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import bpy
from mathutils import Vector

def main():
    
    # specify the object
    ob = bpy.context.object
    
    # change to your desired output location and file name
    filepath = r"D:\temp\bounds_2d.txt"

    scene = bpy.context.scene
    frame_current = scene.frame_current
    frame_start = scene.frame_start
    frame_end = scene.frame_end
    
    write_bounds_3d(filepath, ob, frame_start, frame_end)
    
    scene.frame_set(frame_current)


def write_bounds_3d(filepath, ob, frame_start, frame_end):
    
    file = open(filepath, "w")
    
     for frame in range(frame_start, frame_end + 1):
        bpy.context.scene.frame_set(frame)
        file.write("%f %f %f %f\n" % get_bounds(ob))
        
    file.close()

def get_bounds(ob):
    mat = ob.matrix_world
    bbox = [mat * Vector(b) for b in ob.bound_box]
    
    min_x = min(b.x for b in bbox)
    max_x = max(b.x for b in bbox)
    min_y = min(b.y for b in bbox)
    max_y = max(b.y for b in bbox)
    
    top_left = Vector((min_x, max_y))
    bottom_right = Vector((max_x, min_y))
    
    # make flat tuple, x y width height
    return top_left.to_tuple() + tuple(map(abs, (top_left - bottom_right)))

if __name__ == '__main__':
    main()

import bpy
from mathutils import Vector

def main():
    
    # specify the object
    ob = bpy.context.object
    
    # change to your desired output location and file name
    filepath = r"D:\temp\bounds_2d.txt"

    scene = bpy.context.scene
    frame_current = scene.frame_current
    frame_start = scene.frame_start
    frame_end = scene.frame_end
    
    write_bounds_3d(filepath, ob, frame_start, frame_end)
    
    scene.frame_set(frame_current)


def write_bounds_3d(filepath, ob, frame_start, frame_end):
    
    with open(filepath, "w") as file: 
        for frame in range(frame_start, frame_end + 1):
            bpy.context.scene.frame_set(frame)
            file.write("%f %f %f %f\n" % get_bounds(ob))

def get_bounds(ob):
    mat = ob.matrix_world
    bbox = [mat * Vector(b) for b in ob.bound_box]
    
    min_x = min(b.x for b in bbox)
    max_x = max(b.x for b in bbox)
    min_y = min(b.y for b in bbox)
    max_y = max(b.y for b in bbox)
    
    top_left = Vector((min_x, max_y))
    bottom_right = Vector((max_x, min_y))
    
    # make flat tuple, x y width height
    return top_left.to_tuple() + tuple(map(abs, (top_left - bottom_right)))

if __name__ == '__main__':
    main()

import bpy
from mathutils import Vector

def main():
    
    # specify the object
    ob = bpy.context.object
    
    # change to your desired output location and file name
    filepath = r"D:\temp\bounds_2d.txt"

    scene = bpy.context.scene
    frame_current = scene.frame_current
    frame_start = scene.frame_start
    frame_end = scene.frame_end
    
    write_bounds_3d(filepath, ob, frame_start, frame_end)
    
    scene.frame_set(frame_current)


def write_bounds_3d(filepath, ob, frame_start, frame_end):
    
    file = open(filepath, "w")
    
    for frame in range(frame_start, frame_end + 1):
        bpy.context.scene.frame_set(frame)
        file.write("%f %f %f %f\n" % get_bounds(ob))
        
    file.close()

def get_bounds(ob):
    mat = ob.matrix_world
    bbox = [mat * Vector(b) for b in ob.bound_box]
    
    min_x = min(b.x for b in bbox)
    max_x = max(b.x for b in bbox)
    min_y = min(b.y for b in bbox)
    max_y = max(b.y for b in bbox)
    
    top_left = Vector((min_x, max_y))
    bottom_right = Vector((max_x, min_y))
    
    # make flat tuple, x y width height
    return tuple(top_left) + tuple(map(abs, (top_left - bottom_right)))

if __name__ == '__main__':
    main()

import bpy
from mathutils import Vector

def main():
    
    # specify the object
    ob = bpy.context.object
    
    # change to your desired output location and file name
    filepath = r"D:\temp\bounds_2d.txt"

    scene = bpy.context.scene
    frame_current = scene.frame_current
    frame_start = scene.frame_start
    frame_end = scene.frame_end
    
    write_bounds_3d(filepath, ob, frame_start, frame_end)
    
    scene.frame_set(frame_current)


def write_bounds_3d(filepath, ob, frame_start, frame_end):
    
    file = open(filepath, "w")
    
    for frame in range(frame_start, frame_end + 1):
        bpy.context.scene.frame_set(frame)
        file.write("%f %f %f %f\n" % get_bounds(ob))
        
    file.close()

def get_bounds(ob):
    mat = ob.matrix_world
    bbox = [mat * Vector(b) for b in ob.bound_box]
    
    min_x = min(b.x for b in bbox)
    max_x = max(b.x for b in bbox)
    min_y = min(b.y for b in bbox)
    max_y = max(b.y for b in bbox)
    
    top_left = Vector((min_x, max_y))
    bottom_right = Vector((max_x, min_y))
    
    # make flat tuple, x y width height
    return top_left.to_tuple() + tuple(map(abs, (top_left - bottom_right)))

if __name__ == '__main__':
    main()

And here's some code to write out what you asked for (front view):

import bpy
from mathutils import Vector

def main():
    
    # specify the object
    ob = bpy.context.object
    
    # change to your desired output location and file name
    filepath = r"D:\temp\bounds_2d.txt"

    scene = bpy.context.scene
    frame_current = scene.frame_current
    frame_start = scene.frame_start
    frame_end = scene.frame_end
    
    write_bounds_3d(filepath, ob, frame_start, frame_end)
    
    scene.frame_set(frame_current)


def write_bounds_3d(filepath, ob, frame_start, frame_end):
    
    file = open(filepath, "w")
    
    for frame in range(frame_start, frame_end + 1):
        bpy.context.scene.frame_set(frame)
        file.write("%f %f %f %f\n" % get_bounds(ob))
        
    file.close()

def get_bounds(ob):
    mat = ob.matrix_world
    bbox = [mat * Vector(b) for b in ob.bound_box]
    
    min_x = min(b.x for b in bbox)
    max_x = max(b.x for b in bbox)
    min_y = min(b.y for b in bbox)
    max_y = max(b.y for b in bbox)
    
    top_left = Vector((min_x, max_y))
    bottom_right = Vector((max_x, min_y))
    
    # make flat tuple, x y width height
    return tuple(top_left) + tuple(map(abs, (top_left - bottom_right)))

if __name__ == '__main__':
    main()