How is orthographic projection used in computer graphics technically classified as a projection?

Question

I'm wondering why the orthographic projection we use in computer graphics is called a projection, if all it does is just scale and translate a mesh?

According to wiki orthographic projection is Orthographic projection (sometimes referred to as orthogonal projection, used to be called analemma[a]) is a means of representing three-dimensional objects in two dimensions, but we don't use orthographic projection to project our mesh to 2d space, we just use it to transform our mesh defined in the view box with arbitrarily defined dimensions (left, right, up, bottom, far and near) to a view box of (-1, 1, -1, 1, -1, 1) dimensions. So why do we call it an orthographic projection?

intergula · Accepted Answer

I think it is more of a terminology shared specifically in the computer graphics community. The transformation $P$ results in a vector one-step-ahead from getting the actual projection. From a 3D position transformed with $P$, we can obtain both

the 2D-projected position in normalized device coordinate (NDC) (by obtaining xy component)
the depth (by obtaining the z component) in NDC

This so-called projection matrix is designed specifically to satisfy the needs in the computer graphics pipeline. The key difference between an ordinary N-D-to-(N-1)-D projection is that the projection matrix results in 2D positions with "depth", which is required for obtaining a depth map used for many purposes in the computer graphics pipeline.

How is orthographic projection used in computer graphics technically classified as a projection?

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