Is there a way to use cv2.approxPolyDP to approximate open curve?

I would like to approximate smooth lines with chain of line segments.

cv2.approxPolyDP in OpenCV 3.4 made a good result in the case of closed curve.

Origin close curve: Approximated close curve:

But in the case of open curve, cv2.approxPolyDP did not achieve the desired effect.

Origin open curve: Approximated open curve:

The result I want should be one chain of line segments but not a closed polygon, like this(this picture is created by Photoshop but not Python program):

Is there a way to use cv2.approxPolyDP to approximate open curve?

My Python program is as follow:

import cv2

img = cv2.imread('1.jpg')

gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)

cv2.imshow("gray", gray)
cv2.waitKey(0)

_, binary = cv2.threshold(gray, 10, 255, cv2.THRESH_BINARY)

# cv2.imshow("binary", binary)
# cv2.waitKey(0)

_, contours, _ = cv2.findContours(binary, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)

for contour in contours:
    epsilon = 0.009 * cv2.arcLength(contour, True)
    approx = cv2.approxPolyDP(contour, epsilon, closed=True)
    cv2.drawContours(img, [approx], -1, (0, 255, 255), 1)

cv2.imshow("approx", img)
cv2.waitKey(0)

cv2.destroyAllWindows()

The origin photos used in my program are as follow.

Close curve photo Open curve photo

Answer

Here is how to do that in Python/OpenCV using cv2.approxPolyDP

Input (cropped off screen snap title bar)

import numpy as np
import cv2

# read input
img = cv2.imread('curve.png')
hh, ww = img.shape[:2]

# convert to grayscale
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)

# threshold
thresh = cv2.threshold(gray, 100, 255, cv2.THRESH_BINARY)[1]

# get points
points = np.column_stack(np.where(thresh.transpose() != 0))

# list points
for pt in points:
    ptx = pt[0]
    pty = pt[1]
    print(ptx,pty)

# approximate polygon
poly = cv2.approxPolyDP(points, 0.02 * ww, False)

# list polygon points
for p in poly:
    px = p[0]
    py = p[0]
    print(px,py)

# draw polygon on copy of input
result = img.copy()
cv2.polylines(result, [poly], False, (0,0,255), 1)

# save results
cv2.imwrite('curve_polygon.png', result)

cv2.imshow("thresh", thresh)
cv2.imshow("result", result)
cv2.waitKey(0)