Given the 3D pose of a camera with known field of view get the distance of a point to the plane of view

camera_utils.py

'''
MIT License
Copyright (c) 2019 Michail Kalaitzakis

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
'''

import numpy as np

class Camera_Utils:
    '''
        Given the 3D pose of a camera with known field of view get the distance of a point to the plane of view
    '''

    # Initialize with camera characteristics
    # foV_X -> Field of view on x image axis (rad)
    # foV_Y -> Field of view on y image axis (rad)
    # depthOfField -> Distance of 
    def __init__(self, foV_X, foV_Y, depthOfField):
        # Camera characteristics
        self.fovX = foV_X / 2.0
        self.fovY = foV_Y / 2.0
        self.doF = depthOfField

        self.state = None
        self.R = None
        self.t = None
        self.planeOfView = None
        self.normalV = None
        self.RuL = None
        self.RuR = None
        self.RlR = None
        self.RlL = None
        self.m = None

        # Initialize Rotation matrices
        self.initializeRotations()

    # Updates the camera state
    # newState -> np.array([x, y, z, qw, qx, qy, qz])
    def updateState(self, newState):
        self.state = newState
        self.R = self.quat2R(self.state[3:])
        self.t = np.asmatrix(self.state[:3]).T

        self.getPlaneOfView()

    # Retturns distance from point
    # point -> np.array([x, y, z])
    def getDistance(self, point):
        poi = np.asmatrix(point).T

        poiP = self.getPlaneProjection(poi)

        if self.isInPlaneOfView(poiP):
            return np.linalg.norm(poi - poiP)
        else:
            dMin = 1.0e9

            for i in range(self.planeOfView.shape[0] - 1):
                res = self.getLineProjection(self.planeOfView[i].T, self.planeOfView[i + 1].T, poi)

                if (res[0] >= 0.0 and res[0] <= 1.0):
                    dL = np.linalg.norm(poi - res[1])

                    if dL < dMin:
                        dMin = dL

            if dMin == 1.0e9:
                for i in range(self.planeOfView.shape[0] - 1):
                    dP = np.linalg.norm(self.planeOfView[i].T - poi)

                    if dP < dMin:
                        dMin = dP

            return dMin

    # Updates plane of view corner points and normal vector
    def getPlaneOfView(self):
        self.normalV = self.R * np.matrix([[self.doF], [0.0], [0.0]])

        uLc = self.m * self.R * self.RuL * self.R.T * self.normalV + self.t
        uRc = self.m * self.R * self.RuR * self.R.T * self.normalV + self.t
        lRc = self.m * self.R * self.RlR * self.R.T * self.normalV + self.t
        lLc = self.m * self.R * self.RlL * self.R.T * self.normalV + self.t

        # Push the four corners and an extra copy of the first corner for ease in loops
        self.planeOfView = np.vstack([uLc.T, uRc.T, lRc.T, lLc.T, uLc.T])

    # Returns projection of point on a plane
    def getPlaneProjection(self, point):
        m = ((self.planeOfView[1].T - point).T * self.normalV) / (self.normalV.T * self.normalV)

        return m.item(0) * self.normalV + point

    # Returns the projection of a point to a line along its cos(theta)
    def getLineProjection(self, a, b, p):
        cTheta = ((p - a).T * (b - a)) / ((b - a).T * (b - a))
        pP = a + (b - a) * cTheta

        return cTheta, pP

    # Returns true if the point lies inside the plane of view
    def isInPlaneOfView(self, point):
        theta = 0.0

        for i in range(self.planeOfView.shape[0] - 1):
            v1 = point - self.planeOfView[i].T
            v2 = self.planeOfView[i + 1].T - point

            theta += np.arccos((v1.T * v2) / (np.linalg.norm(v1) * np.linalg.norm(v2)))

        if (np.abs(theta - 2*np.pi) < 1.0e-6):
            return True
        else:
            return False

    # Return the Rotation matrix derived from the quaternion
    # q -> np.array([qw, qx, qy, qz])
    def quat2R(self, q):
        r00 = 1 - 2*(q[2]*q[2] + q[3]*q[3])
        r01 =     2*(q[1]*q[2] - q[3]*q[0])
        r02 =     2*(q[1]*q[3] + q[2]*q[0])

        r10 =     2*(q[1]*q[2] + q[3]*q[0])
        r11 = 1 - 2*(q[1]*q[1] + q[3]*q[3])
        r12 =     2*(q[2]*q[3] - q[1]*q[0])

        r20 =     2*(q[1]*q[3] - q[2]*q[0])
        r21 =     2*(q[2]*q[3] + q[1]*q[0])
        r22 = 1 - 2*(q[1]*q[1] + q[2]*q[2])

        R = np.matrix([[r00, r01, r02], [r10, r11, r12], [r20, r21, r22]])

        return R

    # Initializes the standard rotation matrices
    def initializeRotations(self):
        cosX = np.cos(self.fovX)
        cosY = np.cos(self.fovY)
        sinX = np.sin(self.fovX)
        sinY = np.sin(self.fovY)

        # Initialize vector multiplier
        self.m = 1.0 / (cosX * cosY)

        R_y = np.asmatrix(np.eye(3))
        R_y[0, 0] = cosY
        R_y[2, 2] = cosY
        R_y[0, 2] = sinY
        R_y[2, 0] = -sinY

        R_x = np.asmatrix(np.eye(3))
        R_x[0, 0] = cosX
        R_x[1, 1] = cosX
        R_x[0, 1] = -sinX
        R_x[1, 0] = sinX

        # Initialize matrices
        self.RuL = R_y.T * R_x
        self.RuR = R_y.T * R_x.T
        self.RlR = R_y * R_x.T
        self.RlL = R_y * R_x