2nd/10_Wiki/Topics/Game_Design/Fixed Time Step vs Variable Time Step.md

---
id: wiki-2026-0508-fixed-time-step-vs-variable-time
title: Fixed Time Step vs Variable Time Step
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Game Loop, Timestep, Fixed Update, Variable Update]
duplicate_of: none
source_trust_level: A
confidence_score: 0.95
verification_status: applied
tags: [game-design, game-loop, simulation, physics, determinism]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: cpp
  framework: game-loop
---

# Fixed Time Step vs Variable Time Step

## 매 한 줄
> **"매 simulation 의 fixed Δt 의 advance, render 의 variable Δt 의 interpolate"**. 매 game loop 의 core decision — fixed timestep 매 deterministic physics + reproducibility 의 buy 하되 매 frame variability 의 absorb 위해 accumulator + interpolation 의 require. 2026 매 Glenn Fiedler "Fix Your Timestep!" pattern 매 Unity FixedUpdate, Unreal Tick, Bevy FixedTimestep 의 across canonical.

## 매 핵심

### 매 Fixed Timestep
- 매 simulation 매 constant Δt (e.g. 16.67ms = 60Hz) 의 always advance.
- **Pros**: Deterministic, lock-step multiplayer-friendly, stable physics.
- **Cons**: 매 spiral-of-death (frame slow → catch-up → slower → ...).

### 매 Variable Timestep
- 매 simulation Δt 매 wall-clock frame time 의 follow.
- **Pros**: Simpler, no accumulator, no interpolation.
- **Cons**: Non-deterministic, physics tunneling, replay-incompatible.

### 매 Semi-Fixed (Glenn Fiedler)
- 매 fixed simulation step + accumulator + render interpolation.
- 매 industry standard 의 2026 — Unity, Unreal, Bevy 의 default.

### 매 응용
1. Physics-heavy game (driving, fighting) — fixed mandatory.
2. Lock-step multiplayer (RTS, fighting games) — fixed + deterministic math.
3. Casual single-player — variable acceptable.

## 💻 패턴

### Naive variable timestep
```cpp
double previous = now();
while (running) {
    double current = now();
    double dt = current - previous;
    previous = current;

    update(dt);   // 매 dt 매 frame 의 따라 fluctuate
    render();
}
```

### Fixed timestep with accumulator
```cpp
constexpr double DT = 1.0 / 60.0; // 16.67ms
double accumulator = 0.0;
double previous = now();
State current_state, previous_state;

while (running) {
    double current = now();
    double frameTime = std::min(current - previous, 0.25); // 매 spiral 의 cap
    previous = current;
    accumulator += frameTime;

    while (accumulator >= DT) {
        previous_state = current_state;
        integrate(current_state, DT);
        accumulator -= DT;
    }

    double alpha = accumulator / DT;
    State render_state = lerp(previous_state, current_state, alpha);
    render(render_state);
}
```

### Determinism-safe integration (fixed-point)
```cpp
// 매 lock-step multiplayer — float drift 의 avoid
struct Fixed64 {
    int64_t raw; // 매 32.32 fixed-point
    static constexpr int64_t SCALE = 1LL << 32;
    static Fixed64 from_double(double d) { return {(int64_t)(d * SCALE)}; }
    Fixed64 operator+(Fixed64 o) const { return {raw + o.raw}; }
    Fixed64 operator*(Fixed64 o) const { return {(raw * o.raw) >> 32}; }
};
```

### Physics tunneling guard (continuous collision)
```cpp
// 매 variable / large Δt 매 fast object 매 thin wall 의 tunnel
bool sweepAABB(AABB a, Vec2 vel, AABB b, double dt, double& tHit) {
    Vec2 inv = { vel.x ? 1.0 / vel.x : 1e30, vel.y ? 1.0 / vel.y : 1e30 };
    double tEnter = std::max(
        (b.min.x - a.max.x) * inv.x,
        (b.min.y - a.max.y) * inv.y
    );
    double tExit = std::min(
        (b.max.x - a.min.x) * inv.x,
        (b.max.y - a.min.y) * inv.y
    );
    if (tEnter > tExit || tEnter > dt || tEnter < 0) return false;
    tHit = tEnter;
    return true;
}
```

### Unity-style separation
```csharp
public class Player : MonoBehaviour {
    public float speed = 5f;

    void Update() {
        // 매 input + visuals 의 variable Δt
        float h = Input.GetAxis("Horizontal");
        // 매 input buffer 의 only X 매 visual extrapolation 의 do
    }

    void FixedUpdate() {
        // 매 physics 의 fixed Δt — Time.fixedDeltaTime
        rigidbody.MovePosition(transform.position + dir * speed * Time.fixedDeltaTime);
    }
}
```

### Bevy fixed timestep
```rust
use bevy::prelude::*;
use bevy::time::common_conditions::on_timer;
use std::time::Duration;

fn main() {
    App::new()
        .add_plugins(DefaultPlugins)
        .insert_resource(Time::<Fixed>::from_hz(60.0))
        .add_systems(FixedUpdate, physics_step)
        .add_systems(Update, render_step)
        .run();
}
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Lock-step multiplayer (RTS, fighting) | 매 fixed + fixed-point math 의 mandatory |
| Physics-heavy single-player | 매 fixed + accumulator + interpolation |
| Casual / turn-based | 매 variable timestep 의 acceptable |
| Replay / netcode rollback | 매 fixed + deterministic |
| Educational / prototype | 매 variable 의 simplicity |

**기본값**: 매 Glenn Fiedler 의 fixed-with-accumulator + interpolation pattern.

## 🔗 Graph
- 부모: [[Game Loop]]
- 변형: [[Rollback Netcode]]
- 응용: [[Physics]] · [[Beat Saber]]

## 🤖 LLM 활용
**언제**: Loop architecture sketch, accumulator boilerplate, framework migration plan.
**언제 X**: Hard-realtime kernel scheduling, low-level platform timer tuning.

## ❌ 안티패턴
- **Variable for physics**: 매 driving / fighting / platformer 매 stutter + tunneling.
- **No spiral cap**: 매 GPU stall 매 simulation 의 catch-up loop 의 lock.
- **Float math 의 lock-step multiplayer**: 매 cross-platform desync 의 inevitable.
- **Render-state == sim-state**: 매 interpolation 의 absent 매 visual stutter.

## 🧪 검증 / 중복
- Verified (Glenn Fiedler "Fix Your Timestep!" 2004/2018, Unity Manual, Unreal Tick docs, Bevy book 2025).
- 신뢰도 A+.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — Fix-Your-Timestep canonical pattern, Unity/Bevy examples |