Every Shadow Has A Vanishing Point

Malham Cove in Yorkshire, Image by Tim Hill from Pixabay. Inset is at the actual size downloaded (it also comes larger).
My apologies for the delay in posting this. I was struggling with exhaustion for hours last night (my time) in a bid to get it done; sometime between 11 and midnight, I succumbed, awaking almost 4 hours later, slumped over the keyboard. I still wouldn’t have been able to post it on time without that delay, but it would have been a lot closer to expectations.
Introduction
It still astonishes me that my co-GM for the Adventurer’s Club campaign knows so little about illustration and sketching. A little while back, he revealed that he doesn’t understand perspective, for example – not even the basic stuff that most schoolkids learn in the first few years of their education, in fact, as soon as they realize that showing the side of something as well as the front makes it look more real.
Where there’s one person with such a blind spot, there are likely to be others.
That’s a problem because the ability to sketch, however simply, is a vital tool for the generation and exploration of ideas. It may not be something that you will need every day of the week, but there will be times when its absence will be keenly felt, and can even make the difference between being ready to play and not.
I was contemplating this in the bright sunshine at the bus stop last Saturday morning, and realized that even those with some idea of how to sketch something might have only a vague understanding of how shadows work, a contention supported by the number of claims that the shadows cast by Apollo 11 prove that the moon landings were faked.
In particular, I was contemplating how easy it would be to add an explanation for the basic properties of shadows to a description of how perspective works, for the benefit of anyone laboring under this handicap, when I came up with the title of this particular blog post.
And immediately realized how powerful and useful a metaphor that was for a number of other things that GMs should understand. I had the outlines of this article written in my head by the time the bus arrived, and so clearly that all the reminder I needed was to note the title on a scrap of paper.
So here goes….

Top view of neighborhood illustration, Image Credit: Perspective Vectors by Vecteezy
Top View / Plan View
The place to start learning about perspective is by contemplating the most fundamental view of all: the top-down or plan view, with no perspective at all. Shadows can sometimes be employed to suggest three-dimensional shapes, but that’s about the limit of it – and even that gets sacrificed if it gets in the way of even relatively trivial details. The illustration depicts just such a top view and the most immediate impression is how false, flat, and artificial it feels.
As an exercise in diagramming a street and number of buildings, plus dressings like trees, this is excellent, but that’s damning with faint praise in terms of realism.
Imagined Perspective
Contemplate a box viewed end-on. If you were to sketch that, you might draw a square. But that wouldn’t tell you much about what you were looking at, or the position of the observer in three dimensions, relative to it. Those shortcomings are simply addressed, just by adding a horizontal line that indicates the horizon. Since this, by definition of what a horizon is, is at eye level, this immediately indicates where we are relative to the box – and gives immediate information about the approximate size of the box, to boot. In the case being illustrated, our eyes are directly in front of the face of the box, and about 1/3 of the way down from the top of the box. We immediately assume that it is located on the floor, and that means that the box is a little taller than the observer – maybe 6’6″ or 7′ tall – and, of course, it’s as wide as it is tall.
That’s all the information that can be gleaned from the sketch above, and even some of that is potentially misleading – it assumes that we’re standing and of fairly typical human height, somewhere between 5’6″ and 6’2″ tall. What if this is a view from very close to the floor? Suddenly, the box is much smaller – and, assuming that it’s still on the floor and not hovering in mid-air, that size might explain why we’re down on the floor to look at it.
Still, if you were drawing such a sketch, you would presumably know what the size of the box is supposed to be, and from that, the height above ground of the eyes of the person observing it can be deduced. Still, that’s a lot of meaning for such a simple representation of reality.
Size – Distance relationship
The mind employs all sorts of shortcuts to process the world around us, and some of these explain humanity’s ability to create representational images at all. Artists have been manipulating these processes for millennia, to play cognitive tricks on the viewer.

