Generalities about Visualization

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Jean-François COLONNA

CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, 91120 Palaiseau, France

france telecom, France Telecom R&D

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(CMAP28 WWW site: this page was created on 03/15/2000 and last updated on 06/24/2023 11:21:20 -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. | 3-foil torus knot on its torus. | 5-foil torus knot on its torus. | 7-foil torus knot on its torus. |

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

Distorsion of a sphere. | Distorsion of a sphere. |

Distorsion of a sphere. | Distorsion of a sphere. |

The pseudo-sphere. |

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

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. |

1-foil torus knot -obvious knot- on its torus and its asociated Möbius strip. | 3-foil torus knot on its torus. | 5-foil torus knot on its torus. | 7-foil torus knot on its torus. |

Distorsion of the Möbius strip. | Distorsion of the Möbius strip. |

Distorsion of the Möbius strip. | Distorsion of the Möbius strip. |

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

The Jeener twin bottles. |

Distorsion of the Bonan-Jeener-Klein double bottle. | Distorsion of the Bonan-Jeener-Klein double bottle. |

Distorsion of the Bonan-Jeener-Klein double bottle. | Distorsion of the Bonan-Jeener-Klein double bottle. |

Distorsion of the Bonan-Jeener-Klein double bottle. |

The u=v line on the Bonan-Jeener-Klein triple bottle. | The u=v line on the Bonan-Jeener-Klein triple bottle and a strip. |

Distorsion of the Bonan-Jeener-Klein triple bottle. |

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 Boy surface in motion. | Rotation about the Y axis of the Boy surface with motion blur. | From à rectangle to the Boy surface. | From a sphere to the Boy surface. |

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 parallelepipedic Hyper-Torus. | A Ball. |

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. |

Some elementary symbols used to built labyrinths -with a big black ghost structure at pi/4-. |

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. | A strange and noisy picture with a very simple luminance. | A strange and noisy picture with a very simple 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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