3D Generation Representation Datasheet v2.0¶

In 3D, question #1 is not “which guidance scale?” It is which geometric representation the model is generating. The same prompt may end as a mesh, field, Gaussians, or structured latents — and each format follows different mathematics and failure modes.

1. Representation spaces¶

Explicit mesh¶

\[ \mathcal M=(V,F) \]

\(V\): vertices;
\(F\): faces/triangles.

It may carry:

normals;
UVs;
material IDs;
vertex colors;
textures/PBR maps.

Implicit field¶

A continuous function:

\[ f_\theta(\mathbf x)\rightarrow \rho,\ SDF,\ occupancy,\ radiance \]

Geometry may be extracted as an isosurface:

\[ f(\mathbf x)=\tau \]

NeRF / radiance field¶

\[ F_\theta(\mathbf x,\mathbf d)\rightarrow(\sigma,\mathbf c) \]

Rendering integrates density and color along rays.

3D Gaussian Splatting¶

Each primitive may be represented as:

\[ G_i=(\mu_i,\Sigma_i,\alpha_i,c_i,\ldots) \]

where position, covariance/orientation, opacity, and appearance are explicitly parameterized.

Structured latent / sparse voxel latent¶

State:

\[ Z=\{(p_i,z_i)\}_{i=1}^{N} \]

with sparse positions/voxels + learned latent features. TRELLIS/SLAT demonstrates that a single latent can be decoded into mesh, Gaussian, or radiance representations.

PART I — THE MODERN PIPELINE¶

2. Conceptual graph¶

\[ text/image/multiview\rightarrow condition\ encoder\rightarrow 3D\ latent/structure\rightarrow generator\rightarrow representation\ decoder\rightarrow geometry/material \]

Shape and appearance are often separate subsystems:

\[ Shape\ Generation\neq Texture/Material\ Generation \]

Hunyuan3D 2.1 is an explicit example: Hunyuan3D-DiT for shape and Hunyuan3D-Paint for PBR texture/material generation.

3. Conditioning¶

Possible inputs:

text;
single image;
multiview images;
camera poses;
normal/depth maps;
masks;
existing mesh;
partial latent.

Single-image ambiguity¶

A single 2D image does not uniquely determine 3D geometry:

\[ P(Shape\mid Image) \]

is multimodal.

The model fills unobserved surfaces from a learned prior. “Janus” and backside hallucination are consequences of this observability problem, not merely “bugs.”

PART II — FLOW/DIFFUSION IN 3D¶

4. Latent flow¶

For structured latents:

\[ \frac{dZ_t}{dt}=v_\theta(Z_t,t,C) \]

Integration transforms noise/prior latent into 3D structure.

TRELLIS uses rectified-flow Transformers over SLAT.

Consequence¶

Parameters such as:

steps;
solver;
guidance;
seed;

may exist, but they operate in the 3D latent, not directly on triangles.

PART III — ISOSURFACE AND EXTRACTION¶

5. Isosurface threshold¶

This is fundamental only when the pipeline has an implicit density/SDF/occupancy field that must be converted into a surface.

\[ Surface=\{\mathbf x\mid f(\mathbf x)=\tau\} \]

Changing \(\tau\) may:

inflate/shrink the shape;
open/close cavities;
remove fine features.

Rule¶

Isosurface Threshold is not a universal AI-3D variable. It is a representation-extraction parameter.

6. Marching Cubes¶

Converts a discretized scalar field into a triangular mesh.

Quality depends on:

grid resolution;
threshold;
interpolation;
field smoothness.

Higher grid resolution increases memory/compute approximately with volume:

\[ N_{voxels}\propto N_xN_yN_z \]

Doubling resolution on each axis:

\[ N\rightarrow8N \]

PART IV — MESH QUALITY¶

7. Poly count¶

Poly count is not quality by itself.

\[ Quality\not\propto TriangleCount \]

Millions of triangles may represent surface noise; a good remesh with fewer faces may preserve perceptual shape better.

Evaluate¶

triangle aspect ratio;
curvature preservation;
topology;
normals;
manifoldness;
UV distortion.

8. Manifoldness and watertightness¶

For manufacturing, desirable properties include:

edges with consistent incidence;
correctly oriented normals;
no relevant self-intersections;
closed volume.

A renderable mesh may still be unusable for FDM/resin printing.

\[ RenderValid\not\Rightarrow ManufacturingValid \]

9. Floating components¶

Disconnected components:

\[ \mathcal M=\bigcup_i\mathcal M_i \]

Filtering by connected-component size is often useful:

\[ i^*\in\arg\max_i s(\mathcal M_i),\qquad \mathcal M^*=\mathcal M_{i^*} \]

Choose one scalar size metric \(s\) for the comparison: surface area, or enclosed volume for closed, consistently oriented components without self-intersections. These are alternative metrics with different units, not a volume/area ratio. If several components tie, choose a maximizing index according to a declared tie rule.

