Shape reconstruction from planar cross sections
Computer Vision, Graphics, and Image Processing
A triangulation algorithm from arbitrary shaped multiple planar contours
ACM Transactions on Graphics (TOG)
A Two-Stage Algorithm for Discontinuity-Preserving Surface Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Piecewise optimal triangulation for the approximation of scattered data in the plane
Computer Aided Geometric Design
Computational Line Geometry
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Constructing a dem from grid-based data by computing intermediate contours
GIS '03 Proceedings of the 11th ACM international symposium on Advances in geographic information systems
Multi-Resolution Triangulations with Adaptation to the Domain Based on Physical Compression
SIBGRAPI '04 Proceedings of the Computer Graphics and Image Processing, XVII Brazilian Symposium
Local subdivision of Powell--Sabin splines
Computer Aided Geometric Design
Approximating complex surfaces by triangulation of contour lines
IBM Journal of Research and Development
A continuative variable resolution digital elevation model for ground-based photogrammetry
Computers & Geosciences
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The core of the presented multiresolution method is an algorithm for removing recursively the level curves according to some error criterion. This allows us to obtain a sequence of approximations of the terrain where the difference between two consecutive approximations is only one curve: the less ''important''. In other words, the input curves are sorted in such a way that the n most relevant curves are contained in the n-th resolution level. For a given curve, the relevance criterion is the error computed using a function interpolating the remaining curves. Hence, to fully formulate the multiresolution algorithm a function interpolating the contour lines of the terrain is necessary. We note that a contour line representation has a higher density in the horizontal direction than in the vertical. To alleviate this problem, a horizontal simplification algorithm for each curve is proposed. Computational efficiency concerns arising from the size of the datasets, such as the computation of the distance from a point to a polygon (with a huge number of vertices), and the point location problem, are addressed. To obtain an efficient implementation of the proposed method, it was necessary to use adequate data structures and computational geometry algorithms, in order to solve several subproblems, for instance: the computation of the distance from a point to a polygon (with a huge amount of vertices), the simplification of the level curves and the point location problem. Finally, we show how to visualize the interpolant corresponding to the n-th resolution level.