If you're open to using a library for this, have a look at shapely
: https://github.com/Toblerity/Shapely
As a quick example (points.txt
contains the data you linked to in your question):
import shapely.geometry as geom
import numpy as np
coords = np.loadtxt('points.txt')
line = geom.LineString(coords)
point = geom.Point(0.8, 10.5)
# Note that "line.distance(point)" would be identical
print(point.distance(line))
As an interactive example (this also draws the line segments you wanted):
import numpy as np
import shapely.geometry as geom
import matplotlib.pyplot as plt
class NearestPoint(object):
def __init__(self, line, ax):
self.line = line
self.ax = ax
ax.figure.canvas.mpl_connect('button_press_event', self)
def __call__(self, event):
x, y = event.xdata, event.ydata
point = geom.Point(x, y)
distance = self.line.distance(point)
self.draw_segment(point)
print 'Distance to line:', distance
def draw_segment(self, point):
point_on_line = line.interpolate(line.project(point))
self.ax.plot([point.x, point_on_line.x], [point.y, point_on_line.y],
color='red', marker='o', scalex=False, scaley=False)
fig.canvas.draw()
if __name__ == '__main__':
coords = np.loadtxt('points.txt')
line = geom.LineString(coords)
fig, ax = plt.subplots()
ax.plot(*coords.T)
ax.axis('equal')
NearestPoint(line, ax)
plt.show()
Note that I've added ax.axis('equal')
. shapely
operates in the coordinate system that the data is in. Without the equal axis plot, the view will be distorted, and while shapely
will still find the nearest point, it won't look quite right in the display: