Physics Cutting: Balancing Detection, Performance, and Precision

Physical Cutting: Stable Collisions Matter More Than "CAD-Level Precision"

The One-Sentence Essence

On the surface, it simulates realistic geometric splitting; in reality, the core relies on a "coarse-to-fine" culling strategy and "bounded complexity" fragment rules to ensure stability. This article focuses on how to make hard trade-offs between collision stability and physical performance via configuration parameters.

Why it works: Strong physical feedback; players immediately feel "it cut, it shattered, it fell."

1) Collision Detection: Coarse-to-Fine for Stability

The biggest killer of cutting experience is: The player clearly swiped, but nothing happened (trust broken).

Common detection pipeline (recommended):

1. Coarse cull (AABB/Circle): Quickly exclude 90% of non-intersecting objects
2. Fine check (Segment vs Polygon): Perform exact intersection only on candidates
3. Result handling: Generate split polygons, apply physical impulse, play effects

If your budget is tight, prefer:

• Slightly looser collision detection
• Slightly lower physical precision

Over appearing to hit but getting no reaction.

2) Splitting Strategy: Satisfaction Comes from "It Looks Shattered," Not "Infinite Shards"

Engineering-wise, you must set an upper limit:

• Generate at most N pieces per cut (e.g., 6~10)
• Fragments below the area threshold disappear directly or merge into particles
• If polygon vertex count exceeds the threshold, simplify (to avoid physics calculation explosion)

3) Balancing Performance and Precision: Encode Budget as Rules

Recommend writing these into your config:

• maxPiecesPerCut
• minPieceArea
• maxPolygonVertices
• maxCutChecksPerFrame

One-sentence summary: The "satisfaction" of a cutting mechanic is built on stable detection and controllable performance; chasing extreme precision will ruin the feel.

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4) Segment vs Polygon: Minimal Viable Intersection Detection

When entering the "fine check" phase, the most common approach is:

• Form a line segment (or polyline) from the cutting trajectory
• Detect if it intersects the target polygon edges

Key points for the minimal implementation:

• Allow some tolerance (epsilon) to avoid jitter when grazing the edge
• Sample high-speed swipes: use a polyline segment instead of a single segment (otherwise it will tunnel through)

In terms of feel, it's better to "cut slightly loosely" than to "look like you swiped but nothing happened."

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5) Split Generation: Enforce "Bounded Complexity" Shattering

The real difficulty isn't intersection detection, but ensuring the generated splits maintain:

• Polygon vertex count stays reasonable (otherwise physics explosion)
• Tiny fragments are handled (otherwise jitter everywhere)

Practical rules:

• If generated area < minPieceArea: disappear directly or become particles
• If vertex count > maxPolygonVertices: simplify (e.g., Douglas–Peucker) or degenerate to convex hull
• Generate at most maxPiecesPerCut pieces per cut; merge or discard if exceeded

6) Physics Engine Collaboration: Don't Expect "Shards to Look Good Naturally"

Once splits are generated, to make them "look satisfying," you usually need to manually add a bit of:

• Impulse in the cutting direction, to fling shards apart
• Slight angular velocity, to make shards spin
• Tuned friction/damping for ground contacts, to avoid infinite jitter

These are all part of the "presentation layer"; don't treat them as cheating.

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7) Acceptance Checklist (Stability First)

• [ ] High-speed swipes don't miss detection (sampling/polyline effective)
• [ ] Continuous cutting doesn't let fragment count run out of control (upper limit enforced)
• [ ] Tiny fragments don't cause a performance avalanche (area threshold effective)
• [ ] Cutting edge jitter is acceptable (epsilon/simplification effective)

Edge Cases

• Must handle high-speed swipes where single-segment detection tunnels through: use polyline sampling or tolerance (epsilon) as a fallback.
• Must handle continuous cutting causing fragment count to run out of control: set a max pieces per cut limit and force merge or discard.
• Must handle tiny-area fragments causing a performance avalanche: set a minimum area threshold and make them disappear or convert to particles.
• Must handle excessive polygon vertex counts causing physics calculation explosion: set a vertex count limit and simplify or degenerate.
• Must handle jitter when the cutting edge just grazes the target: introduce a tolerance mechanism to avoid "hit but no reaction."

Design Trade-offs

• Gain: Slightly looser detection, slightly lower physical precision; Cost: Visual/physical presentation is less precise than CAD; Alternative: Use "looks shattered" bounded fragments and manual impulses instead of infinite-shard realistic physics.
• Gain: Encode budget as rules (e.g., maxPiecesPerCut, minPieceArea); Cost: Cannot achieve theoretically perfect cutting effects; Alternative: Use config items to forcibly limit computation and generated object counts, prioritizing frame rate.