ellipse_indices#
- emg3d.maps.ellipse_indices(coo, p0, p1, radius, factor=1.0, minor=1.0, check_foci=True)[source]#
Return bool which points fall within a general ellipse.
The general ellipse is given by
(32)#\[ A (x-x_0)^2 + B (x-x_0) (y-y_0) + C (y-y_0)^2 = 1 \ ,\]where
\[\begin{split}A &= \cos^2\theta / a^2 + \sin^2\theta / b^2 \ , \\ B &= 2 \cos\theta \sin\theta (1/a^2 - 1/b^2) \ , \\ C &= \sin^2\theta / a^2 + \cos^2\theta / b^2 \ . \\\end{split}\]Here,
\((x_0;y_0)\) is the center, the midpoint between the two provided points
p0
andp1
;\(a\) is the semi-major axis, defined as
(33)#\[a = \max(f c, c + r)\ ,\]where \(c\) is the distance between the center and either of the points
{p0;p1}
, \(r\) is the providedradius
, and \(f\) the providedfactor
;\(b\) is the semi-minor axis, defined as \(b = m a\), where \(m\) is provided as
minor
;\(\theta\) is the angle between the two points.
The following figure explains it graphically (only visible in the web version of the API docs on https://emg3d.emsig.xyz).
- Parameters
- cootuple of two ndarrays
Tuple of two arrays defining the points in x and y: - If two vectors are given (of same or different size), they are taken
as the x- and y-values of a regular grid.
If two 2D-arrays are given of the same shape, they are taken as the (regular or irregular) x- and y-values.
- p0, p1array_like
(x, y)-coordinates of two points.
- radiusfloat
Radius of the circle around the points that should be included in the ellipse. This defines also the minimum value for the major and minor axes of the ellipse.
- factorfloat, default: 1.0
The semi-major axis length is defined as a = max(f c, c + r), where f is this factor.
- minorfloat, default: 1.0
The semi-minor axis is defined as the semi-major axis multiplied by
minor
, usually a value <= 1.0, where 1.0 defines a circle. The enforced lower limit of the minor axis is the radius. The providedminor
might be overruled ifcheck_foci=True
.- check_focibool, default: True
If True, it is ensured that {p0;p1} are at least as far from the center as the foci of the ellipse;
minor
is adjusted accordingly if necessary.
- Returns
- indndarray
Boolean with same shape as the provided coordinates containing True where (x;y) are inside or on the ellipse, and False otherwise.