Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Multiresolution hierarchies on unstructured triangle meshes
Computational Geometry: Theory and Applications - Special issue on multi-resolution modelling and 3D geometry compression
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
Mesh forging: editing of 3D-meshes using implicitly defined occluders
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Differential Coordinates for Interactive Mesh Editing
SMI '04 Proceedings of the Shape Modeling International 2004
Mesh editing with poisson-based gradient field manipulation
ACM SIGGRAPH 2004 Papers
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A remeshing approach to multiresolution modeling
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Linear rotation-invariant coordinates for meshes
ACM SIGGRAPH 2005 Papers
Large mesh deformation using the volumetric graph Laplacian
ACM SIGGRAPH 2005 Papers
Discrete differential forms for computational modeling
ACM SIGGRAPH 2006 Courses
Volume and shape preservation via moving frame manipulation
ACM Transactions on Graphics (TOG)
Discrete quadratic curvature energies
Computer Aided Geometric Design
On Linear Variational Surface Deformation Methods
IEEE Transactions on Visualization and Computer Graphics
ACM Transactions on Graphics (TOG)
ACM SIGGRAPH 2009 papers
A simple geometric model for elastic deformations
ACM SIGGRAPH 2010 papers
Spin transformations of discrete surfaces
ACM SIGGRAPH 2011 papers
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We present a linear algorithm to reconstruct the vertex coordinates for a surface mesh given its edge lengths and dihedral angles, unique up to rotation and translation. A local integrability condition for the existence of an immersion of the mesh in 3D Euclidean space is provided, mirroring the fundamental theorem of surfaces in the continuous setting (i.e. Gauss's equation and the Mainardi–Codazzi equations) if we regard edge lengths as the discrete first fundamental form and dihedral angles as the discrete second fundamental form. The resulting sparse linear system to solve for the immersion is derived from the convex optimization of a quadratic energy based on a lift from the immersion in the 3D Euclidean space to the 6D rigid motion space. This discrete representation and linear reconstruction can benefit a wide range of geometry processing tasks such as surface deformation and shape analysis. A rotation-invariant surface deformation through point and orientation constraints is demonstrated as well. © 2012 Wiley Periodicals, Inc.