> For the complete documentation index, see [llms.txt](https://docs.hology.app/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.hology.app/zh-tw/shaders/typescript-shaders/math-functions.md).

# Math functions

Beyond the functions defined on the numeric types, there are other methods which works on most types. These are wrapping functions defined in the GLSL standard library. This page does not describe what each method does. Please see [GLSL documentation](https://www.shaderific.com/glsl-functions) to learn what they do if it is not clear by their signature.

Import functions like this:

```ts
import { dot, radians, saturate } from "@hology/core/shader-nodes"

```

### Trigonometry functions

```ts
radians<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
degrees<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
sin<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
cos<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
tan<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
asin<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
acos<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
atan<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(yOverX: T): T
```

### Exponential functions

```ts
exp<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
log<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
exp2<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
log2<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
sqrt<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
inversesqrt<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
pow<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T, y: T): T
```

### Geometric functions

```ts
length<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): FloatNode
normalize<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
```

### Common functions

```ts
abs<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
sign<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
floor<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
fract<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T
ceil<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T): T

mix<
  T extends FloatNode | Vec2Node | Vec3Node | Vec4Node,
  U extends T | FloatNode
>(x: T, y: T, a: U): T

step<
  T extends FloatNode | Vec2Node | Vec3Node | Vec4Node,
  U extends T | FloatNode
>(edge: U, x: T): T

smoothstep<
  T extends FloatNode | Vec2Node | Vec3Node | Vec4Node,
  U extends T | FloatNode
>(edge0: U, edge1: U, x: T): T

clamp<
  T extends FloatNode | Vec2Node | Vec3Node | Vec4Node,
  U extends T | FloatNode
>(x: T, minVal: U, maxVal: U): T

saturate<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(a: T): T
```

### Vector functions

```ts
dot<T extends FloatNode | Vec2Node | Vec3Node | Vec4Node>(x: T, y: T): FloatNode
```

### Matrix functions

```ts
inverse<T extends Mat2Node | Mat3Node | Mat4Node>(x: T): T
transpose<T extends Mat2Node | Mat3Node | Mat4Node>(x: T): T
```


---

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