colour_hdri.distortion.hyperbolic_cosine_2D_function#

colour_hdri.distortion.hyperbolic_cosine_2D_function(x_y: Tuple, r_x: float, x_0: float, r_y: float, y_0: float, c: float) → NDArrayFloat[source]#

Evaluate a hyperbolic cosine 2D function on given coordinate matrices from coordinate vectors.

The hyperbolic cosine 2D function adopts the following form:

\(I_v(x, y) = 1 - (cosh(r_x * (x - x_0)) * cosh(r_y * (y - y_0))) + c\)

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.

  • r_x (float) – Coefficient \(r_x\) for the hyperbolic cosine equation.

  • x_0 (float) – Coefficient \(x_0\) for the hyperbolic cosine equation.

  • r_y (float) – Coefficient \(r_y\) for the hyperbolic cosine equation.

  • y_0 (float) – Coefficient \(y_0\) for the hyperbolic cosine equation.

  • c_y – Coefficient \(c_y\) for the hyperbolic cosine equation.

  • c (float) – Coefficient \(c\) for the hyperbolic cosine equation.

Returns:

Coordinate matrices with evaluated hyperbolic cosine 2D function.

Return type:

numpy.ndarray

References

[WonpilYu04]

Examples

>>> x_1, y_1 = np.meshgrid(np.linspace(0, 1, 4), np.linspace(0, 1, 3))
>>> hyperbolic_cosine_2D_function(  
...     (x_1, y_1), 1, -0.5, 1, -0.5, 1
... )
array([[ 1.       ...,  0.9439281...,  0.7694244...,  0.4569193...],
       [ 0.8723740...,  0.8091459...,  0.6123710...,  0.2599822...],
       [ 0.4569193...,  0.3703959...,  0.1011226..., -0.3810978...]])