Voronoi Scissors: Approximate Dissection of 2D Shapes
with Continuous Optimization

One set of pieces. Two completely different shapes. (Conditionally accepted to Siggraph Asia 2026)

Anran Qi1,2 Nico Pietroni3 Mikhail Bessmeltsev4 Nobuyuki Umetani1 Adrien Bousseau2 Takeo Igarashi1
1The University of Tokyo 2Centre Inria d’Université Côte d’Azur 3University of Technology Sydney 4Université de Montréal
Paper Video Code soon Supplemental
Two input shapes, their common dissection pieces, and fabricated results

Overview: Our algorithm takes two shapes as input (a) and computes an approximate dissection of these shapes into a common set of pieces (b). Each shape can be reproduced by rearranging the pieces via rigid transformations (c, 3D-printed pieces).

01

Reconfigure

More exaples: Same pieces, different shapes.

A

Arm ⇄ Seahorse

B

Ghost ⇄ Hat

C

Turtle ⇄ Strawberry

02

Method

From Voronoi cells to a common dissection.

Overview of the Voronoi Scissors method
Method overview: Starting from two input shapes, we perform Voronoi-based joint partitioning to obtain approximately isometric piece pairs, followed by coarse geometric dissection to enforce exact isometry, and bijective refinement to better approximate the inputs.
Voronoi-based joint partitioning (b)
We optimize the site positions in the Voronoi diagram so that the corresponding cells agglomerate into compact pieces that are as similar as possible in the two shapes when registered by a rigid transformation.
More results on Voronoi-based joint partitioning
We show more examples of Voronoi partitioning and Results.  The first row is the Voronoi-based joint partitioning Process. The second row visualizes the transformed pieces overlaid on the reference shape. The last row is the final results.
03

Results

A gallery of dissections

The formulation supports different piece counts as well as shapes with holes and disconnected components.

Different piece numbers: 3 → 8 pieces
Duck and Dinosaur dissection results using three to eight pieces
Duck–Dinosaur dissection results using 3–8 pieces.
Topology: input shapes with holes
One shape to two shapes
Results for shapes with holes and multiple disconnected components
Left: shapes containing holes, Ghost–Broccoli. Right: shapes composed of multiple disconnected components, Turtle–Ghost.
04

More applications

Material reuse

The same reconfiguration principle can also support reuse-oriented design scenarios.

Modular design
Zero-waste garment upcycling
Garment panel reuse example
Given two input garment panels, our method generates patches that can be reconfigured into either a top or a pair of pants. By keeping the pant panel unchanged during optimization, it can be directly reused for a top with no material waste. In both cases, the top and pants cannot coexist.
05

Comparision with existing works

Comparison
Comparison with prior automatic dissection results
Compared with the automatic results of Duncan et al. (SIGGRAPH 2017) , both methods visually reproduce the input shapes, while ours generates more compact, well-proportioned pieces and achieves lower geometric error.

Reference

BibTeX

@inproceedings{Qi2026voronoiscissors,
  title     = {Voronoi Scissors: Approximate Dissection of 2D Shapes with Continuous Optimization},
  author    = {Qi, Anran and Pietroni, Nico and Bessmeltsev, Mikhail and Umetani, Nobuyuki and Bousseau, Adrien and Igarashi, Takeo},
  booktitle = {SIGGRAPH Asia 2026 Conference Papers},
  year      = {2026}
}
Expanded figure