Voronoi-based interpolation with higher continuity
Proceedings of the sixteenth annual symposium on Computational geometry
Subdivision Methods for Geometric Design: A Constructive Approach
Subdivision Methods for Geometric Design: A Constructive Approach
Radial Basis Functions
On harmonic and biharmonic Bézier surfaces
Computer Aided Geometric Design
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Computing - Special Issue on Industrial Geometry
Technical Section: Dynamic harmonic fields for surface processing
Computers and Graphics
Discrete Laplace--Beltrami operators and their convergence
Computer Aided Geometric Design
ACM Transactions on Graphics (TOG)
Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
SDE: graph drawing using spectral distance embedding
GD'05 Proceedings of the 13th international conference on Graph Drawing
Natural neighbor coordinates of points on a surface
Computational Geometry: Theory and Applications
Isotropic polyharmonic B-splines: scaling functions and wavelets
IEEE Transactions on Image Processing
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Divided differences play a fundamental role in the construction of univariate B-splines over irregular knot sequences. Unfortunately, generalizations of divided differences to irregular knot geometries on two-dimensional domains are quite limited. As a result, most spline constructions for such domains typically focus on regular (or semi-regular) knot geometries. In the planar harmonic case, we show that the discrete Laplacian plays a role similar to that of the divided differences and can be used to define well-behaved harmonic B-splines. In our main contribution, we then construct an analogous discrete bi-Laplacian for both planar and curved domains and show that its corresponding biharmonic B-splines are also well-behaved. Finally, we derive a fully irregular, discrete refinement scheme for these splines that generalizes knot insertion for univariate B-splines.