GALLERY:

GENERALITIES ABOUT VISUALIZATION

[Généralités sur la Visualisation]

Jean-François COLONNA

CMAP (Centre de Mathématiques APpliquées), Ecole Polytechnique, CNRS
france telecom, France Telecom R&D
91128 Palaiseau Cedex
France

tel = +33.(0)1.69.33.46.45
jean-francois.colonna@polytechnique.edu

http://www.lactamme.polytechnique.fr

http://www.cmap.polytechnique.fr/~colonna

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(this page was created on 03/15/2000)
(this page -belonging to the CMAP28 site- was last updated on 03/15/2010 09:41:42 -CET-)

• Curve Visualization [Visualisation de Courbes]:
• Surface Visualization [Visualisation de Surfaces]:
• Tridimensional Visualization of Bidimensional Scalar Fields [Visualisation de Champs Scalaires Bidimensionnels]:
• Visualization of Tridimensional Scalar Fields [Visualisation de Champs Scalaires Tridimensionnels]:
• Visualization of Tridimensional Vector Fields [Visualisation de Champs de Vecteurs Tridimensionnels]:
• Visualization of Bidimensional Time-Dependent Scalar Fields [Visualisation de Champs Scalaires Bidimensionnels Dépendant du Temps]:
• Visualization of Tridimensional Time-Dependent Scalar Fields [Visualisation de Champs Scalaires Tridimensionnels Dépendant du Temps]:
• Enhancement of the Third Dimension -Fog, Depth of Field,...- [Améliorations de la Perception de la Troisième Dimension -Brouillard, Profondeur de Champ,...]:
• Stereograms and Autostereograms [Stéréogrammes et Autostéréogrammes]:
• Autostereograms of a Volcano [Autostéréogrammes d'un Volcan]:
• Autostereograms of Quaternionic Julia Sets [Autostéréogrammes d'Ensembles de Julia Calcules dans le Corps des Quaternions]:
• More Autostereograms [Autres Exemples d'Autostéréogrammes]:
• Stereograms [Stéréogrammes]:
• Fourth Dimension Visualization [Visualisation de la Quatrième Dimension]:
• N-Dimensional Space Visualization [Visualisation d'Espaces à N Dimensions]:
• Time Visualization [Visualisation du Temps]:
• Relative Motions, Points of View and Virtual (or Subjective) Chaos [Mouvements Relatifs, Points de Vue et Chaos Virtuel (ou Subjectif)]:
• Optical Illusions and Various Problems [Illusions d'optique et Problèmes Divers]:

Generalities about Visualization [Généralités sur la Visualisation]:

Curve Visualization [Visualisation de Courbes]:

• A twisting rope.



• 3-foil knot.



• Random intertwining.
• Intertwining based on a bidimensional square lattice.
• Intertwining based on a conformal mapping of a bidimensional square lattice.



• Intertwining based on the geometry of a disk.
• Intertwining based on the geometry of the sphere.
• Intertwining based on the geometry of the Boy surface.



• Intertwining based on the geometry of a Mobius strip.
• Intertwining based on the geometry of a Klein bottle.
• Intertwining based on the geometry of the Bonan-Jeener's triple Klein bottle.



• Intertwining based on the geometry of a shell (Jeener surface 1).



• Intertwining based on the geometry of the Lorenz attractor.



Surface Visualization [Visualisation de Surfaces]:

• A Peano 'fractal plane' defined by means of three bidimensional fields.



• A sphere defined by means of three bidimensional fields.
• A crumpled sphere defined by means of three bidimensional fields.
• A crumpled sphere defined by means of three bidimensional fields.



• A set of spheres with holes.
• A set of twisted spheres.



• A crumpled torus defined by means of three bidimensional fields.



• 3-foil torus knot on its torus.
• 5-foil torus knot on its torus.
• 7-foil torus knot on its torus.



• A fractal surface defined by means of three bidimensional fields.
• A fractal surface (one iteration) defined by means of three bidimensional fields.
• A fractal surface (two iterations) defined by means of three bidimensional fields.
• A fractal surface (three iterations) defined by means of three bidimensional fields.
• A fractal surface (four iterations) defined by means of three bidimensional fields.
• A fractal surface (five iterations) defined by means of three bidimensional fields.
• A fractal surface (six iterations) defined by means of three bidimensional fields.
• A fractal surface (seven iterations) defined by means of three bidimensional fields.
• A fractal surface (eight iterations) defined by means of three bidimensional fields.



