ConcertoNotes 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
- Define the field signature: point in which space goes in, what value comes out, and what sign convention means.
- Choose whether the function must be a true distance field or only a sign-like implicit function.
- Build primitive fields first, then compose with transforms, Booleans, blends, offsets, or deformation fields.
- Transform the input point by the inverse object transform. Do not rewrite the primitive for every translation, rotation, or scale.
- Track when operations preserve or destroy true distance meaning.
- Decide how the field becomes gameplay or renderable data: direct sampling, raymarching, mesh extraction, voxelization, particles, decals, or collision probes.
- 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.
- Deformation field: returns displacement vectors in the same space as the modeled object.
- Implicit surrogate: returns a sign-like value but not true distance. Useful, but unsafe for operations that require distance magnitude.
SDF Operations
- Union: take the minimum of two fields.
- Intersection: take the maximum of two fields.
- Subtraction: intersect the first field with the negated second field.
- Dilation/erosion on a true SDF: add or subtract a constant according to the project's sign convention.
- Hollowing: convert a boundary band into a shell using absolute distance and shell width.
- Smooth blends: useful for organic shapes but may destroy exact distance semantics.
Distance Validity Rules
- A true SDF can support reliable offsets and gradient-based movement.
- Boolean composition usually keeps the sign behavior but not exact distance everywhere.
- Metaballs, lemniscates, density functions, and many procedural formulas are implicit fields, not true SDFs.
- After distance validity is lost, reinitialize or recompute distance before algorithms that depend on exact distance.
- Gradients on noisy or sampled fields need filtering or robust finite differences.
Game Use Cases
- Procedural rocks, caves, blobs, shields, zones, decals, and organic props.
- Destructible or editable volumes before conversion to mesh or voxels.
- Influence maps for AI, hazard fields, fog density, wind, water currents, and force fields.
- Cheap inside/outside tests for volumes where mesh topology is unreliable.
Common Mistakes
- Treating every implicit function as a true SDF.
- Applying offsets after Booleans without checking distance validity.
- Recomputing transforms or expensive neighbor searches per sample in a hot path.
- Sampling a field at too low a resolution, then blaming the extraction algorithm.
- Shipping field logic without a slice or isoline debug view.