by Joe Farina » Wed Oct 15, 2014 10:15 am
That's a very good point about the distortion apparent in the first picture -- the perspective doesn't look quite right, does it? But I think the explanation is simple.
Perspective is notorious for being difficult to explain, and the more it's put into words, it seems the more confusing it gets. The best thing is to do a few tests. But I will give it a try.
It may help for people with a background in holography or optics to think of "forced perspective" in terms of ray-tracing. A number of things need to be determined precisely before a perspective construction can be made. One important thing which might be overlooked is the precise location of the eye with respect to the "picture plane" (i.e., emulsion). In the above "room" the eye was determined to be exactly 25mm above "ground level" and exactly 8 inches from the picture plane. The picture plane is determined to be exactly 70mm wide X 50mm tall, which is the front open-end of the box. (The picture plane is thus divided into 5mm squares, 14 squares wide and 10 squares tall.) The depth of the "represented" scene needs to be determined also, in this case it's 60mm or 12 squares. Lastly, the amount of foreshortening needs to be established. A simple way of doing this is to determine how much the "floor" will be raised, in degrees. In the above example, it's raised at a 5 degree angle.
Once all of these factors are determined, then the ray-tracing can begin, with a side view of the arrangement on paper. This would show the position of the eye, the 8 inch distance to the picture plane, the picture plane, and the "unforeshortened" ground-plan or floor, which is 60mm deep. If a ray is traced from the eye to the termination of floor (which is 60mm deep), it will intersect the picture plane at a certain point. If an angled floor line is drawn, say at 5 degrees "up," then that same point on the picture plane will determine the depth of the "foreshortened" floor. In the above case, the foreshortened floor is halved in size to about 30mm "real" depth (60mm apparent depth).
Now, the probable reason why the first photo looks distorted is that the photo was taken far too close to the "picture plane" (i.e, the front of the box). It was just a few inches, because if the camera was all the way back to the "correct" viewing distance of 8 inches, the lines wouldn't show up in the photograph. An 8 inch distance is pretty close to the limit where many of us can focus our eyes.
Perspective only provides a true "illusion" when the eye is at an exact position in space, and the perspective is constructed with this in mind. As the eye moves away from this distance, the perspective becomes more and more distorted. However, with holograms, it's a very worthwhile trade-off, because the scene is limited to a front-view, and "real depth" is at a premium (laser power, coherence, etc.).
As you noticed, the diagonals are important. Perfect squares need to be determined somewhere in the scene, then diagonals need to be drawn to establish the correct spacing of other squares. A person needs to become like Sherlock Holmes, and deduce where lines "must" be located. Once the floor, ceiling, and walls have been foreshortened with squares, then any object in the room may be foreshortened by using the corresponding floor, wall, and ceiling squares as a guide, noting particularly where these lines intersect in space (in the room's interior). With regards to the degree of foreshortening applied, any amount can be used, but as the amount goes up (say a 10 degree floor inclination) the more obvious the distortions will be when the eye moves away from the correct position. However, when the eye is in the correct position, and the perspective is done properly, the scene will be pretty much "exactly" the same thing as the real scene.
Probably, what I said above makes little sense. Perspective is extremely difficult to explain, even with words, pictures, and demonstration.
That's a very good point about the distortion apparent in the first picture -- the perspective doesn't look quite right, does it? But I think the explanation is simple.
Perspective is notorious for being difficult to explain, and the more it's put into words, it seems the more confusing it gets. The best thing is to do a few tests. But I will give it a try.
It may help for people with a background in holography or optics to think of "forced perspective" in terms of ray-tracing. A number of things need to be determined precisely before a perspective construction can be made. One important thing which might be overlooked is the precise location of the eye with respect to the "picture plane" (i.e., emulsion). In the above "room" the eye was determined to be exactly 25mm above "ground level" and exactly 8 inches from the picture plane. The picture plane is determined to be exactly 70mm wide X 50mm tall, which is the front open-end of the box. (The picture plane is thus divided into 5mm squares, 14 squares wide and 10 squares tall.) The depth of the "represented" scene needs to be determined also, in this case it's 60mm or 12 squares. Lastly, the amount of foreshortening needs to be established. A simple way of doing this is to determine how much the "floor" will be raised, in degrees. In the above example, it's raised at a 5 degree angle.
Once all of these factors are determined, then the ray-tracing can begin, with a side view of the arrangement on paper. This would show the position of the eye, the 8 inch distance to the picture plane, the picture plane, and the "unforeshortened" ground-plan or floor, which is 60mm deep. If a ray is traced from the eye to the termination of floor (which is 60mm deep), it will intersect the picture plane at a certain point. If an angled floor line is drawn, say at 5 degrees "up," then that same point on the picture plane will determine the depth of the "foreshortened" floor. In the above case, the foreshortened floor is halved in size to about 30mm "real" depth (60mm apparent depth).
Now, the probable reason why the first photo looks distorted is that the photo was taken far too close to the "picture plane" (i.e, the front of the box). It was just a few inches, because if the camera was all the way back to the "correct" viewing distance of 8 inches, the lines wouldn't show up in the photograph. An 8 inch distance is pretty close to the limit where many of us can focus our eyes.
Perspective only provides a true "illusion" when the eye is at an exact position in space, and the perspective is constructed with this in mind. As the eye moves away from this distance, the perspective becomes more and more distorted. However, with holograms, it's a very worthwhile trade-off, because the scene is limited to a front-view, and "real depth" is at a premium (laser power, coherence, etc.).
As you noticed, the diagonals are important. Perfect squares need to be determined somewhere in the scene, then diagonals need to be drawn to establish the correct spacing of other squares. A person needs to become like Sherlock Holmes, and deduce where lines "must" be located. Once the floor, ceiling, and walls have been foreshortened with squares, then any object in the room may be foreshortened by using the corresponding floor, wall, and ceiling squares as a guide, noting particularly where these lines intersect in space (in the room's interior). With regards to the degree of foreshortening applied, any amount can be used, but as the amount goes up (say a 10 degree floor inclination) the more obvious the distortions will be when the eye moves away from the correct position. However, when the eye is in the correct position, and the perspective is done properly, the scene will be pretty much "exactly" the same thing as the real scene.
Probably, what I said above makes little sense. Perspective is extremely difficult to explain, even with words, pictures, and demonstration.