python - Distance for each intersected points of a line in increased order in 2D coordinate -

i calculating distance between a(x0,y0) , b(x1,y1) points in 2d (x,y).

i have following code represents intersected points of each cell in given 2 boundary points, a(x0,y0) , b(x1,y1).

def intersected_points(x0, x1, y0, y1):     # slope      m = (y1 - y0 )/( x1 - x0)     # boundary of selected points     x_ceil = ceil( min (x0, x1 ))     x_floor = floor( max(x0, x1))     y_ceil = ceil( min(y0, y1))     y_floor = floor( max(y0, y1))      # calculate intersected x coordinate     ax = []     x in arange(x_ceil, x_floor + 1, 1):           ax.append([ x, m * ( x - x0 ) + y0 ])     # calculate intersected y coordinate     y in arange(y_ceil, y_floor + 1, 1):           ax.append([ ( y - y0 ) * ( 1./m ) + x0, y ])     return ax 

sample values:

intersected_points(1.5, 4.4, 0.5, 4.1); 

output:

[     [2.0, 1.1206896551724137],     [3.0, 2.3620689655172411],     [4.0, 3.6034482758620685],     [1.9027777777777779, 1.0],     [2.7083333333333335, 2.0],     [3.5138888888888893, 3.0],     [4.3194444444444446, 4.0] ] 

the output got mixed , unsorted values, so, each cell coordinates, line crosses. but, result want should (including boundary points): (x0,y0), intersected points, (x1,y1) x0, y0 - intial, x1,y1 - final point. other values intersected line coordinates!

here's modified version of code. uses numpy bit more, , includes end points in sorted array of points.

import numpy np  def intersected_points(x0, x1, y0, y1):     # slope     m = (y1 - y0) / (x1 - x0)     # boundary of selected points     x_ceil = np.ceil(min(x0, x1))     x_floor = np.floor(max(x0, x1))     y_ceil = np.ceil(min(y0, y1))     y_floor = np.floor(max(y0, y1))      # calculate intersected x coordinate     x = np.arange(x_ceil, x_floor + 1)     y = m * (x - x0) + y0     ax = zip(x, y)     # calculate intersected y coordinate     y = np.arange(y_ceil, y_floor + 1)     x = (y - y0) / m + x0     ax.extend(zip(x, y))     ax.append((x0, y0))     ax.append((x1, y1))     ax.sort()     return np.array(ax)   if __name__ == "__main__":     import matplotlib.pyplot plt      x0, y0 = 1.5, 0.5     x1, y1 = 4.4, 4.1      points = intersected_points(x0, x1, y0, y1)     print points      rect = plt.rectangle((x0, y0), x1 - x0, y1 - y0,                          facecolor="#60ff60", alpha=0.2)     plt.gca().add_patch(rect)     plt.plot([x0, x1], [y0, y1], 'b-')     plt.plot(points[:, 0], points[:, 1], 'bo')     plt.grid(true)     plt.xticks(np.arange(np.floor(x0), np.ceil(x1)))     plt.yticks(np.arange(np.floor(y0), np.ceil(y1)))     plt.show() 

it prints:

[[ 1.5         0.5       ]  [ 1.90277778  1.        ]  [ 2.          1.12068966]  [ 2.70833333  2.        ]  [ 3.          2.36206897]  [ 3.51388889  3.        ]  [ 4.          3.60344828]  [ 4.31944444  4.        ]  [ 4.4         4.1       ]] 

and generates plot: