Femur

Femur

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

extensions/humanoid/spec.mojo, extensions/humanoid/sex.mojo and extensions/humanoid/side.mojo hold the spec. Tissue and visual maps live in extensions/humanoid/skeleton/. The femur solid lives in extensions/humanoid/skeleton/leg/femur/. Shared field, isosurface and occupancy code sit beside them.

This is not a three.js port. See Extensions and Why extensions sit beside the port.

Call it

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

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

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

Length

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

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

Sex	Published line, lengths in cm
Male	stature = 2.38 * femur + 61.41
Female	stature = 2.47 * femur + 54.10

Those are the American White adult formulae from 1952. Forensic tools use them when no population is named. Later samples report different coefficients. This template keeps this pair as its named default.

A six foot male gets a femur of 51.04 cm on this line.

femur_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
Head diameter	0.1030	0.0977	Authored landmark ratio
Neck length, shaft axis to head center	0.1073	0.1065	Authored landmark ratio
Bicondylar width	0.1803	0.1736	Authored landmark ratio
Midshaft anteroposterior diameter	0.0631	0.0602	Authored landmark ratio
Midshaft mediolateral diameter	0.0579	0.0567	Authored landmark ratio
Greater trochanter offset	0.0687	0.0648	Authored construction
Lesser trochanter offset	0.0386	0.0370	Authored construction
Anterior bow	0.0129	0.0120	Authored construction

Neck-shaft angle, anteversion and the bicondylar angle are authored adult means for the two templates.

The code builds the shaft frame first. It then places the neck relative to that frame, including anteversion. measured_neck_shaft_angle reads the generated centerlines. It compares that angle with the reported template value.

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, a neck and a spherical head meet both trochanters. A metaphyseal flare joins the shaft to both condyles. A patellar surface, a linea aspera and a posterior notch complete the distal end. The mesh is a marching-tetrahedra isosurface. Connectivity and smooth normals come from the sampled field.

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

Landmarks

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

Member	Meaning
head_center	Hip joint.
neck_base	Where the neck meets the shaft.
greater_trochanter	Lateral attachment.
lesser_trochanter	Posteromedial attachment.
medial_condyle	Distal medial articular center.
lateral_condyle	Distal lateral articular center.

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

Bone tissue

cortical_tissue() and trabecular_tissue() hold density, porosity and longitudinal moduli. The values come from Morgan, Unnikrishnan and Hussein 2018 (PMC6053074).

Tissue density is 2.0 g/cm³ for both tissues. Apparent density is tissue density times one minus porosity.

Tissue	Porosity	Apparent density	Longitudinal moduli
Cortical	0.10	1.8 g/cm³	17.9 GPa and 18.16 GPa
Trabecular	0.80	0.40 g/cm³	400 MPa

Cortical porosity in the paper is 5% to 15%. The template uses the middle. Table 1 of that review lists two cortical longitudinal moduli from different footnotes. It does not label them tension and compression.

Poisson's ratio 0.62 is a directional cortical figure. It is not an isotropic elastic constant. Do not form a bulk modulus from E and ν with the isotropic formula.

These values are sourced research metadata. This extension does not implement a constitutive model.

BoneKind is CORTICAL or TRABECULAR. A bare integer is a compile error. Tissue data lives in tissue.mojo. The visual maps live in bone.mojo.

Mass and weight

The mesh is the outer surface. The interior is not solid cortical bone. femur_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.femur.mass import femur_mass
from units.si import GRAM, NEWTON, POUND_FORCE

var report = femur_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. That would need a mineral fraction. It does not estimate whole-bone mass with marrow.

A six foot male at a 5 mm step has about 853 g of bone tissue. That is 8.4 N, or 1.9 lbf, on Earth. The value is a grid-sampled estimate under the template tissues. It is not a proven upper bound.

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

Look

bone_albedo is a procedural sRGB map of dry cortical bone. bone_roughness is a linear roughness map. Both are visual approximations. Bone is a dielectric. Metalness is zero.

bone_phong draws the albedo with a dim highlight. bone_physical is a PHYSICAL material: a rough dielectric with an index of refraction of 1.55. See Leg.

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/femur.mojo draws four femurs in a row and writes out/femur.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/femur.mojo out/femur.png