p2, p3)


**Description:**

Calculates a cubic bezier interpolated value for a given parameter `t`, based on four control points. The curve passes through `p0` at `t=0` and `p3` at `t=1`, while `p1` and `p2` act as pull points that shape the curve between those endpoints without necessarily being on it. This makes cubic bezier interpolation well-suited for smooth, art-directed transitions in animations, camera paths, and procedural movement.

[https://medium.com/@adrian_cooney/bezier-interpolation-13b68563313a](https://medium.com/@adrian_cooney/bezier-interpolation-13b68563313a)

**Parameters:**
| name | type | optional | description |
| ---- | ---- | -------- | ----------- |
| t | number | No | The percentage of interpolation, between 0 and 1. |
| p0 | number | No | The start point. |
| p1 | number | No | The first control point. |
| p2 | number | No | The second control point. |
| p3 | number | No | The end point. |


**Returns:** number - The interpolated value.


> Source: [src/math/interpolation/CubicBezierInterpolation.js#L43](https://github.com/phaserjs/phaser/blob/v4.1.0/src/math/interpolation/CubicBezierInterpolation.js#L43)  
Since: 3.0.0


---

### Linear

#### \<static> Linear(v, k)


**Description:**

Performs linear interpolation across an array of values.

Given an array of values `v` and a progress factor `k` in the range 0 to 1, this function maps `k` to a position along the array and returns the linearly interpolated value between the two nearest array elements. A `k` of 0 returns a value near the first element, while a `k` of 1 returns a value near the last. Values of `k` outside the range 0 to 1 are extrapolated beyond the ends of the array.

**Parameters:**
| name | type | optional | description |
| ---- | ---- | -------- | ----------- |
| v | Array.\<number> | No | The input array of values to interpolate between. |
| k | number | No | The percentage of interpolation, between 0 and 1. |


**Returns:** number - The interpolated value.


> Source: [src/math/interpolation/LinearInterpolation.js#L9](https://github.com/phaserjs/phaser/blob/v4.1.0/src/math/interpolation/LinearInterpolation.js#L9)  
Since: 3.0.0


---

### QuadraticBezier

#### \<static> QuadraticBezier(t, p0, p1, p2)


**Description:**

Calculates a single point along a quadratic Bezier curve defined by a start point, a control point, and an end point. The value of `t` determines how far along the curve the returned value sits: 0 returns the start point value, 1 returns the end point value, and values in between are smoothly interpolated. The control point pulls the curve toward it, shaping the arc between the start and end points without the curve passing through it directly.

**Parameters:**
| name | type | optional | description |
| ---- | ---- | -------- | ----------- |
| t | number | No | The interpolation position along the curve, between 0 (start) and 1 (end). |
| p0 | number | No | The start point value. |
| p1 | number | No | The control point value, which pulls the curve toward it and determines its arc. |
| p2 | number | No | The end point value. |


**Returns:** number - The interpolated value at position `t` along the quadratic Bezier curve.


> Source: [src/math/interpolation/QuadraticBezierInterpolation.js#L35](https://github.com/phaserjs/phaser/blob/v4.1.0/src/math/interpolation/QuadraticBezierInterpolation.js#L35)  
Since: 3.2.0


---

### SmootherStep

#### \<static> SmootherStep(t, min, max)


**Description:**

An interpolation method based on Ken Perlin's Smoother Step function, which is an improved variant of the standard Smooth Step curve. Unlike Smooth Step, which has zero first derivatives at the endpoints, Smoother Step also has zero second derivatives at the endpoints, resulting in an even smoother S-curve transition between `min` and `max`. Use this when you need particularly fluid easing with no perceivable acceleration or deceleration artifacts at the start or end of the transition.

**Parameters:**
| name | type | optional | description |
| ---- | ---- | -------- | ----------- |
| t | number | No | The percentage of interpolation, between 0 and 1. |
| min | number | No | The minimum value, also known as the 'left edge', assumed smaller than the 'right edge'. |
| max | number | No | The maximum value, also known as the 'right edge', assumed greater than the 'left edge'. |


**Returns:** number - The interpolated value.


> Source: [src/math/interpolation/SmootherStepInterpolation.js#L9](https://github.com/phaserjs/phaser/blob/v4.1.0/src/math/interpolation/SmootherStepInterpolation.js#L9)  
Since: 3.9.0


---

### SmoothStep

#### \<static> SmoothStep(t, min, max)


**Description:**

A Smooth Step interpolation method that uses the Smoothstep function to produce a smooth, S-shaped transition between the `min` and `max` values. Unlike linear interpolation, Smooth Step eases in and out at both edges, resulting in a gradual start and end to the transition. This makes it well-suited for animations and transitions where abrupt changes at the boundaries would look unnatural.

The interpolation parameter `t` is first remapped via the Smoothstep curve (which clamps and applies a cubic Hermite function), and the result is then used to linearly interpolate between `min` and `max`.

**Parameters:**
| name | type | optional | description |
| ---- | ---- | -------- | ----------- |
| t | number | No | The percentage of interpolation, between 0 and 1. |
| min | number | No | The minimum value, also known as the 'left edge', assumed smaller than the 'right edge'. |
| max | number | No | The maximum value, also known as the 'right edge', assumed greater than the 'left edge'. |


**Returns:** number - The interpolated value.


> Source: [src/math/interpolation/SmoothStepInterpolation.js#L9](https://github.com/phaserjs/phaser/blob/v4.1.0/src/math/interpolation/SmoothStepInterpolation.js#L9)  
Since: 3.9.0


---

---

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