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MathGroup Archive 1995

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Re: Re: finding irregular areas

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1114] Re: [mg1041] Re: finding irregular areas
  • From: Allan Hayes <hay at haystack.demon.co.uk>
  • Date: Mon, 15 May 1995 01:01:43 -0400

Given a list of coordinates  {c1,c2, ...., cn} the area of the  
polygon defined (returning to c1 at the end) is the sum of the  
signed areas of the triangles  {c1,c2,c3},{c1,c3,c4},  
...{c1,cn-1,cn}. So a formula for it is

Area[cds_] :=
	Plus@@Det/@Partition[(# - First[cds])&/@Rest[cds],2,1]/2

Steve's colleague, who needs the areas of fields, can get the list  
of coordinate of points along the field boundary in an  
anti-clockwise direction in the that way Paul suggests. The areas of  
ponds can be be found separately and deleted, or he could make one  
list by jumping onto their edges and going round them them  
clockwise. And, for islands in those ponds, ..

Allan Hayes
hay at haystack.demon.co.uk


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