1. Relativistic Visualisation of Stars
for High-resolution Displays
Nicole Lin 1/16/2009
Examiner: Prof. Dr. Daniel Weiskopf
Supervisors: Prof. Dr. Daniel Weiskopf, Dr. Thomas Müller

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BrightnessBrightness
GeometryGeometry
Introduction
VisualisationVisualisation RelativityRelativity
MassMass
SpeedSpeed
ColorColor

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Outline
 Visualisation of stars
 Special relativistic visualisation
 General relativistic visualisation

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Visualisation of Stars
 Visualisation of stars
 Special relativistic visualisation
 General relativistic visualisation

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Steps of Visualisation
Stellar
Data
Stellar
Data
HDR
Data
HDR
Data
Tone
mapping
Tone
mapping
RenderingRendering

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Stellar Data
Hipparcos
Catalogue
Hipparcos
Catalogue
Spherical
Coordinates
Spherical
Coordinates
TemperatureTemperature
Visual
Magnitude
Visual
Magnitude
Stellar
Data
Stellar
Data
HDR
Data
HDR
Data
Tone
mapping
Tone
mapping
RenderingRendering
ESA*ESA*
* European Space Agency

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Black Body Radiation
Stellar
Data
Stellar
Data
HDR
Data
HDR
Data
Tone
mapping
Tone
mapping
RenderingRendering
Black
Body
Black
Body
Planck
Spectrum
Planck
Spectrum
Star
Spectral
Intensity
Spectral
Intensity

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Stellar Temperature vs. Spectral Intensity
hot / blue star
Stellar
Data
Stellar
Data
HDR
Data
HDR
Data
Tone
mapping
Tone
mapping
RenderingRendering
cool / red star
intensity
visible wavelength

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LensLens
ApertureAperture
Fraunhofer Diffraction
Stellar
Data
Stellar
Data
HDR
Data
HDR
Data
Tone
mapping
Tone
mapping
RenderingRendering
ObservationObservation
Diffraction

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Stellar Color - CIE XYZ
Fraunhofer
Diffraction
Fraunhofer
Diffraction
Spectral
Intensity
Spectral
Intensity
Stellar
Data
Stellar
Data
HDR
Data
HDR
Data
Tone
mapping
Tone
mapping
RenderingRendering
CIE XYZ
Color matching
functions
Color matching
functions
HDR Data
denoted by
(Ix, Iy, Iz)

11. HDR Data
Stellar
Data
Stellar
Data
HDR
Data
HDR
Data
Tone
mapping
Tone
mapping
RenderingRendering
11/32
log
η
10n
0
η distance to the center of a screen
solid angle
Luminance F = Iy * ρ
observer
Ix, Iy, Iz

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Tone Mapping
 Original concept by Reinhard et al.
Ld =
Lw
1 + Lw
Ld =
Lw
1 + Lw G
Stellar
Data
Stellar
Data
HDR
Data
HDR
Data
Tone
mapping
Tone
mapping
RenderingRendering
global operator local operator
Ld Display luminance
Lw World luminance
G Gaussian function
F * φ
φ User scaling

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Global Operator vs. Local Operator
Stellar
Data
Stellar
Data
HDR
Data
HDR
Data
Tone
mapping
Tone
mapping
RenderingRendering
global operator local operator
more local contrast preserved

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Rendering - Constellation of Orion
tone mapping image
Stellar
Data
Stellar
Data
HDR
Data
HDR
Data
Tone
mapping
Tone
mapping
RenderingRendering
photo *
* source: NASA

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Special Relativistic Visualisation
 Visualisation of stars
 Special relativistic visualisation
 General relativistic visualisation

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Special Relativistic Visualisation
aberration of light
Doppler shift
velocityvelocity
changes in
position
color
brightness
observer

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Aberration of Rain
velocityvelocity
DB
remains static

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Aberration of Light
rays of light
remains static

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Classical Aberration of Light
0.5
close to the speed of light
0.999

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Relativistic Aberration of Light
close to the speed of light
0. 5 0.999

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Changes in Position (1/3)
remains static

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Changes in Position (2/3)
0.5

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Changes in Position (3/3)
0.9

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Changes in Color & Brightness
remains statics
0.99
Doppler blue shift & Aberration of Light *
* changes in solid angles

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General Relativistic Visualisation
 Visualisation of stars
 Special relativistic visualisation
 General relativistic visualisation

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General Relativistic Visualisation
MassMass
changes in
position
color
brightness
gravitational red shift
bending of light
Doppler blue shift
aberration of light
velocityvelocity

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Bending of Light
black
hole
black
hole
star
appears infinitely many times

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Around a Black Hole – Constellation of Orion

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Interactive Schwarzschild Black Hole
GPS for
Orion
settings time & position

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Interactive Schwarzschild Black Hole
GPS for
Orion
settings time & position

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Freely Falling into a Black Hole
BHBH BHBH
remains
static
velocity velocity
blue shift, gravitational red shift aberration vs. bending
Color Size

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Conclusion & Future Work
Visualisation Relativity
For high-resolution displays
Tiled display Edge
blending
Geometry
distortion
Intensity
correction

33. Any Questions?
33/32
source: NASA
The Pleiades – well known for its shape of a question mark