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  1. #1
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    Antonio's Sketchbook - Spherical perspectives et al

    Hi,

    I do mathematics and I draw - sometimes simultaneously. I've been drawing and researching spherical perspectives lately. They look like this:

    Name:  cubic_room_s.jpg
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    This is a total (360º) spherical perspective drawing of a cubical room seen from the center. It is drawn in ruler and compass and colored in sketchbook pro.

    People know how to draw these perspectives by ruler and compass since the 1960s, but only up to 180º (so-called "5-point perspectives"). This was a work by two french researchers (Barre and Flocon). When people wanted to do a 360º degree view ("6-point perspective") they just did two of those separately. That's what Dick Termes (of thermesphere fame) used to do in his book, for instance.

    What I did was to generalize the work of these people to 360º so as to draw a full view (by hand - computers could do it easily of course) into a single round canvas, and not just gridding an guessing, but finding all the vanishing points, just as in classical perspective (here's a picture of my building's stairway with some vanishing points shown):

    Name:  stairs_xs.jpg
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    I described the method in this paper:

    Ruler, compass and nail: Constructing a total spherical perspective, Journal of Mathematics and the Arts, 2018

    (by the way, the journal made the paper free access during august, so download the pdf today if you think you'll have use for it later)

    The paper is a bit too mathematical (also, articles have page limits!), so I wanted to do some easier tutorials and drawing experiments to suplement it ; mostly drawings and videos with commented examples, relating special tricks plus the difficulties I still find in doing this (I'm definitely still learning and struggling). I though it might fit well in a conceptart sketchbook, so I finally opened one. We'll see how this goes. The purpose will be to dump the formality of drawings such as these (view of the reading room of the british museum)

    Name:  spherical perspective of brit museum_s2.jpg
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    ...and get more and more to do simpler drawings such as the one below (crop of a 360º of the af chapman ship/hostel) where measurements are inexact, drawn casually on location, but still loosely grounded on the principles of the perspective.

    Name:  af deck scan s.jpg
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    Anyway, I think this is probably enough for a first post. Hope some of you will find this interesting and/or useful.

    All the best,
    António


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  4. #2
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    Your sketches are so amazing! The perspective looks so good, also very intricate
    Welcome to CA.org!

  5. #3
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    Thank you!
    I tend to be too intricate, in fact, and then I take too long to get going. I'll do my best to get some tutorials up, ASAP, even if I have to be more sketchy about it

  6. #4
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    Here is a step-by-step (well, some steps anyway) of an immersive 360-degree drawing of the inner courtyard of ISEL's school of engineering in Lisbon, Portugal.



    This one is done in equirectangular spherical perspective. It is still a total spherical perspective but renders onto a rectangle instead of a circle. You probably have seen it before since it is the projection most commonly used by 360-degree cameras. It turns out that this perspective can also be done by hand (ruler, compass and a protractor). I have solved that here (this article is free access forever unlike the previous one). After rendering you can send these drawings to flickr and see them "from inside" as you do with 360-photos and video. Basically what the software does is this: it wraps the drawing back onto the sphere surface and puts you in the center of the sphere looking out. Just imagine being in the center of a termesphere, but done virtually instead of physically (less charming but far more convenient).

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  8. #5
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    Name:  ScanImage001_proc.jpg
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    Here's a quick sketch of the Santa Justa elevator in Lisbon, Portugal. It's a bit of a freestyle perspective loosely based on the rules of my fisheye perspective paper at the JMA (know the rules, break the rules ).

  9. #6
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    Nice work. Interesting! Gonna have to try some of this.Especially like that last one.

  10. #7
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    Please do and let me know the result! By the way, you can still read the article for free here (hope it helps):

    https://www.tandfonline.com/eprint/Z...Z6Tk2x4V9/full

    (the publisher only allows 50 free downloads from this link so get it and save it to your disk while it works)

    Best of luck,
    A.

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  12. #8
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    A whimsical one, for fun:
    Name:  ScanImage004_proc.jpg
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  13. #9
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    Very interesting and full of character - I especially like the tall ship drawing in your first post. Nicely done - please keep sharing!

  14. #10
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    Thank you, Dave!

  15. #11
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    Sometimes you only have a few minutes. Quick curvilinear perspective of Atrium Saldanha (a mall in Lisbon, Portugal) in my pocket notebook while waiting for a friend.
    Name:  08122018saldanhauto.jpg
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