Calculating three-dimensional position from two-dimensional projections are literal textbook examples in geometry, but those examples are the “assume a spherical cow” type of simplifications. Applicable only in an ideal world where the projections are made with mathematically perfect cameras at precisely known locations with infinite resolution. Making things work in the real world is a lot harder. But not only have [Jingtong Li, Jesse Murray et al.] worked through the math of tracking a drone’s 3D flight from 2D video, they’ve released their MultiViewUnsynch software on GitHub so we can all play with it.
Instead of laboratory grade optical instruments, the cameras used in these experiments are available at our local consumer electronics store. A table in their paper Reconstruction of 3D Flight Trajectories from Ad-Hoc Camera Networks (arXiv:2003.04784) listed several Huawei cell phone cameras, a few Sony digital cameras, and a GoPro 3. Video cameras don’t need to be placed in any particular arrangement, because positions are calculated from their video footage. Correlating overlapping footage from dissimilar cameras is a challenge all in itself, since these cameras record at varying framerates ranging from 25 to 59.94 frames per second. Furthermore, these cameras all have rolling shutters, which adds an extra variable as scanlines in a frame are taken at slightly different times. This is not an easy problem.
There is a lot of interest in tracking drone flights, especially those flying where they are not welcome. And not everyone have the budget for high-end equipment or the permission to emit electromagnetic signals. MultiViewUnsynch is not quite there yet, as it tracks a single target and video files were processed afterwards. The eventual goal is to evolve this capability to track multiple targets on live video, and hopefully help reduce frustrating public embarrassments.
[IROS 2020 Presentation video (duration 14:45) requires free registration, available until at least Nov. 25th 2020.]
You may be familiar with origami, the Japanese art of paper folding, but chances are you haven’t come across smocking. This technique refers to the way fabric can be bunched by stitches, often made in a grid-like pattern to create more organized designs. Often, smocking is done with soft fabrics, and you may have even noticed it done on silk blouses and cotton shirts. There are plenty of examples of 18th and 19th century paintings depicting smocking in fashion.
[Madonna Yoder], an origami enthusiast, has documented her explorations in origami tessellations and smocking, including geometric shapes folded from a single sheet of paper and fabric smocked weave patterns. Apart from flat patterns, she has also made chain-linked smocked scarves stitched into a circular pattern and several examples of origami tessellations transferred to fabric smocking. Similar to folds in origami, the stitches used aren’t complex. Rather, the crease pattern defines the final shape once the stitches and fabric are properly gathered together.
Continue reading “Tessellations And Modular Origami From Fabric And Paper”
You may have seen Simon Beck’s work a few years back. The snow artist, known for creating large-scale works of art with nothing but snowshoes, has been creating geometrically inspired fractals and mathematical forms for years. An orienteer and map-maker by day, he typically plans out his works in advance and chooses sites based on their flat terrain. The lack of slopes prevents skiers from traversing the area beforehand and helps with measuring the lines needed to create the drawing.
He starts off by measuring the distance he has to be from the center by using a compass and walking in a straight line towards a point in the distance, making curves based on relative position to other lines. Once the primary lines are made, he measures points along the way using pace counting and joins secondary lines by connecting the points. The lines are generally walked three times to solidify them before filling in the shaded areas. The results are mesmerizing.
He has since expanded to sand art, using the same techniques that gained him fame in ski resorts and national parks on the sandy shores. Unfortunately, tidal patterns, seaweed, and beach debris make it slightly harder to achieve pristine conditions, but he has managed to create some impressive works of art nonetheless.
Continue reading “This Artist Drags His Feet Across Sand And Snow”
It seems that tensegrity structures are trending online, possibly due to the seemingly impossible nature of their construction. The strings appear to levitate without any sound reason, but if you bend them just the right way they’ll succumb to gravity.
