On: Drawing better-looking Bézier curves

[amelius]

I'm wondering how well one could define curves by using the physical model of a strip of material, and allowing one to change the properties (stiffness) of the material at different points along the curve, or to insert more material at a given point. Of course, there should be the usual constraints that the strip should pass through a bunch of given (x,y) coordinates, and there could be constraint that "pins" the strip to a given (x,y) coordinate.

In a drawing program, the stiffness could be depicted by using grayscale values.

[dhotson → amelius]

It's really interesting if you look at how CAD handles this stuff. It lets you set the degree of curvature-continuity/smoothness you want—and it kind of takes care of filling in the curve for you. You have to give up some direct control over the curve if you need it to meet these constraints.

Here's what different degrees of curvature continuity look like: http://help.autodesk.com/cloudhelp/2017/ENU/Alias-Tutorials/...

.. or in 2d: http://help.autodesk.com/cloudhelp/2017/ENU/Alias-Tutorials/...

To make smooth surfaces you just need the tangents to line up. This is called G1.

But if you also want surface reflections to look smooth you need a higher degree of curvature continuity. G2 or higher.

http://help.autodesk.com/cloudhelp/2017/ENU/Alias-Tutorials/...

[perl4ever → dhotson]

I wonder whether for curvy automobile sheet metal these days they sculpt and then digitize or start out directly creating virtual shapes.

[mkeeter → amelius]

Check out Raph Levien's thesis: http://levien.com/phd/phd.html

It doesn't talk about dynamically varying stiffness along the curve, but is otherwise a very detailed dive into splines.

[Tomte → amelius]

Isn't that the MetaFont model that Knuth used?