Module constraints 

XPBD + Sequential-Impulse constraint solver for 2D/3D rigid bodies.

Implements both:

• Sequential Impulse (SI) solver — velocity-level constraint resolution following Erin Catto / Box2D style iterative impulses.
• Extended Position-Based Dynamics (XPBD) — position-level constraints with compliance, substep integration, and constraint islands.

Constraint types

• ContactConstraint — normal + friction, restitution, Baumgarte, warm-start
• DistanceConstraint — rigid rod (exact) and soft spring (compliance)
• HingeConstraint — single-axis rotation with limits and motor
• BallSocketConstraint — 3-DOF free rotation with cone limit
• SliderConstraint — prismatic joint with translation limits and motor
• WeldConstraint — fully rigid 6-DOF lock
• PulleyConstraint — two bodies through a fixed pulley ratio
• MotorConstraint — angular velocity drive
• MaxDistanceConstraint — soft rope
• GearConstraint — ratio-based angular coupling

Structs

BallSocketConstraint

Ball-and-socket joint: 3-DOF rotation, fixed relative position. Optionally limits the cone angle between the two body Z-axes.

BodyHandle

Reference to a rigid body in the solver.

BodyState

Minimal state the solver needs from a rigid body.

ConstraintId

ConstraintIsland

A group of bodies and constraints that are connected and should be solved together.

ConstraintSolver

Sequential-impulse + XPBD constraint solver.

ConstraintWorld

Manages all bodies and constraints in one place.

ContactConstraint

Contact constraint: normal impulse (non-penetration) + friction impulse.

DistanceConstraint

Maintain a fixed distance between two local anchor points on two bodies. With compliance = 0 this is a rigid rod; compliance > 0 gives spring behavior.

GearConstraint

Couple the angular velocities of two bodies: omega_a + ratio * omega_b = 0.

HingeConstraint

Hinge (revolute) joint: two bodies share a common anchor. Allows rotation around the Z-axis. Supports angular limits and a velocity motor.

MaxDistanceConstraint

Soft rope: only constrains when distance exceeds max_distance.

MotorConstraint

Drive a body at a target angular velocity. Acts as a torque motor.

PinConstraint

Pin a body’s local anchor to a fixed world-space point.

PulleyConstraint

Pulley constraint: body_a and body_b are connected via a rope over two fixed pulley points. Maintains: len_a + ratio * len_b = constant.

SliderConstraint

Prismatic (slider) joint: allows translation along one axis only. Supports translation limits and a linear motor.

SpringConstraint

A spring-damper between two anchor points (Hooke’s law).

WeldConstraint

Weld joint: fully rigid 6-DOF lock. Fixes both relative position and angle.

Constants

WORLD

Sentinel for world-space anchors (infinite mass, immovable).

Traits

Constraint

A constraint imposes a restriction on body state.

Functions

cross2

2D cross product (scalar result): a.xb.y - a.yb.x

detect_islands

Detect constraint islands using union-find.

perp

Perpendicular of a 2D vector: (-y, x)

rotate2

Rotate a Vec2 by angle theta.