# Residual Primitive Fitting of 3D Shapes with SuperFrusta

arXiv: https://arxiv.org/abs/2512.09201 · HTML: https://mlsanity.com/paper/2512.09201/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 47 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Builds on (most cited first, 30 of 30)

- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [Using Shape to Categorize: Low-Shot Learning with an Explicit Shape Bias](https://mlsanity.com/paper/2101.07296/) (2021)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)
- [SAMPart3D: Segment Any Part in 3D Objects](https://mlsanity.com/paper/2411.07184/) (2024)
- [PARTFIELD: Learning 3D Feature Fields for Part Segmentation and Beyond](https://mlsanity.com/paper/2504.11451/) (2025)
- [3D Gaussian Splatting: Survey, Technologies, Challenges, and Opportunities](https://mlsanity.com/paper/2407.17418/) (2024)
- [3D-PRNN: Generating Shape Primitives with Recurrent Neural Networks](https://mlsanity.com/paper/1708.01648/) (2017)
- [Approximate Convex Decomposition for 3D Meshes with Collision-Aware Concavity and Tree Search](https://mlsanity.com/paper/2205.02961/) (2022)
- [LASSIE: Learning Articulated Shapes from Sparse Image Ensemble via 3D Part Discovery](https://mlsanity.com/paper/2207.03434/) (2022)
- [CAPRI-Net: Learning Compact CAD Shapes with Adaptive Primitive Assembly](https://mlsanity.com/paper/2104.05652/) (2021)
- [Unsupervised Learning for Cuboid Shape Abstraction via Joint Segmentation from Point Clouds](https://mlsanity.com/paper/2106.03437/) (2021)
- [Differentiable Blocks World: Qualitative 3D Decomposition by Rendering Primitives](https://mlsanity.com/paper/2307.05473/) (2023)
- [PartNeRF: Generating Part-Aware Editable 3D Shapes without 3D Supervision](https://mlsanity.com/paper/2303.09554/) (2023)
- [Robust and Accurate Superquadric Recovery: a Probabilistic Approach](https://mlsanity.com/paper/2111.14517/) (2021)
- [A Comprehensive Survey on 3D Content Generation](https://mlsanity.com/paper/2402.01166/) (2024)
- [SuperDec: 3D Scene Decomposition with Superquadric Primitives](https://mlsanity.com/paper/2504.00992/) (2025)
- [Marching-Primitives: Shape Abstraction from Signed Distance Function](https://mlsanity.com/paper/2303.13190/) (2023)
- [3DIAS: 3D Shape Reconstruction with Implicit Algebraic Surfaces](https://mlsanity.com/paper/2108.08653/) (2021)
- [PrimitiveAnything: Human-Crafted 3D Primitive Assembly Generation with Auto-Regressive Transformer](https://mlsanity.com/paper/2505.04622/) (2025)
- [3DGen-Bench: Comprehensive Benchmark Suite for 3D Generative Models](https://mlsanity.com/paper/2503.21745/) (2025)
- [Learning to Edit Visual Programs with Self-Supervision](https://mlsanity.com/paper/2406.02383/) (2024)
- [Light-SQ: Structure-aware Shape Abstraction with Superquadrics for Generated Meshes](https://mlsanity.com/paper/2509.24986/) (2025)
- [SweepNet: Unsupervised Learning Shape Abstraction via Neural Sweepers](https://mlsanity.com/paper/2407.06305/) (2024)
- [Point2Primitive: CAD Reconstruction from Point Cloud by Direct Primitive Prediction](https://mlsanity.com/paper/2505.02043/) (2025)
- [Split, Merge, and Refine: Fitting Tight Bounding Boxes via Over-Segmentation and Iterative Search](https://mlsanity.com/paper/2304.04336/) (2023)
- [Controllable Shape Modeling with Neural Generalized Cylinder](https://mlsanity.com/paper/2410.03675/) (2024)

## Built on by (most cited first, 5 of 5)

- [SuperFlex: Deformable Superquadrics for Point Cloud Decomposition](https://mlsanity.com/paper/2607.01015/) (2026)
- [Learning Convex Decomposition via Feature Fields](https://mlsanity.com/paper/2603.09285/) (2026)
- [Articulation in Prime: Primitive-Based Articulated Object Understanding from a Single Casual Video](https://mlsanity.com/paper/2605.18645/) (2026)
- [CADENA: Stepwise CAD Reverse Engineering](https://mlsanity.com/paper/2608.00799/) (2026)
- [Prompting Image Generators for Training-free Primitive Shape Abstraction](https://mlsanity.com/paper/2607.05568/) (2026)

## Abstract (arXiv)

We introduce a framework for converting 3D shapes into compact and editable assemblies of analytic primitives, directly addressing the persistent trade-off between reconstruction fidelity and parsimony. Our approach combines two key contributions: a novel primitive, termed SuperFrustum, and an iterative fiting algorithm, Residual Primitive Fitting (ResFit). SuperFrustum is an analytical primitive that is simultaneously (1) expressive, being able to model various common solids such as cylinders, spheres, cones & their tapered and bent forms, (2) editable, being compactly parameterized with 8 parameters, and (3) optimizable, with a sign distance field differentiable w.r.t. its parameters almost everywhere. ResFit is an unsupervised procedure that interleaves global shape analysis with local optimization, iteratively fitting primitives to the unexplained residual of a shape to discover a parsimonious yet accurate decompositions for each input shape. On diverse 3D benchmarks, our method achieves state-of-the-art results, improving IoU by over 9 points while using nearly half as many primitives as prior work. The resulting assemblies bridge the gap between dense 3D data and human-controllable design, producing high-fidelity and editable shape programs.