Consider the following 3D triangle,

(3.2) |

in which its vertex coordinates are expressed as generic constants.

Let , , and be the amount we would like to change the triangle's position, along the , , and axes, respectively. The operation of changing position is called *translation*, and it is given by

in which denotes that becomes replaced by after the transformation is applied. Applying (3.3) to every triangle in a model will translate all of it to the desired location. If the triangles are arranged in a mesh, then it is sufficient to apply the transformation to the vertices alone. All of the triangles will retain their size and shape.

Steven M LaValle 2020-11-11