# Cross Node


![](../img/cross.png)

### Description

This node computes the cross product of two **float3** vectors A and B, resulting in a vector that is perpendicular to both and serves as the normal to the plane they define.


![](../img/cross_product.png)


This operation is fundamental in 3D graphics and physics calculations. Use it to:


- Generate normal vectors
- Calculate surface normals
- Find the area of a triangle
- Handle rotational effects in simulations
- Determine the orientation of objects in 3D space, such as aligning a camera or defining the axis of rotation.


**Functionality**


The **Cross** node takes two vectors as input and calculates their cross product using the formula:

**Vresult = A x B**
Where:


- A and B are the input vectors.
- The result is a vector perpendicular to both A and B, following the **right-hand rule.**
- The order of input vectors matters: A x B and B x A return different results.


**To Avoid Unexpected Results:**


- Ensure input vectors are **not parallel**, as this would result in a **zero vector**.
- ***[Normalize](../../../../../content/materials/graph/node_library/math/normalize.md)*** input vectors to ensure consistent output scaling.
- Remember that the **physical position of the object does not change** (i.e. its bound is stable) - only the material behavior creates the visual illusion of rotation.


## Usage Examples

**Creating A Material Always Facing The Camera**

[![](../img/cross_ex_1.gif)](../img/cross_ex_1.gif)


To make an object always face the camera, we need to construct a local coordinate system based on the camera's position relative to the object.


1. Compute the **Unit Vector** from the object to the camera:

  - Use the ***[Camera Position](../../../../../content/materials/graph/node_library/input/camera_position.md)*** node and normalize the vector to maintain consistent scaling.
2. Determine the **Side Vector**:

  - Use the **Cross Node** to calculate a perpendicular vector by crossing the unit vector (computed in Step 1) with a fixed up vector.
  - ***[Normalize](../../../../../content/materials/graph/node_library/math/normalize.md)*** the result vector.
3. Compute the **Final Orientation**:

  - Perform another **cross product** between the computed *side vector* (computed in Step 2) and the *unit vector* (computed in Step 1) to get the final perpendicular vector.
  - Use the three orthogonal vectors to construct a ***[transformation matrix](../../../../../content/materials/graph/node_library/matrix/compose_matrix3_by_column.md)*** that aligns the object to face the camera.


By using the **Cross** node in this way, we ensure the object dynamically orients itself toward the camera regardless of its movement, making it ideal for *billboards, particles*, and *UI elements* in 3D environments.


| [**View Fullscreen**](https://matgraph.unigine.com/DocsCross_2.21/fullView) |
|---|