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We revisit the concept of constraint embedding as a means for dealing with kinematic loop constraints during dynamics computations for rigid-body systems. Specifically, we consider the local loop constraints emerging from common actuation…
3D scene graphs have recently emerged as a powerful high-level representation of 3D environments. A 3D scene graph describes the environment as a layered graph where nodes represent spatial concepts at multiple levels of abstraction and…
Recent work has shown that if an isostatic bar and joint framework possesses non-trivial symmetries, then it must satisfy some very simply stated restrictions on the number of joints and bars that are `fixed' by various symmetry operations…
We introduce HYPERPOSE, a novel 3D human pose estimation framework that performs spatio-temporal reasoning entirely within the Lorentz model of hyperbolic space $\mathbb{H}^d$ to natively preserve the hierarchical tree topology of the human…
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple…
Holography has provided valuable insights into the time evolution of strongly coupled gauge theories in a fixed spacetime. However, this framework is insufficient if this spacetime is dynamical. We present a scheme to evolve a…
Starting from the canonical phase space for discretised (4d) BF-theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our construction allows us to study the connection…
While current general-purpose 3D human models (e.g., SMPL-X) efficiently represent accurate human shape and pose, they lacks the ability to physically interact with the environment due to the kinematic nature. As a result, kinematic-based…
Directly learning to model 4D content, including shape, color, and motion, is challenging. Existing methods rely on pose priors for motion control, resulting in limited motion diversity and continuity in details. To address this, we propose…
We describe the idea of studying quantum gravity by means of dynamical triangulations and give examples of its implementation in 2, 3 and 4 space time dimensions. For $d=2$ we consider the generic hermitian 1-matrix model. We introduce the…
In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…
This paper proposes a novel 3D graphical representation for impedance control, called the impedance space, to foster the analysis of the dynamic behavior of robotic compliant controllers. The method overcomes limitations of existing 2D…
A new representation of Quantum Gravity is developed. This formulation is based on an extension of the group of loops. The enlarged group, that we call the Extended Loop Group, behaves locally as an infinite dimensional Lie group. Quantum…
We propose a method for incorporating object interaction and human body dynamics into the task of 3D ego-pose estimation using a head-mounted camera. We use a kinematics model of the human body to represent the entire range of human motion,…
A kinetic theory of classical particles serves as a unified basis for developing a geometric $3+1$ spacetime perspective on fluid dynamics capable of embracing both Minkowski and Galilei/Newton spacetimes. Parallel treatment of these cases…
Robots operating in domestic environments generally need to interact with articulated objects, such as doors, cabinets, dishwashers or fridges. In this work, we present a novel, probabilistic framework for modeling articulated objects as…
We present a formalism for constructing schematic diagrams to depict chaotic three-body interactions in Newtonian gravity. This is done by decomposing each interaction in to a series of discrete transformations in energy- and angular…
Symmetry is an implicit objective in structural form-finding that often reconciles efficiency and aesthetics. This paper identifies the symmetry of polyhedral diagrams in three-dimensional graphic statics (3DGS) as point groups and…
This paper considers to jointly tackle the highly correlated tasks of estimating 3D human body poses and predicting future 3D motions from RGB image sequences. Based on Lie algebra pose representation, a novel self-projection mechanism is…
Reconstructing dynamic 4D scenes from monocular videos is a fundamental yet challenging task. While recent 3D foundation models provide strong geometric priors, their performance significantly degrades in dynamic environments. This…