Game Smooth Curves And Motion

Game Smooth Curves And Motion

Use this skill to design path and curve systems where continuity, control, and game feel matter more than exact mathematical purity.

Primary source: Geometry for Programmers by Oleksandr Kaleniuk (https://www.manning.com/books/geometry-for-programmers), transformed and paraphrased, especially chapters 5-7. Additional source: A Primer on Bezier Curves by Pomax (https://pomax.github.io/bezierinfo/).

Core Workflow

1. Identify what must be smooth: position, tangent direction, speed, curvature, camera orientation, banking, or animation value.
2. Choose the curve family that gives the needed controls with the least state: linear segments, cubic Hermite, Catmull-Rom, Bezier, B-spline, NURBS, or a custom polynomial piece.
3. Define continuity targets:
   • C0: pieces meet at positions.
   • C1: tangents match for visually smooth direction.
   • C2: curvature changes smoothly.
4. Decide parameterization: uniform t, chord length, centripetal, explicit timing, or arc-length lookup.
5. Separate authoring controls from runtime samples. Designers may edit points and handles; the game may use baked lookup tables.
6. Test extreme control points, sharp turns, closed loops, repeated points, and speed variation.

Curve Selection

• Use linear segments for grid motion, debug paths, and intentionally sharp routes.
• Use cubic Hermite when you know endpoint positions and tangent vectors.
• Use Bezier curves when control handles are the natural authoring interface.
• Use Catmull-Rom-style splines when paths should pass through waypoints with minimal handle authoring.
• Use B-splines or NURBS when many control points, high continuity, or exact conic sections matter.
• Avoid one high-degree global polynomial through many points. Split into pieces to avoid oscillation and poor local control.