# Source code for colour.geometry.intersection

```"""
Intersection Utilities
======================

Defines the geometry intersection utilities objects.

References
----------
-   :cite:`Bourkea` : Bourke, P. (n.d.). Intersection point of two line
segments in 2 dimensions. Retrieved January 15, 2016, from
http://paulbourke.net/geometry/pointlineplane/
-   :cite:`Erdema` : Erdem, U. M. (n.d.). Fast Line Segment Intersection.
Retrieved January 15, 2016, from
http://www.mathworks.com/matlabcentral/fileexchange/\
27205-fast-line-segment-intersection
-   :cite:`Saeedna` : Saeedn. (n.d.). Extend a line segment a specific
distance. Retrieved January 16, 2016, from
http://stackoverflow.com/questions/7740507/\
extend-a-line-segment-a-specific-distance
"""

from __future__ import annotations

from dataclasses import dataclass

import numpy as np

from colour.algebra import euclidean_distance, sdiv, sdiv_mode
from colour.hints import ArrayLike, NDArrayFloat
from colour.utilities import as_float_array, tsplit, tstack

__author__ = "Colour Developers"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"

__all__ = [
"extend_line_segment",
"LineSegmentsIntersections_Specification",
"intersect_line_segments",
]

[docs]
def extend_line_segment(
a: ArrayLike, b: ArrayLike, distance: float = 1
) -> NDArrayFloat:
"""
Extend the line segment defined by point arrays :math:`a` and :math:`b` by
given distance and return the new end point.

Parameters
----------
a
Point array :math:`a`.
b
Point array :math:`b`.
distance
Distance to extend the line segment.

Returns
-------
:class:`numpy.ndarray`
New end point.

References
----------
:cite:`Saeedna`

Notes
-----
-   Input line segment points coordinates are 2d coordinates.

Examples
--------
>>> a = np.array([0.95694934, 0.13720932])
>>> b = np.array([0.28382835, 0.60608318])
>>> extend_line_segment(a, b)  # doctest: +ELLIPSIS
array([-0.5367248...,  1.1776534...])
"""

x_a, y_a = tsplit(a)
x_b, y_b = tsplit(b)

d = euclidean_distance(a, b)

with sdiv_mode():
x_c = x_b + sdiv(x_b - x_a, d) * distance
y_c = y_b + sdiv(y_b - y_a, d) * distance

xy_c = tstack([x_c, y_c])

return xy_c

[docs]
@dataclass
class LineSegmentsIntersections_Specification:
"""
Define the specification for intersection of line segments :math:`l_1` and
:math:`l_2` returned by :func:`colour.algebra.intersect_line_segments`
definition.

Parameters
----------
xy
Array of :math:`l_1` and :math:`l_2` line segments intersections
coordinates. Non existing segments intersections coordinates are set
with `np.nan`.
intersect
Array of *bool* indicating if line segments :math:`l_1` and :math:`l_2`
intersect.
parallel
Array of :class:`bool` indicating if line segments :math:`l_1` and
:math:`l_2` are parallel.
coincident
Array of :class:`bool` indicating if line segments :math:`l_1` and
:math:`l_2` are coincident.
"""

xy: NDArrayFloat
intersect: NDArrayFloat
parallel: NDArrayFloat
coincident: NDArrayFloat

[docs]
def intersect_line_segments(
l_1: ArrayLike, l_2: ArrayLike
) -> LineSegmentsIntersections_Specification:
"""
Compute :math:`l_1` line segments intersections with :math:`l_2` line
segments.

Parameters
----------
l_1
:math:`l_1` line segments array, each row is a line segment such as
(:math:`x_1`, :math:`y_1`, :math:`x_2`, :math:`y_2`) where
(:math:`x_1`, :math:`y_1`) and (:math:`x_2`, :math:`y_2`) are
respectively the start and end points of :math:`l_1` line segments.
l_2
:math:`l_2` line segments array, each row is a line segment such as
(:math:`x_3`, :math:`y_3`, :math:`x_4`, :math:`y_4`) where
(:math:`x_3`, :math:`y_3`) and (:math:`x_4`, :math:`y_4`) are
respectively the start and end points of :math:`l_2` line segments.

Returns
-------
:class:`colour.algebra.LineSegmentsIntersections_Specification`
Line segments intersections specification.

References
----------
:cite:`Bourkea`, :cite:`Erdema`

Notes
-----
-   Input line segments points coordinates are 2d coordinates.

Examples
--------
>>> l_1 = np.array(
...     [
...         [[0.15416284, 0.7400497], [0.26331502, 0.53373939]],
...         [[0.01457496, 0.91874701], [0.90071485, 0.03342143]],
...     ]
... )
>>> l_2 = np.array(
...     [
...         [[0.95694934, 0.13720932], [0.28382835, 0.60608318]],
...         [[0.94422514, 0.85273554], [0.00225923, 0.52122603]],
...         [[0.55203763, 0.48537741], [0.76813415, 0.16071675]],
...     ]
... )
>>> s = intersect_line_segments(l_1, l_2)
>>> s.xy  # doctest: +ELLIPSIS
array([[[        nan,         nan],
[ 0.2279184...,  0.6006430...],
[        nan,         nan]],
<BLANKLINE>
[[ 0.4281451...,  0.5055568...],
[ 0.3056055...,  0.6279838...],
[ 0.7578749...,  0.1761301...]]])
>>> s.intersect
array([[False,  True, False],
[ True,  True,  True]], dtype=bool)
>>> s.parallel
array([[False, False, False],
[False, False, False]], dtype=bool)
>>> s.coincident
array([[False, False, False],
[False, False, False]], dtype=bool)
"""

l_1 = as_float_array(l_1)
l_2 = as_float_array(l_2)

l_1 = np.reshape(l_1, (-1, 4))
l_2 = np.reshape(l_2, (-1, 4))

r_1, c_1 = l_1.shape[0], l_1.shape[1]
r_2, c_2 = l_2.shape[0], l_2.shape[1]

x_1, y_1, x_2, y_2 = (np.tile(l_1[:, i, None], (1, r_2)) for i in range(c_1))

l_2 = np.transpose(l_2)

x_3, y_3, x_4, y_4 = (np.tile(l_2[i, :], (r_1, 1)) for i in range(c_2))

x_4_x_3 = x_4 - x_3
y_1_y_3 = y_1 - y_3
y_4_y_3 = y_4 - y_3
x_1_x_3 = x_1 - x_3
x_2_x_1 = x_2 - x_1
y_2_y_1 = y_2 - y_1

numerator_a = x_4_x_3 * y_1_y_3 - y_4_y_3 * x_1_x_3
numerator_b = x_2_x_1 * y_1_y_3 - y_2_y_1 * x_1_x_3
denominator = y_4_y_3 * x_2_x_1 - x_4_x_3 * y_2_y_1

with sdiv_mode("Ignore"):
u_a = sdiv(numerator_a, denominator)
u_b = sdiv(numerator_b, denominator)

intersect = np.logical_and.reduce((u_a >= 0, u_a <= 1, u_b >= 0, u_b <= 1))
xy = tstack([x_1 + x_2_x_1 * u_a, y_1 + y_2_y_1 * u_a])
xy[~intersect] = np.nan
parallel = denominator == 0
coincident = np.logical_and.reduce((numerator_a == 0, numerator_b == 0, parallel))

return LineSegmentsIntersections_Specification(xy, intersect, parallel, coincident)

```