superEllipseProfileType

The profile consists of an upper and a lower semi-superellipse, which meet at their widest point on the line z = z₀ and can be shaped independently. Width and total height are always 1, and the profile is centered at the origin. lowerHeightFraction is the height of the lower half relative to the total height and thus defines where the two halves meet. Order and curve parameter are described for standardProfileType.

The contour is the set of points (y, z) that fulfill

|2y|^m_upper + |(z - z0)/(0.5 - z0)|^n_upper = 1 for z >= z0; |2y|^m_lower + |(z - z0)/(0.5 + z0)|^n_lower = 1 for z < z0; z0 = lowerHeightFraction - 0.5

The exponents m act on the y term and the exponents n on the z term. Both equal to 2 give half an ellipse; larger values give fuller shapes that approach a rectangle, both equal to 1 give straight lines, and values below 1 give concave, pointed shapes. A rectangle cannot be described exactly, since infinite exponents are not allowed; use rectangle instead.

The following figure shows three examples:

Example	mUpper	nUpper	mLower	nLower	lowerHeightFraction
(a) pointed top, flat bottom	0.5	2	5	3	0.25
(b) circle	2	2	2	2	0.5
(c) diamond, i.e. a square rotated by 45°	1	1	1	1	0.5

Three superellipse profiles with upper and lower half: pointed top with flat bottom, circle and diamond

Attributes

Name	Type	Use	Description
`@externalDataDirectory`	`xsd:string`	optional	Directory of the external data file
`@externalDataNodePath`	`xsd:string`	optional	Path of the node inside the external data file
`@externalFileName`	`xsd:string`	optional	Name of the external data file

Child elements

Name	Type	Constraints	OccurrenceHow often the element may appear at this place. The schema writes it as minOccurs and maxOccurs on the declaration.	Description
allThe children below may appear in any order. Each may appear at most once.
`mUpper`	`posExcl0DoubleBaseType`	minExclusive	[1..1] required	Exponent of the y term of the upper half
`nUpper`	`posExcl0DoubleBaseType`	minExclusive	[1..1] required	Exponent of the z term of the upper half
`mLower`	`posExcl0DoubleBaseType`	minExclusive	[1..1] required	Exponent of the y term of the lower half
`nLower`	`posExcl0DoubleBaseType`	minExclusive	[1..1] required	Exponent of the z term of the lower half
`lowerHeightFraction`	`doubleBaseType`	minExclusive, maxExclusive	[1..1] required	Height of the lower half relative to the total height

superEllipseProfileType

Attributes

Child elements

Used by

In a dataset · 3 paths

In the schema · 1 declaration