Visualization of Four-Dimensional Spacetimes
Visualization of Four-Dimensional Spacetimes
复制标题
四维时空的可视化
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
Gerhard J. Wagner
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文献类型：
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作者：
Gerhard J. Wagner
本文提出了一种新的和改进的四维空时可视化方法。本论文的第一部分是关于狭义相对论的平坦时空。为狭义相对论可视化建立了统一的物理基础。讨论了照明、色觉、光性质的转换以及加速物体的运动学等问题。特别是，还包括了辐射度变换的推导。给出了用于特殊相对论可视化的绘制技术。在统一的框架中描述了先前已知的技术--特殊的相对论多边形绘制和特殊的相对论光线跟踪。文中展示了如何在这些技术中加入相对论照明效应，并证明了视觉感知是由探照灯和多普勒效应主导的。相对论光能传递、基于纹理的相对论绘制和基于图像的相对论绘制是新的绘制方法。对于由漫反射材质组成的场景，相对论光能传递可以可视化照明效果，达到任意精度。光能传递非常适合交互式漫游，但也适用于高质量图像。基于纹理的相对论绘制利用纹理映射硬件来实现相对论变换。它最适合于可视化几何和照明上的特殊相对论效果的交互式应用程序。基于图像的相对论绘制弥合了众所周知的非相对论基于图像的技术和相对论可视化之间的差距。基于图像的绘制不需要费力的三维建模，并且在高渲染速度下实现了照片真实感。基于图像的相对论渲染可以非常轻松地生成快速移动的真实世界对象的照片级图像，是为娱乐和教育目的制作电影和快照的强大工具。介绍了用于探索狭义相对论的交互式虚拟环境。第一个环境是一个简单的“相对论飞行模拟器”，它在标准的PC或图形工作站上运行。第二个系统是一个复杂的沉浸式虚拟环境，它利用了多管道和多处理器架构。相对论变换的并行化导致相对论渲染的帧速率与标准非相对论渲染的帧速率相同。为了实现高速航行，引入了相对论车辆控制比喻。这个比喻包含一个基于物理的相机控制，并提供主动和被动运动。论文的第二部分讨论了广义相对论的弯曲四维时空。观察者在一般相对论环境中所看到的东西的直接可视化是通过非线性光线跟踪实现的。提出了一个由单一图表描述的用于时空光线跟踪的通用系统。通过两个例子--尘埃的刚性旋转圆盘和翘曲度规--论证了光线追踪作为可视化工具的适用性。提出了对单图射线追踪的扩展，以结合地图集的微分几何概念。这样，就可以考虑复杂拓扑的时空。其中包括一个例子，展示了虫洞的可视化。光线追迹被应用于引力透镜领域。它展示了如何将标准透镜的可视化包含在光线跟踪系统中。此外，光线跟踪允许研究超出标准透镜近似的偏转对象。例如，可以考虑大角度的偏转。焦散探测仪是一种用于识别引力透镜诱导的二维焦散结构的数值方法。在三维欧氏空间中等距嵌入可以可视化二维空间超曲面的内部几何。描述了一种可以嵌入球面拓扑的方法。该嵌入方案支持可能源自数值模拟的采样度量数据。最后，描述了它在经典可视化中的一个具体应用。经典可视化意味着对来自相对论模拟的数据的可视化表示，而不考虑时空的曲率。为了获得良好的网格质量，开发了一种高度场自适应三角剖分算法，即使在底层函数具有高梯度的区域也是如此。高度场可视化被典型地应用于来自中子星模拟的数据。
In this thesis, new and improved methods for the visualization of four-dimensional spacetimes are presented. The first part of this thesis deals with the flat spacetime of special relativity. A unified physical basis for special relativistic visualization is established. Issues of illumination, color vision, transformation of properties of light, and the kinematics of accelerating bodies are discussed. In particular, a derivation of the transformation of radiance is included. Rendering techniques for special relativistic visualization are presented. Previously known techniques—special relativistic polygon rendering and special relativistic ray tracing—are described in a unified framework. It is shown how relativistic effects on illumination can be incorporated in these techniques and it is demonstrated that visual perception is dominated by the searchlight and Doppler effects. Relativistic radiosity, texture-based relativistic rendering, and image-based relativistic rendering are proposed as new rendering methods. Relativistic radiosity can visualize effects on illumination up to arbitrary accuracy for scenes made of diffuse materials. Radiosity is well suited for interactive walk-throughs, but also for high-quality images. Texture-based relativistic rendering utilizes the texture-mapping hardware to implement the relativistic transformations. It is most appropriate for interactive applications which visualize special relativistic effects on both geometry and illumination. Image-based relativistic rendering closes the gap between well-known non-relativistic image-based techniques and relativistic visualization. Image-based rendering does not require laborious threedimensional modeling and achieves photo-realism at high rendering speeds. Imagebased relativistic rendering allows to generate photo-realistic images of rapidly moving real-world objects with great ease and is a powerful tool to produce movies and snapshots for both entertainment and educational purposes. Interactive virtual environments for the exploration of special relativity are introduced. The first environment is a simple “relativistic flight simulator” which runs on a standard PC or graphics workstation. The second system is a sophisticated immersive virtual environment which exploits multi-pipe and multi-processor architectures. Parallelization of the relativistic transformation results in the same frame rates for relativistic rendering as for standard non-relativistic rendering. The relativistic-vehiclecontrolmetaphor is introduced for navigating at high velocities. This metaphor contains a physics-based camera control and provides both active and passive locomotion. The second part of the thesis deals with curved four-dimensional spacetimes of general relativity. Direct visualization of what an observer would see in a general relativistic setting is achieved by means of non-linear ray tracing. A generic system is presented for ray tracing in spacetimes described by a single chart. The suitability of ray tracing as a visualization tool is demonstrated by means of two examples—the rigidly rotating disk of dust and the warp metric. Extensions to single-chart ray tracing are proposed to incorporate the differential-geometric concept of an atlas. In this way, spacetimes of complex topologies can be considered. An example is included, showing the visualization of a wormhole. Ray tracing is applied to the field of gravitational lensing. It is shown how the visualization of standard lensing can be included in a ray tracing system. Furthermore, ray tracing allows to investigate deflecting objects beyond the approximations of standard lensing. For example, large angles of deflections can be considered. The caustic finder is proposed as a numerical method to identify two-dimensional caustic structures induced by a gravitational lens. The inner geometry of two-dimensional spatial hypersurfaces can be visualized by isometric embedding in three-dimensional Euclidean space. A method is described which can embed surfaces of spherical topology. This embedding scheme supports sampled metric data which may originate from numerical simulations. Finally, a specific application in classical visualization is described. Classical visualization means the visual representation of data from relativistic simulations without taking into account the curvature of spacetime. An algorithm for the adaptive triangulation of height fields is developed in order to achieve a good mesh quality, even in areas where the underlying function has high gradients. Height field visualization is exemplarily applied to data from neutron star simulations.