如何计算FOV？

Question

因此，我有一个板倾斜系统，顶部有喷枪，压力很大，因此我可以将机器人放在至少1.5米的距离处。我目前已经将坐标标准化了xy，我可以在相机上可视化

现在我想将这些坐标转换为真实的帆布，并让泛块朝向它们并最终喷洒。这两个伺服器具有0至180度，但喷枪位于倾斜的顶部90。我正在跟随这个答案 https://stackoverflow.com/a/44269392/444269392/13475623

lx = (2 * canvasXpoint / canvasW - 1) * np.tan(fovX / 2)
ly = (-2 * canvasYpoint / canvasH + 1) * np.tan(fovY / 2) 
lz = 100

tx = np.cos(pan) * np.cos(tilt) * lx - np.cos(tilt) * np.sin(pan) * ly - np.sin(tilt) * lz
ty = np.sin(pan) * lx + np.cos(pan) * ly
tz = np.cos(pan) * np.sin(tilt) * lx - np.sin(pan) * np.sin(tilt) * ly + np.cos(tilt) * lz

tilt = abs(np.arctan2(tz, tx) )*180 /np.pi
pan  = abs(np.arcsin(ty / np.sqrt(tx*tx + ty*ty + tz*tz))) *180 /np.pi

他特别要求使用Fovx和fovy，但我不知道如何放置，而fovx和fovy与canvas Plus Z的中心相同？哪个给出机器人位置？

这是整个代码：

import numpy as np
import random
import cv2

rect = (0,0,0,0)
startPoint = False
endPoint = False

def on_mouse(event,x,y,flags,params):

    global rect,startPoint,endPoint

    # get mouse click
    if event == cv2.EVENT_LBUTTONDOWN:

        if startPoint == True and endPoint == True:
            startPoint = False
            endPoint = False
            rect = (0, 0, 0, 0)

        if startPoint == False:
            rect = (x, y, 0, 0)
            startPoint = True
        elif endPoint == False:
            rect = (rect[0], rect[1], x, y)
            endPoint = True

cap = cv2.VideoCapture(0)
waitTime = 50

#Reading the first frame
(grabbed, frame) = cap.read()

# create a numpy array with coordinates, dtype= np.uint32
points = np.array([
    [0.3791454386035252, 0.5089704263689607], [0.4983802415059109, 0.4865878212776629], [0.4191061040406586, 0.4890729258496474], [0.48898375092596835, 0.6904554156787046], [0.41117320428962, 0.6855686449973655], [0.48969027909831686, 0.8806483247709954], [0.4096722346480175, 0.8725103831012889], [0.45146556567120294, 0.216198952126905], [0.6304876750748412, 0.1994776546413951], [0.6406976694235704, 0.1861724655606558], [0.6199918357274865, 0.18561325370105788], [0.6525936779272056, 0.201758477474465], [0.6013198509477334, 0.20041966221830415], [0.6683290543094758, 0.29699362669473495], [0.5645238852104717, 0.3113999818240313], [0.6545654774178274, 0.49620430200480303], [0.5898070573107588, 0.49659117464889346], [0.6592482998457356, 0.6834740545963035], [0.5840631897032319, 0.6828527784533074], [0.6408640096147972, 0.8299668209407426], [0.5829181988101784, 0.8173392725052692], [0.6197806290284397, 0.30050890733295843], [0.8252923243905792, 0.23409826375167195], [0.835683753646597, 0.2185883280832016], [0.8131540844750428, 0.21904862499113367], [0.8506741192799976, 0.2279991219170517], [0.7959142481709739, 0.22725381616179272], [0.8733570624656342, 0.3256920048853457], [0.7652207837892534, 0.3239122878098148], [0.893097550288673, 0.44273291363944955], [0.7346131146711571, 0.4430594635999311], [0.902709244982588, 0.5343829401117663], [0.8520378940615836, 0.543215423861057], [0.7842126810888624, 0.5430821914771806], [0.8496391467917583, 0.7170072127563635], [0.7934480818135997, 0.7157067918591926], [0.8415470663986131, 0.8790693270711738], [0.7969306654944098, 0.8786970205344115], [0.8191112469834433, 0.32444646417244244], [0.4544294400182521, 0.10802826838116084], [0.4652589441860643, 0.09470838455219986], [0.44184697991125976, 0.09401847354478254], [0.4784184639521475, 0.1113126386155105], [0.42270482157448985, 0.10977393520172159], [0.5101597581790689, 0.21719483055184013], [0.39370939342390643, 0.21645334444157344], [0.3703281257159549, 0.34746637604116004]], np.float64)

while(cap.isOpened()):

    (grabbed, frame) = cap.read()

    cv2.namedWindow('frame')
    cv2.setMouseCallback('frame', on_mouse)    
    panarr=[]
    tiltarr=[]

    #drawing rectangle

    if startPoint == True:
        cv2.circle(frame, (rect[0], rect[1]), 2,(255, 0, 255), 2)
    if startPoint == True and endPoint == True:
        
        cv2.rectangle(frame, (rect[0], rect[1]), (rect[2], rect[3]), (255, 0, 255), 2)
        
        w = rect[2] - rect[0]
        h = rect[3] - rect[1]

        canvasW = 120
        canvasH = 90
        distanceZ = 100
        
        #position machine    
        screenXCenter = (rect[0] + rect[2]) / 2
        screenYCenter = (rect[1] + rect[3]) / 2

        pan = tilt = 90

        servoXcentrepoint = canvasW / 2 
        servoYcentrepoint = canvasH / 2 

        # fov
        fovX =  np.arctan((canvasW * canvasH )/distanceZ)
        
        for x, y in points:
           
            screenX = (x * w) + rect[0] #- differencesqrx
            screenY = (y * h) + rect[1] #- differencesqry

            cv2.circle(frame,(int(screenXCenter),int(screenYCenter)),2,(255, 255, 0),2)    
            cv2.circle(frame,(int(screenX),int(screenY)),2,(255, 45, 250),2)


            canvasXpoint = (x * canvasW)
            canvasYpoint = (y * canvasH)

            # dx =  canvasXpoint - servoXcentrepoint 

            # dy =  canvasYpoint - servoYcentrepoint

            # pan = abs(np.arctan((distanceZ/dx))) * 180/np.pi
            # tilt = abs(np.arctan(distanceZ/dy)) * 180/np.pi

            lx = (2 * canvasXpoint / canvasW - 1) * np.tan(servoXcentrepoint / 2)
            ly = (-2 * canvasYpoint / canvasH + 1) * np.tan(servoYcentrepoint / 2) 
            lz = 10

            tx = np.cos(pan) * np.cos(tilt) * lx - np.cos(tilt) * np.sin(pan) * ly - np.sin(tilt) * lz
            ty = np.sin(pan) * lx + np.cos(pan) * ly
            tz = np.cos(pan) * np.sin(tilt) * lx - np.sin(pan) * np.sin(tilt) * ly + np.cos(tilt) * lz

            tilt = abs(np.arctan2(tz, tx) )*180 /np.pi
            pan  = abs(np.arcsin(ty / np.sqrt(tx*tx + ty*ty + tz*tz))) *180 /np.pi

            

          
            
            tiltarr.append(int(tilt))
            panarr.append(int(pan))
            
   

            # a = [x,y]
    
    cv2.imshow('frame',frame)
    if cv2.waitKey(1)==ord('q'):
        break
print(tiltarr)
print(panarr)

cap.release()
cv2.destroyAllWindows()

最终目标是根据每个点确定锅的角度并倾斜