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• Intro


— 3D World: 2D, 3D, 4D —


Space is described by dimensions. A dot without expansion has no dimension. A line (——) has one dimension, namely its length.

A surface has two dimensions, length and width. The screen surface on which this page is displayed, has two dimensions as has anything printed on paper.

Humans have two eyes and thus the third dimension is added to his/her perception: length, width and height or depth. The video display unit in front of you has three dimensions, every other object, too and even the room in which you are.

3D Pictures
Most pictures we look at are displayed on a surface and therefore appear two-dimensional and flat. The sensation of three-dimensionality can be created with appropriate tools: holograms; two photographs shot at slightly different positions shown side by side and looked at with a special sort of glasses; anaglyphs.

Even if the landscape depicted on a piece of paper appears to be flat, we know that the mountains are farther away than the big flower. With raytracing programs, three-dimensional worlds can be created that are displayed flat. The three-dimensionality exists, however, since the place of observation can be changed at will.

The fourth-dimension is commonly attributed to the time. The movie from last years holidays is four-dimensional in this sense, even if the third dimension is missing when displayed on the screen. Raytracing programs permit the animation of the observing camera and you can create a movie. To those small movies, sound may even be added with an additional program. This is not called 5-D, however.

3D with Raytracers — The three-dimensional world

With raytracing programs you create three-dimensional bodies and place them within a three-dimensional space. The bodies may be objects, parts of landscapes, vegetation or others. The bodies may be hollow or solid. If they are hollow, a material can be put on, if they are solid, they are filled with the material.

Materials may change in relation to the height or steepness of a slope. A material consists of multiple textures. The material consisting of textures interacts with the light it absorbs and reflects. Different raytracing programs offer different tools to create and put on materials and how the material interacts with the environment.

When a scene is finished, it will be rendered, i.e. a two-dimensional picture is created from the vantage point of the one-eyed observing camera. Although the scene appears flat and without depth, it portrays a room nevertheless.

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The example of a simple island landscape shows the three-dimensionality. From left to right: after a long voyage over the sea, the sandbanks of an island are reached and three trees can be made out near the beach. During a flight over the island between mountain ranges a river is discovered. The three trees can be seen in the distance. Seing the end of a long hike through the mountains makes the tired wanderer happy: the trees are not far away anymore. Oops! The trees grow in the seawater. They will not survive long, there. Quite obviously, the work was not carried out with the necessary care.

This series of pictures was created from a simple Bryce 5 project. The materials are all from the library.

Panorama of a Landscape — 360° Spherical View

Landscapes photographed with a very wide angle lens are often called panoramas. A fisheye lens has as widest angle only 180°. A complete panorama covers the environment by full 360° and that is what an observer would see, if he/she turns once around his/her own axis. A panorama has no end at its sides and has to be displayed on the inside of a cylinder or sphere. When it is displayed on a flat screen, the observer has to imagine the left and right edges to be glued together.


Raytracing programs can render a picture as a panorama. The picture shows in the upper part the panorama of the island landscape presented above. For the lower part of the picture, the upper part of the picture was cut in half and re-assembled with the parts swapped, thus the left and the right edges of the upper picture are glued together. Now, the center moved to the opposite edges. What is obvious in those pictures are the distortions. The reason lies in the fact that a picture created to be displayed on a curved surface is shown on a flat screen (example: a world map of the round Earth).

QTVR - Panorama Movies

The picture and movie displaying program QuickTime has from its version 3 onwards the option «Virtual Reality» and can display panoramas interactively. Only a part of the panorama is shown. The content of the window can be moved in all directions, even zooming in and out is possible. This permits to display a panorama on a flat video screen in a sensible manner.

Motion Pictures: the Fourth Dimension — Different types

In a motion picture, objects (cars) or people move and the environment remains unchanged because the camera is still. Sometimes, the camera moves and then, the environment changes. A quick-motion movie shows clouds racing over the sky or how the snow crawls back up to the summit when the season changes.

Also with raytracing programs different elements of a scenery can be animated:

  • Objects,
  • the Camera,
  • the Clouds in the Sky,
  • Materials.

Unfortunately it is seldom possible to animate more than one element at a time.

A hobby of its own

To begin the escapade of creating acceptable movies means starting an entirely new hobby. The landscape must be correctly set up, if the camera is to explore it. The speed of the animation can be varied at any point. The camera can penetrate and speed through objects, something that is not always desired.

First results are as doubtful as the first movie from the holidays with the new camcorder. If you watch the results of your labour you quickly get sick at all that jolting, rocking and shaking.

Rendering an animation can turn out to be a nightmare. Consider a duration of 10 seconds for the movie and 15 frames per second (the minimum), there are 150 individual pictures to be rendered.

  © 2004 - 2018 by Horo Wernli.