Semi-regular mesh extraction from volumes
Proceedings of the conference on Visualization '00
Constrained Centroidal Voronoi Tessellations for Surfaces
SIAM Journal on Scientific Computing
Polyhedral Surface Smoothing with Simultaneous Mesh Regularization
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Volumetric parameterization and trivariate b-spline fitting using harmonic functions
Proceedings of the 2008 ACM symposium on Solid and physical modeling
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
Discrete surface modelling using partial differential equations
Computer Aided Geometric Design
Volumetric geometry reconstruction of turbine blades for aircraft engines
Proceedings of the 7th international conference on Curves and Surfaces
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By a d-dimensional B-spline object (denoted as O^d), we mean a B-spline curve (d=1), a B-spline surface (d=2) or a B-spline volume (d=3). By regularization of a B-spline object O^d we mean the process of relocating the control points of O^d such that it approximates an isometric map of its definition domain in certain directions and is shape preserving. In this paper we develop an efficient regularization method for O^d, d=1,2,3, based on solving weak form L^2-gradient flows constructed from the minimization of certain regularizing energy functionals. These flows are integrated via the finite element method using B-spline basis functions. Our experimental results demonstrate that our new regularization methods are very effective.