Generating textures on arbitrary surfaces using reaction-diffusion
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Using particles to sample and control implicit surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Shape transformation using variational implicit functions
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
Smooth surface reconstruction from noisy range data
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
A Multi-scale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions
SMI '03 Proceedings of the Shape Modeling International 2003
Flows on surfaces of arbitrary topology
ACM SIGGRAPH 2003 Papers
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
An Improvement of a Recent Eulerian Method for Solving PDEs on General Geometries
Journal of Scientific Computing
Diffusion generated motion of curves on surfaces
Journal of Computational Physics
A simple embedding method for solving partial differential equations on surfaces
Journal of Computational Physics
On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere
Journal of Computational Physics
A Stable Algorithm for Flat Radial Basis Functions on a Sphere
SIAM Journal on Scientific Computing
Level Set Equations on Surfaces via the Closest Point Method
Journal of Scientific Computing
Stable computation of multiquadric interpolants for all values of the shape parameter
Computers & Mathematics with Applications
Segmentation on surfaces with the closest point method
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Solving eigenvalue problems on curved surfaces using the Closest Point Method
Journal of Computational Physics
Stable Computations with Gaussian Radial Basis Functions
SIAM Journal on Scientific Computing
CAD and mesh repair with Radial Basis Functions
Journal of Computational Physics
Solving PDEs on manifolds with global conformal parametriazation
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
CAD and mesh repair with Radial Basis Functions
Journal of Computational Physics
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Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper, we investigate methods to solve PDEs on arbitrary stationary surfaces embedded in R^3 using the RBF method. We present three RBF-based methods that easily discretize surface differential operators. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent the most complex geometries in any dimension. Two out of the three methods, which we call the orthogonal gradients (OGr) methods are the result of our work and are hereby presented for the first time.