Tiger (EntityTopic, 11)

From Hi.gher. Space

Revision as of 21:03, 10 December 2013

ExPar: [#img] is obsolete, use [#embed] instead
Diagram created by Keiji, adapted from a sketch from Secret in this forum post.

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:

(√(x² + y²) − a)² + (√(z² + w²) − b)² = r²

• The parametric equations are:

x = a cos(θ₁) + r cos(θ₁)cos(θ₃)
y = a sin(θ₁) + r sin(θ₁)cos(θ₃)
z = b cos(θ₂) + r cos(θ₂)sin(θ₃)
w = b sin(θ₂) + r sin(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.

Cross-sections

Jonathan Bowers aka Polyhedron Dude created these two excellent cross-section renderings: ExPar: [#img] is obsolete, use [#embed] instead ExPar: [#img] is obsolete, use [#embed] instead