TETe – INTERSECTING SILHOUETTES intersecting silhouettes CHALLENGE YOUR STUDENTS TO CREATE AND 3D PRINT AN INTERSECTING SILHOUETTE

echnology and engineering students meaning to a person who sees the object from are often given challenges to design a particular vantage point using the silhouette and create a prototyping for a product of the object. Silhouettes are filled outlines of that meets a particular need. However, an object without any internal distinguishing inT process engineering, there may be instances features. They have been used for millennia where students could instead be asked to refine (Jackson, 1911), with applications in historiogra- BY a particular process and find applications for phy, art, design, and signage. A silhouette can it. This article shares a basic procedure for be cut out of paper, steel, or other flat sheets of JIM creating a product that is the intersection of material. As you walk around it to view it edge- FLOWERS silhouettes, and it is especially appropriate for on, the image disappears into a line. technology labs where students can use 3D design software and 3D printers. Now imagine a physical object where you see a silhouette by looking at the front of the object. BACKGROUND But with this object, as you walk around it or rotate the object in your hand, a completely In two-dimensional graphics, the term “ambig- Intersecting different silhouette appears, a 3D ambigram. ram” refers to “a word, art form, or other symbol- silhouettes are Jonathan Borofsky’s 2004 sculpture at Penn ic representation whose elements retain mean- Station in Bal- sometimes ing when viewed or interpreted from a different timore, MD, direction, , or orientation” (Wikipedia, greeted with Male/Female, n.d., Para. 1). Scott Kim (1981) shared many ““Wow” by shows two original ambigrams in his book called Inversions, those who extruded sil- where the title of the book reads as his name houettes that don’t expect a when viewed upside down (Figure 1). are crossed second image (Figure 2). or second set of text to Figure 2. Male/ Female, 2004, appear. Jonathan Borof- sky, Penn Sta- tion, Baltimore, Figure 1. An Ambigram as Inversions and, MD. Retrieved when rotated 180°, as Scott Kim (Kim, 1981, p.4.). from http:// www.borofsky. com/index. In the design of three-dimensional objects, some php?album= products, such as signs, are designed to convey malefemale

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Another example integrity, greater clarity in the ability of the design to communi- of this is the cover cate, or aesthetics. art for ’s (1979, ESSENTIAL PROCEDURE reprinted in 1999) The essential procedure for creating an intersecting silhouette book, Gödel, was demonstrated at an ITEEA conference and took less than Escher, Bach: An one minute (Flowers, 2015). It is illustrated here with an object Eternal Golden that reads “Top” when viewed from the top, but “Front” when Braid (Figure 3). viewed from the front. In this instance, Rhinoceros™ 3D design The “shadow software was used to create the virtual object, and a Stratasys blocks” depicted uPrint™ SE Plus was used to build the resulting physical model. there cast the shadow of a differ- 1. Two silhouettes were created, one in each of two views ent letter in each of (Figure 4). In this instance, a font was selected that allowed three directions. the letters to be moved so they slightly overlapped, but with-

Figure 3. Shadow out losing the shape of the letter. Fonts will be discussed in blocks as cover art greater detail below. A text command was used to create (Hofstadter, 1999, solid letters in the top view spelling Top, though these could originally published in 1979). have also been created as lines or surfaces and extruded then capped as solids. Solids for the letters in Front were However, longer lines of text can be used than shown in the created in the front view. 1-letter shadow blocks, and the technique could be used with non-text silhouettes. When created with digital design software, the resulting virtual objects can be rotated to reveal first one view, then a surprising second view, and in rare cases, maybe even a third silhouette.

