ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001 
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MULTIRESOLUTION TERRIAN MODEL 
Jin ZHANG 
Dep. Of Surveying and Mapping 
Taiyuan University of Technology (Middle Campus) 030024 
Zhangjingis@yeah.net 
KEY WORDS: DEM Multiresolution LOD GIS 
ABSTRACT: DEM have been studied in the GIS literature for a long time. They have become a major constituent part of geographic 
information processing in the earth and engineering sciences. We use DEM to represent the terrain in GIS. The more data are available, 
the better representations of a terrain can be built. But not all tasks in the framework of a given application necessarily require the same 
accuracy, and even a single task may need different levels of accuracy in different areas of the domain. For instance, in landscape 
visualization, or in flight simulation, the terrain must be rendered at different degrees of resolution depending on their distance from the 
viewpoint. Multiresolution models, such as LOD, offer the possibility of representing and analyzing a terrain at a range of different levels 
of detail. Many papers have published in LOD studying. But in GIS, the most important issue or the key problem, such as combining 
different multiresolution spatial data into single representation and for tiled terrain how to solve tile to tile edge matching in 
multiresolution model and how to fully consider the terrain feature in multiresolution TIN model, has not been solved so good till today. 
The situation in LOD or Multiresolution model first overviewed in this paper. Then we pay more attention in how to fully consider the 
terrain feature in multiresolution TIN model and how to solve the tile-to -tile edge matching. 
1. INTRODUCTION 
(DTMs), sometimes called (DEMs), have been studied in the 
GIS literature for a long time. They have become a major 
constituent part of geographic information processing in the 
earth and engineering sciences. DTMs require specific input 
data, data models and algorithms that are different from those 
needed to represent and process 2D data. On the other hand, 
the activity of modeling and processing digital terrain data 
must be regarded as a component of a GIS which needs to be 
clearly linked to other processing functions of a spatial 
database. 
Elevation data are acquired either directly on a terrain through 
sampling techniques, or through the digitization of existing 
elevation maps (contours). Raw data come in the form of 
points either regularly distributed or scattered on a two 
dimensional domain; sometimes points are arranged to form 
polygonal lines, approximating either lineal features of the 
terrain, or contour lines. On the basis of such data, different 
models can be built, depending on the needs of specific 
applications: contour maps, raster data models on dense grids, 
approximations of the surface over the whole domain. Surface 
models can be defined either piecewise on a partition of the 
domain (either regular or irregular), or through a single 
polynomial function of high order. 
A topographical surface (or terrian) T can be defines as the 
image of a real bivariate function f defined over a domain D in 
the Euclidean plane, i.e., T={( x,y,f(x,y ))| ( x,y)e D}. Given a 
real value q, the set C„ (q ) = {(x,y ) e D | f(x,y )=q} is the set 
of contours T of at elevation q. If q is not an extreme value of f, 
then Co (q ) is a set of simple nonintersecting lines, which are 
either closed or open with endpoints on the boundary of 
domain D . 
The more data are available, the better representations of a 
terrain can be built. Modern acquisition techniques provide 
huge datasets that permit to achieve high accuracy, but this is 
paid high costs for storage and processing. On the other hand, 
not all tasks in the framework of a given application 
necessarily require the same accuracy, and even a single task 
may need different levels of accuracy in different areas of the 
domain. For instance, in landscape visualization, or in flight 
simulation, the terrain must be rendered at different degrees of 
resolution depending on their distance from the viewpoint. The 
concept of multiresolution terrain model is generically related 
to the possibility of using different representations of a 
geometric object (e.g., a terrain), having different levels of 
accuracy and complexity in order to optimize the tradeoff 
between accuracy, and cost of data storage and processing. 
Approximate models represent a terrain at a predefined 
reduced LOD; multiresolution models offer the possibility of 
representing and analyzing a terrain at a range of different 
levels of detail. 
So what is needed is a hierarchy of representations at various 
levels of detail; this makes it possible for a given view point to 
render the terrain at an adequate level of detail. Subsequent 
levels of the hierarchy should not differ too much in 
appearance, switching to more and more detailed 
representations when zooming in (this happens for instance in 
flight simulation, when one is landing) should not cause 
disturbing “jumps" in the image. On the other hand, the 
reduction of the number of triangles in subsequent levels 
should not be too small, otherwise too many levels would be 
needed, resulting in an unacceptable increase in storage. It is 
in general insufficient for rendering purposes to use only one 
level of detail at a time; although some part of the terrain may 
be close to the view point, another part (the horizon, for 
example) can still be far away. Hence, one would like to 
combine parts from different levels into a single representation 
of the terrain, such that each part of the terrain is rendered 
with appropriate detail. This means that the levels cannot be 
completely independent, as it should be possible to glue them 
together smoothly. 
The author studys these issue in the following. We first 
overview the situation of multiresolution terrain model or LOD. 
Then we primary study three main methods, including: 
Hierarchical TIN, Adding or deleting point based Delaunay 
rules and Hierarchical Dynamic Simplification methods. These 
methods have its advantage and disadvantage. Main problems 
may be consistency between adjancet edges and tile edges in 
HTIN model. The other problems are how to divide spatial area 
and code it and how to fully consider the terrain feature in 
adding and deleting points based on Delaunay rule 
retriangulating. We introduce the HOOM and technology of 
tile-to-tile edge match solve these key problem. 
2. THE SITUATION OF SURFACE SIMPLIFICATION: A 
SURVEY OF TRADITIONAL LEVEL-OF-DETAIL 
ALGORITHMS 
Polygonal simplification is a very old topic in computer 
graphics. As early as 1976 James Clark described the benefits 
of representing objects within a scene at several resolutions, 
and flight simulators have long used hand-crafted 
multi-resolution models of airplanes to guarantee a constant 
frame rate [Clark, 76 and Cosman, 81]. Recent years have 
seen a flurry of research into generating such multi-resolution 
representations of objects automatically by simplifying the 
polygonal geometry of the object. 
Note that terrains, or tessellated height fields, are a special 
category of polygonal models. A bewildering variety of 
simplification techniques have appeared in the recent literature; 
this section attempts to classify the important similarities and 
differences among these techniques.