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Area Calculations in the Northern Territory

The NT DIPL rules are follows:
Write an area (in sqm) as a string in NT metric format
(a) if the area is less than 1 hectare – in a complete number of square metres of which each figure,
if any, after the first 3 figures is replaced by a nought; and
(b) if the area is 1 hectare or more – in a number and decimal, if any, of a number, of hectares of which
(i) each figure, if any, after the first 4 figures is replaced by a nought, and
(ii) each decimal part, if any, less than one hundredth is omitted.
After allowing for true mid bearings, areas are computed directly from the dimensions.
The parcel is closed, adjusted by bowditch and a double longitudes method used for the calculations.

Problems

There two edge cases:
1. A computed area is very close to a round value
2. Inexact Computer Representation of floating-point numbers.

Computed Areas Close to a Round Number
This can happen when a parcel is slightly ‘non-rectangular’ and can result in an area very close to a round number. e.g. 47.99998104 sqm
Strictly, this should be rounded down to 47sqm.

However, consider that it is 0.00002 sqm (20 sqm mm) below 48 sqm and the parcel dimensions are usually measured to the nearest 2 cm.
Thus, the rounding here of 1sqcm is well below the accuracy of the measurements (2cm x 2cm = 4sqcm).
47.99998104 sqm would be rounded by 1cm to 448.009 sqm and then the truncation formula at the top of the page is applied to give a result of 448 sqm.

Inexact Number Representation
Computer representation of floating point number can sometimes be inexact.
An area calculation of a square 30x10m lot would give it an area of 299.999999998 sqm.
Any human looking at this would call it 300 sqm.
A computer would strictly round it down to 299sqm.

GeoCadastre adds a very small rounding factor of 1 sq cm to the area before the rounding process at the top of this page.
One square centimetre (0.0001 sq metres) was deemed to be below any significant figures expressed for areas and overcomes the
‘Inexact Computer Representation Issue’ mentioned above.

Examples - test cases used by GeoCadastre
(1) 1.000 sqm becomes 1 sqm
(2) 0.950 sqm becomes 0 sqm
(3) 1.050 sqm becomes 1 sqm
(4) 9.490 sqm becomes 9 sqm
(5) 9.510 sqm becomes 9 sqm
(6) 999.5 becomes 999 sqm
(7) 1000.990 becomes 1000 sqm
(8) 10,000 sqm becomes 1 ha
(9) 10099 sqm becomes 1 ha
(10) 10,100 sqm becomes 1.01 ha
(11) 9999.99 sqm becomes 9999 sqm
(12) 109,999 sqm becomes 10.99 ha
(13) 999,999 sqm becomes 99.99 ha
(14) 1,000,000 sqm becomes 100 ha
(15) 1,099,999 sqm becomes 109.9 ha
(16) 10,999,000 sqm becomes 1099 ha
(17) 109,999,999 sqm becomes 10990 ha
(18) 1,099,999,999 sqm becomes 109900 ha
(19) 10,999,999,999 sqm becomes 1099000 ha

However, we have to be realistic in deciding when rounding down to a lower figure.
This is especially important if there is a misclose, because that can alter the area significantly.
For example should an area of 999.99999 be made 999 square metres?

After some discussion with the surveyors in the NT Government,
it was decided that one square centimetre would be added to the calculated area before rounding.

Conclusion
This approach was taken to avoid ‘silly’ results where area values would be rounded down by one square metre due to the fact the calculation was done by computer.

Note: GeoCadastre uses double precision floating point numbers to store all dimensions and area values.
A double precision floating point number can store 15 significant figures.