It is also possible to use additive prototyping technology such as 3D printers to build physical models of intersecting silhouettes— Figure 4. Initial extrusions (of Words) in the Top and Front views. at least for those that would have sufficient structural integrity. Subtractive methods from scroll saws to lasers could also be 2. In the top view, all the letters in Top were brought to a com- used to cut first one silhouette out of a block in one orientation, mon baseline if they were not already on it. The letters were and then a second using a second orientation. then moved (horizontally in ortho mode so they only moved in one axis) to create what seems like enough overlap be- This is not to be confused with technologies and algorithms for tween letters to provide for structural integrity of the model, 3D modeling an object based on the information in a series of but not so much as to obscure the letters (Figure 5). silhouettes (Rivers, Durand, & Igarashi, 2010; Liang & Wong, 2010). Instead, it is a tool for designing products that appear to change with one’s vantage point.

“A prototype is a working model used to test a design concept by making actual observations and necessary adjustments” (Benchmark 9K from ITEA/ITEEA, 2000/2002/2007, p. 105). With intersecting silhouettes, both the observation of the virtual model prior to building and of the finished model may lead the designer to make refinements regarding font selection, scaling, and other design decisions that could lead to better structural Figure 5. Moving letters so they overlap.

2 technology and engineering teacher May/June 2016 3. A Boolean union was performed on the letters in Top so from the vantage point where they ought to be legible (Fig- they became a single solid. ure 7). 4. In the front view, the letters in Front were brought to a com- 10. Once the virtual model passed inspection, it was exported, mon baseline, overlapped, and unioned. in this case as an .stl file for 3D printing. 5. The lengths of the two objects were compared starting with 11. In the software controlling a 3D printer, the .stl file was a common origin at the left of the object. A decision was loaded, and the object was scaled and oriented as desired. made to scale one or both objects, either 1-dimensionally 3D printing parameters, such as the internal density of the along its length, 2-dimensionally, or 3-dimensionally, so that model, were specified. The software digitally sliced the the final objects had the same length. In this example, only object, created virtual supports, created toolpaths for the slight 1-dimensional scaling was used. extruding head, and sent the object to a 3D printer. 6. The objects were moved so that they intersected in all three 12. The object was built from the bottom layer up (Figure 8). In principal views (Figure 6). this case, the 3D printer laid down spaghetti-like strands of a blue thermoplastic (acrylonitrile butadiene styrene) to cre- ate each layer, with separate white support material used for areas such as overhangs that required support. After each layer the table moved down, and the next layer was built on top of the previous layer.

Figure 6. Repositioning unioned and scaled objects so they intersect.

7. A Boolean intersection was performed so that only those volumes in common to both objects are kept. This some- times does not work, with the software reporting a failed attempt. In those instances, slight adjustments could be made to the position of the objects before re-attempting the intersection. 8. The mouse was used to click on the object, realizing that this might not select non-contiguous areas. The selection The object being built in a uPrint SE Plus™ 3D printer. was then moved to show any remaining non-contiguous Figure 8. areas. Those non-contiguous portions were deleted. 13. After building, the object was removed from the 3D printer.

In this case, the support material was dissolved in a diluted alkali bath (Figure 9), after which the object was washed, rinsed, and dried.

Figure 7. Results of a Boolean Intersection

9. The virtual model was shaded and rotated to look for areas that might be problematic for building or handling, such as very small connective areas between letters or instances where some characters may not be legible when viewed

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manipulated in an attempt to produce a viable model. The big- gest factor, though, is the choice of font face.

FONTS There are many issues concerning the design of fonts used for intersecting silhouettes and physical models that result. In the USA, fonts are not covered by U.S. Copyright law and may be edited as needed.

Most fonts do not work well in silhouette intersections for products that will be manufactured. Many fonts contain line strokes that are so thin that a resulting build lacks the structural integrity for the product to be handled. An object to promote a book manuscript entitled The Selfish Professor was created Figure 9. Dissolving supports with a font face that had rather narrow line strokes (Figure 11). This seemed adequate in a virtual setting, and the object was 14. During a final inspection, touch-up work with pliers, a knife, successfully built. However, the object soon broke because it did or a file improved the model (Figure 10). not have the strength required to endure reasonable handling.

