Modeling surfaces of arbitrary topology using manifolds
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Globally smooth parameterizations with low distortion
ACM SIGGRAPH 2003 Papers
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A simple manifold-based construction of surfaces of arbitrary smoothness
ACM SIGGRAPH 2004 Papers
Direct Anisotropic Quad-Dominant Remeshing
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
Parameterization of triangle meshes over quadrilateral domains
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Discrete conformal mappings via circle patterns
ACM Transactions on Graphics (TOG)
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
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Our algorithm computes two piecewise smooth harmonic scalar functions, whose isolines tile the input surface into well-shaped quadrangles, without any T-junctions. Our main contribution is an extension of the discrete Laplace operator which encompasses several types of line singularities. The resulting two discrete differential 1-forms are either regular, opposite or switched along the singularity graph edges. We show that this modification guarantees the continuity of the union of isolines across the lines, while the locations of the isolines themselves depend on the global solution to the modified Laplace equation over the whole surface.