image of Astroidal ellipsoid

Astroidal ellipsoid



The Astroidal ellipsoid is a three-dimensional surface which is the inverse of the ellipsoid in the sense that it "goes in" where the ellipsoid "goes out."

Object definitions


Mapping of Astroidal ellipsoid
\left\{x\to a \cos ^3(u) \cos ^3(v),y\to b \sin ^3(u) \cos ^3(v),z\to c \sin ^3(v)\right\}
<math> <mrow> <mo>{</mo> <mrow> <mrow> <mi>x</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mrow> <mi>a</mi> <mo>&#8290;</mo> <mrow> <msup> <mi>cos</mi> <mn>3</mn> </msup> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>&#8290;</mo> <mrow> <msup> <mi>cos</mi> <mn>3</mn> </msup> <mo>(</mo> <mi>v</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mo>,</mo> <mrow> <mi>y</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mrow> <mi>b</mi> <mo>&#8290;</mo> <mrow> <msup> <mi>sin</mi> <mn>3</mn> </msup> <mo>(</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>&#8290;</mo> <mrow> <msup> <mi>cos</mi> <mn>3</mn> </msup> <mo>(</mo> <mi>v</mi> <mo>)</mo> </mrow> </mrow> </mrow> <mo>,</mo> <mrow> <mi>z</mi> <semantics> <mo>&#8594;</mo> <annotation encoding='Mathematica'>&quot;\[Rule]&quot;</annotation> </semantics> <mrow> <mi>c</mi> <mo>&#8290;</mo> <mrow> <msup> <mi>sin</mi> <mn>3</mn> </msup> <mo>(</mo> <mi>v</mi> <mo>)</mo> </mrow> </mrow> </mrow> </mrow> <mo>}</mo> </mrow> </math>
{x -> a*Cos[u]^3*Cos[v]^3, y -> b*Cos[v]^3*Sin[u]^3, z -> c*Sin[v]^3}
[x = a*cos(u)^3*cos(v)^3, y = b*cos(v)^3*sin(u)^3, z = c*sin(v)^3]


Constants of Astroidal ellipsoid
<math> <mrow> <mo>{</mo> <mrow> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> </mrow> <mo>}</mo> </mrow> </math>
{a, b, c}
[a, b, c]

Cite this as:

Surfaces: Astroidal ellipsoid from Differential Geometry Library.

Terms of use:

You can use the contents of DG Library pages for education, research, professional needs and enjoyment.
If you use this library, please, cite DG Library as the source of the data.

Pages of DG Library may not be copied, mirrored, redistributed, printed, or reproduced in bulk without permission. Usage for any commercial purposes without permission is prohibited.

DG Library is database of over 580 objects for differential geometry and its applications. Read more...

  • Share via email
  • Share via Twitter
  • Share via Facebook