Computational geometry: an introduction
Computational geometry: an introduction
Direct least-squares fitting of algebraic surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Control points for multivariate B-spline surfaces over arbitrary triangulations
Computer Graphics Forum
An implementation of multivariate B-spline surfaces over arbitrary triangulations
Proceedings of the conference on Graphics interface '92
Box splines
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
SIAM Journal on Numerical Analysis
Automatic reconstruction of surfaces and scalar fields from 3D scans
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Fitting smooth surfaces to dense polygon meshes
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Automatic reconstruction of B-spline surfaces of arbitrary topological type
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Triangular NURBS surface modeling of scattered data
Proceedings of the 7th conference on Visualization '96
Triangular NURBS and their dynamic generalizations
Computer Aided Geometric Design
Localized-hierarchy surface splines (LeSS)
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
Displaced subdivision surfaces
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Triangular G1 interpolation by 4-splitting domain triangles
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
What is the natural generalization of univariate splines to higher dimensions?
Mathematical Methods for Curves and Surfaces
Modeling with Triangular B-Splines
IEEE Computer Graphics and Applications
Computer Aided Geometric Design
Subdivision Surface Fitting to a Range of Points
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Bivariate Simplex B-Splines: A New Paradigm
SCCG '01 Proceedings of the 17th Spring conference on Computer graphics
Surface Reconstruction with Triangular B-splines
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
Hierarchical triangular splines
ACM Transactions on Graphics (TOG)
Smooth Adaptive Fitting of 3D Models Using Hierarchical Triangular Splines
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Meshless Thin-Shell Simulation Based on Global Conformal Parameterization
IEEE Transactions on Visualization and Computer Graphics
Curves-on-Surface: A General Shape Comparison Framework
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Graphical Models - Special issue on SPM 05
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Optimal Surface Parameterization Using Inverse Curvature Map
IEEE Transactions on Visualization and Computer Graphics
Adaptive knot placement in B-spline curve approximation
Computer-Aided Design
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Recently, a new bivariate simplex spline scheme based on Delaunay configuration has been introduced into the geometric computing community, and it defines a complete spline space that retains many attractive theoretic and computational properties. In this paper, we develop a novel shape modeling framework to reconstruct a closed surface of arbitrary topology based on this new spline scheme. Our framework takes a triangulated set of points, and by solving a linear least-square problem and iteratively refining parameter domains with newly added knots, we can finally obtain a continuous spline surface satisfying the requirement of a user-specified error tolerance. Unlike existing surface reconstruction methods based on triangular B-splines (or DMS splines), in which auxiliary knots must be explicitly added in advance to form a knot sequence for construction of each basis function, our new algorithm completely avoids this less-intuitive and labor-intensive knot generating procedure. We demonstrate the efficacy and effectiveness of our algorithm on real-world, scattered datasets for shape representation and computing.