: This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewise-linear surface in 3-D defined by a set of polygons; typically a set of triangles. Methods from computer graphics, computer vision, cartography, computational geometry, and other fields are classified, summarized, and compared both practically and theoretically. The surface types range from height fields (bivariate functions), to manifolds, to non-manifold self-intersecting surfaces. Piecewise-linear curve simplification is also briefly surveyed.

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Survey of Polygonal Surface Simplification Algorithms

A method is developed for surface-fitting from sampled data Surface-fitting is the process of constructing a compact representation to model the surface of an object based on a fairly large number of given data points In our case, the data is obtained from a real object using an automatic three-dimensional digitizing system The method is based on an adaptive subdivision approach, a technique previously used for the design and display of free-form curved surface objects Our approach begins with a rough approximating surface and progressively refines it in successive steps in regions where the data is poorly approximated The method has been implemented using a parametric piecewise bicubic Bernstein-Bezier surface possessing G1 geometric continuity An advantage of this approach is that the refinement is essentially local reducing the computational requirements which permits the processing of large databases Furthermore, the method is simple in concept, yet realizes efficient data compression Some experimental results are given which show that the representation constructed by this method is faithful to the original database

An adaptive subdivision method for surface-fitting from sampled data

Geometric graphs.- The ?-Neighborhood Graph.- Boundary construction.- Boundary from the ?-Graph.- Approximation and localization.- The flintstones.- Smooth curves and surfaces.- G 1 boundary construction.- Conclusions.

Closed object boundaries from scattered points

Computational Morphology is the analysis of form by computational means. This discipline typically uses techniques from Computational Geometry and Computer Aided Geometric Design. The present paper is more specifically about the construction and manipulation of closed object boundaries through a set of scattered points in 3D. Original results are developed in three stages of computational morphology:





impose a geometrical structure on the set of points;




construct a polyhedral boundary surface from this geometrical structure;




build a hierarchy of polyhedral approximations together with localization information;






The economic advantage of this approach is that there is no dependency on any specific data source. It can be used for various types of data sources or when the source is unknown.

/pdf/3d-computational-morphology-u1n3trli6n.pdf

3D Computational Morphology

An effective parallelization algorithm based on the compute-unified-device-architecture (CUDA) is developed for DEM generalization that is critical to multi-scale terrain analysis. It aims to efficiently retrieve the critical points for generating coarser-resolution DEMs which maximally maintain the significant terrain features. CUDA is embedded into a multi-point algorithm to provide a parallel-multi-point algorithm for enhancing its computing efficiency. The outcomes are compared with the ANUDEM, compound and maximum z-tolerance methods and the results demonstrate the proposed algorithm reduces response time by up to 96% compared to other methods. As to RMSE, it performs better than ANUDEM and needs half the number of points to keep the same RMSE. The mean slope and surface roughness are reduced by less than 1% in the tested cases. The parallel algorithm provides better streamline matching. Given its high computing efficiency, the proposed algorithm can retrieve more critical points to meet the demands of higher precision.

An effective parallelization algorithm for DEM generalization based on CUDA

A method is proposed for the determination of a progressive polyhedral approximation of 3-D digitized surfaces whose points are located on a regular lattice. It relies on an iterative and adaptative splitting of the triangular faces of an initial polyhedral surface. Assuming a bijection between the digitized surface and its approximation, a partition of the data base is operated. The algorithm allows for the measurement of the local quality of the approximation and avoids the generation of ill-defined triangles with sharp corners. Its low computational complexity permits the approximation of very large sets of points (hundreds of thousands).

Gholizadeh Behrouz

Papers

Adaptative Polyhedral Approximation Of Digitized Surfaces