• A fractal surface (four iterations) defined by means of three bidimensional fields.
• A fractal surface (four iterations) defined by means of three bidimensional fields.
• A dynamic fractal surface (four iterations) defined by means of three sets of bidimensional fields.



• Tridimensional representation of a quadridimensional Calabi-Yau manifold.



• The Mobius strip.
• The Mobius strip.
• The Mobius strip.



• A gaussian mixing of a sphere and of the Mobius strip defined by means of three bidimensional fields.



• An interpolation between the Mobius strip and a sphere defined by means of three sets of bidimensional fields.



• Rotation about the Y (vertical) axis of a Jeener-Mobuis tridimensional manifold that can also be viewed as a set of 4x3 stereograms.
• A Jeener-Mobuis tridimensional manifold.
• Rotation about the Y (vertical) axis of a Jeener-Mobuis tridimensional manifold that can also be viewed as a set of 4x3 stereograms.
• A Jeener-Mobuis tridimensional manifold.



• The Klein bottle in motion.



• The Klein bottle.
• The Klein bottle in motion.
• The Klein bottle in motion.
• A crumpled Klein bottle defined by means of three bidimensional fields.
• A dynamic crumpled Klein bottle defined by means of three sets of bidimensional fields.



• The double Jeener bottle.



• The quadruple Jeener bottle.



• An interpolation between the Klein bottle and a sphere defined by means of three sets of bidimensional fields.



• An interpolation between the Klein bottle and the double Jeener bottle defined by means of three sets of bidimensional fields.



• The Jeener's triple Klein bottle.
• The Jeener's triple Klein bottle.
• The Jeener's quadruple bilateral bottle.
• The Jeener's quadruple bilateral bottle.
• The Jeener's quintuple Klein bottle.
• The Jeener's quintuple Klein bottle.



• The Bonan-Jeener's triple Klein bottle.
• The u=v line on the Bonan-Jeener's triple Klein bottle.



• Interpolation between the Jeener's quintuple Klein bottle and the Bonan-Jeener's triple Klein bottle.
• An interpolation between the Bonan-Jeener's triple Klein bottle and a sphere defined by means of three sets of bidimensional fields.



• A shell (Jeener surface 1).
• A shell (Jeener surface 1).
• A shell (Jeener surface 1) in motion.



• An interpolation between a shell (Jeener surface 1) and a sphere defined by means of three sets of bidimensional fields.



• An arbitrary surface (Jeener surface 2) in motion.
• An arbitrary surface (Jeener surface 2).
• An arbitrary surface (Jeener surface 2) in motion.



• Rotation about the Y axis of the Boy surface with motion blur.
• The Boy surface.
• The Boy surface in motion.
• Rotation about X and Y axes of the Boy surface.
• The Boy surface.
• From à rectangle to the Boy surface.
• From a sphere to the Boy surface.



• A Lissajous surface.
• A Lissajous surface.
• A Lissajous surface.
• A Lissajous surface in motion.
• A twisting Lissajous surface.



• Archimedian gaussian surface (bird's-eye view).



• Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (bidimensional computation).



Tridimensional Visualization of Bidimensional Scalar Fields [Visualisation de Champs Scalaires Bidimensionnels]:

• A fractal landscape.
• Wavelet transform of a bidimensional fractal field.



Visualization of Tridimensional Scalar Fields [Visualisation de Champs Scalaires Tridimensionnels]:

• A tridimensional twisted torus-like manifold defined by means of three tridimensional fields.
• A tridimensional Mobius-like manifold defined by means of three tridimensional fields.
• A tridimensional fractal manifold defined by means of three tridimensional fields.



• Black and white display of a tridimensional function.
• Black and white display of a tridimensional function.
• Color display of a tridimensional function.
• Color display of a tridimensional function.



Visualization of Tridimensional Vector Fields [Visualisation de Champs de Vecteurs Tridimensionnels]:

• The normal field of a shell (Jeener surface 1).
• The normal field of a shell (Jeener surface 1).
• The normal field of a shell (Jeener surface 1).



• The normal field of the Klein bottle.



• The normal field of the Bonan-Jeener's triple Klein bottle.



• The normal field of a crumpled sphere defined by means of three bidimensional fields.



• The normal field of a tridimensional representation of a quadridimensional Calabi-Yau manifold.



