Small patch that adds some documentation for the area() function.
Specifically, point out that intersecting points in a path will yield
(most likely), unexpected results. Visually these are identical paths,
but mathematically they're not the same. Ex:
area | plan
------
+-----------------------------------------------------------------------
-------------------
-0 | ((0,0),(0,1),(2,1),(2,2),(1,2),(1,0),(0,0))
2 | ((0,0),(0,1),(1,1),(1,2),(2,2),(2,1),(1,1),(1,0),(0,0))
The current algorithm for area(PATH) is very quick, but only handles
non-intersecting paths. I'm going to work on two other functions for
the PATH data type that determines if a PATH is intersecting or not,
and a function that returns the area() for an intersecting PATH. The
intersecting area() function will be considerably slower (I think it's
going to be O(n!) or worse instead of the current O(n), but that comes
with the territory).
-sc
PS Right now I'm developing on OS-X and there's a geometry regression
test that's returning -0. FWIW
*** ./expected/geometry.out Fri Oct 31 19:07:07 2003
--- ./results/geometry.out Thu May 27 22:16:58 2004
***************
*** 117,123 ****
| (5.1,34.5) | [(1,2),(3,4)] | (3,4)
| (-5,-12) | [(1,2),(3,4)] | (1,2)
| (10,10) | [(1,2),(3,4)] | (3,4)
! | (0,0) | [(0,0),(6,6)] | (-0,0)
| (-10,0) | [(0,0),(6,6)] | (0,0)
| (-3,4) | [(0,0),(6,6)] | (0.5,0.5)
| (5.1,34.5) | [(0,0),(6,6)] | (6,6)
--- 117,123 ----
| (5.1,34.5) | [(1,2),(3,4)] | (3,4)
| (-5,-12) | [(1,2),(3,4)] | (1,2)
| (10,10) | [(1,2),(3,4)] | (3,4)
! | (0,0) | [(0,0),(6,6)] | (0,0)
| (-10,0) | [(0,0),(6,6)] | (0,0)
| (-3,4) | [(0,0),(6,6)] | (0.5,0.5)
| (5.1,34.5) | [(0,0),(6,6)] | (6,6)
======================================================================
--
Sean Chittenden
