Weird area calculation

[Didier Bur]

Hi all,

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 ?

[Dan Rathbun]

The 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)

[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).

Math::PI x 2 x 50
=> 314.1592653589793

Math::PI x 0.5 x 0.5
=> 0.7853981633974483

[Dan Rathbun]

You are confounding the calculated circumference of a circle, with the perimeter of a many sided polygon. They are distinct.

A circle (or an closed ArcCurve) is not a Drawingelement subclass object. They are virtual helper objects that are actually a series of edges with some extra data attached that is used by the GUI.