Generalities about Visualization

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Jean-François COLONNA

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, Ecole Polytechnique, CNRS, 91128 Palaiseau Cedex, France

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(CMAP28 WWW site: this page was created on 03/15/2000 and last updated on 04/20/2021 16:37:12 -CEST-)

- Curve Visualization [
*Visualisation de Courbes*]: - Intersection Visualization [
*Visualisation d'Intersections*]: - Surface Visualization [
*Visualisation de Surfaces*]: - Tridimensional Manifold Visualization [
*Visualisation de Variétés Tridimensionnelles*]: - 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*]: - Picture Sharpening [
*Amélioration de la netteté d'une image*]: - Stereograms [
*Stéréogrammes*]: - Autostereograms [
*Autostéréogrammes*]:
[More information]
- Autostereograms of a Volcano [
*Autostéréogrammes d'un Volcan*]: - Autostereograms of Quaternionic Julia Sets [
*Autostéréogrammes d'Ensembles de Julia Calculés dans le Corps des Quaternions*]: - More Autostereograms [
*Autres Exemples d'Autostéréogrammes*]: - Anaglyphs [
*Anaglyphes*]: - Cross-Sections with Translations and/or Rotations [
*Sections avec Translations et/ou Rotations*]: - Enhancement of the Third Dimension -Fog, Depth of Field, Lighting,...- [
*Améliorations de la Perception de la Troisième Dimension -Brouillard, Profondeur de Champ, Eclairage,...-*]: - Third and Fourth Dimensions Visualization and beyond [
*Visualisation de la troisième et de la Quatrième Dimensions et au-delà*]: - N-Dimensional Space Full Visualization [
*Visualisation complète d'Espaces à N Dimensions*]: - Time Visualization [
*Visualisation du Temps*]: - Animation [
*Animation*]:
[ - 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*]:

A Part of the DNA double helix -a tribute to Francis Crick, Rosalind Franklin and James Watson-. |

A twisting rope. |

3-foil knot. |

A straigth line -a monodimensional manifold- or a cylinder -a bidimensional manifold- in the distance?. |
A cylinder -a bidimensional manifold-. |
A cylinder -a bidimensional manifold-. |

Bidimensional cross-sections of a cylinder. |
Bidimensional cross-sections of a cylinder. |

Bidimensional cross-sections of the Klein bottle. |
Bidimensional cross-sections of the Klein bottle. |

Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle. |
Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle. |

Bidimensional cross-sections of the Jeener unilateral node. |
Bidimensional cross-sections of the Jeener unilateral node. |
Bidimensional cross-sections of the Jeener unilateral node. |

A one sheet hyperboloid of revolution -negative curvature-. |
A plane -zero curvature-. |
A sphere -positive curvature-. |

A sphere. |
A set of spheres with holes. |
A set of twisted spheres. |
A sphere defined by means of three bidimensional fields. |
The pseudo-sphere. |

A cylinder. |
A cone. |
A two sheet hyperboloid of revolution. |

A torus. |
A torus. |
A torus by means of three bidimensional fields. |
Four overlaped torus. |
Sixteen overlaped torus. |

Sixty-four overlaped torus. |

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

7-foil torus knot on its torus. |

The Jeener unilateral node. |
The Jeener toric node. |

The double Jeener bottle. |
The Bonan-Jeener double bottle. |
The Jeener twin bottles. |

The Jeener's quadruple bilateral bottle. |
The Jeener's quadruple bilateral bottle. |
The quadruple Jeener bottle. |

The Jeener-Klein quintuple bottle. |
The Jeener-Klein quintuple bottle. |
The Jeener-Klein quintuple bottle. |
Artistic view of the Jeener-Klein quintuple bottle. |

The interlaced epicycloidal Jeener bottle. |
The interlaced epicycloidal Jeener bottle. |
The interlaced epicycloidal Jeener bottle. |

The interlaced hypocycloidal Jeener bottle. |

The Jeener opera -10-Sydney-. |

A Lissajous surface. |
A Lissajous surface. |
A Lissajous surface. |
A Lissajous surface in motion. |
A twisting Lissajous surface. |

Fractal 'celestial body' based on the Bonan-Jeener-Klein triple bottle. |

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

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 fractal structure. |
Bidimensional cross-sections inside a fractal structure. |
Tridimensional fractal structure. |
Bidimensional cross-sections inside a fractal structure. |

