Tootfinder

This https://arxiv.org/abs/2405.12949 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCG_…

Exact predicates, exact constructions and combinatorics for mesh CSG
This article introduces a general mesh intersection algorithm that exactly computes the so-called Weiler model (also called an arrangement) and that uses it to implement boolean operations with arbitrary multi-operand expressions, CSG (constructive solid geometry) and some mesh repair operations. From an input polygon soup, the algorithm first computes the co-refinement, with an exact representation of the intersection points. Then, the decomposition of 3D space into volumetric regions (Weiler …

This https://arxiv.org/abs/2407.15625 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCY_…

Dressed to Gamble: How Poker Drives the Dynamics of Wearables and Visits on Decentraland's Social Virtual World
Decentraland is a blockchain-based social virtual world where users can publish and sell wearables to customize avatars. In it, the third-party Decentral Games (DG) allows players of its flagship game ICE Poker to earn cryptocurrency only if they possess certain wearables. Herein, we present a comprehensive study on how DG and its game influence the dynamics of wearables and in-world visits in Decentraland. To this end, we analyzed 5.9 million wearable transfers made on the Polygon blockchain (…

Uniqueness in determining a convex polygonal source of an elastic body
Jianli Xiang
https://arxiv.org/abs/2506.02870 https://arxiv.or…

Uniqueness in determining a convex polygonal source of an elastic body
In this work, we consider the time-harmonic inverse elastic source problem of a fixed frequency for the Navier equation in two dimensions. We show that a convex polygon can be uniquely determined by a single far field measurement. Our approach relies on the corner singularity analysis of solutions to the inhomogeneous Navier equation with a source term in a sector. This paper also contributes to corner scattering theory for the Navier equation in an non-convex domain.

Conductive homogeneity of locally symmetric polygon-based self-similar sets
J. Kigami amd Y. Ota
https://arxiv.org/abs/2505.23057 https://

Conductive homogeneity of locally symmetric polygon-based self-similar sets
We provide a rich family of self-similar sets, called locally symmetric polygon-based self-similar sets, as examples of metric spaces having conductive homogeneity, which was introduced as a sufficient condition for the construction of counterparts of ``Sobolev spaces'' on compact metric spaces. In particular, our results imply the existence of ``Brownian motions'' on our family of self-similar sets at the same time. Unlike the known examples like the Sierpinski carpet by Barlow-Bass, unconstra…

Computing Diverse and Nice Triangulations
Waldo G\'alvez, Mayank Goswami, Arturo Merino, GiBeom Park, Meng-Tsung Tsai
https://arxiv.org/abs/2506.01323 …

Computing Diverse and Nice Triangulations
We initiate the study of computing diverse triangulations to a given polygon. Given a simple $n$-gon $P$, an integer $ k \geq 2 $, a quality measure $σ$ on the set of triangulations of $P$ and a factor $ α\geq 1 $, we formulate the Diverse and Nice Triangulations (DNT) problem that asks to compute $k$ \emph{distinct} triangulations $T_1,\dots,T_k$ of $P$ such that a) their diversity, $\sum_{i < j} d(T_i,T_j) $, is as large as possible \emph{and} b) they are nice, i.e., $σ(T_i) \leq ασ^* $ …

This https://arxiv.org/abs/2307.07774 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Heptagon relations from a simplicial 3-cocycle, and their cohomology
We introduce new algebraic structures associated with heptagon relations -- higher analogue of the well-known pentagon. The main points we deal with are: (i) polygon relations as algebraic imitations of Pachner moves, on the example of heptagon, (ii) parameterization of heptagon relations by simplicial 3-cocycles, (iii) applications to invariants of pairs "piecewise linear 5-manifold, a 3rd cohomology class on it".

PolyTrack: try try again
PolyTrack is a Trackmania tribute - almost identical gameplay mechanics, but with digital controls, simplified driving model, and a very stripped-back graphical style. It's even simpler than Virtua Racing in many ways, with the car having a polygon count almost in the single digits. This simplicity means that it runs incredibly smoothly, even in-browser at Much like Trackmania, the courses are short but deceptively tricky to complete.

Max/Min Puzzles in Geometry IV
James M Parks
https://arxiv.org/abs/2505.03744 https://arxiv.org/pdf/2505.03744

Max/Min Puzzles in Geometry IV
In the previous paper, Max/Min Puzzles in Geometry III, we searched for the smallest area triangle which contained a regular unit polygon (Square, Pentagon, Hexagon). In this paper we will work in 3-dimensions, and search for the smallest regular Tetrahedron which contains a regular unit polyhedron (Cube, Octahedron, Icosahedron, Dodecahedron).