A texture with one more dimension

The volume density field

A 2D texture is looked up with (u,v) and returns a colour. A 3D texture is looked up with (x,y,z) and returns, here, a single density — how much medium is present at that point in space. It is stored the obvious way, as a stack of 2D slices, and it is filtered the obvious way, by blending the eight texels surrounding the sample point instead of four.

One slice —
Move to probe a texel
0.50
The stack what a 3D texture is

Twelve of the slices, drawn one behind the other. The hardware stores exactly this — a contiguous run of 2D images — and texture(vol, vec3(x,y,z)) is the operation that reaches into two neighbouring slices and blends between them.

Marched through —

The same volume, ray marched with a light. Drop the resolution to 8³ and switch to nearest — the texels become visible as cubes, which is the volumetric version of a pixelated texture.

The eight texels under the pointer —
texelxyzvalueweight

—

What it costs to store memory grows cubically
Texels in this volume—
As 8‑bit density (R8)—
As 16‑bit float (R16F)—
The same volume at 256³, R16F—
At 512³, R16F—

Doubling the resolution costs eight times the memory, not four. That single fact is why production cloud systems rarely store a big uniform grid — they use sparse structures, tile the volume, or generate the density procedurally in the shader and store nothing at all.

Resolution
—
One texel spans
—
Density at the pointer
—
Filtering
—
Trilinear is not eight lookups on a good day. Sampling a 3D texture with filtering enabled is a single instruction on any modern GPU, and the eight-texel blend happens in dedicated hardware — which is precisely why volumetric renderers go to the trouble of storing density in a texture rather than evaluating a noise function per step. The comparison is worth making explicit: the procedural route costs arithmetic and no memory, the texture route costs memory and almost no arithmetic, and a real cloud renderer usually does both, with a coarse texture giving the shape and cheap noise added on top for detail. Switch to nearest above and watch what the filter is actually buying you: without it, every step of the march inside one texel returns an identical value, so the volume renders as a field of blocks.