Ellipse¶
Functionality¶
The ellipse node creates ellipses given a set of main parameters: major/minor radii, eccentricity, focal length. Additional parameters allow you to tweak the ellipse curve: phase, rotation, scale and x/y exponents.
Super Ellipse formula:
(x/a)^n + (y/b)^m = 1
Different values of the x and y exponents (n and m) generate various shapes such as: astroid, square/rhombus, circle/ellipse, squircle/rectellipse.
astroid: 0 < n,m < 1 square/diamond: n/m = 1 circle/ellipse: n/m = 2 squircle/rectellipse: n/m > 2
Inputs¶
All inputs are vectorized and they will accept single or multiple values.
Major Radius
Minor Radius [1]
Eccentricity [2]
Focal Length [3]
Num Verts
Phase [4]
Rotation [4]
Scale
Exponent X
Exponent Y
Notes: [1] : The Minor Radius is available in ab mode [2] : The Eccentricity is available in ae mode [3] : The Focal Length is available in ac mode [4] : The angles are in DEGREES. The Property Panel has option to set angle units as: RADIANS, DEGREES or UNITIES.
Parameters¶
The Mode parameter allows to select one of the three modes of defining the ellipse: ab, ae and ac.
In ab mode the ellipse is defined by the major radius (a) and minor radius (b).
In ae mode the ellipse is defined by the major radius (a) and the eccentricity (e).
In ac mode the ellipse is defined by the major radius (a) and the focal length (c).
Note: when switching modes the main ellipse parameters for the new mode are derived based on the main parameters of the previous mode as to keep the ellipse the same.
The Centering parameter lets you center the ellipse around one of its focal points F1 or F2 or around its center C.
All parameters except Mode and Centering can take values from the node itself or an external input.
The inputs are “sanitized” to restrict their values to valid domains: - Major radius (a) and Minor radius (b) are floats with values >= 0.0 and b <= a - Eccentricity is a float with value in the range [0.0, 1.0] - Focal Length is a float with value in the range [0.0, a] - Number of vertices is an integer with value >= 3 - Scale is a float with values >= 0.0
Param |
Type |
Default |
Description |
|---|---|---|---|
Major Radius |
Float |
1.0 |
Major radius of the ellipse |
Minor Radius |
Float |
0.8 |
Minor radius of the ellipse [1] |
Eccentricity |
Float |
0.6 |
Eccentricity of the ellipse [2] |
Focal Length |
Float |
0.6 |
Distance between the center and one of the foci [3] |
Num Verts |
Int |
36 |
Number of vertices in the ellipse |
Phase |
Float |
0.0 |
Phase the vertices along the ellipse around its center [4] |
Rotation |
Float |
0.0 |
Rotate the ellipse around its centering point [4] |
Scale |
Float |
1.0 |
Scale the ellipse radii by this amount. |
Exponent X |
Float |
2.0 |
Exponent modulating the curve X direction. [5] |
Exponent Y |
Float |
2.0 |
Exponent modulating the curve Y direction. [5] |
Notes: [1] : The Minor Radius is available in ab mode [2] : The Eccentricity is available in ae mode [3] : The Focal Length is available in ac mode [4] : Angles are given by default in DEGREES. The Property Panel has option to set angle units as: RADIANS, DEGREES or UNITIES. [5] : Various combinations of the XY exponents generate different super ellipse curves (e.g. eX = eY = 2 the shape is an ellipse)
Extra Parameters¶
A set of extra parameters are available on the property panel. These parameters do not receive external input.
Extra Param |
Type |
Default |
Description |
|---|---|---|---|
Angle Units |
|
DEGREES |
Interprets the angle values based on the selected angle units: Radians = 0 - 2pi Degrees = 0 - 360 Unities = 0 - 1 |
Outputs¶
Outputs will be generated when connected.
Verts, Edges, Polys These are the vertices, edges and polygons of the ellipse.
F1, F2 These are the locations of the ellipse foci.
Presets¶
A set of super ellipse configuration presets is available for convenience. Once a preset is selected the super ellipse settings are updated with the preset values and the user can modify the settings to further alter the super ellipse shape.
Note: once a setting is altered (after selecting a preset) the preset selection is cleared from the preset drop-down indicating that the new setting configuration is no longer the one corresponding to the previously selected preset.
Preset |
R |
r |
eX |
eY |
N |
|---|---|---|---|---|---|
STAR |
1.0 |
1.0 |
0.3 |
0.3 |
200 |
ASTROID |
1.0 |
1.0 |
0.6 |
0.6 |
200 |
DIAMOND |
1.0 |
0.6 |
1.0 |
1.0 |
100 |
EYELENS |
1.0 |
0.6 |
2.0 |
1.0 |
100 |
SQUARE |
1.0 |
1.0 |
1.0 |
1.0 |
100 |
CIRCLE |
1.0 |
1.0 |
2.0 |
2.0 |
100 |
ELLIPSE |
1.0 |
0.6 |
2.0 |
2.0 |
100 |
SQUIRCLE |
1.0 |
1.0 |
4.0 |
4.0 |
100 |
HYPOELLIPSE |
1.0 |
0.6 |
1.5 |
1.5 |
100 |
HYPERELLIPSE |
1.0 |
0.6 |
2.5 |
2.5 |
100 |
RECTELLIPSE |
1.0 |
0.6 |
4.0 |
4.0 |
100 |
Example of usage¶
Reference¶
https://mathworld.wolfram.com/Superellipse.html https://en.wikipedia.org/wiki/Superellipse https://en.wikipedia.org/wiki/Ellipse