Sharif Digital Repository

Due to increasing quality of satellite images, volume of stored data significantly increased, so speed of statistical and computational processing decreased. For solving this problem, simplification
problem has been suggested. Surface simplification problem is a fundamental problem in computational geometry and it has many applications in other fields such as GIS, computer graphics, and image processing. Major goal of simplification problems is reducing stored information in any surface, Because it improves speed of processes. One of common types in this field is 3D terrain simplification while error of simplified surface be acceptable. Simplification is NP-Hard problem. In this project,... 

A basic technique in data reduction is to approximate a collection of data by another collection of smaller size. Then, the resulted data are easier to be processed or maintained. An example of such large scale data is the ordered sequence of n points describing a path or a region boundary. We are given a sequence of points p , p , ..., p , and we consider the 1 2 n problem of approximating these points by a path with k < n line segments which error of this path is not greater than special value. Various criterions are defined to compute the path simplification error.This problem can be used in GIS, Image Processing and Computer Graphics problems. In this thesis, we consider special case... 

TIN (Triangulated Irregular Network) is a Data Structure for storing and manipulating surfaces like maps in GIS applications or 3D models in game engines or Vector Fields . A TIN contains a set of triangulated vertices (which has irregular distribution) and each vertex shows a point in space . We trying to find the smallest possible set (optimal solution) of vertices from input surface (which given as a TIN) to approximate input surface with epsilon error which is given as input. also, surface simplification problem is a member of NP-Hard class. The hardness of problem makes it infeasible to find an optimal solution in polynomial time. So we try finding an approximate algorithm for this... 

One of the available methods for modeling a geographical area is sampling a series of points whose altitude is measured and the altitude of other points is estimated based on the altitude of sampled points. The use of irregular triangular networks (TIN) is one of the common methods for this estimation. Because the number of sample points is large, it is necessary to reduce them in some applications. This process reduces the number of points. The process of reducing the number of sample points is called simplification. Simplification should be done in such a way as to preserve all the main features of the original space. For this purpose, various methods have been presented, which we will... 

Geographical environments can be modeled through the medium of TINs, in which some discrete points are sampled as vertices, and the union of polygonal faces, particularly triangles, constitutes its surface. As regards the two-dimensional space, the TIN boundary is an x-monotone path and we focus on this case. If the number of vertices is too large to be stored or some sampled points should be removed due to a lack of vital information, the necessity of TIN simplification arises. On top of this situation, if a point observer locates on or above the TIN, the points visible to the observer have more priorities to be considered in the simplified TIN. For example, human eyes can see the closer or...