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[?] Formula to return object area comprised of lines and radii?

Barry Frye
Posted 7 years ago

At one time, I had a formula used in a FORTRAN program that provided the area of an object comprised of lines and radii. I provided an NC input file that contained x-y coordinates along with x-y offsets for a radius and it also indicated CW or CCW circular interpolation. The areas under the lines and radii would be summed when travelling left to right and subtracted when going right to left. I know that I can calculate the areas manually. Can someone point me to where I could find that formula? Thank you.

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POSTED BY: Barry Frye
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Barry Frye
Barry Frye
Posted 7 years ago

I'm sure this will return the accuracy required. Since I no longer have the formula that I used, what I would like to find that formula. The input file contained codes to indicate straight line motion and circular motion (clockwise and counterclockwise) along with the x-y coordinates for destination and x-y offset coordinates for radii location. The program provided the area under the lines and radii. Areas were positive for left-right relative motion (I & II) and negative for relative right-left motion (III & IV).I found the formula in the appendix of a calculus book published ~1970-1973.
POSTED BY: Barry Frye

Another way:

data = Polygon[{{1, 1}, {2, 10}, {4, 10}, {4.15, 9.6}, {4.5, 9}, {5, 
    8.5}, {5.4, 8.3}, {6, 8.2}, {6, 8.6}, {6.1, 9}, {6.25, 9.3}, {6.5,
     9.5}, {9.5, 9}, {9.5, 3}, {7, 2.5}, {6.8, 2.2}, {6.4, 1.9}, {6, 
    1.8}, {5.4, 1.85}, {4.96, 2.2}, {4.8, 2.3}, {4.5, 2.35}, {4.4, 
    2.35}, {3.9, 2.2}, {3.5, 1.8}}];
Graphics[data]

enter image description here

Area[data]
(* 57.6415 *)
POSTED BY: Mariusz Iwaniuk
Barry Frye
Barry Frye
Posted 7 years ago

I would need the accuracy to be +/- 0.001 so the polygon solution would be approximate. Correct?
POSTED BY: Barry Frye

In Wolfram Language(Mathematica) only exact numbers have infinity precision.

A toy example:

     data = Polygon[{{0, 0}, {1, 1}, {1, 1/3}}];(* 1/3 exact value *)
     Graphics[data]
     Area[data, Method -> {"NIntegrate", WorkingPrecision -> 100}]
     (* 0.33333333333333333333333333333333333333333333333333333333333333333333\
     33333333333333333333333333333333 *)


      data = Polygon[{{0, 0}, {1, 1}, {1, 0.3}}];(* 0.3 a numeric value with "MachinePrecision" *)
      Graphics[data]
      Precision[0.3]
      (*  MachinePrecision *)
      Area[data, Method -> {"NIntegrate", WorkingPrecision -> 100}]
      ( *0.35 *)

      data = Polygon[{{0, 0}, {1, 1}, {1,0.33333}}];(* 0.33333 a numeric value with "MachinePrecision" *)
      Graphics[data]
      Precision[0.33333]
      (*  MachinePrecision *)
      Area[data, Method -> {"NIntegrate", WorkingPrecision -> 100}]
      ( *0.333335 *)
POSTED BY: Mariusz Iwaniuk
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