Self-determination theory is a well-established theory of motivation. This theory provides for fundamental concepts related to human motivation, including self-determination. The mathematization of this theory has been envisaged in a series of two papers by the author. The first paper entitled “Mathematical self-determination theory I: Real representation” addressed the representation of the theory in reals. This second paper is in continuation of it. The representation of the first part allows to abstract the results in more general mathematical structures, namely, affine spaces. The simpler real representation is reobtained as a special instance. We take convexity as the pivotal starting point to generalize the whole exposition and represent self-determination theory in abstract affine spaces. This includes the affine space analogs of the notions of internal locus, external locus, and impersonal locus, of regulated and graded motivation, and self-determination. We also introduce polar coordinates in Euclidean affine motivation spaces to study self-determination on radial and angular line segments. We prove the distributivity of the lattice of general self-determination in the affine space formulation. The representation in an affine space is free in the choice of primitives. However, the different representations, in reals or affine, are shown to be unique up to canonical isomorphism. The aim of this paper is to extend on the results obtained in the first paper, thereby to further lay the mathematical foundations of self-determination motivation theory.

自决理论是一种行之有效的动机理论。该理论提供了与人类动机相关的基本概念，包括自决。作者在两篇系列论文中设想了该理论的数学化。第一篇题为“数学自决理论 I：实数表示”的论文讨论了该理论在实数中的表示。第二篇论文是它的延续。第一部分的表示允许将结果抽象为更一般的数学结构，即仿射空间。重新获得更简单的真实表示作为特殊实例。我们以凸性为关键起点来概括整个论述并在抽象仿射空间中表示自决理论。这包括内部轨迹、外部轨迹和非人格轨迹、调节和分级动机以及自我决定等概念的仿射空间类似物。我们还在欧几里得仿射动机空间中引入极坐标来研究径向和角线段的自决。我们证明了格子的分布性仿射空间公式中的一般自决。仿射空间中的表示可以自由选择基元。然而，不同的表示，无论是实数还是仿射，在规范同构方面都被证明是唯一的。本文的目的是扩展第一篇论文所获得的结果，从而进一步奠定自我决定动机理论的数学基础。