On the construction of polynomial minimal surfaces with Pythagorean normals

<abstract><p>In this paper we presented a method of $ G^2 $ Hermite interpolation of offset curves of regular plane curves based on approximating the normal vector fields. We showed that our approximant is also $ C^1 $ Hermite interpolation of the offset curve. Our method is capable of achieving circular precision. Another advantage of our method is that if the input curve is a polynomial curve, then our method also yields a polynomial curve. Our approximation method was applied to numerical examples and its numerical results were compared to previous offset approximation methods. It was observed that our method is almost optimal with respect to the number of control points of the approximation curves for the same tolerance.</p></abstract>

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

On the construction of polynomial minimal surfaces with Pythagorean normals

Cited by 2 publications

References 11 publications

Deformation of surfaces along curves and their applications

Deformation of surfaces along curves and their applications

$ G^2/C^1 $ Hermite interpolation of offset curves of parametric regular curves

Contact Info

Product

Resources

About