[postgis-users] Polygon validity

[Andrea Peri]

first of all: sorry for my poor english ..:(

>>* So a curve with 2 consecutive point like this
*>>* linestring (10 10, 20 20, 20 20, 30 30) is violating this definition
*>I disagree.  In the formal definition of Curve above, note the condition
>that x1 < x2.  In any continuous parameterization f of LINESTRING(10 10,
>20 20, 20 20, 30 30), if f(x1) = pt[1] (20 20) and f(x2 = pt[2] (20 20),
>then x1 must = x2.

Oh no.

x1 and x2 report simply a sequence (or a serial of point),
for example

1 , 2 , 3
is a sequence of points.

but even
1 , 1,  1
is a sequence.

(where x1 = 1, x2 = 1 and x3 = 1)

So

x1 is always differente from x2.

x1 < x2 is needed for saying that it is a sequence, or that matemathically
there is a sequence of point where the first point come in before of the
second point,
and the second point com after the first point.
the 1 and 2 prefix is a positional index in the sequence.

so:

is cannot be true that
if f(x1) = f(x2) then x1 = x2.

Andrea.


-- 
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Andrea Peri
. . . . . . . . .
qwerty àèìòù
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