Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
3D geometric metamorphosis based on harmonic map
PG '97 Proceedings of the 5th Pacific Conference on Computer Graphics and Applications
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
T-spline simplification and local refinement
ACM SIGGRAPH 2004 Papers
ACM SIGGRAPH 2004 Papers
Multiresolution heterogeneous solid modeling and visualization using trivariate simplex splines
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Harmonic coordinates for character articulation
ACM SIGGRAPH 2007 papers
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Volumetric parameterization and trivariate B-spline fitting using harmonic functions
Computer Aided Geometric Design
Technical Section: A divide-and-conquer approach for automatic polycube map construction
Computers and Graphics
Swept Volume Parameterization for Isogeometric Analysis
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Generalized PolyCube Trivariate Splines
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
Restricted Trivariate Polycube Splines for Volumetric Data Modeling
IEEE Transactions on Visualization and Computer Graphics
Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline
Computational Mechanics
Journal of Computational Physics
Isogeometric analysis on triangulations
Computer-Aided Design
An optimization approach for constructing trivariate B-spline solids
Computer-Aided Design
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A comprehensive scheme is described to construct rational trivariate solid T-splines from boundary triangulations with arbitrary topology. To extract the topology of the input geometry, we first compute a smooth harmonic scalar field defined over the mesh, and saddle points are extracted to determine the topology. By dealing with the saddle points, a polycube whose topology is equivalent to the input geometry is built, and it serves as the parametric domain for the trivariate T-spline. A polycube mapping is then used to build a one-to-one correspondence between the input triangulation and the polycube boundary. After that, we choose the deformed octree subdivision of the polycube as the initial T-mesh, and make it valid through pillowing, quality improvement and applying templates to handle extraordinary nodes and partial extraordinary nodes. The T-spline that is obtained is C^2-continuous everywhere over the boundary surface except for the local region surrounding polycube corner nodes. The efficiency and robustness of the presented technique are demonstrated with several applications in isogeometric analysis.