superEllipse Element

Superellipse

Namespace: Empty

Schema: Empty

Type
Parents
Children
NameOccurrencesDescription
All All
      Element lowerHeightFraction

Fraction of height of the lower semi-ellipse relative to the total height

      Element mLower

Exponent m for lower semi-ellipse

      Element mUpper

Exponent m for upper semi-ellipse

      Element nLower

Exponent n for lower semi-ellipse

      Element nUpper

Exponent n for upper semi-ellipse

Attributes
NameTypeRequiredDescription
Attribute externalDataDirectorySimple Type string
Attribute externalDataNodePathSimple Type string
Attribute externalFileNameSimple Type string
Remarks

A profile based on superellipses is composed of an upper and a lower semi-ellipse, which may differ from each other in their parameterization. The total width and height of the profile is always 1, since scaling is performed after referencing (e.g., in the fuselage).

This lowerHeightFraction describes the portion of the lower semi-ellipse on the total height.

The resulting profile is defined by the following set of equations:

Equation for superellipse in positive half-space
Equation for superellipse in negative half-space

with

Equation for superellipse middle line

The following examples indicate the various possibilities of parametric profiles:

Example 1: (mUpper,nUpper,mLower,nLower, lowerHeightFraction) = (0.5; 2; 5; 3; 0.25)

Example of adjacent lower and upper superellipse

Example 2: (mUpper,nUpper,mLower,nLower, lowerHeightFraction) = (2; 2; 2; 2; 0.5) = a circle

Example of a superellipse forming a circle

Example 3: (mUpper,nUpper,mLower,nLower, lowerHeightFraction) = (1; 1; 1; 1; 0.5) = a square / diamond

Example of a superellipse forming a square

Note: For exponents that are infinitely large, the superellipse converges to a rectangle. However, the value Inf is not a valid entry at this point. Use the square element instead.

See Also