Smooth spline surfaces over irregular meshes
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Level set diagrams of polyhedral objects
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Surface Coding Based on Morse Theory
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Anisotropic polygonal remeshing
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Global conformal surface parameterization
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Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
NURBS-based Galerkin method and application to skeletal muscle modeling
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Harmonic functions for quadrilateral remeshing of arbitrary manifolds
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Harmonic volumetric mapping for solid modeling applications
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Computer Aided Geometric Design
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Isogeometric analysis and shape optimization via boundary integral
Computer-Aided Design
Optimal analysis-aware parameterization of computational domain in isogeometric analysis
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SMI 2012: Mixed-element volume completion from NURBS surfaces
Computers and Graphics
Isogeometric simulation of turbine blades for aircraft engines
Computer Aided Geometric Design
A construction of injective parameterizations of domains for isogeometric applications
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
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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
Fitting polynomial volumes to surface meshes with Voronoï squared distance minimization
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We present a methodology based on discrete volumetric harmonic functions to parameterize a volumetric model in a way that it can be used to fit a single trivariate B-spline to data so that simulation attributes can also be modeled. The resulting model representation is suitable for isogeometric analysis [Hughes, T.J., Cottrell, J.A., B., Y., 2005. Isogeometric analysis: Cad, finite elements, nurbs, exact geometry, and mesh refinement. Computer Methods in Applied Mechanics and Engineering 194, 4135-4195]. Input data consists of both a closed triangle mesh representing the exterior geometric shape of the object and interior triangle meshes that can represent material attributes or other interior features. The trivariate B-spline geometric and attribute representations are generated from the resulting parameterization, creating trivariate B-spline material property representations over the same parameterization in a way that is related to [Martin, W., Cohen, E., 2001. Representation and extraction of volumetric attributes using trivariate splines. In: Symposium on Solid and Physical Modeling, pp. 234-240] but is suitable for application to a much larger family of shapes and attributes. The technique constructs a B-spline representation with guaranteed quality of approximation to the original data. Then we focus attention on a model of simulation interest, a femur, consisting of hard outer cortical bone and inner trabecular bone. The femur is a reasonably complex object to model with a single trivariate B-spline since the shape overhangs make it impossible to model by sweeping planar slices. The representation is used in an elastostatic isogeometric analysis, demonstrating its ability to suitably represent objects for isogeometric analysis.