kohido/abc-curvature

ABC Curvature: Large-Scale Discrete Differential Geometry Benchmark

This dataset provides precomputed vertex-level discrete Gaussian ($K$), minimum ($k_1$), and maximum ($k_2$) principal curvature vectors across 751,407 production CAD models (100 chunk archives) from the NYU ABC Dataset.

It is designed for geometric deep learning, 3D shape analysis, CAD feature extraction, normal estimation, neural implicit surface reconstruction (SDF/UDF), and differentiable geometry benchmarking.

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1. Dataset Overview & Key Offerings

• Scale: 751,407 production-grade watertight CAD models.
• Vertex-Level Continuous Signals:
  • *_gauss.npy: Discrete Gaussian curvature ($K = k_1 \cdot k_2$) per mesh vertex.
  • *_k1.npy: Minimum principal curvature ($k_1$) per mesh vertex.
  • *_k2.npy: Maximum principal curvature ($k_2$) per mesh vertex.
• Precision & Numerical Clamping: Float16 arrays finite-range clamped to $[-65504.0, +65504.0]$ to eliminate floating-point infinities and NaNs from high-frequency CAD edge singularities.
• Companion Indices:
  • curvature_investigation_report_mesh_index.json: Fast $O(1)$ lookup index mapping each mesh to its curvature difficulty tier (Tiers 1–5), mean absolute curvature ($\overline{|K|}$), peak curvature ($K_{\max}$), and flat surface ratio ($f_{\text{flat}}$).
  • mesh_analysis.json: Topological census detailing vertex counts ($V$), face counts ($F$), and $F/V$ Euler characteristic ratios.

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2. Repository Structure & File Organization

kohido/abc-curvature/
├── README.md                                          # This Dataset Card
├── curvature_investigation_report_mesh_index.json     # Per-mesh curvature lookup table (172 MB)
├── mesh_analysis.json                                 # Per-mesh topology census (114 MB)
└── curvature/                                         # Chunk archives directory (~55 GB)
    ├── abc_0000_obj_v00.7z
    ├── abc_0001_obj_v00.7z
    └── ...
    └── abc_0099_obj_v00.7z

Inside each abc_XXXX_obj_v00.7z archive, files follow the standard ABC subfolder structure:

abc_XXXX_obj_v00/
└── <model_id>/
    ├── <model_id>_<hash>_trimesh_000_gauss.npy
    ├── <model_id>_<hash>_trimesh_000_k1.npy
    └── <model_id>_<hash>_trimesh_000_k2.npy

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3. Usage & Code Examples

1. Download Metadata & Specific Chunk Archives

from huggingface_hub import hf_hub_download

# Download the curvature index (172 MB)
index_file = hf_hub_download(
    repo_id="kohido/abc-curvature",
    filename="curvature_investigation_report_mesh_index.json",
    repo_type="dataset"
)

# Download a specific chunk archive (~550 MB)
chunk_file = hf_hub_download(
    repo_id="kohido/abc-curvature",
    filename="curvature/abc_0000_obj_v00.7z",
    repo_type="dataset"
)

2. Inspect Model Curvature & Filter by Difficulty Tier

import json

with open("curvature_investigation_report_mesh_index.json", "r") as f:
    curvature_index = json.load(f)

# Example entry lookup
sample_key = list(curvature_index.keys())[0]
print(sample_key, curvature_index[sample_key])
# Output:
# {
#   "tier": "Tier 3: Moderate Curved CAD",
#   "mean_abs_k": 0.9666,
#   "max_abs_k": 87.81,
#   "flat_ratio": 0.964,
#   "num_vertices": 1156522
# }

# Filter high-curvature evaluation set (Tier 4 & Tier 5 only)
complex_models = [
    rel_path for rel_path, meta in curvature_index.items()
    if meta["tier"] in ["Tier 4: High Curvature CAD", "Tier 5: Extreme / Freeform CAD"]
]
print(f"Total complex models: {len(complex_models):,}")

3. Load Curvature Vectors in NumPy / PyTorch

import numpy as np
import torch

# Zero-copy memory mapped load
gauss_k = np.load("00000739_e1b0437a642942c8a4fd9f81_trimesh_000_gauss.npy", mmap_mode="r")

# Convert to PyTorch float32/float64 tensor for neural training
k_tensor = torch.from_numpy(gauss_k.astype(np.float32))
print("Curvature vector shape:", k_tensor.shape)  # (N_vertices,)

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4. GPU Curvature Computation Engine: conquer3d

All discrete differential curvature vectors in this dataset were extracted at high throughput using conquer3d, a high-performance 3D computer vision and geometry processing library for PyTorch and CUDA.

Key Highlights

• GPU-Accelerated Differential Geometry: Fast, vectorized computation of discrete Gaussian curvature and principal curvatures ($k_1, k_2$) directly on CUDA tensors.
• Native PyTorch Integration: Provides TriangleMesh with zero-copy memory transfers, eliminating CPU-GPU serialization bottlenecks.
• High Throughput Scalability: Enabled processing all 751,407 production CAD models with sub-second per-mesh execution on modern GPUs.

Example: Computing Curvature with conquer3d

import torch
from conquer3d.data_structure import TriangleMesh

# Load mesh vertices and triangle indices onto GPU
vs = torch.tensor(vertices, dtype=torch.float32, device="cuda")
fs = torch.tensor(faces, dtype=torch.int32, device="cuda")

# Construct conquer3d GPU TriangleMesh
mesh = TriangleMesh(vs, fs)

# Compute discrete Gaussian curvature and principal curvatures
gaussian_curv = mesh.get_gaussian_curvature()        # Shape: (N_vertices,)
k1, k2 = mesh.get_principal_curvatures().unbind(1)   # Shapes: (N_vertices,), (N_vertices,)

For more details and source code, visit: 👉 https://github.com/KhoiDOO/conquer3d.git