Cortical Surface Area
Sum triangle areas of a supplied cortical mesh with duplicate-face and index auditing; millimetre coordinates yield square millimetres.
Description
A triangulated cortical mesh represents surface area as the sum of triangular faces.
A triangulated cortical mesh represents surface area as the sum of triangular faces. Coordinate units determine the squared unit of area.
The tool returns triangleAreasMm2 (triangle areas mm2); totalAreaMm2 (total area mm2). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Cortical Surface Area
Use Cortical Surface Area when you already have verticesMm, triangles and want triangleAreasMm2, totalAreaMm2. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Cortical Surface Area and understand its results
- Enter verticesMm, triangles using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read triangleAreasMm2, totalAreaMm2. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| verticesMm | Vertices mm | list of list of number | Required |
| triangles | Triangles | list of list of number | Required |
Use three-dimensional vertices in mm and triples of distinct zero-based vertex indexes. Reject duplicate faces regardless of vertex order, then return individual and total areas.
triangle area = ||(b−a) × (c−a)||/2; total = ΣfaceArea The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"verticesMm": [
[
0,
0,
0
],
[
2,
0,
0
],
[
0,
3,
0
]
],
"triangles": [
[
0,
1,
2
]
]
},
"output": {
"triangleAreasMm2": [
3
],
"totalAreaMm2": 3
}
}Limitations and assumptions
Degenerate collinear faces can have zero area. Manifoldness, self-intersection, segmentation and surface registration are not checked.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Gyrification Index: Aggregate independently tessellated pial and enclosing-hull areas for the same region and compute a surface gyrification ratio. Euler Characteristic: Count the unique cells of the union of closed voxel cubes and compute V−E+F−C; edge/corner contacts share cells, unlike a six-connected component convention.
Methodological background: Cross product reference.1
References
-
Cross product reference — NumPy developers
Similar or alternative tools
- Gyrification Index
Aggregate independently tessellated pial and enclosing-hull areas for the same region and compute a surface gyrification ratio.
- Euler Characteristic
Count the unique cells of the union of closed voxel cubes and compute V−E+F−C; edge/corner contacts share cells, unlike a six-connected component convention.