What is a Transformation Matrix

When we talk about transformations in 3D space, we mean altering the position, orientation, or scale of an object. These transformations can include various operations such as translation (shifting the position), rotation (changing the orientation), shear (distorting the shape), scale (changing the size), reflection (flipping the object), and projection (mapping the 3D point onto a 2D plane).

To perform these transformations, a common technique is to use a transformation matrix. A transformation matrix is a mathematical matrix that stores the information about the desired transformation. By multiplying a Vector3 representing a point(x,y,z position) with the transformation matrix, we can apply the transformation to that point.

//Three.js
const transformationMatrix = new THREE.Matrix4(); 
transformationMatrix.set( 11, 12, 13, 14, 
	   21, 22, 23, 24,
	   31, 32, 33, 34, 
	   41, 42, 43, 44 );
	

When we talk about "applying the matrix to the vector," it means that the transformation matrix is multiplied with the Vector3 point to achieve the desired transformation. The resulting Vector3 will reflect the transformed position, orientation, or scale of the original point in 3D space.

Read more

• Matrix4 in Three.js docs

• OpenGL matrices tutorial