I have created a 3D Pie Chart whose major feat (among the others) is to be rotated:
I did it to demonstrate how the visual perception of data in a Pie Chart can be distorted depending on the position, so that with a 3D pie chart, the closer the slices are, the more important they 'seem' perceptively, since they occupy a bigger area (area of ellipse + visible area of cylinder's side), while the more distant they are the less important they look, since they occupy a smaller area (only the ellipse's area, without the cylinder's), despite all numerical weighs being equal.
A method of evaluation of how much a slice's weigh is perceived compared to its basic weigh (the percentage), is the area of the slices of the 3D Pie Chart (inner pie area + outer pie area).
In order to demonstrate my point, I need to calculate the total visual area of the slices.
What approach is best to be used ?
EDIT 1
I was able to calculate the total visible area of the PieChart by using the formulas to calculate the area of a cylinder, as shown below.
Area of Pie Chart = Area of Ellipse + Area of Cylinder's side
AE -> (Area of Ellipse):
PE -> (Perimeter of Ellipse) (It is an approximation):
ACS -> (Area of Cylinder's side):
ACS = PE * H (height of cylinder)
VACS -> Visible part of Cylinder's Area's side: VACS = ACS / 2
Total Visible Area of Pie Chart -> AE + VACS
EDIT 2
I was also able to calculate the slice closest to the viewer (the one having 29.5%):
For each slice: - AE * percentage e.g. if AE is 74.28, then the light blue slice within the Ellipse (29.5%) must be:
then the light blue slice's outer side, with VACS = 25.36:
the result for the light blue slice would be -> 21.9126 + 7.4812 = 29,3938
but what about the other 2 (26% and 10.1%)?