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

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. |

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

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

A set of 4x3 stereograms of a fractal-fractal tree. |

A set of 4x3 stereograms of a fractal Notre-Dame de la Garde, Marseilles. |

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

Anaglyphic glasses. |

Anaglyph -blue=right, red=left- of a fractal Notre-Dame de la Garde, Marseilles. |

Anaglyph -green=right, red=left- of a tridimensional display of the Mandebrot set. |

A cylinder -a bidimensional manifold-. |
A cylinder -a bidimensional manifold-. |

Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -sixteen bidimensional cross-sections-. |
Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') -tridimensional cross-section-. |

Bidimensional cross-sections of a cylinder. |
Bidimensional cross-sections of a cylinder. |

Bidimensional cross-sections of the Klein bottle. |
Bidimensional cross-sections of the Klein bottle. |

Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle. |
Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle. |

Bidimensional cross-sections of the Jeener unilateral node. |
Bidimensional cross-sections of the Jeener unilateral node. |

2.pi rotation about the Y axis of a quaternionic Julia set -tridimensional cross-sections-. |
2.pi rotation about the Y axis of a quaternionic Julia set with motion blur -tridimensional cross-section-. |

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. |

Close-up on a pseudo-octonionic Mandelbrot set (a 'Mandelbulb') for sixteen different lightings -tridimensional cross-section-. |

A straigth line -a monodimensional manifold- or a cylinder -a bidimensional manifold- in the distance?. |
A cylinder -a bidimensional manifold-. |
A cylinder -a bidimensional manifold-. |

Hypercube. |
A 4-cube -an hypercube-. |

Bidimensional cross-sections of a cylinder. |
Bidimensional cross-sections of a cylinder. |

Bidimensional cross-sections of the Klein bottle. |
Bidimensional cross-sections of the Klein bottle. |

Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle. |
Bidimensional cross-sections of the Bonan-Jeener-Klein triple bottle. |

Bidimensional cross-sections of the Jeener unilateral node. |
Bidimensional cross-sections of the Jeener unilateral node. |
Bidimensional cross-sections of the Jeener unilateral node. |

N-dimensional random structure. |
N-dimensional random structure. |

Tridimensional display of the dynamics of the bidimensional John Conway's life game. |
Tridimensional display of the dynamics of the bidimensional John Conway's life game. |

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. |

The Möbius strip. |

Dynamics of the even distribution of 24 points on a sphere by means of simulated annealing. |
Dynamics of the even distribution of 6 points on a sphere -an Octahedron- by means of simulated annealing. |

Bidimensional texture animation by means of the Generalized Product. |
Tridimensional texture animation by means of the Generalized Product. |
Bidimensional geometrical texture animation. |

From Mars to the Sun. |
The journey of an Earth-like virtuel planet (green) from Pluto (grey) to the Sun (yellow) -point of view of the virtual planet-. |

The bidimensional John Conway's life game. |

Monument Valley at sunrise with light cloud dynamics -this sequence being periodical-. |

The random walk of photons escaping the Sun. |

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. |
The Sierpinski carpet -iteration 5-. |

Black dots (inside random white squares) on a square lattice. |
Zollner optical illusion. |

Geometrical distorsion. |
Geometrical distorsion. |
Geometrical distorsion. |

Three ghost squares. |

Vibrations 0001. |
Vibrations 0002. |
Vibrations 0003. |

Heap or hole? |
A pseudo-periodical Penrose tiling of the Golden Decagon with five hidden cubes. |
Cube "in" or cube "out"? |
Perspective anomaly with the RGB cube. |

Artistic view of a bidimensional texture obtained by means of the self-transformation of a fractal process. |

A color palette with an increasing luminance. |
From cold to warm colors. |
From cold to warm colors. |

The same bidimensional scalar field displayed with 4 different color palettes. |
The same bidimensional scalar field displayed with 4 different color palettes. |

The 1.000 first digits -base 10- of 'pi' displayed on an helix -bad point of view-. |
The 1.000 first digits -base 10- of 'pi' displayed on an helix -good point of view-. |

The connexity of the Mandelbrot set. |
The connexity of the Mandelbrot set. |

Bidimensional clouds or height field. |
Different modes of representation of a tridimensional cross-section of a Quaternionic Julia set. |

The defaults of the JPEG encoding. |

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