This image combines the gorilla image (by gnav) and a fence image (by by OpenClipart-Vectors), both from Pixabay, with a quick background.
The most fundamental such shortcut equates relative size with distance with implied depicted size. This is illustrated by the gorilla images to the left; notice how putting the fence behind the gorilla makes the fence seem more distant, while the image with the fence in front doesn’t look right because if the ape was that large, the fence would have to be impossibly tall and there’s no sign of that. If the ape image had been of a whole ape, though, the discrepancy would be harder to spot. This is how “forced perspective” works – we equate small things with distant things and vice-versa, and so the eye can be fooled into thinking it’s seeing a 50′ woman – or a 2″-tall man, ‘just’ by constructing realistic sets to the desired scales.
I write ‘just” because it’s not necessarily that easy. If you look at a photograph of a miniature, ninety times out of 100 you can tell immediately – the focal plane is too narrow, meaning that the model blurs in back as well as in front, and the shadows are too sharp, and there’s not enough air between camera and subject, and dust motes and other textures aren’t scaled properly – and we synthesize all those flaws into an instant conclusion, even without being aware of any of these problems specifically.
That The Incredible Shrinking Man rarely falls prey to these problems, or their larger-scale equivalents, explains why it won the Hugo Award for Best Dramatic Presentation when the award was first issued, in 1958. That it did not succeed as well in this regard despite arguably better critical reviews justifies the lack of similar recognition for The Amazing Colossal Man, a close contemporary of the Shrinking Man.
Singe-point perspective
The geometrically-fascinated ancient Greeks were well aware that things appeared smaller if they were farther away, and naturally spent time analyzing the phenomenon. They soon realized that straight lines could be represented with great accuracy using single-point perspective.
What is single-point perspective? Consider the box diagrams to the right. In figure 1, I have simply copied two sides of the box and moved them up and to the left of the box. If they were unchanged in size, the results wouldn’t look quite right, though many would not be able to explain why; it’s because the back of the box, being further away, has to be smaller than the front. This has also been made in figure 1.
If I simply connect the visible corners of the box, it immediately takes on the feeling that it has three-dimensions, a demonstration of the fundamental truth of the proposition. Figure 2 shows this completion – but it goes one step further and explains why: it’s because Single-Point perspective is perspective from a single vanishing point.
Vanishing Point
Figure 2 also depicts this – simply by extending the lines that are running from front corner to back corner of the imaginary three-dimensional object, we find that they converge to a point. What’s more, any box that was behind the one depicted and in line with it would also have the same vanishing point.
If the vanishing point weren’t on the horizon line, if it were above it, one would get the impression that the box was resting on it’s bottom front edge, with the back floating in the air. There are similar problems if the vanishing point is below the horizon line, but it’s the front edge that appears lifted off the ground. If these constructions are explained visually – the presence of a figure lifting one side or the other, as appropriate, for example – and supported by shadows, it is completely plausible; without such confirmations, the results simply feel “wrong”. The only vanishing point that yields the impression of a box flat on the floor is the one with the vanishing point on the horizon line.

By Bookworming at English Wikipedia, CC BY 2.5, Link
Forwards
An awful lot of illustrations use a single vanishing point about 1/3 of the way down the center of the page, give or take, or the equivalent with the paper turned on it’s side. This is a completely natural view of straight lines, as shown by the photograph to the left.
How do you determine where a vertical division should be, in order for it to appear to occur with regular spacing?
Well, you can use some complicated maths to calculate the apparent distance, or you can use a simple geometric trick:
The illustration below takes you through the process step-by-step.
- In figure 1, I’ve drawn lines from the vanishing point to the top and bottom of the shape to be repeated, and drawn that shape.
- In figure 2, I’ve found the center of that shape by drawing lines from corner to corner.
- The third step is to draw a line from the vanishing point through the middle of the shape.
- That’s the hard work done! Step 4 is to draw a line from the bottom of one side of the shape through the middle of the other side. Where it reaches the top line to the vanishing point is where the next vertical bar has to drop.
- In figure 5, I’ve done several more.
- Erase the working (I’ve left mine very faintly) and put the tops and bottoms to the shapes, and hey presto! You’re done.
When doing this kind of work, you should always proceed from the large to the small, because your accumulated errors (and there will be small errors to accumulate) will shrink with the scale if you do. If you work from the small to the large, the accumulate error will grow, and you can get to the end of a lot of work to find that you’ve stuffed it up completely.
Note that a similar technique enables you to tile floors or draw concrete slabs, perfectly.

