per space. In the upper right corner you draw another dot, and you write "1, 1" next to it. You now have 2 points defined in paper space (uv space).
Ok, lay down the pencil and pick up the paper. You'll notice that the two points have just moved through world-space. They were very close to the desk, but now they are hovering above it. The coordinates you wrote down on the paper or the other hand are still valid.
No matter what you do to this piece of paper; crumple it, fold it, take it on a plane to South Africa, those two points remain fixed in paper space.
A surface is always a rectangle in Rhino. It may be deformed, it may have holes cut into it, but in the end it's always a rectangle, just like your piece of paper. UV coordinates are points that are defined in Surface UV space. They consist of only two numbers, because a surface has no thickness. At any point in time, you can translate these UV points into World XYZ points using what is called a surface evaluator. Where these XYZ points end up depends entirely on the *shape*, *size* and *location* of the surface.
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Surface uv-space (and Curve t-space) are vital when dealing with nurbs geometry. If you do not understand the concept of parameter space, you will have a lot of problems because many components in Grasshopper use these coordinates.
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David Rutten
david@mcneel.com
Seattle, WA…
Added by David Rutten at 6:40pm on September 27, 2009