### Camera calibration With OpenCV - tutorial

i am reading the very interesting tutorial https://docs.opencv.org/3.4.2/d4/d94/tutorial_camera_calibration.html
and i find it ~~seems ~~difficult to ~~me there might be an error in ~~understand the ~~formulas~~formulas for tangential distortion

xdistorted=x+[2p1xy+p2(r^2+2x^2)]

ydistorted=y+[p1(r^2+2y^2)+2p2xy]

~~the reason is that ~~specifically i don't understand the terms p2(r^2+2x^2) and ~~p1(r^2+2y^2)should ~~p1(r^2+2y^2) which seems to me should have always ~~be positive ~~the same sign no matter what sign of p1 or ~~p2
so i don't know might be ~~p2, in all 4 areas of the ~~correct formula are~~Cartesian plane

~~xdistorted=x+[2p1xy+p2^2(r^2+2x^2)]~~

ydistorted=y+[p1^2(r^2+2y^2)+2p2xy]

for instance if the camera is tilted upwards i might assume
p1>0 p2=0

xeffective=x+[2p1xy] (linear correction in x, increasing in half could you please provide a link with more detailed explanation of ~~the plane, decreasing in the other half)~~

yeffective=y+[p1(r^2+2y^2)] (y always corrected increasing it)

and that would quite work i guess

but i i would really not understand the case camera downwards and p1<0 p2=0
in that case y these formulas (and would be ~~wrongly corrected??!!~~

am i misunderstanding the formulas??wonderful also with some special case example)?

please help ~~thanks~~thank you very much