dappled designs

image courtesy Edward Tufte

As sunlight passes through the crown of a tree, every small opening in the crown serves as the aperture of a pinhole camera that casts an image of the sun on the ground. These sun images vary in size and brightness and may overlap, forming shadows of intricate detail and rich intensity gradations.

Artists call this dappled light. As the sun makes its way across the sky, the shapes change relatively quickly (a property of the moiré phenomenon).

If we could carefully design a tree-shaped sculpture with precisely positioned twigs and leaves, we could make a sundial that marks the passage of times and seasons by casting intricately detailed transient shadow images. For example, a tree sculpture installation that casts shadow portraits of persons whose birthday it is on that day — every day of the year, at a specific time.

Wooden shadow mirror

The artist Danny Rozin has created "mirrors" that create shadow images of the viewer by actuating simple elements such as blocks or pegs.

looking for the right shadow renderer...

So far, I have done most of my modeling in Matlab and IDL, but for complex 3D scenes, I need a flexible 3D renderer that would allow me to create intricate 3D detail and cast realistic shadows.

As I am fairly comfortable with C++, I am drawn to one of the incarnations of Open Inventor, although it may be overkill. Any other suggestions?

mesh-and-shadow sculptures

Randy Cooper uses copper mesh as his medium. The resulting figures appear somewhat like three-dimensional pencil drawings. Furthermore, the sculptures cast wispy shadows that often complement the overall composition.


Meshes are also an ideal medium for moiré synthesis. The moirés in this photo are probably an artifact of digital photography. However, the sculptures themselves can generate rich moiré patterns by interfering with themselves or their own shadows. The moirés could make the figures appear to move and shimmer as the viewer moves past them. Or, with a fair amount of craftsmanship, meaningful secret moiré patterns could be integrated in these figures visible only from a specific vantage point.

shadows on curved surfaces

Originally uploaded by alwasaga

Another interesting property of shadow sculptures that can be exploited in computer-aided sculpting to enhance the visual surprise is that shadow shapes depend on the geometry of the surface onto which they are cast and the viewing angle.

I liked the artistic touch: the book appears to be a dictionary opened on imaginary and imagination.

In this piece by Kumi Yamashita titled Landscape, the shadow is cast by a straight edge and the shadow is shaped by the surface.

shadows with multiple meanings (simplest)

Another interesting property of shadows is that their meaning can change as the light source moves, even without resorting to moiré patterns, as in this sculpture by Markuz Raetz.

... or in this God-Ego duality shadow sculpture by Fred Eerdekens.

With the introduction of moiré effects, the number of possible distinct meaningful shadows can quickly multiply. So far, I have not seen anyone trying this medium.

Monstein moiré

I have just posted this video of a moiré pattern I described in an earlier post.

Google:

youtube:

The two gratings encrypt the images of Albert Einstein and Mona Lisa, hence Monstein. I made the gratings in different colors from the opposite sides of the color wheel. Google compresses videos when you submit them, so this animation does not let you see very well how the green and purple lines overlap.

George's moirés

The Chicago Tribune's Seinfeld 10 years later story gave Jason Alexander a serious case of the moirés.

Remember Nyquist: smoothen before subsampling.

But could this have been intentional? The miorés make the jacket much more expressive. Was this a deliberate artistic trick? Have moirés been used by digital photographers to enhance the three-dimensional feel of the image?

Interactive moiré simulations

Here are some online applications that let you play with moiré patterns:

1. Project LITE at Boston University
2. Elisabeth Sylvan student project at MIT
3. Moire videos at phidelity blog
4. iMoire by Vincent Scheib

shadow sculpture

Shadow sculptures are interesting for at least two reasons:

First, the objects that cast the shadows don't have to look as though they have anything in common with the shadows themselves. Such is this piece at the Museum of Fine Arts:

Tim Noble and Sue Webster, Real life is rubbish

Or in this advertisement:

Secondly, the meaning of the sculpture can change as the light source moves or changes. Such is this thesis project of an art student:

Time-lapse Shadow Verse

Both reasons are more mathematical than aesthetic, but the boundary is subtle. According to one definition, beauty is the sense of wonder, whereas art is the expression of that sense. Well, mathematics is all about wonder. Both of these examples are quite primitive from the mathematical point of view and an engineer with good geometrical skills could design something far more impressive. For some reason most engineers rarely give much thought to such projects. Could it be that engineers are less prone to respond to symbolism?

