Tiger (EntityTopic, 11)

From Hi.gher. Space

Revision as of 19:43, 19 November 2007

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Equations

• Variables:

a ⇒ major radius of the tiger in the xy plane
b ⇒ major radius of the tiger in the zw plane
r ⇒ minor radius of the tiger

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

(sqrt(x²+y²) - a)² + (sqrt(z²+w²) - b)² = r²

• The parametric equations are:

x = acos(θ₁) + rcos(θ₁)cos(θ₃)
y = asin(θ₁) + rsin(θ₁)cos(θ₃)
z = bcos(θ₂) + rcos(θ₂)sin(θ₃)
w = bsin(θ₂) + rsin(θ₂)sin(θ₃)

• The hypervolumes of a tiger are given by:

total edge length = Unknown
total surface area = Unknown
surcell volume = Unknown
bulk = Unknown

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

For realms parallel to one of the axes, they are formed by rotating Cassini ovals around a line parallel with their major axis, and not intersecting the ovals.

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