World Space

by William Shoaff with lots of help

Contents

• Contents
• World Space: Where It All Comes Together
  • Conclusions
• Bibliography

World Space: Where It All Comes Together

World space (WS) is the second space in the graphics pipeline. Objects pass through it from model space (MS) and proceed on to view space (VS). World space is a place where we seldom want to stop, yet it is conceptually interesting as the place where all the objects are collected to form a scene, and it provides a mechanism for defining the location of the view of these objects.

We will see that the affine transforms that map objects from model space into world space are concatenated with the view transforms that maps objects from world space into view space. Thus, we never stop in the world to perform other operations. This contrasts with spaces such as view space, where we may compute illumination values (colors) and determine hidden objects, and clip space, where objects are cut to fit the viewport.

There's not much else I can think to say.

Conclusions

World space is a conceptual space used to define the relative location of objects, lights, and viewers. Data flowing down the graphics pipeline never really exists in world space. It goes directly from model space to view space, where some operations are performed on it.

One could map objects to world space and then to view space using two matrix multiplies:

$$(x,\,y,\,z)M_{\mbox{model}\rightarrow\mbox{world}} = (x',\,y',\,z')$$

and

$$(x',\,y',\,z')M_{\mbox{world}\rightarrow\mbox{view}} = (x'',\,y'',\,z'')$$

where the first matrix performs an affine transform that scales, rotates and translated a model coordinate $(x,\,y,\,z)$into a world coordinate $(x',\,y',\,z')$, and then the second matrix performs the view transformation (it's also an affine transform) producing a view space point $(x'',\,y'',\,z'')$. However, this would be efficient in general.

• Where to we go from here? To view space.
• How do we get there? By the viewing transform.
• Although little was covered here, there still some things to practice.

No References!