SPECIFICATION: True Volumetric Sub-Millimeter Mesh Collisions

Hardware-Accelerated Zero-Hitbox Physics Engine

Traditional fighting games rely on 1990s discrete bounding boxes and bone-attached capsules. This document specifies a modern, hardware-accelerated volumetric collision architecture.

Note

All collision calculations execute in parallel on GPU compute workgroups (@workgroup_size(64)) in under 0.1 ms per frame.

1. Mathematical Foundations

Each skeletal limb is enveloped in analytical Signed Distance Fields (SDFs) $ d(\vec{x}) $:

$$ d(\vec{x}) < 0 \implies \text{Inside Flesh (Penetration)} $$

$$ d(\vec{x}) = 0 \implies \text{Exact Surface Contact} $$

$$ d(\vec{x}) > 0 \implies \text{Outside Surface} $$

Continuous Swept-Volume Formula (Zero Tunneling)

To prevent fast strikes from ghosting through targets between frames:

$$ \vec{X}_{\text{swept}}(s, \tau) = (1-\tau)\vec{x}_t(s) + \tau \vec{x}_{t+1}(s), \quad \tau \in [0, 1] $$

2. Hit Severity Classification

Penetration Depth (\delta)	Classification	Gameplay Reaction
0.0 cm ≤ \delta < 0.5 cm	Glancing Graze	15% Damage, spark deflection
0.5 cm ≤ \delta < 3.0 cm	Clean Hit	100% Damage, standard hitstop
3.0 cm ≤ \delta	Crushing Counter	150% Damage, crumple stun & torque

3. Compute Shader Pipeline

wgsl

@compute @workgroup_size(64)
fn solveCollisions(@builtin(global_invocation_id) global_id: vec3u) {
    let ptIndex = global_id.x;
    if (penetrationDepth > 0.0) {
        let slot = atomicAdd(&ledger.count, 1u);
        ledger.contacts[slot].point = vec4f(contactPos, penetrationDepth);
        ledger.contacts[slot].normal = vec4f(contactNormal, impactVelocity);
    }
}

Tip

Use 3D spatial hash grids with $ 5.0\text{ cm} $ cell bounds to query point proximity in $ O(1) $ constant time.