Knot selection for least squares thin plate splines
SIAM Journal on Scientific and Statistical Computing
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Adaptively sampled distance fields: a general representation of shape for computer graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Piecewise optimal triangulation for the approximation of scattered data in the plane
Computer Aided Geometric Design
Meshless parameterization and surface reconstruction
Computer Aided Geometric Design
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Theme Issue Introduction: Challenges in Visualization Research
IEEE Transactions on Visualization and Computer Graphics
Modeling and Visualizing Volumetric and Surface-on-Surface Data
Focus on Scientific Visualization
Adaptive smooth scattered-data approximation for large-scale terrain visualization
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
VIS '04 Proceedings of the conference on Visualization '04
VIS '04 Proceedings of the conference on Visualization '04
Multi-level partition of unity implicits
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Implicit fitting of point cloud data using radial hermite basis functions
Computing - Special issue on Geometric Modeling (Dagstuhl 2005)
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We describe some new methods for obtaining a mathematical representation of a surface that approximates a scattered point cloud, {(x i , y i , z i ) i = 1, . . . , N} without the use or need of normal vector data. The fitting surface is defined implicitly as the level set of a field function which is a linear combination of trivariate radial basis functions. Optimal approximations are based upon normalized least squares criteria which lead to eigenvalue/eigenvector characterizations. The normalized aspect allows for the exclusion of the need of normal vector estimates which is one of the unique features of this new method. Localizing techniques are introduced to allow for the efficient application of these new methods to large data sets. The use of a variety of radial basis functions are introduced through various examples that illustrate the performance and efficiency of the new methods.