高维图形：在四维空间及更远的空间中构思世界
Higher Dimensional Graphics: Conceiving Worlds in Four Spatial Dimensions and Beyond
摘要：
虽然对高维数据集的解释在大多数行业中已经成为必要，并且得到了数据科学和机器学习的不断进步的支持，但高维几何的空间可视化主要仍然是数学家和物理学家的利基研究课题。对这一领域的断断续续的贡献可以追溯到一个多世纪以前，对当代艺术和哲学产生了不可忽视的影响。然而，大多数贡献都集中在理解特定的数学形状，很少有具体的应用。在这项工作中，我们试图通过将焦点从抽象形状的可视化转移到更广泛的超宇宙概念的设计来恢复社区对可视化高维几何的兴趣，其中3D和4D对象可以共存并相互作用。具体来说，我们讨论了与扩展标准3D应用程序以支持4D机制的过程相关的内容定义、创作模式和技术实现。我们通过引入一个新的混合3D/4D视频游戏来实现我们的想法，该游戏名为Across Dimensions，我们通过集成我们自己的4D插件在Unity3D中开发。
英文摘要：
While the interpretation of high-dimensional datasets has become a necessity in most industries, and is supported by continuous advances in data science and machine learning, the spatial visualization of higher-dimensional geometry has mostly remained a niche research topic for mathematicians and physicists. Intermittent contributions to this field date back more than a century, and have had a non-negligible influence on contemporary art and philosophy. However, most contributions have focused on the understanding of specific mathematical shapes, with few concrete applications. In this work, we attempt to revive the community's interest in visualizing higher dimensional geometry by shifting the focus from the visualization of abstract shapes to the design of a broader hyper-universe concept, wherein 3D and 4D objects can coexist and interact with each other. Specifically, we discuss the content definition, authoring patterns, and technical implementations associated with the process of extending standard 3D applications as to support 4D mechanics. We operationalize our ideas through the introduction of a new hybrid 3D/4D videogame called Across Dimensions, which we developed in Unity3D through the integration of our own 4D plugin.
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