Undesirable faceted fillets

Lets say that I have a square and then I fillet the corners, when I go extrude the curve, the rounded corners appear very faceted. I assumed that that was Rhino’s way of making the model easier to display, but when I use my internal rendering engine (Thea Render) to visualize the geometry, the edges are still faceted. I can make it smooth by adjusting the mesh settings in the options window, but Rhino draw the viewport really slow. Do I just have to always jump between jagged and smooth mesh settings or is there a way to make the render engine always use high quality meshes?

Mesh settings are stored in the 3dm file, not with the Rhino application.

The initial settings are seeded by the template file you are using when you created the file.

If you want tighter default mesh settings, open a new file using your desired template and make the change. Use Save As Template to overwrite the file or make a new template.
Once you change the setting in a file (Options - Mesh), they will stay changed.

However, be aware that a tighter mesh will slow down Rhino’s performance. The mesh setting has no effect on the accuracy of the geometry.

It makes more sense to kick up the mesh settings only when you need it.

This sounds like you extruded a single surface from the rounded rectangle which gets meshed differently compared to 4 seperate planar surfaces and 4 fillet surfaces. To try out if you can get better fillet facetting of the extruded result, set _SplitAtTangents=_Yes in the _ExtrudeCrv command.

The global settings under Options / Mesh apply to all meshable objects in your document. You can override them individually if you set them per object under:

Properties / Render Mesh Settings / Custom Mesh / Adjust

c.

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