Camera Footprint Calculator

camera_calculator.py

"""
***************************************************************************
    camera_calculator.py
    ---------------------
    Date                 : August 2019
    Copyright            : (C) 2019 by Luigi Pirelli
    Email                : luipir at gmail dot com
***************************************************************************
*                                                                         *
*   This program is free software; you can redistribute it and/or modify  *
*   it under the terms of the GNU General Public License as published by  *
*   the Free Software Foundation; either version 2 of the License, or     *
*   (at your option) any later version.                                   *
*                                                                         *
***************************************************************************
"""

__author__ = 'Luigi Pirelli'
__date__ = 'August 2019'
__copyright__ = '(C) 2019, Luigi Pirelli'

import math
import numpy as np 

# pip install vector3d
from vector3d.vector import Vector


class CameraCalculator:
    """Porting of CameraCalculator.java

    This code is a 1to1 python porting of the java code:
        https://github.com/zelenmi6/thesis/blob/master/src/geometry/CameraCalculator.java
    referred in:
        https://stackoverflow.com/questions/38099915/calculating-coordinates-of-an-oblique-aerial-image
    The only part not ported are that explicetly abandoned or not used at all by the main
    call to getBoundingPolygon method.
    by: milan zelenka
    https://github.com/zelenmi6
    https://stackoverflow.com/users/6528363/milan-zelenka

    example:

        c=CameraCalculator()
        bbox=c.getBoundingPolygon(
            math.radians(62),
            math.radians(84),
            117.1, 
            math.radians(0),
            math.radians(33.6),
            math.radians(39.1))
        for i, p in enumerate(bbox):
            print("point:", i, '-', p.x, p.y, p.z)
    """

    def __init__(self):
        pass

    def __del__(delf):
        pass

    @staticmethod
    def getBoundingPolygon(FOVh, FOVv, altitude, roll, pitch, heading):
        '''Get corners of the polygon captured by the camera on the ground. 
        The calculations are performed in the axes origin (0, 0, altitude)
        and the points are not yet translated to camera's X-Y coordinates.
        Parameters:
            FOVh (float): Horizontal field of view in radians
            FOVv (float): Vertical field of view in radians
            altitude (float): Altitude of the camera in meters
            heading (float): Heading of the camera (z axis) in radians
            roll (float): Roll of the camera (x axis) in radians
            pitch (float): Pitch of the camera (y axis) in radians
        Returns:
            vector3d.vector.Vector: Array with 4 points defining a polygon
        '''
        # import ipdb; ipdb.set_trace()
        ray11 = CameraCalculator.ray1(FOVh, FOVv)
        ray22 = CameraCalculator.ray2(FOVh, FOVv)
        ray33 = CameraCalculator.ray3(FOVh, FOVv)
        ray44 = CameraCalculator.ray4(FOVh, FOVv)

        rotatedVectors = CameraCalculator.rotateRays(
                ray11, ray22, ray33, ray44, roll, pitch, heading)
        
        origin = Vector(0, 0, altitude)
        intersections = CameraCalculator.getRayGroundIntersections(rotatedVectors, origin)

        return intersections


    # Ray-vectors defining the the camera's field of view. FOVh and FOVv are interchangeable
    # depending on the camera's orientation
    @staticmethod
    def ray1(FOVh, FOVv):
        '''
        tasto
        Parameters:
            FOVh (float): Horizontal field of view in radians
            FOVv (float): Vertical field of view in radians
        Returns:
            vector3d.vector.Vector: normalised vector
        '''
        pass
        ray = Vector(math.tan(FOVv/2), math.tan(FOVh/2), -1)
        return ray.normalize()

    @staticmethod
    def ray2(FOVh, FOVv):
        '''
        Parameters:
            FOVh (float): Horizontal field of view in radians
            FOVv (float): Vertical field of view in radians
        Returns:
            vector3d.vector.Vector: normalised vector
        '''
        ray = Vector(math.tan(FOVv/2), -math.tan(FOVh/2), -1)
        return ray.normalize()

    @staticmethod
    def ray3(FOVh, FOVv):
        '''
        Parameters:
            FOVh (float): Horizontal field of view in radians
            FOVv (float): Vertical field of view in radians
        Returns:
            vector3d.vector.Vector: normalised vector
        '''
        ray = Vector(-math.tan(FOVv/2), -math.tan(FOVh/2), -1)
        return ray.normalize()

    @staticmethod
    def ray4(FOVh, FOVv):
        '''
        Parameters:
            FOVh (float): Horizontal field of view in radians
            FOVv (float): Vertical field of view in radians
        Returns:
            vector3d.vector.Vector: normalised vector
        '''
        ray = Vector(-math.tan(FOVv/2), math.tan(FOVh/2), -1)
        return ray.normalize()

