GLSL built-in function

dot()

Returns the dot product of two vectors. For unit vectors it measures how much they point the same way: 1.0 same direction, 0.0 perpendicular, -1.0 opposite.

Syntax

float dot(vec2 x, vec2 y)
float dot(vec3 x, vec3 y)
float dot(vec4 x, vec4 y)

Parameters

x: The first vector.
y: The second vector, with the same size as x.

Return value

A single float: x.x * y.x + x.y * y.y (+ x.z * y.z ...).

Live example

Edit the code and the preview updates as you type.

How it works

The formula is simple: multiply matching components and add them up.

dot(vec2(1.0, 2.0), vec2(3.0, 4.0)) // 1*3 + 2*4 = 11.0

The useful part is what it means. When both vectors have length 1, dot is the cosine of the angle between them:

directions	dot
the same	1.0
60 degrees apart	0.5
perpendicular	0.0
opposite	-1.0

That is exactly what diffuse lighting needs. In the example, dot(normal, light) is 1.0 where the sphere faces the light, falls toward 0 at the edge of the lit side, and goes negative on the far side, which max clamps to 0.

Typical uses

Diffuse (Lambert) lighting: max(dot(normal, lightDir), 0.0).
Squared length: dot(v, v) is length(v) * length(v) without the square root.
Projecting onto a direction: dot(p, dir) is how far p goes along dir, useful for gradients at any angle.
Hash functions: dot(p, vec2(12.9898, 78.233)) mixes two coordinates into one number before fract(sin(...)).

Common mistakes

Forgetting to normalize. With vectors longer than 1, the result is no longer between -1 and 1, and lighting becomes too bright or too dark.
Not clamping negative values in lighting, which darkens surfaces facing away from the light below the ambient level.
Passing vectors of different sizes. dot(vec3, vec2) does not compile.