---
title: "Interpolation and thresholds"
description: "TapHome LINEAR function for linear interpolation (value mapping, dimming, BOUNDS, INFINITE, STRICT modes) and HYSTERESIS for threshold switching of a heater in smart rules and scripts."
url: "https://taphome.com/en/docs/script/interpolation-and-thresholds/"
language: en
lastmod: 2026-10-13
generator: hugo
ai:
  topics: ["linear-interpolation","hysteresis","value-mapping","thresholds","smart-rules"]
  questions: ["How to use the LINEAR function for value interpolation in TapHome?","How do I map a sensor value to an output range with LINEAR?","What do the BOUNDS, INFINITE, and STRICT parameters do in LINEAR?","How does the LINEAR function behave when the input is out of range?","How to use HYSTERESIS to control a heater in TapHome?","What is the difference between LINEAR and HYSTERESIS?","How do I filter a signal with a hysteresis range?","How does the LINEAR function work and what is it used for in a TapHome script?","How do I use LINEAR for dimming — mapping a value to light brightness?"]
---

# Interpolation and thresholds

LINEAR linear interpolation and HYSTERESIS threshold switching for mapping values, dimming lights and controlling heating in TapHome scripts.

Last updated: 2026-10-13

`LINEAR` converts a value from one range to another along a straight line. `HYSTERESIS` switches between two output values with a dead band, so the output does not flip back and forth around a single threshold.

## LINEAR

`LINEAR` maps a value from an input range to an output range along the straight line through two points, `in1` → `out1` and `in2` → `out2` — for example a raw register value to percent, or daylight to light brightness.

```text
LINEAR(value, in1, out1, in2, out2)
LINEAR(value, in1, out1, in2, out2, LinearType)
```

**Parameters**

| Name | Type | Description |
|---|---|---|
| `value` | number | Input value. |
| `in1`, `out1` | number | First point: input `in1` gives output `out1`. |
| `in2`, `out2` | number | Second point: input `in2` gives output `out2`. |
| `LinearType` | enum, optional | What happens when `value` is outside the range `in1` – `in2`. |

| `LinearType` | Result outside the input range |
|---|---|
| `DEFAULT` (or left out) | Same as `BOUNDS`. On cores older than 2022.2 it extrapolates like `INFINITE`. |
| `BOUNDS` | The value is clamped to the range, so the result stays between `out1` and `out2`. |
| `STRICT` | `NaN`. |
| `INFINITE` | The line continues (extrapolation). |

![LINEAR function graph](https://taphome.com/documentation/script/linear-function.svg)

**Returns** — `double`. A `NaN` input gives `NaN`. When `in1` equals `in2` the slope cannot be computed and `1` is used instead.

**Example — convert a raw value**

```taphome
# raw register 0 ... 1000 -> 0 ... 100 %
LINEAR(MODBUSR(H, 10, Uint16), 0, 0, 1000, 100);
VAR raw := 250;
LINEAR(raw, 0, 0, 500, 50);
# Result: 25
```

The effect of `LinearType` for input 11 with the points 0 → 400 and 10 → 2000:

```taphome
# clamped to the range
LINEAR(11, 0, 400, 10, 2000, BOUNDS);
# Result: 2000
# line continues beyond the range
LINEAR(11, 0, 400, 10, 2000, INFINITE);
# Result: 2160
# outside the range gives NaN
LINEAR(11, 0, 400, 10, 2000, STRICT);
# Result: NaN
```

**Example — dimming: map a value to light brightness**

A dimmer level in TapHome runs from 0 to 1 (0 – 100 %). This formula dims a light from full brightness in darkness to off at 300 lx of daylight; `BOUNDS` keeps the level between 0 and 1 for brighter or darker readings:

```taphome
# Va is the daylight sensor in lx, the result is the dimmer level
LINEAR(Va, 0, 1, 300, 0, BOUNDS);
# Result: 0.5 at 150 lx, 0 at 300 lx and more
```

A dimming curve that never goes below 10 % — a slider value `x` from 0 to 1 is mapped to 0.1 – 1:

```taphome
LINEAR(x, 0, 0.1, 1, 1);
```

The same works for ventilation: `LINEAR(co2, 400, 0, 1200, 1)` gives 0 at 400 ppm, 0.5 (50 %) at 800 ppm and 1 at 1 200 ppm.

**See also** — [HYSTERESIS](https://taphome.com/en/docs/script/interpolation-and-thresholds/#hysteresis), [Rounding and random numbers](https://taphome.com/en/docs/script/rounding-and-random/).

## HYSTERESIS

`HYSTERESIS` returns `lowerState` when a value falls to `lowerThreshold`, `upperState` when it rises to `upperThreshold`, and `previousState` while it stays between them.

```text
HYSTERESIS(value, upperThreshold, lowerThreshold, upperState, lowerState, previousState)
```

Hysteresis filters a signal so that the output reacts more slowly than the input: a thermostat switches a heater on when the temperature drops below one value, but off only when it rises above another.

**Parameters**

| Name | Type | Description |
|---|---|---|
| `value` | number | Measured value, for example a temperature. |
| `upperThreshold` | number | Value at or above which `upperState` is returned. Must be higher than `lowerThreshold`. |
| `lowerThreshold` | number | Value at or below which `lowerState` is returned. |
| `upperState`, `lowerState` | number | Results for the two thresholds — any numbers, not only 0 and 1. |
| `previousState` | number | Result while the value is between the thresholds, usually the previous output. Must not be `Null`. |

**Returns** — `double`: `upperState`, `lowerState` or `previousState`. A value within 0.005 of a threshold counts as reaching it. A `NaN` value returns `previousState`.

**Example — heating**

Keep a room at 20 °C with a hysteresis of ±2 °C: the heater switches on when the temperature drops to 18 °C and off when it rises to 22 °C. In a Script smart rule the heater switch is both read and written:

```taphome
# Te is the room temperature, Sw the heater switch
Sw := HYSTERESIS(Te, 22, 18, 0, 1, Sw);
```

In a Formula smart rule the previous result is `LastState`, which is `Null` on the first run and after a script error:

```taphome
HYSTERESIS(Te, 22, 18, 0, 1, IF(ISNULL(LastState), 0, LastState));
```

**Errors**

- *Upper threshold must be higher than lower threshold* — when you save a script whose thresholds are fixed numbers.
- *Upper threshold (X) must be higher than lower threshold (Y)* — at run time, when the thresholds come from variables.

**See also** — [Scripts in smart rules](https://taphome.com/en/docs/script/smart-rules/), [Hysteresis-based filling control of a tank](https://taphome.com/en/docs/configuration/hysteresis-equation/).