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Title
The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics
Author
Chen, Jun

ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001
366
indicates whether the algorithm is topology-tolerant, that is,
whether the presence of non-manifold mesh regions will
catastrophically affect the algorithm. An asterix (*) under
fidelity-based or polygon-budget simplification indicates that
the algorithm can be easily extended to support that use of the
error metric, even though the algorithm’s original publication
does not mention it.
Tablel The feature of Simplification Algorithms[Luebke,97]
Algorithm
Reference
Mechanism
Use of
Error Metric
Topology
Style
Sampling
Adaptive
Subdivision
Decimation
Vertex
Merging
Fidelity-base
d
Polygon
Budget
Preserving
Modifying
Tolerant
View-depen
dent
View-lndepe
ndent
Multi-Resolution 3D
Approximation
Rossignac 92
V

V
Decimation of Triangle
Mesh
Schroeder 92
V
V
*
V
V
V
Re-tiling Polygonal
Surface
Turk 92
V
V
V
V
V
Mesh Optimization
Hoppe 93
V
V
V
V
V
Multiresolution Analysis of
Arbitrary Meshes
Eck 95
V
V
V
Voxel-Based Object
Simplification
He 95
V
V
V
Simplification Envelopes
Cohen 96
V
V
Pregressive Meshes
Hoppe 96
V
V
V
Model Simplification Using
Vertex Clustering
Low 97
V
V
V
V
View-Dependent
Refinement of
Progressive Meshes
Hoppe 97
V
V
V
V
V
Progressive Simplicial
Complexes
Popovic 97
V
V
V
V
V
Surface Simplification
Using Quadric Error
Metrics
Garland 97
V
V
V
V
V
Dynamic View-Dependent
Simplification
Xia 96
V
V
V
V
Hierarchical Dynamic
Simplification
Luebke 97
V
V
V
V
V
V
Note: An asterix means that the algorithm could easily be extended to include the specified use of error metric.
3. MULTIRESOLUTION TERRAIN MODEL THEORY
3.1. Hierarchical tin model (htin) [leila de floriant, 97 ]
A terrain is a surface in three dimensions, which can be
characterized as the graph G of a continuous bivariate function
z=f(x,y), defined over a compact and connected subset D of
the xy-plane:
G={(x, y, f(x,y)) | (x,y)e D}
Set D is called the domain of the terrain. In practice, a terrain
G is known at a finite set s cG of data points. Based on
such points, DEMs are built. A DEM consists of a plane
subdivision £ , with vertices at the projections of the data
points, and a family of functions which f locally, on each region
of X ■ An approximation terrain model is a model that does not
interpolate all data available, but only a subset. An
approximation error is associated with each triangle ti of a TIN
D. Such error is defined as the maximum approximation error
measured at those points of S-R whose vertical projection lies
inside or on he boundary of t
Err(ti)=max{Err(P) | P=(x,y,x)e S-R | (x,y)s tj
HTIN organize several TINs at different levels of resolution in a
compact structure. Let e 0 . e R predefined decreasing sequence of tolerances on the
approximation error( e ¡>e l+1 for all 0 of an HTIN is the following: starting from an initial coarse TIN
Do, whose approximation error is withine 0 , any triangle tj of D 0 ,
with Err(tj)>=e iis separately refined into a local TIN Dj, whose
domain covers tj, and such that Err(Dj)<= e 1; the process is
recursively iterated on the triangles of Dj, until the finest
resolution levels h is reached.
In HTIN, how to guarantee the consistency of edge or
boundary is a keypoint for constructive HTIN. [Leila de Foriant
and Paola Magillo,97] give us follow suggestion.
An HTIN is consistent if, for each pair of adjacent triangles t
and tj of H, sharing an edge e, one of the following conditions
holds:
Rule 1: The death errors oft and t are equal, and both t and tj
are simple triangles (i.e., tand tare both unrefined);
Rule 2: The death errors of t and t are equal, both t and t are
macro-triangles, (i.e., t and t are refined at the same step),
and the direct expansions of t and tj insert the same vertices
on edge e;