# An overview of some mathematical techniques and problems linking 3D vision to 3D printing

arXiv: https://arxiv.org/abs/2309.10549 · HTML: https://mlsanity.com/paper/2309.10549/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 91 references that are in the map.
- First posted on arXiv 19 Sep 2023.

## Builds on (most cited first, 6 of 6)

- [Normal Integration: A Survey](https://mlsanity.com/paper/1709.05940/) (2017)
- [Variational Methods for Normal Integration](https://mlsanity.com/paper/1709.05965/) (2017)
- [Shapes In A Box -- Disassembling 3D objects for efficient packing and fabrication](https://mlsanity.com/paper/2104.05281/) (2021)
- [Analysis and approximation of some Shape-from-Shading models for non-Lambertian surfaces](https://mlsanity.com/paper/1502.05197/) (2015)
- [A level set based method for fixing overhangs in 3D printing](https://mlsanity.com/paper/1409.1714/) (2014)
- [From 3D Models to 3D Prints: an Overview of the Processing Pipeline](https://mlsanity.com/paper/1705.03811/) (2017)

## Abstract (arXiv)

Computer Vision and 3D printing have rapidly evolved in the last 10 years but interactions among them have been very limited so far, despite the fact that they share several mathematical techniques. We try to fill the gap presenting an overview of some techniques for Shape-from-Shading problems as well as for 3D printing with an emphasis on the approaches based on nonlinear partial differential equations and optimization. We also sketch possible couplings to complete the process of object manufacturing starting from one or more images of the object and ending with its final 3D print. We will give some practical examples of this procedure.