The “meschers” tool visualizes and modifies “physically impossible” objects

Mc Escher’s work is a bridge in a world of optical illusions defying depth, with “impossible objects” which violate the laws of physics with convoluted geometries. What you perceive his illustrations depends on your point of view – for example, a person who apparently works upstairs can go down the steps if you tilt the head laterally.

IT scientists and designers can recreate these 3D illusions, but only by folding or cutting a real shape and positioning it from a particular angle. However, this bypass has drawbacks: the modification of the softness or lighting of the structure will expose that it is not really an optical illusion, which also means that you cannot precisely solve geometry problems.

Researchers from the IT and artificial MIT (CSAIL) computer laboratory have developed a unique approach to represent “impossible” objects in a more versatile manner. Their “meschers” tool converts 3D images and models into 2.5 -dimensional structures, creating representations of the type of things like windows, buildings and even donuts. The approach helps users to rehabilitation, to smooth and study unique geometries while preserving their optical illusion.

This tool could help researchers in geometry to calculate the distance between two points on an impossible curved surface (“geodesic”) and simulating how heat dissipates on it (“heat diffusion”). This could also help artists and computer scientists to create breaking conceptions in physics in several dimensions.

Principal author and doctorate of MIT. The student Ana Dodik aims to design infographic tools which are not limited to the replication of reality, allowing artists to express their intention independently of the realization of a form in the physical world. “Using meschers, we unlocked a new class of shapes so that artists can work on the computer,” she said. “They could also help scientists from perception to understand the point where an object becomes really impossible.”

Dodik and his colleagues will present their article during the Siggraph conference held in Vancouver from August 10 to 14. It is published in ACM transactions on graphicsAnd the full text is available on GitHub.

Make it possible impossible possible

Impossible objects cannot be fully reproduced in 3D. Their constituent parts often seem plausible, but these parts do not stick properly when assembled in 3D. But what can be imitated by calculation, as Csail researchers have discovered it is the process of the way we perceive these forms.

Take the Penrose triangle, for example. The object as a whole is physically impossible because the depths do not “add up”, but we can recognize the 3D forms of the real world (like its three corners in the form of L). These smaller regions can be carried out in 3D – a property called “local coherence” – but when we try to assemble them together, they do not form a coherent world form.

The meschers approach locally coherent regions of models without forcing them to be coherent worldwide, bringing together an Escher structure. Behind the scenes, the meschers represent impossible objects as if we knew their X and Y coordinates in the image, as well as differences in the Z (depth) coordinates between the neighboring pixels; The tool uses these differences in depth to reason on impossible objects indirectly.

Many uses of meschers

In addition to making objects impossible, meschers can subdivide their structures into smaller shapes for more precise geometry calculations and smoothing operations. This process allowed researchers to reduce visual imperfections of impossible forms, such as a red heart contour, they lightened.

The researchers also tested their tool on an “impossible”, where a bagel is shaded in a physically impossible way. Meschers helped Dodik and his colleagues simulate heat diffusion and calculate geodesic distances between different points of the model.

“Imagine that you are an ant that crosses this bagel, and you want to know how long it will take you to cross, for example,” explains Dodik. “In the same way, our tool could help mathematicians to analyze the underlying geometry of close-up forms, a bit like the way we study real.”

Like a magician, the tool can create optical illusions from otherwise practical objects, which facilitates the creation of impossible objects. It can also use “reverse” tools to convert drawings and images of impossible objects into high -dimension conceptions.

“Meschers shows how the infographic tools do not have to be forced by the rules of physical reality,” said the main author Justin Solomon, an associate professor of electrical and computer engineering and leader of the CSAIL Geometric Data Processing Group. “Incredibly, artists using meschers can reason on the forms that we will never find in the real world.”

Meschers can also help IT artists refine the shade of their creations, while preserving an optical illusion. This versatility would allow creatives to change the lighting of their art to represent a greater variety of scenes (such as a sunrise or sunset) – as the meschers demonstrate by razing a dog model on a roller board.

Despite his versatility, Meschers is only the start of Dodik and his colleagues. The team plans to design an interface to make the tool easier to use while building more elaborate scenes. They also work with scientists from perception to see how the IT tool can be used more widely.

This story is republished with the kind authorization of Mit News (Web.mit.edu/newsoffice/), a popular site that covers news of research, innovation and MIT teaching.