Efficient Fitting and Rendering of Large Scattered Data Sets Using Subdivision Surfaces

Abstract

We present a method to efficiently construct and render a smooth surface for approximation of large functional scattered data. Using a subdivision surface framework and techniques from terrain rendering, the resulting surface can be explored from any viewpoint while maintaining high surface fairness and interactive frame rates. We show the approximation error to be sufficiently small for several large data sets. Our system allows for adaptive simplification and provides continuous levels of detail, taking into account the local variation and distribution of the data.

Locally refined spline surfaces for representation of terrain data

“…However, a few approaches can be found and Ref. [32] focuses on the approximation of large data sets primarily for visualization.…”

Multilevel regularization of wavelet based fitting of scattered data ? some experiments

“…There is no explicit grid construction: the data representation is in this sense independent of the original data points. These benefits have made approaches on structured grids a well established, much followed and universally applicable procedure, covering the gamut from strictly mathematical analysis to applications in various areas of sciences, see, e.g., [15,[18][19][20]23,24,29,30,33,34,37,44]. Employing wavelets as basis functions for the data representation provides additional features in the problem formulation regarding computational efficiency and sparseness of the representation, such as good conditioning and a natural built-in potential for adaptivity (see, e.g., [7] for an introduction to basic wavelet theory).…”

Compression of Large‐Scale Terrain Data for Real‐Time Visualization Using a Tiled Quad Tree

“…The results given show that the algorithm is capable of compressing terrain data at high accuracy by a factor of approximately 100:1 over a standard binary representation. Subdivision surfaces [32] can also be used for large areas of smooth terrain without steep discontinuities with the advantage of adaptive continuous level of detail and a simple rendering method.…”