Verlet (Static Class)

Utility class providing core Verlet integration functionality for particle motion and physics simulations. Supports time-corrected integration and spring-like acceleration via Hooke's Law.

The Verlet class contains:

• A stable time-corrected Verlet integration method, designed for variable deltaTime.

• A helper for computing restoring acceleration based on spring-like elasticity.

csharpCopyEditpublic static class Verlet
{
    public static float3 TimeCorrectedVerletIntegration(...);
    public static float3 ElasticityAcceleration(...);
}

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Methods

Time Corrected Verlet Integration

csharpCopyEditpublic static float3 TimeCorrectedVerletIntegration(
    float3 currentPosition,
    float3 priorPosition,
    float3 acceleration,
    float currentTimestep,
    float priorTimestep)

Description

Performs time-corrected Verlet integration, which maintains stability when deltaTime changes frame-to-frame. This avoids the instability common in basic Verlet integration under variable framerate conditions.

Parameters

• currentPosition (float3) Current position of the particle.

• priorPosition (float3) Position of the particle in the previous frame.

• acceleration (float3) Current acceleration (e.g., gravity or other forces).

• currentTimestep (float) Delta time (Time.deltaTime) for the current frame.

• priorTimestep (float) Delta time from the previous frame.

Returns

• float3 — New particle position.

Notes

This method assumes consistent scaling of forces over time, and works well with dynamic frame rates.

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Elasticity Acceleration

csharpCopyEditpublic static float3 ElasticityAcceleration(
    float mass,
    float3 displacement,
    float elasticity)

Description

Computes acceleration due to a spring force using Hooke's Law:

F = -k * x → a = F / m

Used to simulate spring-like connections, restoring forces, or soft constraints.

Parameters

• mass (float) Mass of the object. Must be greater than 0.

• displacement (float3) Offset from equilibrium (zero force) position.

• elasticity (float) Spring constant (stiffness).

Returns

• float3 — Acceleration vector pointing back toward the equilibrium.

Notes

Returns float3.zero if mass <= 0 to avoid division errors.