Rotope (EntityClass, 3)
From Hi.gher. Space
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=== Tapertopes === | === Tapertopes === | ||
Tapertopes were coined by [[Keiji]], and invented by him and [[Paul Wright]]. | Tapertopes were coined by [[Keiji]], and invented by him and [[Paul Wright]]. | ||
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| + | Tapertopes are the line and shapes formed by [[tapering]] other tapertopes to a point. | ||
== Finding rotopes == | == Finding rotopes == | ||
Revision as of 19:27, 17 June 2007
Sets of rotopes
Rotopes are combinations of rotatopes, toratopes and tapertopes. A rotope may be any combination of these, with the exception that a toratope may never be a tapertope and vice versa. There are also rotopes that are none of these. An example is the torinder. The number of non-tapertopes in any dimension is always twice the number of toratopes. In the table below, 'x' denotes the cartesian product, '#' denotes the torus product and '~' denotes tapering. Note that the CSG Notation column shows the notation for a completely solid form of the object.
Rotatopes
A rotatope, invented by Garrett Jones is an object formed by linear extensions or rotations about the origin.
Toratopes
Toratopes were coined by Paul Wright, and invented by him and Marek14. A toratope is an object formed by spheration, i.e. putting a new k-sphere at every point in an object. This is also called the "torus product", #. A#B is the result of replacing every point in A with a copy of B, oriented along the normal space of A.
Tapertopes
Tapertopes were coined by Keiji, and invented by him and Paul Wright.
Tapertopes are the line and shapes formed by tapering other tapertopes to a point.
Finding rotopes
There are currently two main methods for finding rotopes:
