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Comic relief... The trisector...

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  Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-17 15:16 -0700
    Re: Comic relief... The trisector... Max <maxturv26@gmx.net> - 2021-09-18 16:31 +0200
      Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-19 13:32 -0700
        Re: Comic relief... The trisector... Max <maxturv26@gmx.net> - 2021-09-19 22:42 +0200
          Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-19 20:07 -0700
            Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-19 20:10 -0700
        Re: Comic relief... The trisector... Phil Carmody <pc+usenet@asdf.org> - 2021-09-20 16:58 +0300
          Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-22 12:31 -0700
    Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-19 20:13 -0700
    Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-19 23:56 -0700
      Re: Comic relief... The trisector... "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2021-09-22 21:53 -0700

#50011 — Comic relief... The trisector...

The trisector master recently received a massive head wound... It thinks 
this crap is a solution. I coded this up to make you laugh, joke around. 
Or, is it so stupid, it makes you accidentally spill coffee on your 
keyboard? YIKES. Beware.

The, mess, lol:
_____________________________
// LOL! Just a joke, jest. :^D
namespace ct_trisect_LOL
{
     void do_it_lol(
         ct::plot::cairo::plot_2d& plot,
         glm::vec2 p0,
         float angle
     ) {
         glm::vec2 p0_circle = {
             glm::cos(0), glm::sin(0)
         };

         glm::vec2 p1_circle = {
             glm::cos(angle), glm::sin(angle)
         };


         glm::vec2 dif = p1_circle - p0_circle;

         glm::vec2 dif_p0 = p0_circle + dif / 3.f;
         glm::vec2 dif_p1 = p1_circle - dif / 3.f;

         plot.line(p0, p0_circle, CT_RGBF(1, 0, 0), 5.f);
         plot.line(p0, p1_circle, CT_RGBF(0, 1, 0), 5.f);


         plot.line(p0_circle, p1_circle, CT_RGBF(0, 0, 1), 5.f);

         plot.circle(dif_p0, .02, CT_RGBF(1, 1, 0));
         plot.circle(dif_p1, .02, CT_RGBF(0, 1, 1));


         plot.line(p0, dif_p0, CT_RGBF(1, 1, 1), 5.f);
         plot.line(p0, dif_p1, CT_RGBF(1, 1, 1), 5.f);
     }



     void manifest(
         ct::plot::cairo::plot_2d& plot
     ) {
         std::cout << "ct_trisect_LOL::manifest()\n";

         do_it_lol(plot, { 0, 0 }, CT_PI / 4.f);
     }
}
_____________________________

Here is a rendering:

https://i.ibb.co/nn83q6g/ct-tri-shit-lol.png

I am wondering if this is worth a laugh at all...

YIKES! ;^)

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#50031

On 18.09.21 00:16, Chris M. Thomasson wrote:
> The trisector master recently received a massive head wound... It thinks 
> this crap is a solution. I coded this up to make you laugh, joke around. 
> Or, is it so stupid, it makes you accidentally spill coffee on your 
> keyboard? YIKES. Beware.
> 
> The, mess, lol:
> _____________________________
> // LOL! Just a joke, jest. :^D
> namespace ct_trisect_LOL
> {
>      void do_it_lol(
>          ct::plot::cairo::plot_2d& plot,
>          glm::vec2 p0,
>          float angle
>      ) {
>          glm::vec2 p0_circle = {
>              glm::cos(0), glm::sin(0)
>          };
> 
>          glm::vec2 p1_circle = {
>              glm::cos(angle), glm::sin(angle)
>          };
> 
> 
>          glm::vec2 dif = p1_circle - p0_circle;
> 
>          glm::vec2 dif_p0 = p0_circle + dif / 3.f;
>          glm::vec2 dif_p1 = p1_circle - dif / 3.f;
> 
>          plot.line(p0, p0_circle, CT_RGBF(1, 0, 0), 5.f);
>          plot.line(p0, p1_circle, CT_RGBF(0, 1, 0), 5.f);
> 
> 
>          plot.line(p0_circle, p1_circle, CT_RGBF(0, 0, 1), 5.f);
> 
>          plot.circle(dif_p0, .02, CT_RGBF(1, 1, 0));
>          plot.circle(dif_p1, .02, CT_RGBF(0, 1, 1));
> 
> 
>          plot.line(p0, dif_p0, CT_RGBF(1, 1, 1), 5.f);
>          plot.line(p0, dif_p1, CT_RGBF(1, 1, 1), 5.f);
>      }
> 
> 
> 
>      void manifest(
>          ct::plot::cairo::plot_2d& plot
>      ) {
>          std::cout << "ct_trisect_LOL::manifest()\n";
> 
>          do_it_lol(plot, { 0, 0 }, CT_PI / 4.f);
>      }
> }
> _____________________________
> 
> Here is a rendering:
> 
> https://i.ibb.co/nn83q6g/ct-tri-shit-lol.png
> 
> I am wondering if this is worth a laugh at all...
> 
> YIKES! ;^)


:-)

Good job! You found a pretty approximation there. ;-)

Cheers,

Max


P.S.: Pi = 3    ;-)

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#50049

On 9/18/2021 7:31 AM, Max wrote:
> On 18.09.21 00:16, Chris M. Thomasson wrote:
>> The trisector master recently received a massive head wound... It 
>> thinks this crap is a solution. I coded this up to make you laugh, 
>> joke around. Or, is it so stupid, it makes you accidentally spill 
>> coffee on your keyboard? YIKES. Beware.
>>
>> The, mess, lol:
>> _____________________________
>> // LOL! Just a joke, jest. :^D
>> namespace ct_trisect_LOL
>> {
>>      void do_it_lol(
>>          ct::plot::cairo::plot_2d& plot,
>>          glm::vec2 p0,
>>          float angle
>>      ) {
>>          glm::vec2 p0_circle = {
>>              glm::cos(0), glm::sin(0)
>>          };
>>
>>          glm::vec2 p1_circle = {
>>              glm::cos(angle), glm::sin(angle)
>>          };
>>
>>
>>          glm::vec2 dif = p1_circle - p0_circle;
>>
>>          glm::vec2 dif_p0 = p0_circle + dif / 3.f;
>>          glm::vec2 dif_p1 = p1_circle - dif / 3.f;
>>
>>          plot.line(p0, p0_circle, CT_RGBF(1, 0, 0), 5.f);
>>          plot.line(p0, p1_circle, CT_RGBF(0, 1, 0), 5.f);
>>
>>
>>          plot.line(p0_circle, p1_circle, CT_RGBF(0, 0, 1), 5.f);
>>
>>          plot.circle(dif_p0, .02, CT_RGBF(1, 1, 0));
>>          plot.circle(dif_p1, .02, CT_RGBF(0, 1, 1));
>>
>>
>>          plot.line(p0, dif_p0, CT_RGBF(1, 1, 1), 5.f);
>>          plot.line(p0, dif_p1, CT_RGBF(1, 1, 1), 5.f);
>>      }
>>
>>
>>
>>      void manifest(
>>          ct::plot::cairo::plot_2d& plot
>>      ) {
>>          std::cout << "ct_trisect_LOL::manifest()\n";
>>
>>          do_it_lol(plot, { 0, 0 }, CT_PI / 4.f);
>>      }
>> }
>> _____________________________
>>
>> Here is a rendering:
>>
>> https://i.ibb.co/nn83q6g/ct-tri-shit-lol.png
>>
>> I am wondering if this is worth a laugh at all...
>>
>> YIKES! ;^)
> 
> 
> :-)
> 
> Good job! You found a pretty approximation there. ;-)
[...]

