def project_point_line_xy(point, line):
"""Project a point onto a line in the XY plane.
Parameters
----------
point : list of float
XY(Z) coordinates of the point.
line : tuple
Two points defining the projection line.
Returns
-------
list
XYZ coordinates of the projected point, with Z=0.
Notes
-----
For more info, see [1]_.
References
----------
.. [1] Wiki Books. *Linear Algebra/Orthogonal Projection Onto a Line*.
Available at: https://en.wikibooks.org/wiki/Linear_Algebra/Orthogonal_Projection_Onto_a_Line.
"""
a, b = line
ab = subtract_vectors_xy(b, a)
ap = subtract_vectors_xy(point, a)
c = vector_component_xy(ap, ab)
return add_vectors_xy(a, c)
def mirror_point_point_xy(point, mirror):
"""Mirror a point about a point.
Parameters:
point (sequence of float): XY coordinates of the point to mirror.
mirror (sequence of float): XY coordinates of the mirror point.
"""
return add_vectors_xy(mirror, subtract_vectors_xy(mirror, point))
def mirror_point_point_xy(point, mirror):
"""Mirror a point about a point.
Parameters
----------
point : list of float
XY(Z) coordinates of the point to mirror.
mirror : list of float
XY(Z) coordinates of the mirror point.
Returns
-------
list of float
The mirrored point, with Z=0.
"""
return add_vectors_xy(mirror, subtract_vectors_xy(mirror, point))
def mirror_point_line_xy(point, line):
"""Mirror a point about a line.
Parameters
----------
point : list of float
XY(Z) coordinates of the point to mirror.
line : tuple
Two points defining the line.
XY(Z) coordinates of the two points defining the mirror line.
Returns
-------
list of float
The mirrored point, with Z=0.
"""
closest = closest_point_on_line_xy(point, line)
return add_vectors_xy(closest, subtract_vectors_xy(closest, point))
def project_point_line_xy(point, line):
"""Project a point onto a line.
Parameters:
point (sequence of float): XY coordinates.
line (tuple): Two points defining a line.
Returns:
list: XY coordinates of the projected point.
References:
https://en.wikibooks.org/wiki/Linear_Algebra/Orthogonal_Projection_Onto_a_Line
"""
a, b = line
ab = subtract_vectors_xy(b, a)
ap = subtract_vectors_xy(point, a)
c = vector_component_xy(ap, ab)
return add_vectors_xy(a, c)
def closest_point_on_line_xy(point, line):
"""Compute closest point on line (continuous) to a given point lying in the XY-plane.
Parameters
----------
point : sequence of float
XY(Z) coordinates of a point.
line : tuple
Two XY(Z) points defining a line.
Returns
-------
list
XYZ coordinates of closest point (Z = 0.0).
"""
a, b = line
ab = subtract_vectors_xy(b, a)
ap = subtract_vectors_xy(point, a)
c = vector_component_xy(ap, ab)
return add_vectors_xy(a, c)
def translate_points_xy(points, vector):
"""Translate points and in the XY plane.
Parameters
----------
points : list of point
A list of points.
vector : vector
A translation vector.
Returns
-------
list of point
The translated points in the XY plane (Z=0).
Examples
--------
>>>
"""
return [add_vectors_xy(point, vector) for point in points]
def translate_points_xy(points, vector):
return [add_vectors_xy(point, vector) for point in points]
