Humans inhabit a world defined by interactions -- with other humans, objects, and environments. These interactive movements not only convey our relationships with our surroundings but also demonstrate how we perceive and communicate with the real world. Therefore, replicating these interaction behaviors in digital systems has emerged as an important topic for applications in robotics, virtual reality, and animation. While recent advances in deep generative models and new datasets have accelerated progress in this field, significant challenges remain in modeling the intricate human dynamics and their interactions with entities in the external world. In this survey, we present, for the first time, a comprehensive overview of the literature in human interaction motion generation. We begin by establishing foundational concepts essential for understanding the research background. We then systematically review existing solutions and datasets across three primary interaction tasks -- human-human, human-object, and human-scene interactions -- followed by evaluation metrics. Finally, we discuss open research directions and future opportunities.

This is part II of a two-part paper. Part I presented a universal Birkhoff theory for fast and accurate trajectory optimization. The theory rested on two main hypotheses. In this paper, it is shown that if the computational grid is selected from any one of the Legendre and Chebyshev family of node points, be it Lobatto, Radau or Gauss, then, the resulting collection of trajectory optimization methods satisfy the hypotheses required for the universal Birkhoff theory to hold. All of these grid points can be generated at an $\mathcal{O}(1)$ computational speed. Furthermore, all Birkhoff-generated solutions can be tested for optimality by a joint application of Pontryagin's- and Covector-Mapping Principles, where the latter was developed in Part~I. More importantly, the optimality checks can be performed without resorting to an indirect method or even explicitly producing the full differential-algebraic boundary value problem that results from an application of Pontryagin's Principle. Numerical problems are solved to illustrate all these ideas. The examples are chosen to particularly highlight three practically useful features of Birkhoff methods: (1) bang-bang optimal controls can be produced without suffering any Gibbs phenomenon, (2) discontinuous and even Dirac delta covector trajectories can be well approximated, and (3) extremal solutions over dense grids can be computed in a stable and efficient manner.