:^D

Its radically simple and seems to approximate kind of "decent'ish" for 
angles [0...pi/2]. Here is one for .5 radians:

https://i.ibb.co/JxM8M0k/ct-tri-shit-lol-p1.png

It seems to do a much better job for small angles... ;^)

Shit hits the fan for larger angles. Here is 2.5 radians:

https://i.ibb.co/xs6gpjK/ct-tri-shit-lol-p2.png

Oh wow! Shit happens. LOL! ;^)


> P.S.: Pi = 3    ;-)
> 

;^)

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#50050

On 19.09.21 22:32, Chris M. Thomasson wrote:

[....]

> 
> Its radically simple and seems to approximate kind of "decent'ish" for 
> angles [0...pi/2]. Here is one for .5 radians:
> 
> https://i.ibb.co/JxM8M0k/ct-tri-shit-lol-p1.png
> 
> It seems to do a much better job for small angles... ;^)

No kidding? ;-)

> 
> Shit hits the fan for larger angles. Here is 2.5 radians:
> 
> https://i.ibb.co/xs6gpjK/ct-tri-shit-lol-p2.png
> 
> Oh wow! Shit happens. LOL! ;^)
> 
> 
>> P.S.: Pi = 3    ;-)
>>
> 
> ;^)
> 

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#50052

On 9/19/2021 1:42 PM, Max wrote:
> On 19.09.21 22:32, Chris M. Thomasson wrote:
> 
> [....]
> 
>>
>> Its radically simple and seems to approximate kind of "decent'ish" for 
>> angles [0...pi/2]. Here is one for .5 radians:
>>
>> https://i.ibb.co/JxM8M0k/ct-tri-shit-lol-p1.png
>>
>> It seems to do a much better job for small angles... ;^)
> 
> No kidding? ;-)
[...]

:^D

Fwiw, I thought it would be fun to use circle intersections to bisect 
the angle. Also, it happens to be compatible with my experimental circle 
intersection fractal. I posted a link to my fractal plotted on the 
bisection diagram; its the third one:

(.5 radians)
https://i.ibb.co/pyj2XGR/ct-bi-p0.png

(2.5 radians)
https://i.ibb.co/yVDG8DY/ct-bi-p1.png

(2.5 radians with my fractal)
https://i.ibb.co/rfzmwzH/ct-bi-p2.png

Just having some fun. :^)


Fwiw, my fractal was named Thomasson's Turbulent Rings by a friend of mine.

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#50053

On 9/19/2021 8:07 PM, Chris M. Thomasson wrote:
> On 9/19/2021 1:42 PM, Max wrote:
>> On 19.09.21 22:32, Chris M. Thomasson wrote:
>>
>> [....]
>>
>>>
>>> Its radically simple and seems to approximate kind of "decent'ish" 
>>> for angles [0...pi/2]. Here is one for .5 radians:
>>>
>>> https://i.ibb.co/JxM8M0k/ct-tri-shit-lol-p1.png
>>>
>>> It seems to do a much better job for small angles... ;^)
>>
>> No kidding? ;-)
> [...]
> 
> :^D
> 
> Fwiw, I thought it would be fun to use circle intersections to bisect 
> the angle. Also, it happens to be compatible with my experimental circle 
> intersection fractal. I posted a link to my fractal plotted on the 
> bisection diagram; its the third one:
> 
> (.5 radians)
> https://i.ibb.co/pyj2XGR/ct-bi-p0.png

I cannot remember if this is actually .5 radians! I got lost in my own 
code. However, here is .5 radians for sure, with my fractal plotted on it:

https://i.ibb.co/zFKrFqf/ct-bi-p3.png

> 
> (2.5 radians)
> https://i.ibb.co/yVDG8DY/ct-bi-p1.png
> 
> (2.5 radians with my fractal)
> https://i.ibb.co/rfzmwzH/ct-bi-p2.png
> 
> Just having some fun. :^)
> 
> 
> Fwiw, my fractal was named Thomasson's Turbulent Rings by a friend of mine.