Figure 11. Inadequate structural integrity of The Selfish Professor promotional object.

Conversely, fonts could be too bold to allow open areas in let- ters to remain open after scaling compresses them, models are built, and support is attempted to be dissolved away from narrow crevices in the model. More often it is the narrow stroked fonts that result in poor structural integrity.

The easiest fonts to use may be ones with moderately broad strokes because there is a greater probability that there will Figure 10. Final inspection and touch-up be enough mass to keep the model from falling apart after it is fabricated. Selecting boldface can sometimes help. It could be NON-VIABLE INTERSECTIONS that the strokes in a font become indistinguishable when the As noted, an intersection command in 3D modeling software letters are moved so they overlap. Consider letters like MIN in a might result in a failed attempt reported by the software. This font face such as Arial, where they appear without serifs: MIN. can sometimes be overcome by slightly repositioning one of the If these letters are moved so close together that they overlap a virtual objects. little bit with each other, this becomes a blurry zigzag. But with other fonts it might just be possible for each letter to be distinct. Even when the software reports an intersection command Due to the requirement of discerning the letters when they are as successful, the result might not be viable. This could hap- moved to overlap each other, script fonts with broad strokes pen where a significant portion of one of the silhouettes is not may be particularly well suited here. maintained in the intersection. Such an intersection would not be viable even in a virtual setting. Letter spacing, the angles of If there are multiple bonds between two letters, like a capital intersection, and scaling, are among the factors that could be "B" followed by a lowercase "l" where there are two points of intersection, the model may well have more strength. But with

4 technology and engineering teacher May/June 2016 script fonts, there is typically only a tail to provide a single bond. too fragile to remove the supports without breaking the model. In many script fonts, the tail that connects letters is rather thin. However, some 3D printers allow two different materials to be Therefore, it might be wise to edit the font face for each charac- extruded in a single model. This facilitates the use of a support ter to increase the thickness (i.e., height) of the tail. material that can be dissolved away in a bath that does not dis- solve the model material. This greatly increases the intricacy a In some fonts, a character does not touch the baseline, so it is physical model can have, and decreases the minimum size for a likely higher than some other characters in the line. This could viable model. make for a model that does not sit flat on a table. So it is a good idea to place all characters down to the baseline. Some additive modeling technologies do not require separate supports, such as powder-based systems and stereolithogra- Some characters, like g, q, y, and p, typically have descenders phy. In these instances, the model is constructed surrounded by that dip below the baseline. These can be problematic. What if either powder or liquid that provides temporary support. a job calls for a model that stands on a desk and is a top/front intersection of the names Joy and Abby? Had the names been OTHER MODELING TECHNOLOGIES Joy and Bob, then Bob could have been assigned to the front As mentioned, it is possible to use subtractive methods with view and Joy to the top view, so that the model would sit evenly scroll saws, lasers, or other technologies to create a silhou- on the coplanar base of Bob. But with Joy and Abby, each name ette in one orientation, then re-assemble and flip the object to has a descender that would prevent the model from sitting flat position it for a second machining operation where the second without creating a cradle for it. One option is to use all caps, silhouette is cut. since a capital Y typically does not have a descender, or to use reduced-size caps for lower case. It is possible to cut flat sheets of a material out using the geom- etries of successive horizontal cross-sections. These could be THE NEED FOR SUPPORTS layered one on top of the other, possibly using an armature or For nearly all of the intersecting silhouettes I’ve designed, there adhesives, in a process called laminated object manufacture. would be a problem trying to build the object without supports. Alternatively, waffle construction (Figure 12) can be used to 3D printers extrude thermoplastic onto a surface a tiny distance design flat pieces that might be laser cut, then assembled at from the model. But a model that has overhangs, like the letter angles into a finished part. T, would need supports if it is built upright. In that case, turn- ing the letter T upside down lets it be built without supports, but custom intersections may have multiple overhangs in every orientation, so it can be futile to try to build most of these without supports.