• The normal field of a fractal surface defined by means of three bidimensional fields.
• The normal field of a fractal surface defined by means of three bidimensional fields.



Visualization of Bidimensional Time-Dependent Scalar Fields [Visualisation de Champs Scalaires Bidimensionnels Dépendant du Temps]:

• Dynamics of a bidimensional fractal structure.
• Tridimensional fractal structure.



Visualization of Tridimensional Time-Dependent Scalar Fields [Visualisation de Champs Scalaires Tridimensionnels Dépendant du Temps]:

• Tridimensional display of the dynamics of a linear superposition of 6 eigenstates of the Hydrogen atom (tridimensional computation).



Enhancement of the Third Dimension -Fog, Depth of Field,...- [Améliorations de la Perception de la Troisième Dimension -Brouillard, Profondeur de Champ,...]:

• Cauliflowers, seaweeds, shells,... with fog.



• Depth of field effect.
• Depth of field effect with motion blur.
• A 'spiraling plane' defined by means of three bidimensional fields with depth of field effect.



Stereograms and Autostereograms [Stèrèogrammes et Autostèrèogrammes]:

[more information ]
[do you want to know how to generate an autostereogram with a C test program?]

Autostereograms of a Volcano [Autostéréogrammes d'un Volcan]:

• Autostereogram with an hidden volcano and 64 self-portraits.
• Autostereogram with an hidden volcano.
• Autostereogram with an hidden volcano.
• Autostereogram with an hidden volcano.
• Autostereogram with an hidden volcano.
• Autostereogram with an hidden volcano and fractal phenomenon.
• Autostereogram with an hidden volcano.
• Autostereogram with an hidden volcano.
• Autostereogram with an hidden volcano.



• Autostereogram with an hidden volcano by means of only 231 random points.



Autostereograms of Quaternionic Julia Sets [Autostereogrammes d'Ensembles de Julia Calculés dans le Corps des Quaternions]:

• Autostereogram of a quaternionic Julia set.
• The first autostereogram movie about quaternionic Julia sets.
• True colors autostereogram of a quaternionic Julia set.
• The first true colors autostereogram movie about quaternionic Julia sets.
• Autostereogram of a quaternionic Julia set and fractal phenomenon.
• Autostereogram of a quaternionic Julia set.



More Autostereograms [Autres Exemples d'Autostéréogrammes]:

• Autostereogram with an hidden ring and ghost bows.
• Autostereogram of 8 color-multiplexed quaternionic Julia sets.
• Two multiplexed autostereograms by means of a pi/2 rotation.



• Autostereogram with an hidden volcano and an animated disguise texture.



• True colors autostereogram of a fractal landscape.
• Autostereogram of Monument Valley.



Stereograms [Stéréogrammes]:

• Rotation about the Y (vertical) axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms.
• Rotation about the Y (vertical) axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms.
• Rotation about the Y (vertical) axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms.
• Rotation about the Y (vertical) axis of a tridimensional representation of a quadridimensional Calabi-Yau manifold that can also be viewed as a set of 4x3 stereograms.



• A set of 4x3 stereograms of the quaternionic Julia set computed with A=(0,1,0,0).
• A set of 4x3 stereograms of the quaternionic Julia set computed with A=(-0.5815147625160462,0.6358885017421603,0,0).



• Rotation about the Y (vertical) axis of a foggy pseudo-quaternionic Mandelbrot set (a 'MandelBulb') that can also be viewed as a set of 4x3 stereograms.



• Rotation about the Y (vertical) axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms.
• Rotation about the Y (vertical) axis of the Lorenz attractor that can also be viewed as a set of 4x3 stereograms.



• A set of 4x3 stereograms of the Solar System with a green virtual planet -virtual planet point of view-.
• A set of 4x3 stereograms of the Solar System with a green virtual planet -virtual planet point of view-.
• A set of 4x3 stereograms of the Solar System with a green virtual planet -virtual planet point of view-.
• A set of 4x3 stereograms of the Solar System with a green virtual planet -virtual planet point of view-.
• A set of 4x3 stereograms of the Solar System with a green virtual planet -virtual planet point of view-.



• Rotation about the Y (vertical) axis of the Klein bottle that can also be viewed as a set of 4x3 stereograms.
• Rotation about the Y (vertical) axis of the Jeener's triple Klein bottle that can also be viewed as a set of 4x3 stereograms.



