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Bezier curves, Bezier surfaces, b-splines, NURBS

AG
andrew goh
Fri, Sep 2, 2022 11:59 AM

hi all,

well my 1st post here, hope this is ok and not too 'off topic'.

I'd guess this is an 'old' topic. a search in the mailing list archives
shows a large number of threads. But are there any plans to make Bezier
curves, Bezier surfaces and/or even b-splines and better still NURBS
into OpenSCAD?

There are apparently many libraries shared on the web, and some in
Github, some in Thingiverse etc. These are mainly 'libraries' in
openscad codes to make the Bezier curves, surfaces etc.

While I'm not in any feeble way good with the 'technology' (and math)
about these, Bezier curves, surfaces and preferably b-splines, NURBS are
well known means to make "organic" looking models that is very difficult
otherwise. many models has 'mechanically geometrically rigid' looks
otherwise, e.g. fix patterns of circles, elipses etc .

Some of the well known articles found from a google search are like these

https://raphaelluckom.com/posts/bezier_curves.html

https://openhome.cc/eGossip/OpenSCAD/BezierCurve.html

and one of those 'famous' models that has been done with Bezier (curves,
surfaces) is non other than the Utah teapot

https://www.scratchapixel.com/lessons/geometry/bezier-curve-rendering-utah-teapot

Accordingly, we can't really put the Bezier control points and hope to
make affine transforms (rotate, translate, scale, etc) without breaking
the orginal shapes, is that true?
And accordingly NURBS is less affected by those affine transforms and is
able to be transformed with the model components.

This is a further reason I'd think having NURBS in as model components
in OpenSCAD is probably a good idea.

just 2 cents,
� andrew

hi all, well my 1st post here, hope this is ok and not too 'off topic'. I'd guess this is an 'old' topic. a search in the mailing list archives shows a large number of threads. But are there any plans to make Bezier curves, Bezier surfaces and/or even b-splines and better still NURBS into OpenSCAD? There are apparently many libraries shared on the web, and some in Github, some in Thingiverse etc. These are mainly 'libraries' in openscad codes to make the Bezier curves, surfaces etc. While I'm not in any feeble way good with the 'technology' (and math) about these, Bezier curves, surfaces and preferably b-splines, NURBS are well known means to make "organic" looking models that is very difficult otherwise. many models has 'mechanically geometrically rigid' looks otherwise, e.g. fix patterns of circles, elipses etc . Some of the well known articles found from a google search are like these https://raphaelluckom.com/posts/bezier_curves.html https://openhome.cc/eGossip/OpenSCAD/BezierCurve.html and one of those 'famous' models that has been done with Bezier (curves, surfaces) is non other than the Utah teapot https://www.scratchapixel.com/lessons/geometry/bezier-curve-rendering-utah-teapot Accordingly, we can't really put the Bezier control points and hope to make affine transforms (rotate, translate, scale, etc) without breaking the orginal shapes, is that true? And accordingly NURBS is less affected by those affine transforms and is able to be transformed with the model components. This is a further reason I'd think having NURBS in as model components in OpenSCAD is probably a good idea. just 2 cents, � andrew