An adaptive subdivision method for surface-fitting from sampled data
SIGGRAPH '86 Proceedings of the 13th annual conference on Computer graphics and interactive techniques
Radial basis functions for multivariable interpolation: a review
Algorithms for approximation
Smooth interpolation to scattered data by bivariate piecewise polynomials of odd degree
Computer Aided Geometric Design
Piecewise planar surface models from sampled data
Scientific visualization of physical phenomena
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curve and surface fitting with splines
Curve and surface fitting with splines
Piecewise smooth surface reconstruction
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Approximation of scattered data using smooth grid functions
Journal of Computational and Applied Mathematics
Surface fitting with hierarchical splines
ACM Transactions on Graphics (TOG)
Real-time, continuous level of detail rendering of height fields
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Multiresolution BSP trees applied to terrain, transparency, and general objects
Proceedings of the conference on Graphics interface '97
ROAMing terrain: real-time optimally adapting meshes
VIS '97 Proceedings of the 8th conference on Visualization '97
Improved error bounds for scattered data interpolation by radial basis functions
Mathematics of Computation
Least squares surface approximation using multiquadrics and parametric domain distortion
Computer Aided Geometric Design
Local Lagrange interpolation by bivariate C1 cubic splines
Mathematical Methods for Curves and Surfaces
D-NURBS: A Physics-Based Framework for Geometric Design
IEEE Transactions on Visualization and Computer Graphics
Scattered Data Interpolation with Multilevel B-Splines
IEEE Transactions on Visualization and Computer Graphics
Modelling Non-Rectangular Patches using Box Splines
Proceedings of the 3rd IMA Conference on the Mathematics of Surfaces
Scattered Data Techniques for Surfaces
Dagstuhl '97, Scientific Visualization
Hierarchical Visibility in Terrains
Proceedings of the Eurographics Workshop on Rendering Techniques '97
Reconstruction of B-Spline Surfaces from Scattered Data Points
CGI '00 Proceedings of the International Conference on Computer Graphics
Adaptive Hierarchical B-spline Surface Approximation of Large-Scale Scattered Data
PG '98 Proceedings of the 6th Pacific Conference on Computer Graphics and Applications
Interpolating scattered data using 2D self-organizing feature maps
Graphical Models
Adaptive hierarchical RBF interpolation for creating smooth digital elevation models
Proceedings of the 12th annual ACM international workshop on Geographic information systems
Dimension of C1-splines on type-6 tetrahedral partitions
Journal of Approximation Theory
Quasi-interpolation by quadratic piecewise polynomials in three variables
Computer Aided Geometric Design
Visualization of Volume Data with Quadratic Super Splines
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Fitting B-spline curves to point clouds by curvature-based squared distance minimization
ACM Transactions on Graphics (TOG)
Spline approximation of general volumetric data
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Local hybrid approximation for scattered data fitting with bivariate splines
Computer Aided Geometric Design
Similarity-Guided Streamline Placement with Error Evaluation
IEEE Transactions on Visualization and Computer Graphics
A multiple B-Spline representation for progressive 3D mesh compression
ICCOM'05 Proceedings of the 9th WSEAS International Conference on Communications
Quasi-interpolation by quadratic piecewise polynomials in three variables
Computer Aided Geometric Design
A tension approach to controlling the shape of cubic spline surfaces on FVS triangulations
Journal of Computational and Applied Mathematics
Adaptive quasi-interpolating quartic splines
Computing - Geometric Modelling, Dagstuhl 2008
Dimension of C1-splines on type-6 tetrahedral partitions
Journal of Approximation Theory
Fast B-spline curve fitting by L-BFGS
Computer Aided Geometric Design
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We present an efficient method to automatically compute a smooth approximation of large functional scattered data sets given over arbitrarily shaped planar domains. Our approach is based on the construction of a C1-continuous bivariate cubic spline and our method offers optimal approximation order. Both local variation and nonuniform distribution of the data are taken into account by using local polynomial least squares approximations of varying degree. Since we only need to solve small linear systems and no triangulation of the scattered data points is required, the overall complexity of the algorithm is linear in the total number of points. Numerical examples dealing with several real world scattered data sets with up to millions of points demonstrate the efficiency of our method. The resulting spline surface is of high visual quality and can be efficiently evaluated for rendering and modeling. In our implementation we achieve real-time frame rates for typical fly-through sequences and interactive frame rates for recomputing and rendering a locally modified spline surface.