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    Weird area calculation

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    • Didier BurD Offline
      Didier Bur
      last edited by

      Hi all,

      AreaAccuracy.gif

      Look at these 2 circles: one made of 16 segments and the other made of 50 segments, both have a radius of 50cm.
      Faces within these circles have the same circumference, but not the same area.
      None of these areas are exact, and even a circle made of 10000 segments will not output the exact area.
      PI * R * R gives 0.7853981633974483 m²
      The less the number of segments, the greater the error…
      Same goes for any face that have curve(s) in its outer loop, and this is a great issue when we need accurate areas calculations.
      Disapointed…
      When will SketchUp have a good integral calculator ?

      DB

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      • Dan RathbunD Offline
        Dan Rathbun
        last edited by Dan Rathbun

        I main reason is that SketchUp does not have true arcs and circle objects like a Nurbs CAD application does. In SketchUp your circles are really many sided polygons, so πr² will never return the true area of the enclosing face.

        The AI says:

        If a regular polygon has n sides of length s, the area is:
        A = (n * s²) / (4 * tan(π / n))

        Alternatively, if you know the radius r of the circle that circumscribes the polygon:
        A = (1/2) * n * r² * sin(2π / n)

        I'm not here much anymore.

        Didier BurD 1 Reply Last reply Reply Quote 1
        • Didier BurD Offline
          Didier Bur @Dan Rathbun
          last edited by Didier Bur

          @Dan-Rathbun

          Hi Dan,
          I agree with all what you say about Sketchup being a polygonal modeler, but what is not consistent IMHO is the fact that the circumference (outer loop of a disc) of a circle is exact while the area of the circular face is not.
          If SU 'knows' how the perimeter of a circle is calculated, why doesn't it know how to compute the area (assuming the outer loop of a face is a circle).
          circle 1.jpg
          Math::PI x 2 x 50
          => 314.1592653589793
          circle 2.jpg
          Math::PI x 0.5 x 0.5
          => 0.7853981633974483

          DB

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