Texture mapping progressive meshes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Optimization by Vector Space Methods
Optimization by Vector Space Methods
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Smoothing an overlay grid to minimize linear distortion in texture mapping
ACM Transactions on Graphics (TOG)
Seamster: inconspicuous low-distortion texture seam layout
Proceedings of the conference on Visualization '02
ABF++: fast and robust angle based flattening
ACM Transactions on Graphics (TOG)
Preconditioners for generalized saddle-point problems
Preconditioners for generalized saddle-point problems
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
Pattern computation for compression garment
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Local versus Global in Quasi-Conformal Mapping for Medical Imaging
Journal of Mathematical Imaging and Vision
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
A note on least-norm solution of global WireWarping
Computer-Aided Design
Pattern computation for compression garment by a physical/geometric approach
Computer-Aided Design
Spectral conformal parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
A local/global approach to mesh parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
Mesh parameterization based on one-step inverse forming
Computer-Aided Design
Efficient packing of arbitrarily shaped charts for automatic texture atlas generation
EGSR'11 Proceedings of the Twenty-second Eurographics conference on Rendering
Efficient texture mapping by homogeneous patch discovery
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
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In the field of mesh parameterization, the impact of angular and boundary distortion on parameterization quality have brought forward the need for robust and efficient free boundary angle preserving methods. One of the most prominent approaches in this direction is the Angle Based Flattening (ABF) which directly formulates the problem as a constrained nonlinear optimization in terms of angles. Since the original formulation of the ABF, a steady research effort has been dedicated to improving its efficiency. As for any well posed numerical problem, the solution is generally an approximation of the underlying mathematical equations. The economy and accuracy of the solution are to a great extent affected by the kind of approximation used. In this work we reformulate the problem based on the notion of error of estimation. A careful manipulation of the resulting equations yields for the first time a linear version of angle based parameterization. The error induced by this linearization is quadratic in terms of the error in angles and the validity of the approximation is further supported by numerical results. Besides performance speedup, the simplicity of the current setup makes re-implementation and reproduction of our results straightforward.