Related papers: Closed Bounded Rational Framing Motions
A novel algorithm for creating a mathematical model of curved shapes is introduced. The core of the algorithm is based on building a graph representation of the contoured image, which occupies less storage space than produced by raster…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
Space curve motion describes dynamics of material defects or interfaces, can be found in image processing or vortex dynamics. This article analyses some properties of space curves evolved by the curve shortening flow. In contrast to the…
The `linear orbit' of a plane curve of degree d is its orbit in P^{d(d+3)/2} under the natural action of PGL(3). We classify curves with positive dimensional stabilizer, and we compute the degree of the closure of the linear orbits of…
Motion polynomials (polynomials over the dual quaternions with nonzero real norm) describe rational motions. We present a necessary and sufficient condition for reduced bounded motion polynomials to admit factorizations into monic linear…
Let $C$ be an irreducible projective plane curve in the complex projective space ${\mathbb{P}}^2$. The classification of such curves, up to the action of the automorphism group $PGL(3,{\mathbb{C}})$ on ${\mathbb{P}}^2$, is a very difficult…
This paper develops an invariant--geometric interpretation of the canonization problem for simple undirected weighted graphs based on the {discrete moving frame method} for finite groups. We consider the action of the {pair group}…
A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…
A finite-dimensional Hilbert space is usually described in terms of an orthonormal basis, but in certain approaches or applications a description in terms of a finite overcomplete system of vectors, called a finite tight frame, may offer…
The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion.…
Cartan's moving frames method is a standard tool in riemannian geometry. We set up the machinery for applying moving frames to cotangent bundles and its sub-bundles defined by non-holonomic constraints.
Text-driven human motion generation in computer vision is both significant and challenging. However, current methods are limited to producing either deterministic or imprecise motion sequences, failing to effectively control the temporal…
Character animation in real-world scenarios necessitates a variety of constraints, such as trajectories, key-frames, interactions, etc. Existing methodologies typically treat single or a finite set of these constraint(s) as separate control…
We prove that every real algebraic action on a smooth real algebraic variety has a prolongation with a "moving frame".
Motion in-betweening, a fundamental task in character animation, consists of generating motion sequences that plausibly interpolate user-provided keyframe constraints. It has long been recognized as a labor-intensive and challenging…
We consider the motion of a rigid body due to the pressure of a surrounded two-dimensional irrotational perfect incompressible fluid, the whole system being confined in a bounded domain with an impermeable condition on a part of the…
This letter studies a distributed collision avoidance control problem for a group of rigid bodies on a sphere. A rigid body network, consisting of multiple rigid bodies constrained to a spherical surface and an interconnection topology, is…
We consider the propagation of a flame front in a solid periodic medium. The model is governed by a free boundary system in which the front's velocity depends on the temperature via a kinetic rate which may degenerate. We show the existence…
This paper develops a generalized formulation of Lagrangian mechanics on fibered manifolds, together with a reduction theory for symmetries corresponding to Lie groupoid actions. As special cases, this theory includes not only Lagrangian…
We present a novel, deterministic, and efficient method to detect whether a given rational space curve is symmetric. By using well-known differential invariants of space curves, namely the curvature and torsion, the method is significantly…