Game Vector Math Primitives

Game Vector Math Primitives

Use this skill when game code depends on vector operations whose geometric meaning matters. Prefer clear primitives and named intent over opaque formula paste.

Primary source: Geometry for Programmers by Oleksandr Kaleniuk (https://www.manning.com/books/geometry-for-programmers), transformed and paraphrased, especially chapters 2 and 9.

Core Workflow

1. Identify the geometric question: angle, projection, side, area, normal, volume, distance, facing, or interpolation.
2. Choose the primitive that answers that question directly.
3. Check the input assumptions: dimensionality, coordinate space, units, handedness, normalization, and zero-length vectors.
4. Preserve sign when orientation or sidedness matters. Discard sign only when the caller truly needs magnitude.
5. Name intermediate values by meaning: normal, signed_area2, light_factor, plane_distance, facing, projection_t.
6. Add tests that exercise orientation, reversed winding, orthogonal vectors, parallel vectors, and zero-length inputs.

Primitive Guide

Dot Product

Use dot products for:

• Projection onto a direction.
• Angle/facing tests.
• Lambert-style lighting coefficients.
• Distance along a ray or segment.
• Checking orthogonality: dot equals zero under the numeric policy.

If both vectors are normalized, the dot product is the cosine of the angle between them. Clamp before inverse cosine if a display angle is needed.

Cross Product And 2D Cross Scalar