A butterfly subdivision scheme for surface interpolation with tension control
ACM Transactions on Graphics (TOG)
Cubic spline fitting using data dependent triangulations
Computer Aided Geometric Design
Smooth spline surfaces over irregular meshes
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
SIAM Journal on Numerical Analysis
Surface fitting with hierarchical splines
ACM Transactions on Graphics (TOG)
Interpolating Subdivision for meshes with arbitrary topology
SIGGRAPH '96 Proceedings of the 23rd 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
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Polynomial Surfaces Interpolating Arbitrary Triangulations
IEEE Transactions on Visualization and Computer Graphics
On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree
Computer Aided Geometric Design
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The construction of surfaces from dense data points is an important problem encountered in several applications, such as computer vision, reverse engineering, computer graphics, terrain modeling, and robotics. Moreover, the particular problem of approximating digital images from a set of selected points allows to employ methods that are directed specifically to this task, which take advantage of the fact that all points belong to a common 2D domain. This paper describes a method for approximating images by fitting smooth surfaces to scattered points, where the smooth surfaces are constructed using piecewise cubic approximation. An incremental triangulation algorithm is used to iteratively refine a mesh until a specified error tolerance is achieved. The resulting surface is represented by a network of piecewise cubic triangular patches possessing C1 continuity. The proposed method is compared against other surface approximation approaches and applied to several data sets in order to demonstrate its performance.