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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.

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

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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.

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  • $\begingroup$ in transformation both have same dimension? $\endgroup$
    – user17337
    Oct 27, 2021 at 9:29
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    $\begingroup$ @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. $\endgroup$
    – wychmaster
    Oct 28, 2021 at 7:32
  • $\begingroup$ @Nicol Bolas Can you give some references ? $\endgroup$
    – Adam
    Nov 21, 2021 at 9:45