ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
The displacement method for implicit blending surfaces in solid models
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Volumetric shape description of range data using “Blobby Model”
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Higher-order interpolation and least-squares approximation using implicit algebraic surfaces
ACM Transactions on Graphics (TOG)
Describing Complicated Objects by Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Simple constrained deformations for geometric modeling and interactive design
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
Real functions for representation of rigid solids
Computer Aided Geometric Design
Adapted wavelet analysis from theory to software
Adapted wavelet analysis from theory to software
Surface approximation of a cloud of 3D points
Graphical Models and Image Processing
Implicit surfaces for semi-automatic medical organ reconstruction
Computer graphics
Implicit reconstruction of solids from cloud point sets
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
ACM Transactions on Graphics (TOG)
Spline approximations of real algebraic surfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Fitting Curves and Surfaces With Constrained Implicit Polynomials
IEEE Transactions on Pattern Analysis and Machine Intelligence
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
2D piecewise algebraic splines for implicit modeling
ACM Transactions on Graphics (TOG)
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In this paper, we present a constructive method for fitting both an explicit and an implicit curve or surface to a set of scattered points by using gate functions. With this technique, the data are first partitioned with geometric primitives into small data sets such that each sub-data set can be well fitted by a simple algebraic or nonalgebraic shape. These simple shapes are then blended to form an overall fitting for the given data. Compared with some conventional fitting techniques, the proposed method has the following distinct features. First of all, a preset accuracy can always be achieved if the data set is sufficiently finely partitioned. Secondly, a large data set can be dealt with as several small data sets, which can significantly reduce the complexity of the shape to be fitted. Thirdly, the proposed fitting technique can also be used to increase the fitting speed by using simple fitting techniques for each sub-data set. Fourthly, the degree of smoothness of the fitted function can be adjusted to be as smooth as one wishes. Furthermore, the fitting technique provides direct support for parallel computation in curve and surface fitting. When a large data set is partitioned into smaller data sets, these small data sets can then be fitted simultaneously over a parallel system. This will greatly reduce computation time.