Tapering (InstanceTopic, 3)
From Hi.gher. Space
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The shape formed from tapering a base shape ''x'', represented in [[CSG notation]] as ''x''T is the [[set]] of all points included in the [[linear sweep]] between the base object and a given point. | The shape formed from tapering a base shape ''x'', represented in [[CSG notation]] as ''x''T is the [[set]] of all points included in the [[linear sweep]] between the base object and a given point. | ||
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| + | After the tapering, the number of elements change similarly to going down a row in [[wikipedia:Pascal's triangle|Pascal's triangle]]. Each count is increased by the count one dimension below it, with the number of vertices increasing by one and a single cell of the shape's dimension being formed. For example, when extruding the [[cube]] (which has 8 vertices, 12 edges, 6 faces and of course 1 cell), a [[cubic pyramid]] is formed, which will have 8+1 = 9 vertices, 12+8 = 20 edges, 6+12 = 18 faces, 1+6 = 7 cells and a single new teron. | ||
[[Category:Geometric operations]] | [[Category:Geometric operations]] | ||
Revision as of 21:57, 29 May 2010
Tapering is the process of creating a hyperpyramid from a base shape.
The shape formed from tapering a base shape x, represented in CSG notation as xT is the set of all points included in the linear sweep between the base object and a given point.
After the tapering, the number of elements change similarly to going down a row in Pascal's triangle. Each count is increased by the count one dimension below it, with the number of vertices increasing by one and a single cell of the shape's dimension being formed. For example, when extruding the cube (which has 8 vertices, 12 edges, 6 faces and of course 1 cell), a cubic pyramid is formed, which will have 8+1 = 9 vertices, 12+8 = 20 edges, 6+12 = 18 faces, 1+6 = 7 cells and a single new teron.