    @staticmethod
    def rotateRays(ray1, ray2, ray3, ray4, roll, pitch, yaw):
        """Rotates the four ray-vectors around all 3 axes
        Parameters:
            ray1 (vector3d.vector.Vector): First ray-vector
            ray2 (vector3d.vector.Vector): Second ray-vector
            ray3 (vector3d.vector.Vector): Third ray-vector
            ray4 (vector3d.vector.Vector): Fourth ray-vector
            roll float: Roll rotation
            pitch float: Pitch rotation
            yaw float: Yaw rotation
        Returns:
            Returns new rotated ray-vectors
        """
        sinAlpha = math.sin(yaw)
        sinBeta = math.sin(pitch)
        sinGamma = math.sin(roll)
        cosAlpha = math.cos(yaw)
        cosBeta = math.cos(pitch)
        cosGamma = math.cos(roll)
        m00 = cosAlpha * cosBeta
        m01 = cosAlpha * sinBeta * sinGamma - sinAlpha * cosGamma
        m02 = cosAlpha * sinBeta * cosGamma + sinAlpha * sinGamma
        m10 = sinAlpha * cosBeta
        m11 = sinAlpha * sinBeta * sinGamma + cosAlpha * cosGamma
        m12 = sinAlpha * sinBeta * cosGamma - cosAlpha * sinGamma
        m20 = -sinBeta
        m21 = cosBeta * sinGamma
        m22 = cosBeta * cosGamma
        
        # Matrix rotationMatrix = new Matrix(new double[][]{{m00, m01, m02}, {m10, m11, m12}, {m20, m21, m22}})
        rotationMatrix = np.array([[m00, m01, m02], [m10, m11, m12], [m20, m21, m22]])

        # Matrix ray1Matrix = new Matrix(new double[][]{{ray1.x}, {ray1.y}, {ray1.z}})
        # Matrix ray2Matrix = new Matrix(new double[][]{{ray2.x}, {ray2.y}, {ray2.z}})
        # Matrix ray3Matrix = new Matrix(new double[][]{{ray3.x}, {ray3.y}, {ray3.z}})
        # Matrix ray4Matrix = new Matrix(new double[][]{{ray4.x}, {ray4.y}, {ray4.z}})
        ray1Matrix = np.array([[ray1.x], [ray1.y], [ray1.z]])
        ray2Matrix = np.array([[ray2.x], [ray2.y], [ray2.z]])
        ray3Matrix = np.array([[ray3.x], [ray3.y], [ray3.z]])
        ray4Matrix = np.array([[ray4.x], [ray4.y], [ray4.z]])
        
        res1 = rotationMatrix.dot(ray1Matrix)
        res2 = rotationMatrix.dot(ray2Matrix)
        res3 = rotationMatrix.dot(ray3Matrix)
        res4 = rotationMatrix.dot(ray4Matrix)
        
        rotatedRay1 = Vector(res1[0, 0], res1[1, 0], res1[2, 0])
        rotatedRay2 = Vector(res2[0, 0], res2[1, 0], res2[2, 0])
        rotatedRay3 = Vector(res3[0, 0], res3[1, 0], res3[2, 0])
        rotatedRay4 = Vector(res4[0, 0], res4[1, 0], res4[2, 0])
        rayArray = [rotatedRay1, rotatedRay2, rotatedRay3, rotatedRay4]
        
        return rayArray

    @staticmethod
    def getRayGroundIntersections(rays, origin):
        """
        Finds the intersections of the camera's ray-vectors 
        and the ground approximated by a horizontal plane
        Parameters:
            rays (vector3d.vector.Vector[]): Array of 4 ray-vectors
            origin (vector3d.vector.Vector): Position of the camera. The computation were developed 
                                            assuming the camera was at the axes origin (0, 0, altitude) and the 
                                            results translated by the camera's real position afterwards.
        Returns:
            vector3d.vector.Vector
        """
        # Vector3d [] intersections = new Vector3d[rays.length];
        # for (int i = 0; i < rays.length; i ++) {
        #     intersections[i] = CameraCalculator.findRayGroundIntersection(rays[i], origin);
        # }
        # return intersections

        # 1to1 translation without python syntax optimisation
        intersections = []
        for i in range(len(rays)):
            intersections.append( CameraCalculator.findRayGroundIntersection(rays[i], origin) )
        return intersections

    @staticmethod
    def findRayGroundIntersection(ray, origin):
        """
        Finds a ray-vector's intersection with the ground approximated by a planeç
        Parameters:
            ray (vector3d.vector.Vector): Ray-vector
            origin (vector3d.vector.Vector): Camera's position
        Returns:
            vector3d.vector.Vector
        """
        # Parametric form of an equation
        # P = origin + vector * t
        x = Vector(origin.x,ray.x)
        y = Vector(origin.y,ray.y)
        z = Vector(origin.z,ray.z)
        
        # Equation of the horizontal plane (ground)
        # -z = 0
        
        # Calculate t by substituting z
        t = - (z.x / z.y)
        
        # Substitute t in the original parametric equations to get points of intersection
        return Vector(x.x + x.y * t, y.x + y.y * t, z.x + z.y * t)

Hi, just here to say that it was not immediately clear that if the horizon is visible, some (usually two) ray-traced points actually never intersect the ground plane (since they go into the sky). However, if we follow the actual computations, they virtually intersect the plane behind the camera, which is indicated by a negative value of t.

good point, I didn't considered that case