Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Finite Element Methods with B-Splines
Finite Element Methods with B-Splines
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Texture transfer during shape transformation
ACM Transactions on Graphics (TOG)
Weak Approximate Implicitization
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Volumetric parameterization and trivariate B-spline fitting using harmonic functions
Computer Aided Geometric Design
Swept Volume Parameterization for Isogeometric Analysis
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
A construction of injective parameterizations of domains for isogeometric applications
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
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In this paper, we propose a new method for parameterizing a contractible domain (called the computational domain) which is defined by its boundary. Using a sequence of harmonic maps, we first build a mapping from the computational domain to the parameter domain, i.e., the unit square or unit cube. Then we parameterize the original domain by spline approximation of the inverse mapping. Numerical simulations of our method were performed with several shapes in 2D and 3D to demonstrate that our method is suitable for various shapes. The method is particular useful for isogeometric analysis because it provides an extension from a boundary representation of a model to a volume representation.