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Computing in Geographic Information Systems
book

Computing in Geographic Information Systems

by Narayan Panigrahi
July 2014
Intermediate to advanced content levelIntermediate to advanced
303 pages
8h 34m
English
CRC Press
Content preview from Computing in Geographic Information Systems
144 Computing in Geographic Information Systems
basic properties of a Delaunay triangulation. Recall that a triangle ∆abc is
in the Delaunay triangulation, if and only if the circumcircle of this triangle
contains no other point in its interior. (We will make the usual general po-
sition assumption that no 4 points are co-circular.) How to test whether a
point d lies within the interior of the circumcircle of ∆abc? It turns out that
this can be reduced to a computable determinant. The point d lies within the
circumcircle defined by ∆abc if and only if:
ln(a, b, c, d) = det
a
x
a
y
a
x
2
+ a
y
2
1
b
x
b
y
b
x
2
+ b
y
2
1
c
x
c
y
c
x
2
+ c
y
2
1
d
x
d
y
d
x
2
+ d
y
2
1
<0 (7.10)
Assuming that this primitive In(a,b,c,d) is available to us when we add the
next point, p
i
, the major steps used ...
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Publisher Resources

ISBN: 9781482223149