Renka, Robert J.Chen, Min and Zhang, Hao (Richard)2016-09-272016-09-2720161467-8659https://doi.org/10.1111/cgf.12731https://diglib.eg.org:443/handle/10.1111/cgf12731We present two simple and efficient local methods that reposition vertices of a triangle mesh surface with the goal of producing good triangle shapes while preserving the enclosed volume and sharp features. The methods involve minimizing a quadratic energy functional with respect to variations in a tangent plane (or in the direction of a crease) at each free vertex. One of the methods is aimed at producing uniform angles, while the other method is designed to produce uniform triangle areas, or more generally, to force relative triangle areas to conform to curvature estimates or estimates of local feature size so that vertex density is low in flat spots and relatively high in regions of large curvature. Test results demonstrate the effectiveness of both methods, especially when combined.We present two simple and efficient local methods that reposition vertices of a triangle mesh surface with the goal of producing good triangle shapes while preserving the enclosed volume and sharp features. The methods involve minimizing a quadratic energy functional with respect to variations in a tangent plane (or in the direction of a crease) at each free vertex. One of the methods is aimed at producing uniform angles, while the other method is designed to produce uniform triangle areas, or more generally, to force relative triangle areas to conform to curvature estimates or estimates of local feature size so that vertex density is low in flat spots and relatively high in regions of large curvature. Test results demonstrate the effectiveness of both methods, especially when combined.mesh improvementmesh smoothingsurface meshfeature‐preservingI.3.5 [Computer Graphics]: Computational Geometry and Object Modelling—Curve, surface, solid and object representations10.1111/cgf.1273146-58