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""" | |
*************************************************************************** | |
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) |
Hello everyone,
Very nice code and easy to understand!!!
Is someone here requested Flask + ... for this code, please take a look the started conversation, it's ready … fin!
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.
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
Great work here. Such a pity its not a version that just work with only FOV (Im stuck with some camera that just don't give hFOV and vFOV). It would be really great if anybody know anything to get both hFOV and vFOV from FOV.