I actually like both pieces for their artistic value too. Shadows and the motion of the sun across the sky do convey a sense of the passing of time and the illusory nature of perception.

Any artists/mathematicians care to brainstorm a few ideas? For example, in the shadow sculpture above, it would not be too difficult to modify the pile of junk so that it casts for different meaningful shadows onto four different walls simultaneously, but that's just the beginning.

Shadow of communism at University of Chicago

According to this NPR story, the sculpture titled Dialogo on the University of Chicago's campus contains a hidden message.



Supposedly, every year, on May 1, at noon, it casts a hammer-and-sickle-shaped shadow:



As the sculptor Virginio Ferrari confesses, the effect was unintentional, although he enjoys the humor in it. I believe him because he could have done much better than the rather unrealistic version of the Soviet symbol.

Question: Do you know of a sculpture with an unmistakably intentional elaborate hidden message in its shadow that appears on a specific day of the year?

Full-grayscale morphing moiré shadows

A common misconception of shadows is that they must be binary, producing images comprising only black and white areas.

The following figures are adapted (with some conceptual changes) from a patent application I filed while employed at General Electric (US 20080037709A1: METHOD AND SYSTEM FOR CONTROLLING RADIATION INTENSITY OF AN IMAGING SYSTEM). The invention uses shadows from superposed opaque gratings to control the spatial distribution of x-ray radiation intensities in an x-ray beam.

First, we produce two gratings comprising curved opaque bars:



Then, we superpose them with some distance separating them and shine light through them at different angles as shown:



The bars are curved so that the same two gratings together cast shadows containing two different detailed images (not just contours):



Yet, this is not the whole story. If the light comes not from a point source but from a somewhat diffuse source (e.g. the sun), then the shadow will be blurred somewhat by penumbra or half-shadows producing a full-grayscale image:



The blur removes the sharp edges and, paradoxically, improves the images. Notice for example the wrinkles on Albert's face that only come through after the images has been blurred.

Another way to achieve blurring is to rapidly shake the gratings perpendicularly to the bars. Motion blur will then remove the sharp edges from the image producing a similarly smooth image.

You can print the gratings in (a) and (b) on transparencies and superpose them with slight offsets to see the effect for yourselves.

What if such gratings are built as sculpture pieces or are integrated into the facade of a building or as sundials that would cast various artistic shadows at various times of the day at various seasons? What do you think?

Moirés in architecture

Moirés in architecture can add a sense of motion to the building. As you walk past the building, the pattern will appear to move and dance – I can almost see it.

Such patterns could be dramatically improved by using color, generating meaningful images instead of simple geometric patterns, and making the patterns vary with the position of the sun.

Introduction to moirés

Before exploring moiré patterns more systematically and mathematically, let's look at a few examples.

Most moirés are incidental: they arise naturally when two or more gratings, sheets of fabric, wire screens, fences, or dot screens are superposed.

Fence moiré, by Prof. David Eppstein at UC Irwine

In signal processing and imaging, moiré patterns are often known as aliasing. They arise when the sampling rate of a digitized signal is too low to accurately represent the signal. This effect may be a big nuisance in photography and television. In this case in the role of the two gratings play the periodic features in the image and the regular arrangement of pixels in the camera.




Moiré patterns are responsible for adding funky colors to Al Gore's collar in this photo, arguably improving its appearance:



These aliasing artifacts can be easily resolved by either increasing the sampling resolution or by applying proper filtering techniques prior to sampling as described by the Nyquist theorem.

Moiré patterns are commonly treated as a problem. However, they also have many useful applications. For example, their ability to magnify small offsets is exploited for strain and deformation analysis of materials by means of moiré interferometry.


The intentional synthesis of moirés appears to be largely unexplored. The most interesting and sophisticated examples of moiré art I have found to date are animated pictures in children's books:

Animated Illusion, Solved! - The most popular videos are a click away

Invariably, the words magic and amazing are used to describe moiré phenomena, even the most basic ones.

These examples are but a small fraction of what could be done with moirés. Through this blog, I would like to expand the definition of moirés and their applications.

Digital sundials

A company already markets moiré-based digital sundials. As any other sundial, it has no moving parts and no electronic components – only shadows and reflections.




The idea is computationally simple yet the the design is slick!

What else can be done with this? Color? Full grayscale? Larger scale? Artistic expression?