# Full text: The 3rd ISPRS Workshop on Dynamic and Multi-Dimensional GIS & the 10th Annual Conference of CPGIS on Geoinformatics

```ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS", Bangkok, May 23-25, 2001
163
№
a(s,t) = (U(s,t)-m i )SC x + < l l (x)-P i (t),x(t) >
b(s, t) = (V(s,t) - m 3 )SC y + < / 3 (*) - P 2 (/),3>(0 >
2. Distortion of two polygons
We should distort the line included in the two polygons.
3. Displacement of polygon
Displace points in lines related to this polygon.
The special methods of 2 and 3 can be the same as 1.
4. Point selection
Filter the point information through the selection algorithm.
For example, there are two classifications, consider the
geometrical properties, first, computer the expectation
of samples in co, and the expectation
M, =
x2 ] of samples in co . Then make the perpendicular
M, =
bisector of the two points and use the perpendicular bisector as
the criterion function g(X).
The linear equation is:
2x(m xl ~m x2 ) + 2y(m yX -m y2 ) + m 2 x2 - m] x + m] 2 - m) x = 0
is just the criterion function of Bayes classification when we
suppose P{co x ) = P{co 2 ) = 0.5, p{X I co,) is the planar
probability density function which obeys .That is:
p(X/co,) =
2 *l E
T exp{ ^ }(/ = 1,2)
(2.1)
V
This geometrical classification is rational because the Bayes
classification is the best classification.
There are still other means, because of the length of the
paper,we don't give uncecessary details, just narrate simply as
follows:
5. Distort merging of two polygons
Distort lines included in these two polygons, and change
the geographic object signs of related strikethroughs by
topological table.
6. Combination of some regions
7. Substitue polygon for point set, and change the
topology of the corresponding polygon.
8. Substitue one polygon for multi-polygon, and change
the corresponding outer polygon.
9. Elimination of the same region
10. Scale-up the lines which composed the polygon, but
don’t add the number of the lines.
11. Enlarge the region needed to display, so that minish
the corresponding polygon.
12. Simplify the complicated information of lines’ shape.
4. CONCLUSION
Through these approaches above, we can resolve 12 kinds of
geometrical deformation in map generalization. Because these
approaches reserve the topological relations of geographic
objects, it can resolve the varying map scale information
automatic generalization in GIS preferably.
5. REFERENCES
Dan Liu, etc., 1999, A kind of Perception Algorithm, International
g(X) = W T X
Flere, _ w _ f m* ] is the expectation of o) j , 2 is the 2x2
x I is the
07
covariance matrix,|£|is the determinant of 2, ^ _
training sample ,and x,y with the same variance is statistical
independence(correlation function p-Q ).That is:
Marc van Kreveld, 1997,Twelve Computational Geometry
Problems from Cartographic Generalization,
http://www.geo.unizh.ch/ICA-bin/documents
Yin lianwang et al.1999.Research on WebGIS Base Geospatial
Information Generalization with Varying Map Scale. Journal of
Image and Graphics
```

## Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.