Game SDF And Field Modeling

Game SDF And Field Modeling

Use this skill when a game system is better represented as a function over space than as explicit triangles. Treat fields as gameplay and content tools, not only rendering tricks.

Primary source: Geometry for Programmers by Oleksandr Kaleniuk (https://www.manning.com/books/geometry-for-programmers), transformed and paraphrased, especially chapters 2, 8, 10, and 11. Additional sources: NVIDIA GPU Gems 3 chapter 34, "Signed Distance Fields Using Single-Pass GPU Scan Conversion of Tetrahedra" (https://developer.nvidia.com/gpugems/gpugems3/part-v-physics-simulation/chapter-34-signed-distance-fields-using-single-pass-gpu), and "Designing with Distance Fields" by Perry, Frisken, and Jones (https://merl.com/publications/TR2006-054).

Core Workflow

1. Define the field signature: point in which space goes in, what value comes out, and what sign convention means.
2. Choose whether the function must be a true distance field or only a sign-like implicit function.
3. Build primitive fields first, then compose with transforms, Booleans, blends, offsets, or deformation fields.
4. Transform the input point by the inverse object transform. Do not rewrite the primitive for every translation, rotation, or scale.
5. Track when operations preserve or destroy true distance meaning.
6. Decide how the field becomes gameplay or renderable data: direct sampling, raymarching, mesh extraction, voxelization, particles, decals, or collision probes.
7. Add visual debugging: slices, isolines, gradient arrows, sample points, and sign colors.

Field Types

• Scalar field: returns a number at each point. Use for terrain height, influence, heat, fog, danger, signed distance, or density.
• SDF: returns negative inside, zero on the boundary, positive outside, and magnitude as distance when it remains a true SDF.
• Vector field: returns a vector at each point. Use for wind, currents, steering, force fields, deformation, and flow.