The clue is in the name. Tensegrity is a pormanteau of “tension” and “integrity”. It’s easiest to understand if you have a model in your hand — cut the strings and the structure falls apart. We’re used to thinking of integrity in terms of compression. Most man-made structures rely on this concept of engineering, from the Empire State Building to the foundation of apartment building.
Tensegrity allows strain to be distributed across a structure. While buildings built from continuous compression may not show this property, more elastic structures like our bodies do. These structures can be built on top of smaller units that continuously distribute strain. Additionally, these structures can be contracted and retracted in ways that “compressionegrities” simply can’t exhibit.
How about collapsing the structure? This occurs at the weakest point. Wherever the load has the greatest strain on a structure is where it will likely snap, a property demonstrable in bridges, domes, and even our bodies.
Fascinated? Fortunately, it’s not too difficult to create your own structures.
Continue reading “Building Your Own Tensegrity Structure”
[Scott Cramer] is a retired professional woodworker who specializes in geometric art made from beautifully joined wood. In this project he’s carving four interlocked cloverleaf rings from a block of basswood. First he made a series of cuts to turn the block into a cuboctahedron, a geometric solid comprising six squares and eight triangles. Then he drew on the basic lines of the rings on the wood and went to work with a chisel, smoothing and separating the rings and carving out the interior. You can see more shots of the project on his Facebook post, which is included after the break.
To see more of [Scott]’s projects you can follow his Twitter feed. Our favorites include this 70″ pentagonal icosatetrahedron built out of hemlock that [Scott] says is the “largest in Coös County, NH” — what, there are others? He also made a magogany representation of a Hamiltonian circuit of a dodecahedron’s vertices.
We love math art on Hackaday — see our interview with Francisco do Comité we ran earlier this year.
Continue reading “Hand-Carving Geometric Art”
It is pretty easy to go to a big box store and get a digital speedometer for your bike. Not only is that no fun, but the little digital display isn’t going to win you any hacker cred. [AlexGyver] has the answer. Using an Arduino and a servo he built a classic needle speedometer for his bike. It also has a digital display and uses a hall effect sensor to pick up the wheel speed. You can see a video of the project below.
[Alex] talks about the geometry involved, in case your high school math is well into your rear view mirror. The circumference of the wheel is the distance you’ll travel in one revolution. If you know the distance and you know the time, you know the speed and the rest is just conversions to get a numerical speed into an angle on the servo motor. The code is out on GitHub.
Continue reading “Arduino + Geometry + Bicycle = Speedometer”
Spirals, fractals, and even bone length proportions whisper of a consistent ratio woven into the universe. Math is hidden in the fabric of things, and when this fact is observed in art, magic happens. Professor, artist, and inventor [John Edmark] draws inspiration from geometric patterns found in nature and builds sculptures using the golden ratio as a standard for design. In this project, he expresses these characteristics through animated biomorphic zoetropes.
[John] modeled several 3D sculptures in Rhino containing similar geometric properties to those found in pinecones and palm tree fronds. As the segments grow from those objects in nature, they do so in approximately 137.5 degree intervals. This spacing produces a particular spiral appearance which [John] was aiming to recreate. To do so, he used a Python script which calculated a web of quads stretched over the surface of a sphere. From each of the divisions, stalk-like protrusions extend from the top center outward. Once these figures were 3D printed, they were mounted one at a time to the center of a spinning base and set to rotate at 550 RPM. A camera then films the shape as it’s in motion at a 1/2000 sec frame rate which captures stills of the object in just the right set of positions to produce the illusion that the tendrils are blooming from the top and pouring down the sides. The same effect could also be achieved with a strobe light instead of a camera.
[John] has more information on his instructables page. He also provides a video of this trick working with an actual artichoke; one of the living examples of the golden ratio which this project was inspired by. Thank you, [Charlie Nordstrom] for helping him document these awesome sculptures and for telling us about them!
Continue reading “Animate Your Artichoke With A Lathe And Camera”