Geometry nodes: Binormals & cross products

13 May, 2025

Cross Products

We can sample the tangent (forwards) and normal (outwards) vectors at a point on a curve. Those are orthogonal to one another but since we're in 3D space there must be a third 'direction' too. That's the binormal¹!

Given any 2 vectors $𝐚$ and $𝐛$ we can find a third $𝐜$ which is orthogonal to the plane the first two form by taking the cross product: $𝐜 = 𝐚 \times 𝐛$

Binormal of a point on a curve

The binormal is therefore just the cross of the tangent and normal. And it takes just one node to calculate it: A Vector Math node.

Tangent and normal from a Sample Curve node are fed to a vector Math cross-product node to calculate the binormal.

Or in other words. $𝐛 = 𝐭 \times 𝐧$

The operation can also be done on the left side of the sample node too, which could be handy if you'll feed the calculation to some other operation too:

Binormal from a Sample Curve node by feeding the Cross Product of the Tangent and Normal into the Value input, with the attribute type set to Vector

Note the attribute type is set to Vector.

I've seen bitangent too, in the context of sampling a surface.↩

#blender