Related papers: Tangled Splines
We consider causal 3-dimensional triangulations with the topology of $S^2\times [0,1]$ or $D^2\times [0,1]$ where $S^2$ and $D^2$ are the two-dimensional sphere and disc, respectively. These triangulations consist of slices and we show that…
To endow machines with the ability to perceive the real-world in a three dimensional representation as we do as humans is a fundamental and long-standing topic in Artificial Intelligence. Given different types of visual inputs such as…
We explore geometric and topological properties of 3d surfaces swept by Poncelet triangles, as well as tangles formed by associated points.
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects in stochastic geometry. A natural geometric question is…
We propose an unexpected twist to description of the geometry and topology of configurations of n straight lines considered as a whole 3D entity (because the lines are inseparably linked pairwise while having linking numbers 1/2 or -1/2)…
The interest in matching non-rigidly deformed shapes represented as raw point clouds is rising due to the proliferation of low-cost 3D sensors. Yet, the task is challenging since point clouds are irregular and there is a lack of intrinsic…
In computer vision and medical imaging, the problem of matching structures finds numerous applications from automatic annotation to data reconstruction. The data however, while corresponding to the same anatomy, are often very different in…
We investigate the behaviour of vertices and inflexions on 1-parameter families of curves on smooth surfaces in the 3-space, which include a singular member. In particular, we discuss the context where the curves evolve as sections of a…
Shape is an important physical property of natural and manmade 3D objects that characterizes their external appearances. Understanding differences between shapes and modeling the variability within and across shape classes, hereinafter…
Real-life man-made objects often exhibit strong and easily-identifiable structure, as a direct result of their design or their intended functionality. Structure typically appears in the form of individual parts and their arrangement.…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label…
It is shown that a smooth n dimensional manifold with a boundary in R^n admits a Boolean representation in terms of closed half spaces defined by the tangent hyperplanes at the points on its boundary. A similar result is established for…
Existing 3D foundation models typically align point clouds to frozen vision-language spaces like CLIP, which achieve strong cross-modal retrieval by compressing 3D shape into a global vector. However, this global-only alignment cannot…
It is generally believed that the space has a nontrivial structure which is apparent on the order of the Planck length. There is a class of models of three-dimensional quantum spaces constructed using different mathematical tools. Also,…
Ruled surfaces play an important role in various types of design, architecture, manufacturing, art, and sculpture. They can be created in a variety of ways, which is a topic that has been the subject of much discussion in mathematics and…
A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This…
We propose the first algorithm for non-rigid 2D-to-3D shape matching, where the input is a 2D shape represented as a planar curve and a 3D shape represented as a surface; the output is a continuous curve on the surface. We cast the problem…
We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In…