Calculate Constraint Tension Force in Matter.js

Matter.js does not provide an out-of-the-box property that reports the real-time tension force acting on a constraint. However, you can determine this force by calculating the displacement between the constraint's current anchor points relative to its rest length and applying Hooke's Law (\(F = k \cdot \Delta x\)) using the constraint's stiffness value.

Understanding the Physics

A constraint in Matter.js behaves like an elastic spring or a rigid rod depending on its stiffness setting. The tension force arises when the distance between its two connection points exceeds its resting length (constraint.length).

To calculate the tension force magnitude:

1. Determine the world-space coordinates of both attachment points, accounting for body translation and rotation.
2. Measure the current Euclidean distance between the two points.
3. Compute the extension (\(\Delta x = \text{current distance} - \text{rest length}\)).
4. Multiply the extension by the constraint's stiffness (\(F = \text{stiffness} \times \Delta x\)).

If the current distance is less than or equal to the resting length, the tension force is zero (the constraint is either slack or under compression).

Implementation

The following function takes a Matter.js Constraint and returns the scalar tension force currently acting upon it:

const { Vector } = Matter;

function getConstraintTension(constraint) {
    // 1. Calculate world-space position for Point A
    let pointA = constraint.pointA;
    if (constraint.bodyA) {
        pointA = Vector.add(
            constraint.bodyA.position,
            Vector.rotate(constraint.pointA, constraint.bodyA.angle)
        );
    }

    // 2. Calculate world-space position for Point B
    let pointB = constraint.pointB;
    if (constraint.bodyB) {
        pointB = Vector.add(
            constraint.bodyB.position,
            Vector.rotate(constraint.pointB, constraint.bodyB.angle)
        );
    }

    // 3. Compute current distance between the anchors
    const delta = Vector.sub(pointB, pointA);
    const currentDistance = Vector.magnitude(delta);

    // 4. Determine extension relative to rest length
    const extension = currentDistance - constraint.length;

    // If extension is negative or zero, there is no tension
    if (extension <= 0) {
        return 0;
    }

    // 5. Calculate tension force (Hooke's Law)
    const stiffness = constraint.stiffness !== undefined ? constraint.stiffness : 1;
    const tensionForce = extension * stiffness;

    return tensionForce;
}

Reading Tension During the Engine Loop

Because constraints update every simulation step, you should read the tension inside the afterUpdate event of the Matter.js engine:

Matter.Events.on(engine, 'afterUpdate', () => {
    const tension = getConstraintTension(myConstraint);
    
    // Example: Break the constraint if tension exceeds a threshold
    const breakingThreshold = 25;
    if (tension > breakingThreshold) {
        Matter.Composite.remove(engine.world, myConstraint);
    }
});

Using this approach allows you to implement breakable ropes, stress-based visual cues, or custom joint-failure mechanics inside your physics simulation.