Topic 8Feb 2025SDF · Implicit Surfaces · Foundational Study

SDF Research —
Points, Sphere, Cuboid, GANs.

Foundational geometry-representation study. Compared point-cloud and mesh representations to signed-distance fields (SDFs); built analytic SDFs for sphere and cuboid; explored GAN-based SDF generation. Pre-thesis-line preparation that informs every subsequent SDF-using topic (Six-Plane Mesh, Hexplane AE, Hierarchical Triplane, the UODF deep-dive).

00 — Motivation

Pick an implicit-surface representation before the thesis line touches it.

By February 2025 the thesis line was starting to think about 3-D shape representations for ML use. The choices on the table: point clouds (raw scan data), meshes (Houdini-native), and SDFs (implicit surfaces with smooth gradients). The SDF study session was the literacy-and-compare exercise before committing.

01 — Representation Comparison

Representation	Pros	Cons
Point cloud	Direct from LiDAR / photogrammetry; PointNet++ input	No topology; sparse; hard to texture
Mesh (triangles)	Explicit topology; rendering / texturing / Houdini-native	Variable-vertex-count breaks batched NN training
SDF	Smooth gradient (‖∇SDF‖ ≈ 1); differentiable; marching-cubes extractable	Closed surfaces only (use UDF / UODF for open surfaces)

02 — Analytic SDFs Built

// Sphere SDF
float sdSphere(vec3 p, float r) { return length(p) - r; }

// Cuboid SDF (axis-aligned, half-extents b)
float sdBox(vec3 p, vec3 b) {
    vec3 q = abs(p) - b;
    return length(max(q, 0.0)) + min(max(q.x, max(q.y, q.z)), 0.0);
}

// Union / intersection / difference
float opUnion(float a, float b) { return min(a, b); }
float opIntersect(float a, float b) { return max(a, b); }
float opSubtract(float a, float b) { return max(a, -b); }

03 — GAN-Based SDF Generation (exploratory)

Briefly explored using a GAN to generate SDFs (DeepSDF-class). Conclusion at the time: training a GAN on SDFs is unstable; the diffusion alternative (Topic 6 red-square, later JiT) is more promising and was pursued instead.

Full Technical Paper

White paper · SDF foundation study · analytic SDFs + CSG · GAN-SDF dead end · thesis-line propagation

Read Paper →

Appendix — Raw Materials

Transcripts & Source References

████████████████████████████████████████████████

Restricted Access

Interactive Demo · Live

Slide between sphere SDF and cuboid SDF. Click a CSG button to combine them via union, intersection, or subtract.

01 — Sphere radiusr = 0.5

cuboid half-size = 0.4

02 — CSG operationUNION

03 — SDF slicey = 0

SDF Research —Points, Sphere, Cuboid, GANs.

Pick an implicit-surface representation before the thesis line touches it.

Full Technical Paper

Interactive Demo · Live

SDF Research —
Points, Sphere, Cuboid, GANs.