In rare instances, it is possible to take advantage of the mate- rial properties that allow us to slightly step out successive layers Figure 12. Waffle construction. on a 3D printer without using supports. Picture the letter Y and look at the angles of the two upper stokes. As these approach Ideally, designs would facilitate easy injection molding, allowing the vertical, building the object without supports becomes less low-cost mass production of products, such as the promotional of a problem than as they approach the horizontal. Thus, some item mentioned here. However, the intricacies of many intersect- 3D printer users have created test pieces showing how much of ing silhouettes would make this prohibitive. Metal-based additive an incline can be successfully built by their particular 3D printer prototyping technologies exist, though the cost and scale may with the polymer and the settings they are using. These are not not fit this application well. Investment casting may be used to universal, and changing the temperature, extrusion rate, nozzle produce a mold, and then a metal object or a 3D-printed object size, polymer, or even the temperature of the build chamber could have a metal coating applied to it, typically increasing its may create different results. density, hardness, and strength.

Where supports have to be removed manually with pliers, knives, and files, the intersecting silhouette model may prove

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PLAYING WITH GEOMETRIES Cross-cultural sensitivity sparked the creation of the desk nameplate seen in Figure 15. From the front it shows the name “Engineering design is influenced by personal characteristics, of Dr. Ren Mei Xu, and then when viewed from the top her name such as creativity, resourcefulness, and the ability to visual- is visible in Chinese. Notice how the Chinese characters used ize and think abstractly” (Benchmark 9J from ITEA/ITEEA, here do not touch each other, sometimes having line strokes 2000/2002/2007, p. 104). One of the distinct advantages of this that also do not touch the rest of the character. Altering the design challenge for middle school and high school technology character so that these strokes all touched may have changed and engineering students is that it asks them to play with ge- the meaning and appearance of the Chinese name too much, ometry. The following illustrate some geometric variations. The so instead a subtractive method was used. Here, the Chinese first shows a 2-way 90° vertical intersection of words: Vertical + characters were altered only slightly so they behaved the same Intersect. Imagine a store called “Vertical Intersect” and outside way a stencil font behaves, that is, without any non-contiguous the storefront, a 20-foot chrome sign made from this design. background. After each name was unioned, a Boolean subtrac- tion rather than an intersection was used to subtract the Chinese name from the extruded block reading Ren Mei Xu.

Figure 13. Vertical left/right of Vertical + Intersect. Figure 15. A Nameplate for Ren Mei Xu, showing her name also in Chinese with Stencil (i.e., Subtracted) Characters. Ambigrams are often word art, whereas silhouettes are more typically non-textual images. This 3D technique has ability both Shorter words may allow for increased flexibility and creativity. with words and with non-textual images, as seen in the extrusion Shown in Figure 16 is an intersection for a man named Dan of two clipart images that were then interesected and 3D printed Boots, with Dan visible from the top and Boots from the front. In (Figure 14). this case, a silhouette of a boot was drawn and extruded along

the width (x-axis). After the initial intersection of Dan + Boots, a second Boolean intersection of the result with the boot extrusion was performed. Other 3-way intersections have also been cre- ated, often with three names, though the few letters and simple shape in this example proved more successful.

Figure 16. Nameplate for Dan Boots, showing boots silhouette in a third axis. Figure 14. Intersecting Shape Silhouettes of a Couple. Clipart Copyright (c) 2010, Corel Corporation and its licensors; all rights reserved. To support a presentation called “Humor in Technology Educa- tion,” the object seen in Figure 17 was created. This illustrates

6 technology and engineering teacher May/June 2016 how two different lines of text can be unioned prior to their Another example of color solid object printing is seen in Figure intersection. In this instance, Humor is seen from the top of the 19, where a brick-face surface texture was mapped to a virtual object, and Technology Education when the object is seen from object before it was built. the front.

