Torinder (EntityTopic, 11)

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Revision as of 07:19, 20 June 2007

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Geometry

A torinder is the linear extension of a torus.

Equations

• Variables:

R ⇒ major radius of the torinder
r ⇒ minor radius of the torinder
h ⇒ height of the torinder

• All points (x, y, z, w) that lie on the surcell of a torinder will satisfy the following equation:

h ≥ |w|
r² = (sqrt(x² + y²) - R)² + z²

• The parametric equations are:

x = (R + r cos(θ)) cos(Φ)
y = (R + r cos(θ)) sin(Φ)
z = r sin(θ)
w = w

• The hypervolumes of a torinder are given by:

surface area of margin = 8π²Rr
surcell volume = 4πRr(πr + h)
bulk = 2π²Rr²h

• The realmic cross-sections (n) of a torinder are:

Unknown

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