Illumination and acceleration in the visualization of special relativity: a comment on fast rendering of relativistic objects

Weiskopf, Daniel; Kraus, Ute; Ruder, H.

doi:10.1002/1099-1778(200009)11:4<185::aid-vis224>3.0.co;2-2

Cited by 5 publications

(7 citation statements)

References 23 publications

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“…By evaluating the apparent shape of many such points and joining them together, we can retain the original mesh of the shape. Figure (18) shows a series of snapshots of the cube with β = (0.7, 0, 0), a = (1, 0, 0), and l = 1 at times x 0 obs = −1, x 0 obs = 0, x 0 obs = 0.5, x 0 obs = 1, and x 0 obs = 3. In the case of an icosahedron, we can set S as the center of the icosahedron.…”

Section: Apparent Shapes Of Other Objectsmentioning

confidence: 99%

“…Exploring the regions of redshift and blueshift on the apparent shape of an object travelling near the speed of light may help us understand the distortion. In [18], illumination in special relativity is explored and factors such as brightness and radiance are also considered. In this paper, however, we will only consider the apparent change in wavelength of received light due to the relative motion of the observer and source.…”

Section: The Doppler Effect and Relativistic Aberrationmentioning

confidence: 99%

“…We can also compute the metric tensor through equation (18). To quantify the curvature of the surface of the sphere, we compute the scalar curvature R for the resulting 2-dimensional metric above:…”

Section: Other Observationsmentioning

confidence: 99%

“…However, visualising accelerating objects in Special Relativity has been widely ignored, as mentioned by D. Weiskopf et al in [18]. They implement acceleration by proposing a virtual environment in which the user can control the camera's movement by changing its speed.…”

Section: Introductionmentioning

confidence: 99%

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Visual Appearance of Extended objects in Special Relativity

Bajaj

2021

Preprint

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The Lorentz transformation is a spontaneous measurement. We first highlight the difference between "measuring" and "seeing", where the latter considers the time light rays (emitted by each point on the object) take to reach the observer. We compute the apparent position of a point given its velocity, initial position, and observation time. The apparent speed of a point is calculated, and we obtain that it exceeds the speed of light when approaching the observer, similar to superluminal motion. For parameterizable surfaces, we analyze properties (such as curvature and torsion) of apparent shapes.The observation that a sphere retains its circular silhouette when transformed to its apparent shape, independent of the initial conditions, is proved mathematically. Plots describing the apparent speed and length of objects are made, and the metric tensor for a distorted sphere is calculated. A generalized equation for the Doppler effect and relativistic aberration is derived to analyze regions of redshift and blueshift. Using the Born-rigidity conditions, we compute the hyperbolic trajectories of each point on an extended object given an initial velocity, position, and proper acceleration for any reference point. The claim that a rigid body, accelerating in Special Relativity, cannot exceed a given length in certain circumstances is justified. We obtain many non-trivial results, which are proved algebraically and using light cones, that are tested by taking the limit of acceleration approaching 0 to retrieve results in the constant velocity scenario. In conclusion, these visualizations may be used by teachers to explain SR intuitively. Finally, we provide an overview of extending the same problem to curved spacetime and explain the potential applications of this project.

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Section: Apparent Shapes Of Other Objectsmentioning

confidence: 99%

Section: The Doppler Effect and Relativistic Aberrationmentioning

confidence: 99%

Section: Other Observationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Visual Appearance of Extended objects in Special Relativity

Bajaj

2021

Preprint

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“…This pipeline, with an application to a virtual reality environment, is described in [Wei00b], while special relativity renderings of accelerated extended objects are considered in [WBE*06, KRWZ02] (English version available at http://www.spacetimetravel.org/tompkins/tompkins.html). Acceleration is further dealt with [WKR00b], correcting earlier work by Betts [Bet98]. Related work simulates relativistic effects in synthetic scenes modelled with image‐based techniques, by applying the relativistic transformations directly on the light field [WKR00a].…”

Section: Related Workmentioning

confidence: 99%

Relativistic Effects for Time‐Resolved Light Transport

Jarabo

Masiá

Velten

et al. 2015

Computer Graphics Forum

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We present a real-time framework which allows interactive visualization of relativistic effects for time-resolved light transport. We leverage data from two different sources: real-world data acquired with an effective exposure time of less than 2 picoseconds, using an ultrafast imaging technique termed femto-photography, and a transient renderer based on ray-tracing. We explore the effects of time dilation, light aberration, frequency shift and radiance accumulation by modifying existing models of these relativistic effects to take into account the time-resolved nature of light propagation. Unlike previous works, we do not impose limiting constraints in the visualization, allowing the virtual camera to explore freely a reconstructed 3D scene depicting dynamic illumination. Moreover, we consider not only linear motion, but also acceleration and rotation of the camera. We further introduce, for the first time, a pinhole camera model into our relativistic rendering framework, and account for subsequent changes in focal length and field of view as the camera moves through the scene.

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Introduction to Mathematica

Trott

2004

The Mathematica GuideBook for Programming

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Illumination and acceleration in the visualization of special relativity: a comment on fast rendering of relativistic objects

Cited by 5 publications

References 23 publications

Visual Appearance of Extended objects in Special Relativity

Visual Appearance of Extended objects in Special Relativity

Relativistic Effects for Time‐Resolved Light Transport

Introduction to Mathematica

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