RE: Algorithm for Area of a closed polygon.

[Sandeep Koranne <skoranne@tanner.com>]

Hi TEd,

Here is a simple method,

 

let us say the polygon is given by { (0,0), (10,0), (10,10), (0,10) }

Gven the array of [x,y] write then in 2 columns

 

X  Y

--------

0    0

10  0

10  10

0   10

0   0

 

do cross multiplication as you march down the column and sum the results on left side and right side

eg

0*0 + 10*10+10*10+0*0 = 200 on left column

0*10+ 0*10 +10*0 + 10*0 = 0 on right column

subtract the left column from right column = 0 - 200 = -200

divide this by 2 to get area = -100 (if you want absolute area use abs)

 

HTH

sandeep

btw: this can be programmed in 4way SIMD on Intel and others to run "extremely fast"

 

 

 

-----Original Message-----
From: Ted Hill [mailto:thill@tomotherapy.com]
Sent: Wednesday, November 12, 2003 7:00 AM
To: compgeom-discuss@research.bell-labs.com
Subject: Algorithm for Area of a closed polygon.

I want to be able to calculate the area inside a closed many-sided polygon.

 

Given an array of the (x,y) vertices that define the polygon, is there a well-known algorithm that can calculate the enclosed area quickly?

 

Thanks,

 

Ted Hill