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This paper presents a fast algorithm for smooth digital elevation model interpolation and approximation from scattered elevation data. The global surface is reconstructed by subdividing it into overlapping local subdomains using a perfectly balanced binary tree. In each tree leaf, a smooth local surface is reconstructed using radial basis functions. Finally a hierarchical blending is done to create the final C 1 -continuous surface using a family of functions called Partition of Unity. We present two terrain data sets and show that our method is robust since the number of data points in the Partition of Unity blending areas is explicitly specified.

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A point-based 3D surface modelling technique combined with a new point rendering technique is presented. Surfaces are modelled by specifying a set of unorganized points on the surface. An implicit representation of the surface through these points minimizing the bending energy is then calculated using radial basis functions while guaranteeing a specifiable continuity. The surface is directly rendered view-dependently in an output-sensitive multiresolution manner without the creation of a polygonal mesh representation. This is done by the local generation of 3D surface points for the rendering adapted to the output device. A new texturing technique using the material properties of the points is presented.

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