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Reconstructing Escher's cubic space division

Cubic Space Division in action

POSTED BY: Silvia Hao
5 Replies

Thanks Silvia for showing how to create these impressive pictures. They remind me of post-industrial Escher influenced artwork.

POSTED BY: Michael Kelly

Fantastic! Really fun read!

POSTED BY: Sander Huisman

Wonderful work, Silvia, thanks for sharing! This reminded me a bit of Yu-Sung Chang and David G. Stork work: Warping realist art to ensure consistent perspective: A new software tool for art investigations:

There is a notebook and PDF attached at the link showing code an applications. Here is a screenshot of an app painting analysis and the abstract below it:

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ABSTRACT: We developed a software tool for art scholars studying geometrical perspective in realist art. Our software, written in Mathematica, accepts a digital image of an artwork that may not obey the rigorous rules of geometrical prospective. The user/scholar marks perspective lines on the work and then adjusts a control slider, thereby warping this image so as to ensure consistent perspective, i.e., so that perspective lines indeed meet at proper vanishing points, such vanishing points lie along a horizon lines, and so forth. Scholars can adjust the amount of warping dynamically and continuously between no warping and full geometric correction. Moreover, the user can select the polynomial order of image interpolation. In this way, the software helps reveal where and how the artist has deviated from the rigorous rules of geometrical perspective, and thus sheds light upon the artist’s compositional style. We demonstrate our method on pre-Renaissance paintings, such as works by Pietro Lorenzetti.

POSTED BY: Vitaliy Kaurov

Wow! Thank you very much, Vitaliy! I didn't know about that! I remember having learnt a lot from Yu-Sung's post years ago.

Regarding perspective views in classical arts, I'm actually quite interested in some of them with multiple projection schema, or even with "conflicted" ones. Such as Escher's Up and Down and Convex and Concave, maybe even Picasso's Brick Factory at Tortosa. It should be fun to try reproducing the ideas behind them. :)

POSTED BY: Silvia Hao

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