#### Translations

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

 (3.3)

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 2020-01-06