I couldn’t find an answer to this question by researching on the internet, so perhaps some of you can shed some light on this subject.
I am curious to understand: just how do proximity loops help the object to retain its shape after a subdivision modifier is applied? My understanding is that by creating these supporting loops we create new geometry that prevents the subdivision algorithm from being able to subdivide certain areas? But then how come does the algorithm subdivide everything that falls in between those created supporting loops (the edges of a cube), but never the flat areas outside those loops (the original faces of the cube)?
My educated guess just tells me: “complex math” and “just accept it as is,” but the curiosity inside of me is trying to understand the process!
Indeed, just accept it, it works, which is all that matters. Basically, all it is doing is restricting where the smoothing occurs. Think of a sheet of metal, if it is 1 mtr long, bending it, you get a large curve, if it is 5 cm long, you get a tight curve. Applying edge loops is the same as this, no edge loop, big curve, the closer the edge loop the tighter the curve.
Catmull-Clarke subd subdivides the face, then pulls the existing points toward their neighboring vertices. A vertex will not be pulled past it’s nearest neighbor. Close neighbors means less deformation. If you look into the math, it’s actually kind of elegant. It’s just simple weighted average of surrounding vertices, that calculates very quickly, and ALMOST makes a perfect circle out of a square.
You may find this video helpful. It addresses the question you’re asking and more, although in a visual format.
Now, to answer more directly, consider this shape:
It’s two faces from the default cube. If we were to subdivide this, we’d get a curvature which looks nothing like the right angle we may have been expecting. But notice what happens when we scale that geometry down:
As the distance gets smaller between the verts, the interpolation/curvature scales as well. The angles don’t change, and there’s no change to the number of subdivisions. No fancy, ‘smart’ algorithm or math required. Now you can imagine, that instead of scaling the whole of our geometry, we could add extra geometry closer to the angle we want to preserve. This new geo would ‘compress’ the interpolation in the same way scaling in our geometry did. And that is exactly what support loops are and what they do.
Basically, all it is doing is restricting where the smoothing occurs. Think of a sheet of metal, if it is 1 mtr long, bending it, you get a large curve, if it is 5 cm long, you get a tight curve. Applying edge loops is the same as this, no edge loop, big curve, the closer the edge loop the tighter the curve.