But do not blindly remove small components if the object intentionally contains separate parts.

PART V — MATERIAL AND TEXTURE¶

10. UV texture¶

A 2D image mapped over a local surface chart \(c\):

\[ (u,v)=\phi_c(\mathbf x_{surface}) \]

At UV seams, the same surface point may have different coordinates in adjacent charts. Mesh implementations can therefore store UV coordinates per face corner rather than one pair per geometric vertex.

Texture resolution affects memory and appearance, but not geometry.

PBR¶

Separate maps:

base color/albedo;
normal;
roughness;
metallic;
AO;
emissive.

Baked lighting¶

Texture may contain “photographed-in” illumination:

\[ Color\approx Albedo\times Illumination \]

For correct relighting, we want an estimate closer to intrinsic albedo/material.

11. Delighting¶

Conceptual objective:

\[ ObservedAppearance\rightarrow MaterialIntrinsic \]

Reduces baked shadows/highlights before using the asset in a physically based renderer.

PART VI — GAUSSIANS VS MESH¶

12. Gaussian splats¶

Advantages:

efficient neural rendering;
view synthesis;
rich appearance.

Limitations for manufacturing:

not directly a solid surface;
requires conversion/reconstruction to mesh;
“visual geometry” may not correspond to physical volume.

Rule¶

\[ PhotorealisticView\not\Rightarrow AccurateGeometry \]

PART VII — SCALE AND COORDINATES¶

13. Physical units¶

Models may generate normalized/arbitrary coordinates.

Transform to physical units:

\[ \mathbf x_{mm}=sR\mathbf x+t \]

Before printing:

define millimeters;
check bounding box;
minimum wall thickness;
tolerances;
base/orientation.

PART VIII — CAD VS GENERATIVE 3D¶

14. The essential boundary¶

Generative models primarily produce approximate/perceptual geometry.

Functional engineering requires:

parametric constraints;
exact dimensions;
tolerances;
geometric relationships;
analytic surfaces;
assemblies.

\[ GenerativeMesh\neq ParametricCAD \]

Use AI 3D for concepts/organic shapes; rebuild or parameterize in CAD when functional requirements exist.

PART IX — GUIDANCE¶

15. Guidance scale¶

It exists only according to the generative core.

If CFG-like guidance is used:

\[ f_g=f_u+s(f_c-f_u) \]

Do not assume universal ranges such as 7–15.

Artifact surfaces depend on model training, representation, solver, and decoder.

PART X — SYMMETRY¶

16. Symmetry¶

It may be:

conditioning;
data prior;
explicit geometric postprocess;
model-specific option.

It is not a universal variable.

Explicit geometric postprocessing, shown here only at the vertex-set level:

\[ V'=V\cup Mirror(V,plane) \]

This differs from “asking for symmetry” from the generative model. A complete mirrored mesh also needs mirrored face connectivity, corrected winding/normals under reflection, and welding at the mirror plane where a continuous surface is intended. The vertex union alone does not establish those properties.

PART XI — COUPLING MATRIX¶

Qualitative tendencies within a suitable operating regime; arrows are not monotonic guarantees. More resolution creates capacity for detail but does not guarantee accurate geometry, valid topology, or better textures.

Control ↑	Geometry detail	Manifold risk	Compute	Texture quality
latent/grid resolution	↑	may ↓/↑	↑ sharply	~
mesh extraction resolution	↑	may ↑ noise	↑	=
poly count	potential ↑	does not solve	downstream ↑	=
texture resolution	=	=	↑	↑
guidance	adherence ↑	non-monotonic	↑	may ↑
decimation	detail ↓	may simplify	downstream ↓	UV risk

PART XII — 3D-PRINTING WORKFLOW¶

17. From latent to plastic¶

Generate shape.
Convert/export mesh.
Remove unwanted components.
Fix normals/self-intersections.
Remesh if necessary.
Make watertight.
Set physical scale.
Verify wall thickness.
Create base/orientation.
Run slicer manifold check.
Add supports and print.

For dimensionally constrained parts: rebuild in CAD before step 8.

PART XIII — DIAGNOSTICS¶

Symptom	Investigate
good front / invented back	single-view ambiguity
“spiky” mesh	latent/model/extraction threshold
many triangles without detail	extraction/remesh
slicer complains	non-manifold/self-intersection
render has fixed shadow	baked lighting/material
fragile print	wall thickness/scale, not “AI quality”

18. Snapshot 2026¶

TRELLIS/SLAT: structured sparse 3D latent decodable into radiance fields, Gaussians, and meshes; rectified-flow Transformers.
Hunyuan3D 2.1: explicit separation of shape generation and PBR texture synthesis.
The field no longer fits the description “NeRF/point cloud → marching cubes.”

References¶

TRELLIS / Structured 3D Latents — https://arxiv.org/abs/2412.01506
Hunyuan3D 2.1 — https://arxiv.org/abs/2506.15442