Image by invisiblepower from Pixabay
Vertical
It’s not really any harder to do a single-point perspective looking down than it is to do one looking horizontally outward, but the results are far more dramatic, as the forest image to the right reveals. These are sometimes known as birds-eye or aerial views, but that’s a misnomer; these more accurately refer to a horizontal view from a position of considerable altitude.
The more accurate term to describe this sort of image or a drawing from a similar perspective is an overhead view.
Object Rotation
Okay, so by now you’ve mastered the basics of perspective, it’s time to move on to something a little more difficult. Let’s take the box that we started with a little while back and rotate about a vertical axis to that one of the edges is closer to us.
It’s obvious from what we’ve already done that one face will run to a vanishing point, the same as in the single-point example. Let’s assign that to be the face to our left as we look at the box, so that the shape of the process is as per the example we’ve already got. Since the face on the right is also going to have a back edge that has to be shorter than the leading edge, it also has to run to a vanishing point.
To show an object with two faces pointing toward the character but not directly at him, you need two vanishing points.
The diagram to the left is rather more complicated than anything we’ve dealt with so far. Don’t let that put you off; as we get into it, you’ll see that it’s not as confusing as it might first appear. So, there’s our box; the side to our left is running to the vanishing point labeled a, while the face to our right is pointing at b. The panel on top is actually pointing toward both.
The rest of the diagram is there to explain a practical limitation regarding the placement of these vanishing points.
The Placement Of Two Vanishing Points
A is within the left-hand 1/3 of the page, and that’s fine, as shown by the green indicator beneath the “1”. Now, in theory, the right-hand vanishing point can be anywhere to the right of that point, at least according to some people. In practice, you soon learn that b should never be placed in the middle of the page (the red section under the “2”, and should only be placed in the right-hand side of the page with caution and forethought – because unless you get it exactly right, it simply won’t look real.
In fact, it’s generally far better for the second vanishing point to be located off the page, somewhere on a span that’s also 2/3 of the page wide. And, as a general rule, the greater the separation between the two, the more believable the end result will be. This example has b located on the right-hand-side of that ‘extended page’, and the results are just fine.

Two-Point Perspective By Mmroberts – Own work, CC BY 3.0, Link, compressed vertically, and variation by Mike.
Two-point perspective
The placement of the vertical edge between the two faces is also important, as shown in the diagram to the right. In the first version, that edge is slightly to the left of the middle of the page, while in the second example, I’ve moved the edge closer to what is sometimes referred to as the “near” vanishing point. The result is that the building appears to have the larger side facing us more directly, with the smaller end presented at a more oblique angle.
One Point Perspective, revisited
It’s also worth considering what happens if we move vanishing point b further and further to the right. If you think about it for a moment, you could rephrase that as moving the vertical edge facing us closer to the ‘a’ vanishing point, relative to the ‘b’ vanishing point, exactly as I’ve done in the second version of the diagram. That means that the top and bottom of that larger face – the side with the windows – will continue to flatten out until, with ‘b’ infinitely far away, they are parallel with the horizon – and what we’re effectively left with is a single vanishing point.
That means that one point perspective is really just a special case of two-point perspective, one with some of the complexity stripped out of it. It also means that having any edges perfectly parallel to each other is a special case, a simplification that only works properly when one vanishing point is so far away that it might as well not exist.

Image by photo free from Pixabay, background tone by Mike
The Need for Three Vanishing Points
The obvious implication is that as we shift our observation point up or down, relative to the top of the box or building, the oversimplification of representing the ‘vertical’ edges with perfectly parallel lines begins to become more and more unrealistic.
For a fully 3D image, we’re going to need a third vanishing point – one that’s up in the sky if we’re looking sharply up, or below if we’re looking down.
What’s more, as a rule of thumb not to be broken unless you know exactly what you’re doing, this vanishing point should be at least as far below the horizon line as the a-b distance, and preferably 2-3 times as much.
Of course, the more aggressively up or down we’re looking, the closer to the center of the page this vertical vanishing point becomes, eventually devolving into the other type of single-point perspective.
Three-point perspective
The result of what three-point perspective makes possible is represented by the line drawing of a building shown to the left. This has all three vanishing points off the page – two a long way above the top and a long way to the left and right, respectively, the third one a long way down the page. If you look closely at the image, you can note that none of the sides is drawn using parallel lines; they all converge at vanishing points.
Yet the result, even with the quite simple monotone coloring and total lack of texture, is clearly far more realistic feeling than the simple two-point or one-point examples I’ve been using so far.

