# Vector lerp

`vector-lerp` · version 1.0.0 · Vectors & matrices · free, no key needed

Linearly interpolate (or extrapolate) between two equal-length finite-number vectors.

**Use when you need to: vector linear interpolation · lerp between two vectors · vector extrapolation.**

## Supported

- vector linear interpolation
- lerp between two vectors
- vector extrapolation

## Not supported

- vectors of different lengths
- spherical (slerp) interpolation
- non-linear interpolation curves

## Behavior

- Inputs a and b are arrays of finite JSON numbers with the same length, from 1 to 64 entries, magnitude bounded to at most 1000000.
- Input t is a finite number with magnitude at most 1000; t is not clamped to [0, 1], so values outside that range extrapolate.
- The result is result[i] = a[i] + t * (b[i] - a[i]), computed in IEEE-754 double precision. t=0 returns a; t=1 returns b.
- A result entry of -0 is normalized to 0.

## Input

- `a` (array of number, required): min items 1; max items 64
- `b` (array of number, required): min items 1; max items 64
- `t` (number, required)

## Output

- `result` (array of number, required)

## Limits

- max dim: 64
- max abs value: 1000000
- max abs t: 1000

## Example

Request input:

```json
{
  "a": [
    0,
    0
  ],
  "b": [
    10,
    20
  ],
  "t": 0.5
}
```

Response:

```json
{
  "result": {
    "result": [
      5,
      10
    ]
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "vector-lerp",
  "version": "1.0.0",
  "input": {
    "a": [
      0,
      0
    ],
    "b": [
      10,
      20
    ],
    "t": 0.5
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/vector-lerp/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"a":[0,0],"b":[10,20],"t":0.5}'
```

The machine-readable contract is at [/v1/tools/vector-lerp/versions/1.0.0](/v1/tools/vector-lerp/versions/1.0.0).

### CLI

```sh
node cli.mjs run vector-lerp 1.0.0 --input input.json --base-url https://computefirst.net
```

Get the client at [/clients/cli/](/clients/cli/).

## Related tools

- [Vector add](/tools/vector-add): Add two equal-length finite-number vectors elementwise.
- [Vector angle](/tools/vector-angle): Compute the angle in radians between two equal-length finite-number vectors.
- [Vector dot](/tools/vector-dot): Compute the dot (scalar) product of two equal-length finite-number vectors.
- [Vector outer product](/tools/vector-outer-product): Compute the outer product of two finite-number vectors, producing a matrix.
- [Matrix vector multiply](/tools/matrix-vector-multiply): Multiply an MxN finite-number matrix by a length-N finite-number vector, producing a length-M vector.
- [Vector approx equal](/tools/vector-approx-equal): Compare two equal-length finite-number vectors for approximate equality within an absolute tolerance.