colour.algebra.geometry Module

Geometry

Defines objects related to geometrical computations:

colour.algebra.geometry.normalise_vector(a)[source]

Normalises given vector \(a\).

Parameters:a (array_like) – Vector \(a\) to normalise.
Returns:Normalised vector \(a\).
Return type:ndarray

Examples

>>> a = np.array([0.07049534, 0.10080000, 0.09558313])
>>> normalise_vector(a)  
array([ 0.4525410...,  0.6470802...,  0.6135908...])
colour.algebra.geometry.euclidean_distance(a, b)[source]

Returns the euclidean distance between point arrays \(a\) and \(b\).

Parameters:
  • a (array_like) – Point array \(a\).
  • b (array_like) – Point array \(b\).
Returns:

Euclidean distance.
Return type:

numeric or ndarray

Examples

>>> a = np.array([100.00000000, 21.57210357, 272.22819350])
>>> b = np.array([100.00000000, 426.67945353, 72.39590835])
>>> euclidean_distance(a, b)  
451.7133019...
colour.algebra.geometry.extend_line_segment(a, b, distance=1)[source]

Extends the line segment defined by point arrays \(a\) and \(b\) by given distance and return the new end point.

Parameters:
  • a (array_like) – Point array \(a\).
  • b (array_like) – Point array \(b\).
  • distance (numeric, optional) – Distance to extend the line segment.
Returns:

New end point.
Return type:

ndarray

References

[1]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

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)  
array([-0.5367248...,  1.1776534...])
class colour.algebra.geometry.LineSegmentsIntersections_Specification[source]

Bases: colour.algebra.geometry.LineSegmentsIntersections_Specification

Defines the specification for intersection of line segments \(l_1\) and \(l_2\) returned by intersect_line_segments() definition.

Parameters:
  • xy (array_like) – Array of \(l_1\) and \(l_2\) line segments intersections coordinates. Non existing segments intersections coordinates are set with np.nan.
  • intersect (array_like) – Array of bool indicating if line segments \(l_1\) and \(l_2\) intersect.
  • parallel (array_like) – Array of bool indicating if line segments \(l_1\) and \(l_2\) are parallel.
  • coincident (array_like) – Array of bool indicating if line segments \(l_1\) and \(l_2\) are coincident.

Create new instance of LineSegmentsIntersections_Specification(xy, intersect, parallel, coincident)

colour.algebra.geometry.intersect_line_segments(l_1, l_2)[source]

Computes \(l_1\) line segments intersections with \(l_2\) line segments.

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

Line segments intersections specification.
Return type:

LineSegmentsIntersections_Specification

References

[2]Bourke, P. (n.d.). Intersection point of two line segments in 2 dimensions. Retrieved January 15, 2016, from http://paulbourke.net/geometry/pointlineplane/
[3]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

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  
array([[[        nan,         nan],
        [ 0.2279184...,  0.6006430...],
        [        nan,         nan]],

       [[ 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)