pysdic.compute_bouguer_law

compute_bouguer_law(surface_points, surface_normals, light_positions)

Compute the Bouguer law ratio between irradiance \(E\) at source intensity \(I\) for a set of \(N_p\) surface points and a set of \(N_l\) light source positions.

\[\frac{E}{I} = \frac{\cos \theta}{r^2}\]

where \(\theta\) is the angle between the surface normal and the light direction computed as the positive dot product between the surface normal and the direction vector. Note that \((A \cdot B)\) denotes the positive dot product between vectors \(A\) and \(B\) given by \(\max(0, A^T B)\).

Note

The inputs arrays will be converted to numpy.float64 for computation. The output array will be also of type numpy.float64.

Parameters:

• surface_points (ArrayLike) – An array of shape \((N_p, 3)\) or \((3,)\) representing the coordinates of \(N_p\) surface points in 3-dimensional space. If a 1D array is provided, it is treated as a single surface point \((1, 3)\).

• surface_normals (ArrayLike) – An array of shape \((N_p, 3)\) or \((3,)\) representing the normal vectors at each surface point. Must have the same shape as surface_points.

• light_positions (ArrayLike) – An array of shape \((N_l, 3)\) or \((3,)\) representing the position(s) of the light source(s). If a 1D array is provided, it is treated as a single light source \((1, 3)\).

Returns:

An array of \((N_p, N_l)\) representing the Bouguer law ratio \(\frac{E}{I}\) at each surface point for each light source.

Return type:

numpy.ndarray

Raises:

• TypeError – If the inputs cannot be converted to floating-point numpy arrays.

• ValueError – If the dimensions of the input arrays are inconsistent.

Examples

Lets compute the Bouguer law ratio for a set of surface points and normals with a single light source:

import numpy
from pysdic import compute_bouguer_law

surface_points = numpy.array(
    [[0.0, 0.0, 0.0],
     [1.0, 0.0, 0.0],
     [0.0, 1.0, 0.0]]
)
surface_normals = numpy.array(
    [[0.0, 0.0, 1.0],
     [0.0, 0.0, 1.0],
     [0.0, 0.0, 1.0]]
)
light_positions = numpy.array([0.0, 0.0, 10.0])

bouguer_ratios = compute_bouguer_law(
    surface_points,
    surface_normals,
    light_positions
)

print(f"Bouguer ratios (Shape: {bouguer_ratios.shape}):")
print(bouguer_ratios)

Bouguer ratios (Shape: (3, 1)):
[[0.01      ]
 [0.00985185]
 [0.00985185]]