Visualizing Quaternions

TL;DR: In this article, a discrete treatment of adapted framed curves, parallel transport, and holonomy is presented for a discrete geometric model of thin flexible rods with arbitrary cross section and undeformed configuration.

TL;DR: An essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing, and it also serves as an excellent self-study guide for statistical researchers.

TL;DR: This article presents a novel skinning algorithm based on linear combination of dual quaternions that does not exhibit any of the artifacts inherent in previous methods and still permits an efficient GPU implementation.

TL;DR: This paper presents a novel GPU-friendly skinning algorithm based on dual quaternions and shows that this approach solves the artifacts of linear blend skinning at minimal additional cost.

Abstract: This chapter applies our reasoning about structure in physics to two formulations of classical mechanics, Lagrangian and Newtonian mechanics, that are generally taken to be completely equivalent. It argues that these two formulations differ in both the type and amount of structure presupposed by their dynamical laws, as revealed by the invariances of the equations representing the laws as well as the theories’ statespace structures. This suggests that these are not fully equivalent theories: they differ in dynamical structure. There are also various metaphysical differences between them. The chapter goes on to argue that the minimize-structure rule tells us to choose one over the other. Along the way, the idea that preferred or natural coordinate systems indicate underlying structure is discussed.

TL;DR: In this paper, the angular momentum, one of the most fundamental quantities in all of quantum mechanics, is introduced and a concise introduction to its application in atomic, molecular, and nuclear physics is provided.

TL;DR: In this article, the angular momentum, one of the most fundamental quantities in all of quantum mechanics, is introduced and a concise introduction to its application in atomic, molecular, and nuclear physics is provided.