colour_hdri.distortion.parabolic_2D_function#
- colour_hdri.distortion.parabolic_2D_function(x_y: Tuple, a_x2: float, a_x1: float, a_x0: float, a_y2: float, a_y1: float, a_y0: float)[source]#
Evaluate a parabolic 2D function on given coordinate matrices from coordinate vectors.
The parabolic 2D function adopts the following form as given by [KPB16]:
\(I_v(x, y) = \cfrac{1}{2}(a_{x2}x^2 + a_{x1}x + a_{x0}) + \cfrac{1}{2}(a_{y2}y^2 + a_{y1}y + a_{y0})\)
- Parameters:
x_y (Tuple) – Coordinate matrices from coordinate vectors to evaluate the parabolic 2d function on. The coordinate matrices can be generated with the
numpy.meshgrid()definition.a_x2 (float) – Coefficient \(a_{x2}\) for the parabolic equation.
a_x1 (float) – Coefficient \(a_{x1}\) for the parabolic equation.
a_x0 (float) – Coefficient \(a_{x0}\) for the parabolic equation.
a_y2 (float) – Coefficient \(a_{y2}\) for the parabolic equation.
a_y1 (float) – Coefficient \(a_{y1}\) for the parabolic equation.
a_y0 (float) – Coefficient \(a_{y0}\) for the parabolic equation.
- Returns:
Coordinate matrices with evaluated parabolic 2D function.
- Return type:
References
[KPB16]
Examples
>>> x_1, y_1 = np.meshgrid(np.linspace(0, 1, 4), np.linspace(0, 1, 3)) >>> parabolic_2D_function( ... (x_1, y_1), -0.5, 0, 1, -0.5, 0, 1 ... ) array([[ 1. , 0.9722222..., 0.8888888..., 0.75 ], [ 0.9375 , 0.9097222..., 0.8263888..., 0.6875 ], [ 0.75 , 0.7222222..., 0.6388888..., 0.5 ]])