Tibia

Tibia

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

extensions/humanoid/skeleton/leg/tibia/{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 Femur.

Call it

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

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

side picks RIGHT or LEFT. A right tibia 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 tibia is the right shape with x flipped.

Length

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

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

Sex	Published line, lengths in cm
Male	stature = 2.52 * tibia + 78.62
Female	stature = 2.90 * tibia + 61.53

Those are the American White adult formulae from 1952. Trotter omitted the medial malleolus from the length she used. This template still inverts the published coefficients. The generated solid includes an authored medial malleolus beyond that length.

A six foot male gets a tibia of 41.37 cm on this line.

tibia_dimensions(stature, sex, side) returns the lengths, angles 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
Proximal ML width	0.182	0.174	Authored landmark ratio
Proximal AP depth	0.118	0.112	Authored landmark ratio
Midshaft anteroposterior diameter	0.072	0.068	Authored landmark ratio
Midshaft mediolateral diameter	0.054	0.052	Authored landmark ratio
Distal ML width	0.128	0.122	Authored landmark ratio
Tuberosity offset	0.032	0.030	Authored construction
Malleolus drop	0.038	0.036	Authored construction
Anterior bow	0.008	0.007	Authored construction

Torsion and plateau retroversion are authored adult means. The male template uses 23 degrees of external torsion and 7 degrees of retroversion. The female template uses 27 degrees and 8 degrees.

The code builds the plateau first. It then twists the distal end. measured_torsion reads the generated distal chord.

The shaft cross-section is an ellipse. The AP and ML diameters are independent.

The solid is a smooth union of anatomical parts. A bowed shaft meets a flat plateau, both condyles and the intercondylar eminence. A broad ridge joins the tibial tuberosity to the shaft. A plafond and medial malleolus form the distal end. A fibular notch is cut from the distal lateral face. Connectivity and smooth normals come from the sampled field.

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

Landmarks

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

Member	Meaning
medial_condyle	Proximal medial plateau center.
lateral_condyle	Proximal lateral plateau center.
eminence	Intercondylar eminence.
tuberosity	Anterior attachment.
plafond	Distal tibial plafond.
medial_malleolus	Distal medial process.
fibular_notch	Distal lateral notch for the fibula.

tibia_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. tibia_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.tibia.mass import tibia_mass
from units.si import GRAM, NEWTON, POUND_FORCE

var report = tibia_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.cortical_region and report.trabecular_region include pore space. 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 450 g of bone tissue. That is 4.4 N, or 0.99 lbf, on Earth. The value is a grid-sampled estimate under the template tissues. It is not a proven upper bound.

Left and right tibias 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/tibia.mojo draws four tibias in a row and writes out/tibia.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/tibia.mojo out/tibia.png