!4DSolids is a small demo program that runs in the WIMP environment. It
rotates 3-Dimensional and 4-Dimensional shapes in a window.
There are 8 shapes displayed, the first 5 are 3D, the 5 Platonic Solids.
Then there is a Pentahedroid ( like a HyperTetrahedron ) and a Hypercube
( sometimes known as a Tesseract ). These are kind of like Platonic
HyperSolids I think. Then finally there is a Klein Bottle, this is a
topological structure which requires 4 dimensions to exist properly.
Instructions
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When run, !4Dsolids installs itself and its icon will apper on the icon
bar. Clicking Select on this icon will open the main view window, and you
will see a rotating Tetrahedron. Clicking either Select or Menu with the
pointer within this window will open the Control window ,full control of
the program is available through the icons in this window.
Current Shape - The name of the current shape is displayed at the top of
the control window. Clicking on this will change the
current shape, rotating through all 8 shapes.
Surfaces - Clicking on this will remove various surfaces from the
Displayed display, so the structure of the current shape can be
examined. The number displayed represents the number of
surfaces that can be seen, except in the case of the
Klein bottle where it just represents 1/3rd 2/3rds or
the whole of the figure displayed.
There are four different ways the shapes can be rendered on the screen,
selected by clicking on the icon by each option.
Straight - The surfaces of the shape are drawn as they are, opaque
with no shading.
Depth shaded - The surfaces are shaded by becoming darker the further
away they are from the viewer.
Clear Coloured - The shape is rendered as if the surfaces were pieces of
coloured glass, allowing more of the structure to be seen.
Clear White - The shape is rendered as with the Clear Coloured option,
except the surfaces are treated as if they were grey and
not coloured.
The rotation of the shape can be controlled in all 6 axes by the 'meter'
type icons at the bottom of the control menu. The picture to the left of
the icon shows which axis it controls. The first three are the normal 3D
axes, whereas those on the right control rotions in plane which include
the fourth dimension.
When the needle of the meters points straight up,this means no movement
in that axis of rotation. Clicking to the left or right of the needle
causes the needle to move to the left or right. The rotion speed in the
particular axis is proportional to the position of the needle.
NOTE: the program works by keeping a list of the current rotation in each
axis, and then for each image applies the rotation for each axis, in order, to the original basic description of the shape. The basic upshot of this is
that if you stop the shape rotating, and then try to rotate it a bit in a
particular axis you may find it doesn't move in the direction you expect.
This will be because of later rotation angles turning the shape around
after the rotation you're trying to do. Sorry about this.
And Finally...
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I haven't explained very much about the idea of 4D shapes, and I'm not
going to here. But I would like to know if anyone is interested about
using computers to handle higher dimensional structures, it seems to me
an ideal way to think about these things, as the computer can work things
out, without our human bias towards thinking 3-dimensionally.
I have loads of ideas for 4D programs, 4D Rendrers, where you can make
3d templates and fold them up into 4D shapes, 4D Raytracers , etc. But I
also have ideas for loads of other programs and I've got to decide what to
I'm going to write. So if anyone is interested or has any comments, contact
