Multistep scattered data interpolation using compactly supported radial basis functions
Journal of Computational and Applied Mathematics - Special issue on scattered data
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
Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
Reconstructing Surfaces by Volumetric Regularization Using Radial Basis Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multi-scale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions
SMI '03 Proceedings of the Shape Modeling International 2003
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Multi-Scale Reconstruction of Implicit Surfaces with Attributes from Large Unorganized Point Sets
SMI '04 Proceedings of the Shape Modeling International 2004
SMI '04 Proceedings of the Shape Modeling International 2004
Interpolating and approximating implicit surfaces from polygon soup
ACM SIGGRAPH 2004 Papers
VIS '04 Proceedings of the conference on Visualization '04
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We present a novel hierarchical spatial partitioning method for creating interpolating implicit surfaces using compactly supported radial basis functions (RBFs) from scattered surface data. From this hierarchy of functions we can create a range of models from coarse to fine, where a coarse model approximates and a fine model interpolates. Furthermore, our method elegantly handles irregularly sampled data and hole filling because of its multiresolutional approach. Like related methods, we combine neighboring patches without surface discontinuities by overlapping their embedding functions. However, unlike partition-of-unity approaches we do not require an additional explicit blending function to combine patches. Rather, we take advantage of the compact extent of the basis functions to directly solve for each patch's embedding function in a way that does not cause error in neighboring patches. Avoiding overlap error is accomplished by adding phantom constraints to each patch at locations where a neighboring patch has regular constraints within the area of overlap (the function's radius of support). Phantom constraints are also used to ensure the correct results between different levels of the hierarchy. This approach leads to efficient evaluation because we can combine the relevant embedding functions at each point through simple summation. We demonstrate our method on the Thai statue from the Stanford 3D Scanning Repository. Using hierarchical compactly supported RBFs we interpolate all 5 million vertices of the model.