How to Simulate a Roller Coaster in Matter.js

This article explains how to build a 2D physics-driven roller coaster in Matter.js by constructing smooth curved tracks, coupling multiple train cars with constraints, keeping the train anchored to the rails, and applying dynamic forces for propulsion. By combining segmented static collision geometry with high-iteration constraint solvers, you can create a stable, realistic coaster simulation in a standard HTML5 canvas environment.

1. Constructing the Track Geometry

Matter.js does not have a native continuous rail primitive, so tracks are generated using segmented static bodies.

• Spline-Based Generation: Define the coaster path using cubic Bézier curves or Catmull-Rom splines. Sample points at uniform intervals along the curve to generate coordinates.
• Segment Assembly: Between each sampled point \((x_1, y_1)\) and \((x_2, y_2)\), create a thin static rectangular body using Bodies.rectangle. Compute the angle using Math.atan2(y2 - y1, x2 - x1) and set isStatic: true.
• Surface Properties: Set the friction on track segments close to zero (e.g., 0.001 to 0.01) to allow the train to maintain momentum across slopes and loops.

2. Building and Coupling the Train Cars

A roller coaster train consists of multiple individual chassis linked together to articulate smoothly across curves.

• Car Bodies: Create rectangular bodies for each car (Bodies.rectangle) with rounded corners or chamfers to prevent sharp edges from snagging on track joints.
• Constraints (Couplers): Link adjacent cars using Constraint.create. Attach the constraint points to the rear of the leading car and the front of the trailing car. Set the stiffness to a high value (e.g., 0.8 to 1.0) and length to the desired distance between cars.
• Collision Groups: Assign all cars to the same negative collisionFilter.group so that individual train cars do not collide with one another while turning or compressing.

3. Preventing Derailment

At high speeds, a rigid body sliding along a one-sided surface will launch off hills or tunnel through tracks. Two primary methods ensure the train remains on the rails:

• Dual-Sided Rails (Physical Channel): Build a parallel top and bottom rail segment, placing the train's wheel bodies between them. This mirrors physical coaster construction, where upstop wheels prevent the train from lifting off the track.
• Normal Force Clamping: In an Events.on(engine, 'beforeUpdate', ...) callback, calculate the train's distance to the nearest point on the track spline. If the car separates from the track, apply a corrective vector force pulling the car back down along the track's normal vector.

4. Simulating Lift Hills and Propulsion

Gravity drives the coaster through drops and inversions, but mechanical sections require artificial force application.

• Lift Hills: Detect when a car is on a designated incline segment. Use Body.setVelocity or Body.applyForce directed along the segment's tangent vector to pull the train at a constant, controlled speed.
• Launch Tracks: Apply a strong instantaneous force to the cars along the track vector to simulate magnetic (LSM) or hydraulic launches.
• Brakes: Reduce velocity progressively on designated brake run segments by setting higher friction on specific static track bodies or damping the velocity directly via script.

5. Engine Tuning for High-Speed Stability

Roller coasters reach velocities that can overwhelm standard physics engine timesteps. To prevent physics artifacts:

• Increase engine.positionIterations and engine.velocityIterations to at least 8 or 10 to avoid constraint stretching and track tunneling.
• Run the engine at smaller sub-steps (e.g., updating the engine twice per animation frame at half the delta time) to maintain collision accuracy through tight loops and intense transitions.