Muscles

Muscles

muscle_mesh builds a named skeletal muscle from stature, sex and athleticism. Tapered elliptical sections give each belly independent width and depth.

extensions/humanoid/athleticism.mojo holds UNTONED and TONED. The solids live in extensions/humanoid/skeleton/leg/muscles/. add_leg can draw bones, muscles, or both. See Leg for the other layers.

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

Call it

from extensions.humanoid.athleticism import TONED
from extensions.humanoid.sex import MALE
from extensions.humanoid.spec import HumanoidSpec
from extensions.humanoid.skeleton.leg.contents import MUSCLES
from extensions.humanoid.skeleton.leg.muscles.dimensions import RECTUS_FEMORIS
from extensions.humanoid.skeleton.leg.muscles.geometry import muscle_mesh
from units.si import FOOT, Length

var person = HumanoidSpec(Length(6.0, FOOT), MALE, TONED)
var quad = muscle_mesh(person, RECTUS_FEMORIS)

A two-argument spec stores untoned muscle. side picks RIGHT or LEFT. A right leg is the default.

The solids live in the leg frame. The origin is the tibiofemoral joint line. Plus y is proximal. Plus x is body-right. Plus z is anterior.

Athleticism

Athleticism is UNTONED or TONED. A bare integer is a compile error.

The templates scale belly radius. They do not change bone length. Untoned muscle uses scale 0.80. Toned muscle uses scale 1.00, so it carries about half again the volume. Studies of trained and untrained adults report gaps of about that size.

The scales are authored. They are not a cited regression.

Volume

Untoned muscle is calibrated toward typical adult muscle volumes measured by MRI, such as those of Handsfield et al. (2014), scaled to height. The table gives the sampled volume of a six-foot untoned male at a 4 mm step. Treat each value as approximate. People differ by a quarter or more.

Muscle	Volume (cm³)
Gluteus maximus	815
Gluteus medius	272
Tensor fasciae latae	79
Sartorius	180
Rectus femoris	321
Vastus lateralis	617
Vastus medialis	441
Vastus intermedius	445
Pectineus	75
Adductor longus	188
Adductor magnus	602
Gracilis	119
Biceps femoris	318
Semitendinosus	230
Semimembranosus	292
Gastrocnemius	466
Soleus	499
Tibialis anterior	159
Tibialis posterior	109
Extensor digitorum longus	103
Peroneus longus	124
Peroneus brevis	55
Flexor hallucis longus	128
Flexor digitorum longus	69
Extensor hallucis longus	40

Packing

The authored bellies do not fill the space around the bones by themselves. muscle_dimensions packs them. The belly stations nearest a bone go first. Each moves straight toward its bone until it presses into a bone, or a belly already placed at a similar height. A press of PACK_OVERLAP, 15 percent of the two reaches, is allowed, because muscle is soft. Attachments do not move.

Above the knee the bellies pack toward the femoral shaft. Below it each packs toward the nearer of the tibia and the fibula, so the lateral compartment settles on the fibula.

A belly that meets no neighbor then spreads into a sheet. It widens around its bone and thins away from it, up to 1.6 times, and keeps its cross-sectional area. A muscle spreads as far as its tightest station allows, so it widens evenly along its length. Then it packs inward again. MuscleDimensions.bellies holds each station's move and spread. A MuscleField applies them.

The gluteus medius is below the reported mean. It is a thin fan, and a fuller belly would bulge. The soleus runs down to the calcaneal tendon a hand's breadth above the heel.

Named parts

The labeled set follows a standard dissection of the lower limb.

Part	Role
GLUTEUS_MAXIMUS	Back of the ilium and the sacrum, behind the hip, to the gluteal tuberosity.
GLUTEUS_MEDIUS	Outer ilium below the crest to the greater trochanter.
TENSOR_FASCIAE_LATAE	Anterior superior iliac spine into the iliotibial tract.
ILIOTIBIAL_TRACT	Fascia from the trochanter to Gerdy's tubercle.
SARTORIUS	Anterior superior iliac spine to the pes anserinus.
RECTUS_FEMORIS	Anterior inferior iliac spine to the patella.
VASTUS_LATERALIS	Lateral thigh to the patella.
VASTUS_MEDIALIS	Medial thigh to the patella.
VASTUS_INTERMEDIUS	Deep anterior femur to the patella.
PECTINEUS	Pectineal line of the pubis to the lesser trochanter.
ADDUCTOR_LONGUS	Front of the pubic body to the medial femoral shaft.
ADDUCTOR_MAGNUS	Deep medial thigh to the medial femoral condyle.
GRACILIS	Inferior pubic ramus to the pes anserinus.
BICEPS_FEMORIS	Ischial tuberosity to the fibular head.
SEMITENDINOSUS	Ischial tuberosity to the pes anserinus.
SEMIMEMBRANOSUS	Ischial tuberosity to the medial tibial condyle.
GASTROCNEMIUS	Both femoral condyles to the Achilles origin.
SOLEUS	Posterior tibia and fibula to the heel analog.
TIBIALIS_ANTERIOR	Proximal tibia to the medial midfoot analog.
TIBIALIS_POSTERIOR	Deep calf to the medial ankle.
EXTENSOR_DIGITORUM_LONGUS	Fibular head to the anterior ankle.
PERONEUS_LONGUS	Fibular head, along the fibula's lateral surface, then behind the lateral malleolus.
PERONEUS_BREVIS	Behind the distal fibula, then behind the lateral malleolus.
FLEXOR_HALLUCIS_LONGUS	Back of the fibula's lower two thirds to behind the ankle: the lowest belly of the calf.
FLEXOR_DIGITORUM_LONGUS	Back of the tibia to behind the medial malleolus.
EXTENSOR_HALLUCIS_LONGUS	Front of the fibula's middle half to the front of the ankle.
ACHILLES_TENDON	Distal calf to the heel analog.
PATELLAR_TENDON	Patella to the tibial tuberosity.

Vastus intermedius and adductor magnus fill the deep thigh compartments. Tibialis posterior fills the deep calf compartment.

Origins on the pelvis

The pelvic origins come from the pelvis that holds the femur. See Pelvis. Each landmark keeps its offset from the right hip joint center. A left leg mirrors that offset.

Landmark	Where on the pelvis	Muscles
asis	Anterior superior iliac spine	Tensor, sartorius
aiis	Anterior inferior iliac spine	Rectus femoris
iliac	Iliac tubercle	Gluteus medius, and the top of the leg's skin
psis, sacral	Posterior superior spine and the sacrum's lateral border	Gluteus maximus
ischial	Low on the back of the ischial tuberosity	The hamstrings, adductor magnus
pubis	Front of the pubic body	Adductor longus
pectineal	Pectineal line	Pectineus
pubic_arch	Inferior pubic ramus	Gracilis, adductor magnus

The heel comes from the foot's calcaneal tuberosity.

MuscleDimensions is editable. Editing a landmark does not rebuild the others. Call muscle_dimensions to resolve a template. Call validate before a field, mesh or mass consumes an edited copy.

Tissue

muscle_tissue() holds wet density 1.06 g/cm³ from Mendez and Keys 1960 as a named adult template. Water fraction is 0.75. Passive modulus is 0.02 MPa. Poisson's ratio is 0.45.

tendon_tissue() holds wet density 1.12 g/cm³. Water fraction is 0.62. Longitudinal modulus is 500 MPa. The three connective-tissue solids use this tissue.

Water fraction is metadata. Mass uses wet density times envelope volume. Do not scale by one minus water fraction again.

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

Mass

from extensions.humanoid.skeleton.leg.muscles.mass import muscle_mass
from units.si import GRAM

var report = muscle_mass(person, RECTUS_FEMORIS)
report.mass.to(GRAM)

Toned muscle is heavier than untoned muscle at the same stature, sex and step.

Layers

LegContents selects what add_leg attaches.

Value	Draws
BONES	Four bones and five knee tissues.
MUSCLES	The labeled muscles and three connective-tissue solids.
VESSELS	Arteries and veins. See Vessels.
LYMPH	Lymph nodes and trunks. See Lymph.
NERVES	Named peripheral nerves. See Nerves.
SKIN	Skin envelope. See Integument.
HAIR	Thigh and calf hair shafts. See Integument.
BOTH	Bones, knee tissues and muscles.
INTEGUMENT	Skin envelope and hair shafts.
ALL	Every named layer.

A bare integer is a compile error. Both is the default.

Example

examples/muscles.mojo draws three six foot male right legs. The row is bones, untoned muscle and toned muscle. It writes out/muscles.png. Run it with:

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