# Understanding orthographic projection matrix clip coordinates

I'm confused about what orthographic projection matrix outputs. Based on what I know so far, orthographic projection matrix converts vertexes in eye coordinates into clip coordinates. But what exactly are clip coordinates? What are its bounds of x, y, z values? I read somewhere that its x, y, z are all in range [-1...1]. Is it true? Also, how and why axes are orientated in clip coordinates? right handed (z goes out of page) or left handed (z goes into page)? What are main differences between clip coordinates and normalized device coordinates?

Edit: I think the primary difference between clip coordinates and NDC is that NDC can be obtained by dividing clip coordinates by w (ie. $$x_{ndc}=x_{clip}/w$$, $$y_{ndc}=y_{clip}/w$$, and $$z_{ndc}=z_{clip}/w$$. But what I don’t understand here is that even though clip coordinates x,y,z values obtained by projection matrix are in range [-1...1], is it still necessary to divide them by w to get NDC?

• May 23, 2022 at 9:30
• @lightxbulb I already read these pages but they still didn't answer some of my questions like why coordinates are left handed in NDC and is it still necessary to homogenize vertexes after passing them in projection matrix (which produces values in range -1 to 1) May 23, 2022 at 19:26
• The left vs right handed thing differs between APIs. The clip coordinates resulting from the projection matrix do not have to be in [-1,1]. May 23, 2022 at 21:46