Figure 17. Two-line text in an intersection: Technology Education + Humor.

The word Cool was extruded in both the top and front view for the next object. After the letters were moved so they overlapped, placing the two examples' letter o in line with the center of the word rather than aligning baselines, a Boolean intersection was performed. The result was an object that read Cool regardless of how it was flipped, as long as the C was on the left. This is Figure 19. A Color-solid object with a brick surface texture: True + False. due to the vertical bilateral of each of the letters in this word, where their bottom half is a mirror image of their top half. Two different colors were then applied to the virtual object, APPLICATIONS and it was then grown on a Z-Corp Spectrum Z510 Color Solid This discussion began by mentioning artistic silhouettes. Object Printer. This is a rapid prototyper that grows objects However, the derivative methods described in this article are from the bottom up in a vat of powder, with print heads laying mechanical. This parallels the use of machines that helped in down colored liquid binder on every layer. The resulting object the creation of paper portrait silhouettes, though it might be said was dried, excavated, and dipped in cyanoacrylate, a glue that that these did not help, but were a “contrivance” and “general is recommended as an infiltrant to strengthen these powdered abracadabra methods” that would not appeal “to any artist objects. The object also can stand on its end (Figure 18), or be proper” (Coke, 1913, p. 43). Still, meaningful applications of this suspended by a string that passes through a tiny hole in end of process can be found: the object through the middle of the C. • Wedding and anniversary gifts with the names of the two people intersected • Name plates showing first and last names of an individual • Nameplates showing a name in different languages • Nameplates showing a name intersected with a title or department • Nameplates showing the connection between a person and a company or institution, as in intersecting the name of an alumnus/alumna with the name of the institution he or she attended • Street signage where different names or terms are needed when viewed from two different directions • Switches that say ON/OFF or other pairs of terms • Designs where two terms are deliberately juxtaposed in an attempt to show that one is a path to or required by the other, as in Effort + Reward or College + Success Figure 18. Cool, no matter how you see it. Radial Symmetry: Cool + Cool.

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CONCLUSION International Technology Education Association (ITEA/ITEEA). (2000/2002/2007). Standards for technological literacy: Technology and engineering students can be empowered with Content for the study of technology. Reston, VA: Author. this simple technique, and may come up with some fascinating Jackson, E. (1911). The history of silhouettes. London, England: designs as well as new applications. Intersecting silhouettes The Connoisseur. are sometimes greeted with “Wow” by those who don’t expect a Kim, S. (1981). Inversions. Peterborough, NH: Byte Books. second image or second set of text to appear. Thus, this can be Liang, C. & Wong, K. (2010). 3D reconstruction using silhou- attractive to students who are empowered to design a product ettes from unordered viewpoints. Image and Vision Com- that they and others could consider cool, akin to designing a puting, 28(4), 579-589. doi:10.1016/j.imavis.2009.09.012 puzzle. In doing so, they learn about prototyping, gain facility Rivers, A., Durand, F., & Igarashi, T. (2010). 3D modeling with with product design software, and express their creativity. Even silhouettes. ACM Transactions on Graphics, 29(4), Article if the students do not make a physical object but design only vir- 109, 1-8. doi:10.1145/1833349.1778846 tual objects, they may well be enriched by the design challenge. Wikipedia. (n.d.). Ambigram. Retrieved from http://en.wikipedia. org/wiki/Ambigram REFERENCES Coke, D. (1913). The art of the silhouette. London, England: Martin Secker. Jim Flowers is a Professor in the Department Douglis, P. (2011). Finding symbolism in signage: Signs point of Technology at Ball State University. He the viewer in the right direction—or provide unintended can be reached at [email protected]. An meaning. Communication World, 28(4), 44-45. ambigram of his name is pictured here. Flowers, J. (2015). Intersecting silhouettes. Presentation at the International Technology & Engineering Education Confer- ence, Milwaukee, WI.

This is a refereed article.

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