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19-Tanzanite
May 10, 2024
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How to calculate each colored area for this graph made by points?

  • May 10, 2024
  • 3 replies
  • 4924 views

Hello,

I have these points:

Cornel_1-1715330011989.png


How to calculate each colored area from below plot made with above points?

Cornel_0-1715330587262.png

 

Mathcad Prime 9 fille attached.

Best answer by Werner_E

A1 is quite different from the rest so it has to be treated separately:

Werner_E_0-1715334008430.png

 

3 replies

23-Emerald IV
May 10, 2024

If it weren't for the weird placement of A1, you could use an integral over the (absolute value of the) function.

So what's left is brute force. like this:

LucMeekes_0-1715331552035.png

Success!
Luc

Cornel19-TanzaniteAuthor
19-Tanzanite
May 10, 2024

@LucMeekes wrote:

If it weren't for the weird placement of A1, you could use an integral over the (absolute value of the) function.


And how A1 should look like in order to be able to use an integral over the (absolute value of the) function?

ttokoro
21-Topaz I
21-Topaz I
May 10, 2024

Same with unit.

image.pngimage.pngimage.png

t.t.
Werner_E25-Diamond IAnswer
25-Diamond I
May 10, 2024

A1 is quite different from the rest so it has to be treated separately:

Werner_E_0-1715334008430.png

 

Cornel19-TanzaniteAuthor
19-Tanzanite
May 10, 2024

And for this?

Cornel_1-1715335285204.png

 

Cornel_0-1715335595907.png

 

25-Diamond I
May 10, 2024

@Cornel wrote:

And for this?

 


Are you sure about A4???

Otherwise the answer would be here: https://community.ptc.com/t5/Mathcad/How-to-calculate-each-colored-area-for-this-graph-made-by-points/m-p/948887/highlight/true#M211719

16-Pearl
May 10, 2024

Just a thought - I'd think that since any solution is going to have the vertices known - you could then use the surveyor formula/shoelace formula to find the area.  A nifty trick Werner taught me years ago that has helped me a lot.

2024-05-10_08-44-04.jpg

 

(OR = origin)

Cornel19-TanzaniteAuthor
19-Tanzanite
May 10, 2024

Hm,,,I to make also the Area(x,y) to give the same answer as Area2 or maybe Area3? Do not know what is the correct answer in this case..

Cornel_4-1715352572816.png


Even if I put like that the answer is different than Area(x,y):

Cornel_6-1715352631825.png

16-Pearl
May 10, 2024

only a guess, but since the shoelace formula closes itself (i.e. back to (0,0) the negative y values act as a negative area - since the lines cross themselves.  But if you define A1, A2, etc as unique closed areas of vertices those areas should give the same values as integrating or other geometry.  Since you have a mix of triangles and rectangles and others, this one formula will suffice once your have the vertices defined.