Spheration (InstanceTopic, 3)
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| + | '''Spheration''' is a kind of modeller's finish, like a paint. It is not intended to add new topology to the shape, but to give a thin thing substance. | ||
| - | This particular | + | This particular finish converts thin things into solid objects. One can see an example of spheration at the [http://www.atomium.be Atomium], a left-over from the Brussels Expo. This shows the vertices and edges of a cube, which are all connected to a central cell. To make these real, there are spheres at the vertices, and thinner lines connecting the spheres. |
| - | The popular [http://zometool.com Zometool is an example of a tool for making solid examples of vertices and lines, which in turn indicate the shape to build. | + | The popular [http://zometool.com Zometool] is an example of a tool for making solid examples of vertices and lines, which in turn indicate the shape to build. |
The mathematical specification is that all points at some distance ''r'' from a thin thing (like a line), is part of the solid representation of that thing. One might use different values of ''r'' for different dimensions, usually in descending order (a point's ''r'' is bigger than a line's ''r''). | The mathematical specification is that all points at some distance ''r'' from a thin thing (like a line), is part of the solid representation of that thing. One might use different values of ''r'' for different dimensions, usually in descending order (a point's ''r'' is bigger than a line's ''r''). | ||
Latest revision as of 20:51, 6 February 2014
Spheration is a kind of modeller's finish, like a paint. It is not intended to add new topology to the shape, but to give a thin thing substance.
This particular finish converts thin things into solid objects. One can see an example of spheration at the Atomium, a left-over from the Brussels Expo. This shows the vertices and edges of a cube, which are all connected to a central cell. To make these real, there are spheres at the vertices, and thinner lines connecting the spheres.
The popular Zometool is an example of a tool for making solid examples of vertices and lines, which in turn indicate the shape to build.
The mathematical specification is that all points at some distance r from a thin thing (like a line), is part of the solid representation of that thing. One might use different values of r for different dimensions, usually in descending order (a point's r is bigger than a line's r).
A torus is a spherated circle. This is the result of points a sphere might cut if it travels around the circle.
A tiger is a spherated bi-glomolatric prism. A 'glomolatrix' is a round line-fabric as itself, that is, a circle's circumference. The bi- means that you use two of them. The prism is a product, which creates a cartesian intersection (points in A plus points in B are in the product points in AB). This is still a thin 2d surface in 4D. To give it substance, we need to flesh it out or puff it up, by including points at some distance r from it.
The section of a spherated object, when taken at right angles to the object, gives a spheric (eg circular, spheric, glomic), cross-section.
