Collinearity of points

erik

This is an attempt at determining collinearity of a series of points. Rather than compare tangents, one stackoverflower suggested calculating areas of triangles. Other strategies?

def polygon_area(points):  
    area = 0
    q = points[-1]
    for p in points:  
        area += p[0] * q[1] - p[1] * q[0]
        q = p
    return area / 2
    
def plot(points):
    if len(points) < 3:
        return None
    a = 0
    for pi, p in enumerate(points[:-2]):
        npt = points[pi+1]
        nnpt = points[pi+2]
        a += abs(polygon_area([points[pi], npt, nnpt]))
    return a
        
pts = [
    (725,417),
    (548, 440),
    (414, 458),
    (261, 479)
    ]

# tolerance for error
margin = 200

v = plot(pts)

print("plotted area", v)
fontSize(100)
if -.5*margin < v < .5*margin:
    text("colinear",(100,100))
else:
    text("not colinear",(100,100))

# draw the dots
fill(0,0,1)
stroke(1,0,0)
translate(100,100)
newPath()
moveTo(pts[0])
for p in pts[1:]:
    lineTo(p)
drawPath()

ds = 10
fill(0,0,1)
stroke(None)
for p in pts:
    oval(p[0]-.5*ds, p[1]-.5*ds, ds, ds)

jo

what would be 'compare tangents'?
—
comparing angles is probably more expensive?

def get_angle(p1, p2): return atan2((p2[1] - p1[1]), (p2[0] - p1[0]))
        
pts = [
    (725,417),
    (548, 440),
    (414, 458),
    (261, 479)
    ]

angles = [ get_angle(point, pts[p+1]) for p, point in enumerate(pts[:-1])]
angle = get_angle(pts[0], pts[-1])


# tolerance for error
margin = pi/180

fontSize(100)
if all(abs(a - angle) < margin for a in angles):
    text("colinear",(100,100))
else:
    text("not colinear",(100,100))

# draw the dots
fill(0,0,1)
stroke(1,0,0)
translate(100,100)
newPath()
moveTo(pts[0])
for p in pts[1:]:
    lineTo(p)
drawPath()

ds = 10
fill(0,0,1)
stroke(None)
for p in pts:
    oval(p[0]-.5*ds, p[1]-.5*ds, ds, ds)

MauriceMeilleur

That animation of the KABK crown I did: was looking into this question so as to avoid having to define the collinear = invalid segments explicitly — having the code test the combinations is a more elegant solution.
https://twitter.com/MauriceMeilleur/status/973090865882296325