The Python Book

angle point atan
20151022

# Angle between 2 points

Calculate the angle in radians, between the horizontal through the 1st point and a line through the two points

``````def angle(p0,p1):
dx=float(p1.x)-float(p0.x)
dy=float(p1.y)-float(p0.y)
if dx==0:
if dy==0:
return 0.0
elif dy<0:
return math.atan(float('-inf'))
else:
return math.atan(float('inf'))
return math.atan(dy/dx)``````
collinear point
20151022

# Generate an array of collinear points plus some random points

• generate a number of points (integers) that are on the same line
• randomly intersperse these coordinates with a set of random points
• watchout: may generate dupes! (the random points, not the collinear points)

Source:

``````import random

p=[(5,5),(1,10)]    # points that define the line

# warning: this won't work for vertical line!!!
slope= (float(p[1][1])-float(p[0][1]))/(float(p[1][0])-float(p[0][0]) )
intercept= float(p[0][1])-slope*float(p[0][0])

ar=[]
for x in range(0,25):
y=slope*float(x)+intercept

# only keep the y's that are integers
if (y%2)==0:
ar.append((x,int(y)))

# intersperse with random coordinates
r=3+random.randrange(0,5)

# only add random points when random nr is even
if r%2==0:
ar.extend( [ (random.randrange(0,100),random.randrange(0,100)) for j in range(r) ])

print ar``````

Sample output:

``````[(1, 10), (97, 46), (94, 12), (33, 10), (9, 71), (9, 0), (28, 34),
(2, 94), (30, 29), (69, 28), (82, 31), (79, 86), (88, 46), (59, 24),
(2, 78), (54, 88), (94, 78), (99, 37), (75, 48), (91, 1), (67, 61),
(12, 11), (55, 55), (58, 82), (95, 99), (56, 27), (12, 18), (99, 25),
(77, 84), (31, 39), (64, 84), (4, 13), (80, 63), (43, 27), (78, 43),
(24, 32), (17, -10), (73, 15), (6, 97), (0, 74), (16, 97), (6, 77),
(60, 77), (19, 83), (19, 82), (19, 40), (58, 63), (64, 62), (14, 53),
(57, 21), (49, 24), (66, 94), (82, 1), (29, 39), (55, 64), (85, 68),
(39, 24)]``````
point class
20151022

# Define a point class

• with an x and y member
• with methods to 'autoprint'

## Definition

``````import math

class P:
x=0
y=0
def __init__(self,x,y):
self.x=x
self.y=y

# gets called when a print is executed
def __str__(self):
return "x:{} y:{}".format(self.x,self.y)

# gets called eg. when a print is executed on an array of P's
def __repr__(self):
return "x:{} y:{}".format(self.x,self.y)

# convert an array of arrays or tuples to array of points
def convert(in_ar) :
out_ar=[]
for el in in_ar:
out_ar.append( P(el[0],el[1]) )
return out_ar``````

## How to initialize

Eg. create a list of points

``````# following initialisations lead to the same array of points (note the convert)
p=[P(0,0),P(0,1),P(-0.866025,-0.5),P(0.866025,0.5)]
q=convert( [[0,0],[0,1],[-0.866025,-0.5],[0.866025,0.5]] )
r=convert( [(0,0),(0,1),(-0.866025,-0.5),(0.866025,0.5)] )

print type(p), ' | ' , p[2].x, p[2].y,  ' | ', p[2]
print type(q), ' | ' , q[2].x, q[2].y,  ' | ', q[2]
print type(r), ' | ' , r[2].x, r[2].y,  ' | ', r[2]``````

Output:

``````<type 'list'>  |  -0.866025 -0.5  |  x:-0.866025 y:-0.5
<type 'list'>  |  -0.866025 -0.5  |  x:-0.866025 y:-0.5
<type 'list'>  |  -0.866025 -0.5  |  x:-0.866025 y:-0.5``````

## How to use

eg. Calculate the angle between :

• the horizontal line through the first point
• and the line through the two points

Then convert the result from radians to degrees: (watchout: won't work for dx==0)

``print math.atan( ( p[3].y - p[0].y ) / ( p[3].x - p[0].x ) ) * 180.0/math.pi``

Output:

``30.0000115676``

Notes by Willem Moors. Generated on momo:/home/willem/sync/20151223_datamungingninja/pythonbook at 2019-07-31 19:22