spring-vrm

Our spring chains as glTF: VRMC_springBone, plus our own record of them. A rigged body's springs (a tail, a ponytail, a strand hung from a bone) go out in the standard every VRM loader reads (three-vrm's VRMSpringBoneLoaderPlugin, UniVRM, Godot's VRM importer), so they swing in those engines with no setup. Beside it goes TOSIJS_spring_chains, which holds the springs exactly as our model has them, so a file read back here swings as it did when it was made. riggedBodyGlb writes both (pass it the rig recipe); this module is the conversion and the schema, pure.

Where the two models differ

Our chain (spring-chain) is Verlet at a fixed 120 Hz: velocity kept at 1 - damping per second, gravity an acceleration, and each point PULLED toward its rest place by a fraction that grows with stiffness, so the restoring force grows with how far it is out. VRM's (three-vrm's VRMSpringBoneJoint.update, once a frame) adds the last frame's movement times 1 - dragForce, then stiffness × dt metres along the bone's rest axis and gravityPower × dt metres along gravityDir, then keeps the length. So:

• Drag is per FRAME there, per second here: dragForce = 1 - (1 - damping)^(1/60), exact at 60 frames a second. VRM's motion depends on the frame rate (the specification says so); ours does not.
• Gravity adds displacement times dt there, so it acts like an acceleration of gravityPower / dt: gravityPower = gravity / 60, exact at 60 frames a second.
• Stiffness cannot be matched exactly: VRM pushes the tip back with the same force however far it is out, ours with a force in proportion. We match how far a LEVEL segment droops under gravity: ours settles where the pull balances gravity, VRM's where tan θ = gravityPower / stiffness. Swings away from that settle differently (VRM's springs come back at a constant speed and do not ring as ours do).
• Measured on the weasel's tail (five joints, our default settings, the file read by three-vrm with nothing set up by hand): standing, the tip settles 26 cm lower in three-vrm and 43 cm lower in ours; run sideways at 3 m/s for half a second and stopped, it swings about as far and as long in both (still ±0.3 m two seconds later, which is what our defaults are). VRM bends each joint from its parent's current direction, ours from the anchor's, so a long chain droops less there.
• Colliders are spheres in both, on a joint, with an offset in the joint's own frame; VRM gives each spring the collider GROUPS it meets. Our chain radius is VRM's hitRadius.