• Rotation about the Y (vertical) axis of sixteen interlaced torus that can also be viewed as a set of 4x3 stereograms.



• Rotation about the Y (vertical) axis of a Jeener-Mobuis tridimensional manifold that can also be viewed as a set of 4x3 stereograms.
• Rotation about the Y (vertical) axis of a Jeener-Mobuis tridimensional manifold that can also be viewed as a set of 4x3 stereograms.



• Rotation about the Y (vertical) axis of a tridimensional fractal aggregate that can also be viewed as a set of 4x3 pseudo-stereograms.



• Visualization by means of a set of 4x3 stereograms of the density iso-surfaces (density=0.42) during a tridimensional diffusion process of 128312 particles.



• A set of 4x3 stereograms of a tridimensional integration of an anisotropic gaussian Fourier filtering of a random field with a 2.pi rotation of the kernel.



• Rotation about the Y (vertical) axis of the CMAP logo that can also be viewed as a set of 4x3 stereograms.



• Rotation about the Y (vertical) axis of a tridimensional fractal structure that can also be viewed as a set of 4x3 stereograms.



• A set of 4x3 stereograms of a fractal mountain.
• A set of 4x3 stereograms of a few Babel Towers.
• A set of 4x3 stereograms of a few Monument Valleys at sunset.
• A set of 4x3 stereograms of a few Monument Valleys at sunset.



• A set of 4x3 stereograms of a tridimensional fractal structure.



Fourth Dimension Visualization [Visualisation de la Quatrième Dimension]:

• Hypercube.



• Translation along the fourth axis of a quaternionic Julia set.
• Integration of 128 tridimensional cross-sections of a quaternionic Julia set computed along its fourth axis.
• 2.pi rotation about the Y axis of a quaternionic Julia set.
• 2.pi rotation about the Y axis of a quaternionic Julia set with motion blur.



N-Dimensional Space Visualization [Visualisation d'Espaces à N Dimensions]:

• 32 points on a trigonometric circle.



• The 2 vertices of a 1-cube.
• The 4 vertices of a 2-cube.
• The 8 vertices of a 3-cube.
• The 16 vertices of a 4-cube.
• The 32 vertices of a 5-cube.



• Rotation about the X axis of the 32 vertices of a 5-cube.
• Rotation about the Y axis of the 32 vertices of a 5-cube with fog.



• N-dimensional random structure.
• N-dimensional random structure.



Time Visualization [Visualisation du Temps]:

• N-body problem integration (N=10) displaying the actual Solar System with its simultaneous 2.pi rotation.



• The Solar System with a dark blue virtual planet -virtual planet point of view-.



• Tridimensional visualization of a bidimensional turbulent flow.



• A shell (Jeener surface 1) in motion.
• The Klein bottle in motion.
• An arbitrary surface (Jeener surface 2) in motion.
• A Lissajous surface in motion.
• The Lorenz attractor in motion.



• Synthesis of tridimensional textures.
• Dynamics of a bidimensional fractal structure.



Relative Motions, Points of View and Virtual (or Subjective) Chaos [Mouvements Relatifs, Points de Vue et Chaos Virtuel (ou Subjectif)]:

• From the Sun to Pluto (linear scales).
• The journey of a sphere (dark blue) in a system of pure uniform concentric circular motions -moving point of view (dark blue)-.
• The journey of a sphere (dark blue) in a system of pure uniform non concentric circular motions -moving point of view (dark blue)-.



• From the Sun to Pluto -extrapolation 2- (non linear scales).
• Simulation of 'from the Sun to Pluto -extrapolation 2-' with pure uniform circular motions (non linear scales).



Optical Illusions and Various Problems [Illusions d'optique et Problèmes Divers]:

• 2 identical grey squares moving over a grey scale.
• Two identical grey rectangles in front of a grey scale.
• A uniform grey stripe on a grey scale.



• Black dots (inside random white squares) on a square lattice.



• Zollner optical illusion.



• Vibrations 0001.
• Vibrations 0002.
• Vibrations 0003.



• Heap or hole (bird's-eye view).



• Bidimensional clouds or height field.
• The same bidimensional scalar field displayed with 4 different color palettes.

Copyright (c) Jean-François Colonna, 2000-2010.
Copyright (c) France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) / Ecole Polytechnique, 2000-2010.