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Physically interacting with four dimensions.

机译：与四个维度进行物理交互。

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摘要

People have long been fascinated with understanding the fourth dimension. While making pictures of 4D objects by projecting them to 3D can help reveal basic geometric features, 3D graphics images by themselves are of limited value. For example, just as 2D shadows of 3D curves may have lines crossing one another in the shadow, 3D graphics projections of smooth 4D topological surfaces can be interrupted where one surface intersects another.;The research presented here creates physically realistic models for simple interactions with objects and materials in a virtual 4D world. We provide methods for the construction, multimodal exploration, and interactive manipulation of a wide variety of 4D objects. One basic achievement of this research is to exploit the free motion of a computer-based haptic probe to support a continuous motion that follows the local continuity of a 4D surface, allowing collision-free exploration in the 3D projection. In 3D, this interactive probe follows the full local continuity of the surface as though we were in fact physically touching the actual static 4D object.;Our next contribution is to support dynamic 4D objects that can move, deform, and collide with other objects as well as with themselves. By combining graphics, haptics, and collision-sensing physical modeling, we can thus enhance our 4D visualization experience. Since we cannot actually place interaction devices in 4D, we develop fluid methods for interacting with a 4D object in its 3D shadow image using adapted reduced-dimension 3D tools for manipulating objects embedded in 4D. By physically modeling the correct properties of 4D surfaces, their bending forces, and their collisions in the 3D interactive or haptic controller interface, we can support full-featured physical exploration of 4D mathematical objects in a manner that is otherwise far beyond the real-world experience accessible to human beings.
机译：人们早已着迷于对第四维度的理解。通过将4D对象投影到3D来制作图片可以帮助揭示基本的几何特征，而3D图形图像本身的价值有限。例如，就像3D曲线的2D阴影可能在阴影中具有彼此相交的线一样，光滑的4D拓扑表面的3D图形投影可以在一个表面与另一个表面相交的地方中断。;此处提出的研究创建了物理上逼真的模型，用于与虚拟4D世界中的物体和材料。我们提供了多种4D对象的构造，多模式探索和交互操作的方法。这项研究的一项基本成就是，利用基于计算机的触觉探针的自由运动来支持遵循4D表面局部连续性的连续运动，从而实现3D投影中的无碰撞探索。在3D中，这种交互式探针遵循表面的整个局部连续性，就像我们实际上在物理上触摸实际的静态4D对象一样;我们的下一个贡献是支持动态4D对象，该对象可以像其他对象一样移动，变形和碰撞以及与自己。通过组合图形，触觉和碰撞感应物理模型，我们可以增强4D可视化体验。由于我们实际上无法将交互设备放置在4D中，因此我们开发了使用自适应的降维3D工具来处理嵌入4D的对象的流体方法，以便与3D阴影图像中的4D对象进行交互。通过在3D交互式或触觉控制器界面中对4D曲面的正确属性，其弯曲力及其碰撞进行物理建模，我们可以以一种远远超出现实世界的方式支持4D数学对象的全功能物理探索人类可以接触到的经验。

著录项

  • 作者

    Zhang, Hui.;

  • 作者单位

    Indiana University.;

  • 授予单位 Indiana University.;
  • 学科 Computer Science.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 216 p.
  • 总页数 216
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 自动化技术、计算机技术;
  • 关键词

  • 入库时间 2022-08-17 11:38:30

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