This will be a simplified description to make relatively simple reflections.We will be thinking of shapes as cylinders, but you can extend it easlily to rectangles, and then organics. We are going to avoid tapered foreshortening issues and the like and just focus on "the backs of things"In all the sections I will refer to the "pivot". This is the central point that an object would sitting on if you put it on a mirror, and the point that doesn't move if you observed it head on or from any angle. For instance the pivot for a wine glass would be the centre of the bottom of the base. Inverted reflections all have to be considered from this point.Head on reflection--------------------
This is the simplest, you don't have to worry about perspective because everything is flat. Most amateurs try to do reflections like this even when the pivot is NOT head on. With the resulting horror of the educated viewer.The math for head on reflection is simple distances to similar points are equal on both sides of the reflecting line (the head on mirror). In these examples the blue object is the real object and the red one is the reflection in the mirror.
Angled Mirror Reflection. -------------------------We will assume the mirror is basically tilted only up and down in one direction. This would be the case of looking at something on a shiny table. The table surface will be represented by the green trapezoid shape, the centre green line is the horizon at the pivot point, vertical lines are the imaginary line that is at right angles (perpendicular) to the mirror. Angle of incidence on the extended lines from the object will meet these lines and will be the same as the angle of exit.We will look at 3 cases. A cylinder lifted vertically off the mirror, a cylinder lifted at an angle (tipped) and raised, and how circles in the cylinder can be used to formulate a wineglass inside the cylinder. You can extrapolate that convention to ANY shape to model a reflection.
Here we have three cases of a vertical cylinder being lifted off the mirror and showing the results. The first is right on the surface, the second slightly above (notice the blue object obscures the top of the red), and the last object is well above the mirror. The pivot on both ends of the object is marked with a black dot and its central line is the purple line.You will note the reflected object in the last two has a pink circle. This surface is a reflection of the BOTTOM of the real object. If you have a photo of just the real object, to make the reflection you will have to FAKE this surface because it will not be IN the original photo. The pivot (note: the pivot, not just the bottom edge - that changes with perspective, the pivot does not change distance with angle) of the real and reflected objects will be the same distance from the mirror horizon (distance X)You will note that when the image is sitting ON the surface, a cylinder will reflect like it is one long continuous cylinder. If you are looking from above, the real object top will be a squashed circle, and you will not see the bottom surface. That side ofthe cylinder will bulge Down in the middle. (vice versa if viewing the cylinder from low perspective)[Edited by User on 6/9/2011 5:47:09 AM]
Now if the object is tilted the same rules apply. There will always be in the reflection a surface that is NOT in the original photo, if you are not creating a surface, your reflection is wrong. A is what most people do. They just use INVERT in photoshop and call it a day. If you are not creating a surface of the bottom of the real object, you still have work to do. Again the distances from the pivot points are the same to the mirror horizon (x) , and the angle of the central pivot line should be the same (@)(and you never thought you would ever use that geometry your teacher insisted you learn in grade 6! Ha! Math and art are completely related!)
If you move the real object farther up from the mirror, it reacts just the same as the vertical cylinder. The far left of the real object will be the same distance left in the reflection, the far right will be the farthest right in the reflection. If you drop imaginary lines (a & b ) straight down, you will get your boundaries for the reflection. The angle lines will also be equal but opposite.[Edited by User on 6/9/2011 5:53:34 AM]
So how about a wine glass?We will idealize the wine glass to just be sections of the cylinder. You can move some squashed circles on the ends of the cylinder up and down inside to create the areas of the ideal wineglass, and the stem is just a narrower cylinder.
When you remove the chunks of the glass that really shouldn't be part of the cylinder you go from A to B (diagram below)
To see the difference between this and what most people do, I duplicated the blue glass from B and inverted it made it red and matched the pivot point at the bottom to see how C differed from B. This revealed A MAGICAL PROPERTY. For simple ideal reflections, the SILHOUETTE of the reflection (ie. if you changed the image to be all the same colour with no detail) is identical for the BAD reflection most people try to get away with, but the surfaces are showing wrong. This is shown by looking at D. You can see easily that just having photoshop invert the image makes it wrong, everything is twisted the wrong direction and your head hurts because the reflection looks "bent".[Edited by User on 6/9/2011 7:17:28 AM]
The real world.Head on photoshop invert vs. the tipped photoshop invert for amateur reflections.
The water glass reflection is just fine with the simple inversion, because the pivot on the bottom of the glass is head on. You don't have any work to do.If you look at the wine glass slightly from above, the pivot is NOT head on, and if you just invert and match the pivots, you will see that the opening of the glass is on the wrong side, the wine level is on the wrong tilt (you shouldn't be able to see the flat surface of the liquid). You didn't have to do any work, so of course this means the reflection is wrong, because art is for mathematicians not artists. :)
The left glass is a simple inversion. The right glass I used dodge to make the current front of the inversion seem like it is at the back, and I removed the line that indicated the surface of the wine (because you would only see the SIDE of the liquid in a proper reflection at this angle. (As an experiment, go get a glass of wine, and a mirror and see the difference).But that was easy, the glass is clear, and not much contrast, there was nothing really occluded and hidden. Let's try a more difficult teacup.
[Edited by User on 6/9/2011 4:35:59 PM]
So here we have the isolated teacup. I duplicated the image, inverted it and matched the pivot points.AWESOME!!!! Reflections at right angles it would seem.Most people would recognize this and just move the reflection down to be more "realistic"! Super AWESOME!
FAIL.So what do you have to do?
the teacup is kind of like a whole bunch of cylinders. the cup, and the saucer are two different things and you can think of sections of them as being sort of like cylinders. In this case just nice vertical cylinders. the cup is like the one sitting on the mirror, and the saucer like the second one slightly raised off the mirror.
I put in the pivots along the central axis and made some squashed circles to indicate the flat surfaces if I tried to think of the parts as cylinders.You can think of the cup as just a bunch of squashed circles. We know how THOSE reflections will work out mathematically. Equal distances, and angles, and each will have a surface that goes from visible to invisible, or invisible to visible.
Inverting with our imaginary squashed circles
now match up the main pivot point at the bottom of the saucer.
[Edited by User on 6/9/2011 7:44:23 AM]
We know from our MAGIC PROPERTY discovered earlier, that the reflection will have the same SILHOUETTE as our simple inversion with matched pivots, so you can actually make a silhouette of that and you will know where the boundaries of the reflection will have to be. You can go ahead and just put in the silhouette whenever you do this.
We also know from our imaginary cylinders that the greenish ring we used to simulate the saucer when we laid out the cup will be the upper part of the reflection and hide most of the cup. So the area in green below is what we will see of the saucer reflection.
So we get that image using the real source photo and getting artistic.First mask out the source around ITs green area.
Unless you have another photo of the bottom of a saucer, you will have to clone and smudge and paint that section into your best version of an upside down saucer.voila
Now you can slide that under the real image onto the silhouette in the green ring area. This will be the uppermost layer in the layers palette of your reflection folder (you are putting all the separate parts in proper folders and labelling and colouring everthing for ease of finding right? right? )[Edited by User on 6/9/2011 7:22:23 AM]
So the saucer part of the reflection is done and in place:
Now let's pretend there is no saucer and model the cup.
visible circles become invisible and invisible circles become visible. In this case the circle of the open end of the teacup is VISIBLE so in the reflection it will be INVISIBLE. Again, lacking another source, we will have to use the warp tool to change the direction of the circle perspective. First cut the inside of the cup out completely (i used a large circle eraser) Select the isolated cup initiate the warp tool and pull up on all the central nodes in the tool, and then tweak it to turn it inside out as it were.
Then invert the new cup and try to match it up with the silhouette of our reflection. Some minor warp tweaking may be needed. The cup reflection layer will be LOWER on the layer palette, since the saucer hides it.
The handle is also inside out, so go look at a real one and see what you should do. For now I just cut it out onto a new layer and matched the silhouette. Leaving us this.
Looking at a real reflection it seems that the handle is almost the same, but the upper edge should be the INNER edge of the handle. Since it is just some grey and white, I just masked it and smudged out the white, to a dull grey. I then dodged a bit of an edge. I also darkened the saucer a bit because the bottom of the saucer would have less light than the top.
[Edited by User on 6/9/2011 7:48:00 AM]
Now to see what this would look like in more of an environment, I have addded a simple mirror with a bit of dull sky.
But the cup would still cast a bit of a shadow, so I found the silhouette of the original picture and put in a bit of a cast shadow. You will note that the shadow should ALSO be darkening the reflected saucer in the most logical way you can work out.After that, you can clean up a few things and take some artistic licence with the highlights and dark edges.
voila!YOu can extrapolate all these processes. Try it out diagraming a box, do your best and then verify using a real box and a mirror. For the most part you just have to remember. What is visible becomes invisible, and what is invisible becomes visible - on the side AWAY from the mirror.[Edited by User on 6/9/2011 7:51:29 AM]