Description
Calculate signed planar traverse area by double-meridian distances after an explicit closure check.
Geodesy distinguishes a mathematical reference ellipsoid, a realized coordinate datum and the physical gravity field. Geodetic latitude follows the ellipsoid normal; geocentric latitude follows a radius from the center. Ellipsoidal height, orthometric height and geoid undulation are separate signed quantities. Keep the declared ellipsoid, coordinate axes, angular units and time scale with a result.
Calculate signed planar traverse area by double-meridian distances after an explicit closure check.
When to use this tool
Use this tool when you need to calculate signed planar traverse area by double-meridian distances after an explicit closure check.
How to use the tool and how it works
- Enter northIncrementsMeters, eastIncrementsMeters using the definitions below.
- Run the operation. Resolve input-format errors before interpreting an output.
- Read result.doubleMeridianDistancesMeters, result.signedAreaSquareMeters, using the stated boundary, ordering, sign and absence conventions.
Require at least three aligned north/east leg increments and closure within scale×10⁻¹⁰, where scale is the largest absolute increment or one. Start DMD at the first east increment, recur DMD_j=DMD_(j−1)+east_(j−1)+east_j, and return Σ(DMD×north)/2 as signed area.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| northIncrementsMeters | At least three ordered signed north increments in meters, each magnitude≤10⁶, aligned to east increments. | Dense list of at most 128 finite numbers, under the stated integer/range rules. |
| eastIncrementsMeters | Aligned signed east increments in meters, each magnitude≤10⁶, with explicit closure required. | Dense list of at most 128 finite numbers, under the stated integer/range rules. |
| Output field | Interpretation |
|---|---|
| result | Object containing the fields below. |
| result.doubleMeridianDistancesMeters | DMD recurrence values per ordered traverse leg, in meters. |
| result.signedAreaSquareMeters | Signed planar DMD area in square meters under the supplied leg order. |
{
"input": {
"northIncrementsMeters": [
0,
1,
0,
-1
],
"eastIncrementsMeters": [
1,
0,
-1,
0
]
},
"output": {
"result": {
"doubleMeridianDistancesMeters": [
1,
2,
1,
0
],
"signedAreaSquareMeters": 1
}
}
}Limitations and assumptions
- Each increment magnitude≤10⁶ m. This sign follows the tool’s DMD recurrence and ordered traverse; use an absolute value only if unsigned area is intended. No closure adjustment, self-intersection repair or geodetic surface area is inferred.
- All quantities are finite and retain the units stated for this operation. Ellipsoid-parameter tools use semi-major axis 1–10⁸ m and dimensionless flattening 0–0.02; explicit-axis tools use 0.9a≤b≤a unless a tighter bound is stated. These tools do not fetch datums, geoid grids, satellite observations or Earth-orientation updates.
- Every declared outer field is required and unknown outer fields are rejected. Strings and JSON text have size limits, lists are bounded to 128 entries, and JSON nesting/node counts are bounded. Tighter operation-specific bounds stated above take precedence.
- Numeric results must be finite. Large physical magnitudes are allowed by the output evidence checks, while integer fields and source schemas retain their exactness rules. Source indexes are zero-based. Floating-point residues can remain even where an ideal formula gives an exact zero.
Alternative or Complementary methods
Use a coordinate transform for a change of representation and explicit datum parameters for a change of reference frame. Preserve model and convergence metadata, and use observation and datum information appropriate to a real survey before interpreting a computed tolerance as accuracy.
References
Similar or alternative tools
- Traverse Misclosure Lat Departure Closure Calculator
Calculate planar north/east traverse increments, perimeter and closure-vector magnitude.
- Compass Rule Adjustment Distributor for Traverse
Distribute planar traverse closure by leg length using the Bowditch or compass rule.