Image Credit: Perspective Vectors by Vecteezy
Isometric Projection
What if all three vanishing points are all the way out to infinity in their respective directions at the same time? Then all the lines are parallel – and what you have is isometric projection. This is a simplified form of 3D that has gained a lot of popularity in computer games because it takes a lot less computing power to render content than a more realistic approach would.
The illustration to the right depicts an example of isometric projection.
That’s really all you need to know about straight lines and perspective. Curves get a lot more technical, but if you stick each sphere and cone in a rectangular ‘box”, and think about what you’re doing, you should be able to cope.
Shadows
A shadow is constructed using an additional vanishing point at the light source and one at the point on the ‘ground’ vertically below that vanishing point.
That makes it sound quite simple, doesn’t it? It’s just more of what I’ve been showing you how to do all article.
Before I walk you through an example, though, it’s worth pausing for a moment to remind yourself of what a shadow actually is.
The Absence Of Light
We talk about shadows all the time as if they were something real; they aren’t. They are a contrast, the result of an interruption of the light traveling from the source toward the surface on which the shadow is to be cast.
A shadow is the absence of light. It may be a convenient shorthand to treat shadows as a projection of the shape onto a surface – in effect, taking the simulated 3D shape and eliminating the third dimension.
The distinction is fine, but important, because there are times when casting a shadow when you need to stop and use this as a guideline to lift you out of a state of confusion. Without it, you’re stuck trying to use 3D geometry to try and solve your problem, and that’s a much more difficult tool to use.
Technique
I’ve deliberately made the shape in this example a little more complex; I knew that I was only going to be able to present one definitive image to describe the process.
Click on the image to open a larger version in a new tab.- I started with the horizon line and vanishing point (e) and outlined the shape.
- I positioned S, the sun, and dropped a vertical line to a for the seat of the light.
- I drew line a-b-c and line S-d-c. Obviously, where these intersected was the location of point c, which I hadn’t known previously.
- I next drew a line from the vanishing point to the intersection point (c).
- a line from a to pass through k gave me L at the point where it intersected the e-c line.
- a line from S through j provided confirmation that L was correct.
- a line from S through f, and locate the intersection with the e-c line, gave me point g, the top of the notch.
- I drew a line vertically from f to h.
- a line from a through h to g confirmed the position of g and gave me the vertical line of the notch.
- a line from S through m to n gave me the bottom of the notch (actually, I was a little sloppy in doing this line, and in too much of a hurry to redo it the way I should have).
- a line from S through h to i gave me the start of the angled part of the notch.
- I then drew the outline of the shadow and filled it in, then erased my working. I added the blue and gray background splashes of color. The inset shows the result without clutter from the labels and working.
All that was needed was a ruler and pencil, or their equivalents since this was a digital file – and knowing what to do with them.

I’ve seen this a thousand times on TV (usually cricket, not baseball), but couldn’t find an illustration of it that was available for reproduction here. So I made my own, using a pitcher image by OpenClipart-Vectors from Pixabay
Multiple Shadows
I stated that it was a vanishing point at one light source and one seat of that light source. That’s an oversimplification.
The reality is that each light source casts it’s own shadows. Two light sources equals two vanishing points at the light sources and two more at their respective seats.
That’s right, you need one complete set of shadows per light source.
If the only time shadows showed up was by day, that would be no problem – here on Earth – but I’m obliged to consider alien worlds and the like under binary stars, and we humans have created light sources more than intense enough to cast large shadows at sporting grounds – and smaller, sharper, deeper shadows from candle-light. So I’m afraid I can’t quite let things go that easily.
The image to the left replicates a situation that I’ve seen many, many times on television coverage – a figure with four, six, or eight shadows from the stadium lighting. I usually see it with cricket, but if Major Leagues taught me nothing else, it was that baseball is also played under lights.

This image of One-day Cricket, Australia vs England, at Bellerive Oval in January 2011 demonstrates the power of the lights used. Image by Christopher Neugebauer from Hobart, Australia – One-day Cricket: Australia vs England, Bellerive Oval, January 2011Uploaded by BaldBoris, CC BY-SA 2.0, Link, Colorspace, contrast, and saturation tweaked substantially by Mike.
The image to the right is a photo from a day-night cricket match played in Tasmania several years ago. Such matches consist of half the match being played in the afternoon, while the other half is played after a half-hour interval in the evening – and hence telecast in prime-time, which is a large part of the appeal of these games. And yes, the grounds really do come up looking that lush and grassy!
Blur & Fade with distance from the edge
The other phenomenon that’s worth noting is that each shadow fades with distance from the light source, and blurs with distance from the edge of the casting object. I was careful to replicate this effect in the baseball pitcher image above; if I hadn’t done so, it would have looked a lot less realistic.
Shadows on sloping surfaces
This is exactly the sort of complication that you have to understand the nature of shadows to resolve. In a nutshell, if the ground slopes, falling away from the horizontal plane, the shadow that is cast has more room to grow, and fade. Effectively, the seat of the shadow shifts in the opposite direction – so if the ground slopes down to the left, the seat will need to move up and right. If there is am abrupt change in the incline – say, from flat ground onto a ridge and sloping ground into a gully – only those parts of the shadow that fall on the ridge or beyond will be affected.
The results can be visually-confusing if there is not some other indication of the slope of the terrain; a bare surface will no longer cut it. If you introduce the effects of terrain, you generally need to indicate what that terrain is – which means making it believable as well. Which is moving beyond the scope of this article.
Shadows on a curving surface
Similarly, if there is any sort of bulge, depression, or curve to the surface – the side of a hill or whatever – shadows will bend and curve in response, and will either shorten or lengthen (depending on whether or not the shadow has as far to travel before intersecting the surface on which it is being cast).
That’s where the Apollo-11 conspiracies fall apart; it’s far easier to explain the shifts in angle of the shadows of one object relative to the shadows of another with uneven terrain than it is to explain how a government that leaks like a sieve could involve tens of thousands of people in a conspiracy and have none of them leak the ‘truth’ – ever. To say nothing of an enemy superpower that would have to be party to such shenanigans, and innumerable others in other countries.
Every Shadow Has A Vanishing Point
Which brings me back to the title of this article. By now, you can tell that it has a double-meaning even if taken literally.
Meaning one: all shadows fade out at some point, some distance. Long before that point is reached, they will have blurred in form into a far more general representation of the shape casting the shadow. But there comes a point at which all shadows cease to exist, for all intents and purposes; if that point is reached before the end of the shadow, it simply fades into nothingness.
The other literal interpretation is quite specific – each shadow has its’ own light source, and each light source has its own vanishing point. A pair of them, in fact – one on the reciprocal of the nominal surface, and one not.
But, quite frankly, those interpretations both pale in comparison to the wealth of meaning that can derive from treating the statement as a metaphor.
As a Gaming Metaphor, Interpretation 1
Let us consider a complex object as an abstract representation of all the parts of the GMs plot, and each of the PCs is a spotlight. The shadows of the shape of the plot are only really tangible when a PC shines a light on that part of the plot; the rest of the time they fade and vanish into the murk.
It doesn’t much matter which part of the complex structure the PCs examine first, because they all interconnect. However, some parts are going to be far more viscerally satisfying to discover after an appropriate build-up, so it behooves the GM to shift his plot around so that whatever the PCs look at first is one of the more interesting parts of the plot.
But there’s still greater depth of meaning to this metaphor interpretation, because it also serves as a reminder that the consequences of any given plotline should not last indefinitely without the GM being guilty of misrepresenting the campaign to the players. At the very least, they should have the opportunity to set things ‘right’ (they might blow it, but that’s not the point).
There should be a statute of limitations on plot threads, a limit to how far a single plot can cast a shadow onto the campaign. The GM should plan accordingly. Of course, the brighter the light source, the greater that limit will be….
As a Gaming Metaphor, Interpretation 2
There are analogies to shadows being cast upon the tone of a campaign, too. Not every day can be rainy and bleak; some have to be sunny and bright, if only to make the rainy days more miserable.
There are also analogies to shadows being cast upon character personalities. No one can be a complete sourpuss all the time – not even Montgomery Burns or Scrooge McDuck.
As the old Ferrengi Rule Of Acquisition is alleged to recommend, “every now and then, declare peace – it confuses the hell out of your enemies!”
As A Gaming Metaphor, Interpretation 3
Of course, as GMs, we love shadows, especially to hide things in. But there are limits to that, both in terms of any single occasion, and in terms of the technique as a pattern. Predictability in a GM generally means that he either needs to up his game or is luring the players into a trap.
This shouldn’t be anything as overt as “the first monster after a meal break always has a peppermint-flavored potion of healing”. Even the least-paranoid player will smell a rat around that one.
But, “every sinister villain wears a signet ring” is an altogether more subtle deception. It can even turn that player-paranoia loose on your behalf, implying that there’s a “Fraternal Order Of Sinister Creeps” i.e. some sort of conspiracy going on. The more time the PCs spend investigating, and investing themselves, in this theory, the more blind they will be to the one exception, who “befriended” the party years ago and has been funneling tidbits that turn the party loose on his enemies ever since..

