# Sphere (EntityTopic, 15)

(Difference between revisions)
 Revision as of 14:36, 16 September 2007 (view source)Keiji (Talk | contribs)m (add)← Older edit Revision as of 07:21, 22 September 2007 (view source)Keiji (Talk | contribs) m (→Mapping)Newer edit → Line 19: Line 19: === Mapping === === Mapping === - When the surface of a sphere is mapped onto a [[rectangle]] {(-1,-1),(1,-1),(1,1),(-1,1)}, the surface will be horizontally stretched such that the further away from the equator of the sphere a point is, the more it is stretched. The top and bottom edges of the rectangle will converge into a single point. Leaving the top edge of the rectangle will continue entering from the top edge at the position (x±1,1). Similarly, leaving the bottom edge of the rectangle will continue entering from the bottom edge at the position (x±1,-1). + When the surface of a sphere is mapped onto a [[square]] centered at the origin with side length 2, the surface will be horizontally stretched such that the further away from the equator of the sphere a point is, the more it is stretched. The top and bottom edges of the rectangle will converge into a single point. Leaving the top edge of the rectangle will continue entering from the top edge at the position (x±1,1). Similarly, leaving the bottom edge of the rectangle will continue entering from the bottom edge at the position (x±1,-1). {{Trishapes}} {{Trishapes}} {{Rotope Nav|6|7|8|II'
Square pyramid|(III)
Sphere|I'I
Triangular prism|hedra}} {{Rotope Nav|6|7|8|II'
Square pyramid|(III)
Sphere|I'I
Triangular prism|hedra}} {{Bracketope Nav|12|13|14|(z)
Narrow crind|(xyz)
Sphere|[xyzw]
Tesseract|hedra}} {{Bracketope Nav|12|13|14|(z)
Narrow crind|(xyz)
Sphere|[xyzw]
Tesseract|hedra}}

## Geometry

A sphere refers to the surface of a perfectly symmetrical realmic object.

• Variables: