Variational shape approximation

By David Cohen-Steiner, Pierre Alliez, Mathieu Desbrun. ACM Transactions on Graphics, 2004

834 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/1d262c871b775990a34dbfe8b8f07db69f31deb6

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

In Computer Vision and Pattern Recognition

Citations in the corpus

Convergence of the Lloyd Algorithm for Computing Centroidal Voronoi Tessellations (2006, background): “CVTs are indeed special as they enjoy very natural optimization properties which make them very popular in diverse scientific and engineering applications that include art design, astronomy, clustering, geometric modeling, image and data analysis, resource optimization, quadrature design, sensor net”
Hierarchical mesh segmentation based on fitting primitives (2006, methodology): “In this latter case, it might be more appropriate to integrate the squared distances over the whole surface [7].”
Variational tetrahedral meshing (2005, methodology): “A few of these variational methods [Cohen-Steiner et al. 2004; Du and Wang 2003] have an attractive theoretical property resulting in remarkable results: vertex positions and connectivity updates are performed alternately to minimize the same quadratic energy.”
Consistent mesh partitioning and skeletonisation using the shape diameter function (2008, background): “These attributes include curvature and geodesic distances [13, 16, 21, 25, 26, 37], dihedral angles [28], planarity and normal direction [3, 5], slippage [10] etc.”
Architectural geometry (2007, background): “[23], seek to produce general polyhedral meshes that approximate the surface without necessarily being hexagonally-dominant or structured.”
Mesh Segmentation - A Comparative Study (2006, background): “Mesh segmentation has become an important and challenging problem in computer graphics, with applications in areas as diverse as modeling [7], metamorphosis [10, 35], compression [13], simplification [6], 3D shape retrieval [36, 29], collision detection [18], texture mapping [17] and skeleton extrac”
Model Composition from Interchangeable Components (2007, methodology): “To generate the parts we use a Lloyd iteration scheme [17, 4].”
Recent Advances in Remeshing of Surfaces (2008, background): “[16] proposed an error-driven clustering approach that does not resort to any estimation of differential quantities or any parameterization.”
Mesh parameterization: theory and practice (2007, background): “planes are developable by definition, one possible approach is to segment the surface into nearly planar charts [Maillot et al., 1993; Garland et al., 2001; Sander et al., 2003; Cohen-Steiner et al., 2004].”
SimpleTree —An Efficient Open Source Tool to Build Tree Models from TLS Clouds (2015, methodology): “With the flooding algorithm [68] the point cloud is segmented into clusters.”
Mesh segmentation using feature point and core extraction (2005, background): “Some of these applications require segmentation into higher level meaningful components while others require segmentation into lower level disk-like patches [5, 10, 26, 34].”