Hi Maciej,
Here's a puzzle for you and others on the list. Does the usual
'co-latitude' rule for other plane sundials hold for
Oughtred/stereograph dials? I've tried a quick empirical experiment
using _Orologi Solari_ creating a vertical stereograph for my latitude
(35S) and a horizontal for the co-latitude (55N). The two seem identical
(except for the numbering of hours). It's not a 'geometric proof' but it
seems entirely reasonable.
I had meant to add in my earlier post that a few years ago I, too, wrote
a DeltaCad macro for an Oughtred dial. Unlike the elegant trigonometry
used by Valentin, I tried to replicate the protractor, compass and
straightedge methods in a traditional construction. Once it worked for
my Southern Hemisphere location, I stopped working on it, so it is
really a beta version, but I'm happy to forward it to anyone who is
interested.
best wishes,
Peter
On 2/11/2022 5:25:29, ml...@interia.pl wrote:
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Hi Peter,
Thank You for the links.
My plea concerned vertical stereographic sundials - not the horizontal
ones. I'm aware that there are a number of programs to construct
horizontal sterographic dials.
Helmut Sonderegger kindly proposed to include vertical ones in Sonne,
when he finds a time for it, and the info form Valentin was that for
the vertical plane he actually worked on a spider dial, which is most
interesting but of different type than stereographic.
But I must admit that I was unaware of construction possibilty of
vertical stereographic dials (under the name "vertical astrolabe") in
Oroligi Solari.
Though, the program doesn't give any limits for the gnomon - which in
this type of instruments is no longer that 1/2 the dial's radius, as
discussed in my paper, irrespective of walls' declination, latitude
and sundial's plane inclination. It doesn't also give options for
inclining dials. So there is some space for it to be upgraded making
this very nice typology more approachable for sundial makers. Also,
derivatives like the four-sided, "gnomon-less" stereographic vertical
sundial could be included.
Drawing by hand (with CAD) is obviously time consuming, but it allows
for understanding of geometrical relations behind and allows for
inclusion of elements not available in the custom software. So not
being a skilful programmer, I will rather stay with that ! But for the
sundial makers it is obviously easier to use a software.
Regards,
Maciej
Od: "Peter Mayer" <a1000...@adelaide.edu.au>
Do: sundial@uni-koeln.de; ml...@interia.pl;
Wysłane: 5:58 Poniedziałek 2022-10-31
Temat: Re: Vertical stereographic sundial
Hi Maciej,
Thanks for your recent post. Since no one seems to have replied to
your plea in the final paragraph for software to draw a
stereographic/Oughtred dial, here are some existing open software
options:
* Gian Casalegna's _Orologi Solari_ will draw one: azimuth:
horizontal/vertical: astrolabe
*Helmut Sondereggers' Sonne will draw at least a horizontal
stereograph: Azimuthal: Sun Altitude
* Valentin Hristov has written some elegant code for DeltaCad
:www.math.bas.bg/complan/valhrist/az-ht.bas
<http://www.math.bas.bg/complan/valhrist/az-ht.bas>
[When I tried to re-run it a few minutes ago, it now seems to be
stuck in a loop which I haven't had time to debug. I've attached
an example which I created about 4 years ago].
So: no need to create a stereograph by hand!
best wishes,
Peter
On 27/10/2022 4:02:34, ml...@interia.pl wrote:
CAUTION: External email. Only click on links or open attachments
from trusted senders.
Dear All,
As proven in a separate tread on "Sun elevation tool/
horizontoscope", stereographic projection is
a fascinating geometric construction with great potential in
gnomonics.
During last year I explored the idea of vertical stereographic
sundial and it resulted in
a paper describing several stereographic sundial types:
- vertical stereographic sundial, for walls of any declination
and for any latitude,
- four-sided stereographic vertical sundial, attractive for its
“gnomon-less” form,
- double – stereographic & polar – vertical sundial for walls of
any declination, a vertical reference to Oughtred’s horizontal
design,
- folded pocket, double stereographic & polar – vertical sundial
- inclined, proclined and polyhedral stereographic sundials
The paper can be downloaded free of charge from Cursiva
publishers website:
http://cursiva.pl/e-ksiegarnia/vertical-stereographic-sundial-properties-construction-and-related-instruments/
<http://cursiva.pl/e-ksiegarnia/vertical-stereographic-sundial-properties-construction-and-related-instruments>
or from Academia.edu website:
https://www.academia.edu/88820719/Vertical_stereographic_sundial_Properties_construction_and_related_instruments
<https://www.academia.edu/88820719/Vertical_stereographic_sundial_Properties_construction_and_related_instruments>
Have fun with it !
Vertical stereographic sundials offer plenty of possibilities for
sundial makers
and I believe might be a very interesting addition to existing
sundial types.
As the geometric construction of vertical stereographic sundials
with CAD software is time-consuming,
it would be great to include it in existing sundial design software.
I kindly ask sundial list members running such software, please
consider it !
Regards,
Maciej Lose
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The University of Adelaide, AUSTRALIA 5005
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