Translation (geometry)

Summary

In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation is an isometry. As a function Displacement (geometry) If \mathbf{v} is a fixed vector, known as the translation vector, and \mathbf{p} is the initial position of some object, then the translation function T_{\mathbf{v}} will work as T_{\mathbf{v}}(\mathbf{p})=\mathbf{p}+\mathbf{v}. If T is a translation, then the of a subset A under the function T is the translate of A by T . The translate of A by T_{\mathbf{v}} is often written A+\mathbf{v} . Horizontal and vertical

Official source

https://en.wikipedia.org/wiki/Translation_(geometry)

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One Step from the Locomotion to the Stepping Pattern

Ronan Boulic, Utku Evci, Eray Molla

The locomotion pattern is characterized by a translation displacement mostly occurring along the forward frontal body direction, whereas local repositioning with large re-orientations, i.e. stepping, may induce translations both along the frontal and the lateral body directions (holonomy). We consider here a stepping pattern with initial and final null speeds within a radius of 40% of the body height and re-orientation up to 180°. We propose a robust step detection method for such a context and identify a consistent intra-subject behavior in terms of the choice of starting foot and the number of steps.

ACM Press2016

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Reconstructing 3D shape from 2D sketches has long been an open problem because the sketches only provide very sparse and ambiguous information. In this paper, we use an encoder/decoder architecture for the sketch to mesh translation. When integrated into a user interface that provides camera parameters for the sketches, this enables us to leverage its latent parametrization to represent and refine a 3D mesh so that its projections match the external contours outlined in the sketch. We will show that this approach is easy to deploy, robust to style changes, and effective. Furthermore, it can be used for shape refinement given only single pen strokes. We compare our approach to state-of-the-art methods on sketches---both hand-drawn and synthesized---and demonstrate that we outperform them.

IEEE2021

Combined Nuclear Magnetic Resonance and Molecular Dynamics Study of Methane Adsorption in M-2(dobdc) Metal-Organic Frameworks

Efrem Daniel Braun, Amber Kashan Mace, Rocio Mercado, Berend Smit

We examine the diffusion of methane in the metal organic frameworks M-2(dobdc) (M = Mg, Ni, Zn; dobdc(4-) = 2,5-diwddo-1,4-benzenedicarboxylate) as a function of methane loading through a combination of nuclear magnetic resonance and molecular dynamics simulations. At low gas densities, our results suggest that favorable CH4-CH4 interactions lower the free energy barrier for methane hopping between coordinatively unsaturated metal sites and thus enhance the translational motion of methane down the c-axis. At higher gas densities, CH4-CH4 interactions become more significant, CH4-CH4 collisions become more frequent, and the gas self-diffusion begins to decrease. Finally, we observe that the self-diffusion coefficient of methane is inversely related to the binding energy at the coordinatively unsaturated metal sites, such that diffusion is most rapid in the Zn-2(dobdc) framework.

2019