Fibula

Fibula

fibula builds a fibula mesh from a humanoid's stature and sex.

extensions/humanoid/skeleton/leg/fibula/{dimensions,geometry,mass}.mojo. Shared field, isosurface and occupancy code lives under extensions/humanoid/skeleton/.

This is not a three.js port. See Extensions and Tibia.

Call it

from extensions.humanoid.sex import MALE
from extensions.humanoid.spec import HumanoidSpec
from extensions.humanoid.skeleton.leg.fibula.geometry import fibula
from units.si import FOOT, Length

var person = HumanoidSpec(Length(6.0, FOOT), MALE)
var bone = fibula(person)

side picks RIGHT or LEFT. A right fibula is the default. detail sets the marching-tetrahedra grid along the bone. Twenty-four is the default. Eight is the least. Sixty-four is the most.

The bone stands on y. The origin is mid-shaft. Plus y is proximal. Plus x is lateral. Plus z is anterior. A left fibula is the right shape with x flipped.

Length

Length is a modeling choice. Trotter and Gleser 1952 predict stature from fibular length. This template inverts that published line.

That inverse is not the regression of fibula length on stature. The two estimates agree only when the relationship is effectively exact.

Sex	Published line, lengths in cm
Male	stature = 2.68 * fibula + 71.78
Female	stature = 2.93 * fibula + 59.61

Those are the American White adult formulae from 1952. A six foot male gets a fibula of 41.46 cm on this line.

fibula_dimensions(stature, sex, side) returns the lengths and landmarks without building a mesh.

The accepted stature interval is 1.2 m through 2.5 m. That is the software range. It is not the calibration range of the 1952 sample.

Shape

The other linear measures are sex-specific ratios of that length. They are authored template parameters. They are not a cited osteometric table.

Measure	Male ratio	Female ratio	Role
Head diameter	0.062	0.058	Authored landmark ratio
Midshaft anteroposterior diameter	0.028	0.026	Authored landmark ratio
Midshaft mediolateral diameter	0.024	0.022	Authored landmark ratio
Malleolus AP	0.055	0.052	Authored landmark ratio
Malleolus ML	0.040	0.038	Authored landmark ratio
Malleolus height	0.072	0.068	Authored construction
Styloid length	0.022	0.020	Authored construction
Lateral bow	0.012	0.011	Authored construction

The shaft is a thin ellipse. The AP and ML diameters are independent. A proximal head and styloid meet a distal lateral malleolus.

The shaft slants medially and forward as it descends, as the tibia narrows from its plateau to its plafond. The lateral malleolus hugs the talus: about 2.5 cm lateral of the plafond's center and 1.5 cm behind it.

The mesh is a marching-tetrahedra isosurface. Connectivity and smooth normals come from the sampled field.

FibulaDimensions is editable. Editing a length does not rebuild landmarks. Call fibula_dimensions to resolve a template. Call validate before a field, mesh or mass consumes an edited copy.

Landmarks

FibulaDimensions stores joint and attachment points in meters, as a Vector3 always does.

Member	Meaning
head_center	Proximal head.
styloid	Proximal styloid process.
lateral_malleolus	Distal lateral process.

fibula_distance(dimensions, point) is the signed distance in meters. Negative is inside.

Bone tissue

Tissue data is the same as the femur. See Femur.

Mass and weight

The mesh is the outer surface. The interior is not solid cortical bone. fibula_mass(spec) samples the field. Each cell is empty, cortical region, trabecular region or marrow.

Apparent density already includes porosity. The mass formula applies that factor once.

from extensions.humanoid.skeleton.leg.fibula.mass import fibula_mass
from units.si import GRAM, NEWTON, POUND_FORCE

var report = fibula_mass(person)
report.mass.to(GRAM)
report.weight().to(NEWTON)
report.weight().to(POUND_FORCE)

report.envelope is the volume inside the surface, including marrow. report.solid_tissue is the tissue volume after porosity. report.mass is bone-tissue mass.

The report does not estimate a mineral-component mass. It does not estimate whole-bone mass with marrow.

A six foot male at a 5 mm step has about 72 g of bone tissue. That is 0.70 N, or 0.16 lbf, on Earth. The value is a grid-sampled estimate under the template tissues. It is not a proven upper bound. A thin shaft needs a finer step than a femur for a stable left and right comparison.

Left and right fibulas match in mass at the same step, within sampling error.

Limits

Stature must lie in 1.2 m through 2.5 m. Sex must be MALE or FEMALE. BodySide must be RIGHT or LEFT. A bare integer is a compile error. Edited zero or non-finite dimensions fail at validate.

Example

examples/fibula.mojo draws four fibulas in a row and writes out/fibula.png. The row is a five foot female, a five foot six female, a six foot male and a six foot six male. Run it with:

.venv/bin/mojo run -I . examples/fibula.mojo out/fibula.png