Scattered Data Techniques for Surfaces

This survey presents several techniques for solving variants of the following scattered data interpolation problem: given a nite set of N points in R3, nd a surface that interpolates the given set of points. Problems of this variety arise in numerous areas of applications such as geometric modeling and scienti c visualization. A large class of solutions exists for these problems and many excellent surveys exist as well. The focus of this survey is on presenting techniques that are relatively recent. Some discussion of two popular variants of the scattered data interpolation problem { trivariate (or volumetric) case and surface-on-surface { is also included. Solutions are classi ed into one of the ve categories: piecewise polynomial or rational parametric solutions, algebraic solutions, radial basis function methods, Shepard's methods and subdivision surfaces. Discussion on parametric solutions includes global interpolation by a single polynomial, interpolants based on data depend...

• Type: Conference
• Year: 1997
• Where: DAGSTUHL
• Authors: Suresh K. Lodha, Richard Franke
• Keywords: DAGSTUHL 1997, DAGSTUHL 2007, Data Interpolation Problem, Radial Basis Functions, Scattered Data Interpolation