game-spatial-queries

Game Spatial Queries

Use this skill to turn game picking, collision, containment, and distance

questions into small geometric systems with explicit constraints and failure

cases.

Primary source: Geometry for Programmers by Oleksandr Kaleniuk

(https://www.manning.com/books/geometry-for-programmers), transformed and

paraphrased, especially chapters 3, 4, and 9. Additional source: "Fast,

Minimum Storage Ray-Triangle Intersection" by Tomas Moller and Ben Trumbore

(https://dl.acm.org/doi/10.1145/1198555.1198746).

Core Workflow

1. State the query as a predicate or measured value: hit/miss, inside/outside,

closest distance, signed side, intersection point, or parameter value.

1. Move into the simplest local basis when possible. Triangle, segment, plane,

and object-local bases often reduce the query to bounds checks.

1. Derive parameters first, then apply constraints. Keep constraints visible in

code instead of burying them in one large expression.

1. Identify denominator, orientation, or length values that signal degeneracy.
2. Choose a numeric policy: exact integer predicate, scale-aware epsilon,

inclusive boundary, exclusive boundary, or conservative fallback.

1. Test hit, miss, boundary, parallel, degenerate, and near-degenerate cases.
2. Add a debug visualization when the query affects gameplay feel.

Query Patterns

Ray Against Triangle

Model the ray as R = P + t*d with t >= 0. Model triangle points as

S = A + uAB + vAC with u >= 0, v >= 0, and u + v <= 1.

Solve R = S, then:

• Reject when the shared denominator is zero or too small for the numeric policy.
• Reject when t < 0.
• Reject when u < 0, v < 0, or u + v > 1.
• Return hit distance t, barycentric-like parameters u and v, and the hit

point when needed.

Point In Triangle

Prefer one of these approaches:

• Transform the triangle to its local basis and check 0 <= u, 0 <= v,

u + v <= 1.

• Use consistent edge orientation signs from 2D cross products.
• Use barycentric coordinates when the caller needs interpolation weights too.

Decide whether points on edges count as inside. Tests must cover both the chosen

edge policy and reversed triangle winding.

Signed Point To Plane

Build a plane normal from two nonparallel edges. Dot the normalized normal with

the vector from any plane point to the query point. Keep the sign when side

matters; take absolute value only for unsigned distance.

Segment And Closest-Point Queries

Project onto the segment direction, clamp the parameter to [0, 1], then measure

distance to the clamped point. Reject or special-case zero-length segments before

normalization.

Degenerate Geometry Policy

• Zero-length vectors must not be normalized.
• Degenerate triangles must not create unstable bases or normals.
• Parallel ray/plane cases need a deliberate answer: no hit, coplanar handling,

or fallback query.

• Very small denominators need a scale-aware policy. A fixed epsilon is often

wrong across different world scales.

• Boundary inclusion must match gameplay: selection tools often want inclusive

checks; collision separation often wants conservative checks.

Implementation Checklist

• Function name states geometry and boundary policy.
• Inputs document coordinate space and units.
• Winding assumptions are explicit.
• Denominator and zero-length cases are handled before division.
• Return type exposes enough detail for the caller: bool, distance, hit point,

normal, barycentric weights, or rejection reason.

• Tests include normal case, miss case, edge/vertex case, reversed winding,

parallel case, degenerate case, and large/small scale case.

Common Mistakes

• Computing a global-space query when object-local coordinates make it trivial.
• Returning only bool from a query that later needs hit distance or normal.
• Comparing floats to zero with no policy.
• Forgetting that normals and barycentric coordinates depend on winding.
• Treating "not hit" and "invalid input geometry" as the same debugging signal.