G0-G3 corners, visualised: learn what "Apple corners" are

You might have seen this image before (it's hard to attribute, my best guess is among the links below):

The two corners look and feel different, but why? The difference is in the degree of surface continuity.

Surfaces can be joined at different levels of continuity. The most common levels are G0, G1, G2, and G3. There are plenty of videos and articles online and I link some below, but nothing beats seeing the difference with our own eyes and feeling it with our fingers. 

This model is a sample of the four most common levels of continuity: G0 (straight joint), G1 (an arc), G2 (a spline with two collinear control points on each side), and G3 (same but with three control points). Print the model, and you will see and feel the difference.

After that, come back and read and watch more from the links below.

Gentle introduction

As far as I can tell, this article is the source of the image above: https://hackernoon.com/apples-icons-have-that-shape-for-a-very-good-reason-720d4e7c8a14

On aesthetics of continuity, my personal favourite: https://www.core77.com/posts/12752/a-periodic-table-of-form-the-secret-language-of-surface-and-meaning-in-product-design-by-gray-holland-12752

Going deeper

Incredible video by Freya Holmér on splines and continuity in general: 

Or more applied in this video, using Fusion:

And here's an example of fairly involved surface work by Andrew Jackson (the entire channel is solid gold):

The last video is quite advanced, but the path to this level of surfacing starts with just learning how continuity feels.

This model will help you start your journey. Best of luck!

P.S.: There is an additional benefit to super-smooth corners in 3D printing that is not covered in the videos and links above. Besides pure aesthetics of the surface, G3 continuous corners mean that the print head experiences smooth acceleration while printing such corners. This eliminates any possibility of ringing, which further improves the look of the printed model and might improve printing speed.