A fast algorithm for particle simulations
Journal of Computational Physics
An implicit surface polygonizer
Graphics gems IV
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Global and local deformations of solid primitives
SIGGRAPH '84 Proceedings of the 11th annual conference on Computer graphics and interactive techniques
A Multi-scale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions
SMI '03 Proceedings of the Shape Modeling International 2003
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
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When we use a Radial Basis Function (RBF) implicit surface, we may need to transform it. The conventional algorithm to transform an RBF implicit surface is to apply inverse transformation to the given point and to evaluate the original function at the inversely transformed point. The algorithm keeps the initial RBF centers. Sometimes, we need the transformed RBF centers. In these cases, if we still use the conventional algorithm, we need to keep both the initial and the transformed RBF centers. Obviously, this is a problem that wastes the memory. We have derived the relationship between the initial and the transformed RBF coefficients, which can solve the previous problem. Our method only needs to keep the transformed RBF centers, and save much memory. Our method works for both globally and compactly supported RBF. We also compare our algorithm with the conventional algorithm about the time efficiency in details. The theoretical analysis and experiment results show that our algorithm is faster than the conventional algorithm in many cases. We also applied our method on RBF-based CSG operations and improved the RBF-based Boolean operation algorithm to be more efficient. Moreover, we present a solution to relieve the bumps in CSRBF Boolean operations.