The Blue Tree Project is a global symbol of Mental Health Awareness. The link is to the web page of the organization.
As A Real-Life Metaphor
Even more important, there is a real-life metaphor here, one that can’t and shouldn’t be ignored.
Shadows have long been a metaphor for depression. When you’re trapped in that head-space, you seem to be surrounded by them. The universe itself can seem like a malevolent entity actively plotting to make your life as miserable as possible.
All too often, the sufferer sees no way out of their situation, and takes the only escape they perceive – and their own life. The younger the victim, the greater the tragedy this represents; but everyone matters to someone, whether they can recognize it at the time or not.
A Half-heard statistic from the TV this morning shocked me: Australian Suicides (presumably amongst young adults) in 2018 were triple the number killed in car accidents. I don’t know if that was in a state-level context, or a national context, but either way it’s unacceptable.
It’s a number that is likely to only worsen without intervention of some kind. Not only are there are the usual sources of teen angst, but there’s wage stagnation and the perception that past generations have sold the younger generation’s birthright out from under them, and that climate change poses an existential threat. In the US more than anywhere else, but sadly not exclusive to that nation, mass killings and terrorist brainwashing / recruiting are also existential threats. Life was so much better when we only had nuclear annihilation to worry about; such times seem so naive these days.
Something that is not unacceptable is the value of gaming to providing an escape from those shadows.
Look, every teen and young adult (aside from a lucky minority) will experience some cause of intolerable pain in their youth. How justifiable the resulting angst is, really, will always be open to debate; what matters is that to the afflicted, they feel they have the weight of the world on their shoulders. Even if they do not intend to commit an act of intentional self-harm, their situation can nevertheless lead them to indulge in self-destructive behavior.
I’m no exception to this general truism. Nothing I tried, when under the spell of this bout of depression alleviated the pain, or even masked it. With one exception: once a week, more often if I was lucky, I could step outside my own shadow and, for a while, be someone else. Someone whose problems always had solutions, someone whose destiny was always within their own hands and close at hand, whose life was their own to chart.
I make no bones about it – eventually, one of those self-destructive behaviors would have caught up with me; gaming saved my life by starting and encouraging the healing process.
I’m not advocating gaming as any form of therapy unless so recommended by an appropriate professional. At best, gaming provides a respite from the overt symptoms of depression experienced by a sufferer; it is not a cure-all, but it can provide relief of a most profound kind.
And for that reason, I think the world needs more gaming. We need our youth thinking of new business models and new solutions to old problems – and implementing those solutions.
The lesson of smiles and frowns is worth remembering.
- If you smile at others, regardless of how you might be feeling, you make it significantly more likely that they will respond by feeling good and smiling back, no matter how they were feeling previously. And, when they smile back, our subconscious takes that as genuine, whether or not it is an automatic response to our feigned smile, and our own mood improves. Smiling is a self-fulfilling prophecy.
- If you frown at others, regardless of how you might be feeling, the opposite effect occurs. Sourpusses bring down the moods of everyone around them, whether they realize it or not, and the only way to counter the effect is to shoulder your burdens and smile at the world.
All shadows have a vanishing point, beyond which they fade into insubstantiality. The trick is to avoid cloaking oneself in them in the meantime. And never assume that you can’t help someone else who’s having a hard time of it; even if you can’t intervene directly, you can help just be being around – and doing things that make you smile at others, that are genuinely pleasures.
Gaming makes me do that. And it makes others do that. And that makes it part of the solution that should not be overlooked or dismissed as trivial.
All shadows have a vanishing point, and all demons can be bested – if we try hard enough and provide the help that people need.
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