An algorithm for smoothly filling holes in 3D meshes

In plain words

This is an algorithm for repairing damaged 3D meshes by filling holes with smooth surfaces using variational calculus and surface fairing techniques. It is designed for developers and researchers working with 3D mesh data who need to restore broken geometric models. The approach is explained accessibly without assuming prior knowledge of variational calculus, making the mathematical foundations clear to practitioners in computer graphics and 3D modeling.

written from the facts on this page · September 2026

From the sources

$\newcommand{\mvec}[1]{\mathbf{#1}}\newcommand{\gvec}[1]{\boldsymbol{#1}}\definecolor{eqcol2}{RGB}{114,0,172}\definecolor{eqcol1}{RGB}{172,0,114}\definecolor{eqcol3}{RGB}{0,172,114}\definecolor{eqcol4}{RGB}{230,190,120}$In this article, we describe an approach to smoothly filling holes in broken meshes that is based on variational calculus . However, do note that it is not assumed that the reader has experience in variational calculus, and we will instead introduce the necessary concepts from this topic when they are needed. Most of the techniques described in this article are based the description of Surface Fairing in section 4.3 of [1] . In the below image, it is shown how our described…from erkaman.github.io

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