OpenCV-Python: Draw Parabolical Line

Question

I'm trying to draw a curved line, but I just can't figure out how to do that.

In my code, I ask the user to press anywhere withing the white rectangle - Then I take the pressed coordinates and (try to) create a parabolical line starting at the edges of the medial line in the center of the rectangle.

I've got 3 coordinates to work with - [line_start_x, line_start_y], [clicked_x, clicked_y], and [line_end_x, line_end_y]:

pts = np.array(
        [
            [line_start_x, line_start_y],
            [clicked_x, clicked_y],
            [line_end_x, line_end_y],
        ], np.int32)
image = cv2.polylines(image, [pts], True, (0, 255, 0), 2)
cv2.imshow(window_name, image)

As you can see in the attached image, I get a triangle and not a parabolical line.

I'd appricated any help with that matter!

Answer 1

assuming I understand the problem, 2 points will be ever fixed (line_start,line_end). when you have 3 points an a 2nd grade polinomial you there's only onse solution. you can calculate the expresion using numpy and then draw it evaluating this is a toy example with fixed image an point (change it's coords and try diferent solutions). I didn't put any condition on clicked_point so it could be out of the rect.

1. create image, rectangle and put bias points

    import cv2 import numpy as np width,height = 900,600 img = np.zeros((height,width,3), np.uint8) white_rect = np.array([[100, 100], [width-100, 100], [width-100, height-100], [100, height-100], [100, 100] ], np.int32) img = cv2.polylines(img, [white_rect], True, (255,255,255), 3) line_start_x = int(white_rect[0:2,0].mean()) line_start_y = int(white_rect[0:2,1].mean()) line_end_x = int(white_rect[2:4,0].mean()) line_end_y = int(white_rect[2:4,1].mean()) clicked_x = 555 clicked_y = 192 img =cv2.circle(img, (clicked_x, clicked_y), 5, (0,0,255), -1) img =cv2.circle(img, (line_start_x, line_start_y), 5, (0,0,255), -1) img =cv2.circle(img, (line_end_x, line_end_y), 5, (0,0,255), -1) cv2.imshow('fr', img) cv2.waitKey(1)

2. Then create point array 'pts' fit parabola and evaluate with numpy.

    pts = np.array([ [line_start_x, line_start_y], [clicked_x, clicked_y], [line_end_x, line_end_y] ], np.int32) #side parabola coeffs coeffs = np.polyfit(pts[:,1], pts[:,0], 2) poly = np.poly1d(coeffs) yarr = np.arange(line_start_y, line_end_y) xarr = poly(yarr)

3. create parab points as int to draw with polylines (might be other choices but i'm gonna use this for simplicity).

    parab_pts = np.array([xarr, yarr],dtype=np.int32).T cv2.polylines(img, [parab_pts], False, (255,0,0), 3) cv2.imshow('fr', img) cv2.waitKey(1)

The output !!!