# Difference between transformation and projection? [closed]

We know that world coordinates $$(x_w, y_w)$$ transform to viewport coordinates $$(x_v, y_v)$$ which are the physical device coordinates. And during projection, any point $$(x, y, z)$$ projects to $$(x, y)$$ onto the projection plane. My question is: Are projection and transformation both the same? Please explain it with a small example. I want to understand intuition rather than details proof.

• This question is an exact copy from another network site. See this link. Closing here to avoid further scattering of information. Commented Nov 4, 2021 at 9:22

A projection is a kind of transformation.

A transformation is any modification of a coordinate that expresses that coordinate relative to a coordinate system that is different from its original coordinate system. As such, a transformation involves two coordinate systems: the source and the destination.

A projection is any transformation where the destination coordinate system has fewer dimensions than the source coordinate system. That is, it removes one or more dimensions from the coordinate.

• in transformation both have same dimension?
– user17337
Commented Oct 27, 2021 at 9:29
• @User4567 A transformation could result in any dimension: more, less, the same. Transformation and projection behave like the words "plant" and "tree". Trees are a subcategory of plants. Projections are a subcategory of transformations. Commented Oct 28, 2021 at 7:32
• @Nicol Bolas Can you give some references ?