def project_xy(xy_coords, pvec):
# get cubic polynomial coefficients given
#
# f(0) = 0, f'(0) = alpha
# f(1) = 0, f'(1) = beta
alpha, beta = tuple(pvec[CUBIC_IDX])
poly = np.array([
alpha + beta,
-2*alpha - beta,
alpha,
0])
xy_coords = xy_coords.reshape((-1, 2))
z_coords = np.polyval(poly, xy_coords[:, 0])
objpoints = np.hstack((xy_coords, z_coords.reshape((-1, 1))))
image_points, _ = cv2.projectPoints(objpoints,
pvec[RVEC_IDX],
pvec[TVEC_IDX],
K, np.zeros(5))
return image_points
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