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#50059

"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
> On 9/18/2021 7:31 AM, Max wrote:
>> On 18.09.21 00:16, Chris M. Thomasson wrote:
>>> https://i.ibb.co/nn83q6g/ct-tri-shit-lol.png

>> Good job! You found a pretty approximation there. ;-)

> Its radically simple and seems to approximate kind of "decent'ish" for
> angles [0...pi/2]. Here is one for .5 radians:
>
> https://i.ibb.co/JxM8M0k/ct-tri-shit-lol-p1.png
>
> It seems to do a much better job for small angles... ;^)
>
> Shit hits the fan for larger angles. Here is 2.5 radians:
>
> https://i.ibb.co/xs6gpjK/ct-tri-shit-lol-p2.png

Of course, this means that with just a single iterative step it can be
incredibly accurate. First, by eyeballing or any technique, construct
any angle that is a goodish approximation to theta/3, say a_0. Now
3.a_0 ~= theta, and therefore delta_0 = |3.a_0 - theta| is small.
Trisect delta_0 using your technique. Add or subtract this new sliver
from your original a_0 approximation to get a_1, a better approximation.

If this is too complicated, there's an even simpler hack - you never
need to trisect obtuse angles, as you can just trisect their complement
(this is just a special case of the above where you chose a_0 = pi/3).
And it's no great leap to retrict yourself to only having to consider
angles in [0..pi/4].

I'd be willing to bet this converges very quickly, as I said at the
start, probably just one iteration is enough for government work.
Maybe you'd like to code it up and plot a few images?

Phil
-- 
We are no longer hunters and nomads. No longer awed and frightened, as we have
gained some understanding of the world in which we live. As such, we can cast
aside childish remnants from the dawn of our civilization.
-- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/

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#50086

On 9/20/2021 6:58 AM, Phil Carmody wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>> On 9/18/2021 7:31 AM, Max wrote:
>>> On 18.09.21 00:16, Chris M. Thomasson wrote:
>>>> https://i.ibb.co/nn83q6g/ct-tri-shit-lol.png
> 
>>> Good job! You found a pretty approximation there. ;-)
> 
>> Its radically simple and seems to approximate kind of "decent'ish" for
>> angles [0...pi/2]. Here is one for .5 radians:
>>
>> https://i.ibb.co/JxM8M0k/ct-tri-shit-lol-p1.png
>>
>> It seems to do a much better job for small angles... ;^)
>>
>> Shit hits the fan for larger angles. Here is 2.5 radians:
>>
>> https://i.ibb.co/xs6gpjK/ct-tri-shit-lol-p2.png
> 
> Of course, this means that with just a single iterative step it can be
> incredibly accurate. First, by eyeballing or any technique, construct
> any angle that is a goodish approximation to theta/3, say a_0. Now
> 3.a_0 ~= theta, and therefore delta_0 = |3.a_0 - theta| is small.
> Trisect delta_0 using your technique. Add or subtract this new sliver
> from your original a_0 approximation to get a_1, a better approximation.

Sounds good. I should have more time tonight or tomorrow to give it a go.


> If this is too complicated, there's an even simpler hack - you never
> need to trisect obtuse angles, as you can just trisect their complement
> (this is just a special case of the above where you chose a_0 = pi/3).
> And it's no great leap to retrict yourself to only having to consider
> angles in [0..pi/4].
> 
> I'd be willing to bet this converges very quickly, as I said at the
> start, probably just one iteration is enough for government work.
> Maybe you'd like to code it up and plot a few images?

I will. Also, I was thinking of a way to get a loose approximation using 
only a compass. It involves drawing at a constant speed for three units 
of time. Say, seconds. So, place the compass, and start slowly rotating 
it as you count to three. Now, we have an angle. Then, repeat the 
process using the same speed. At one, put a mark using the compasses 
nib. At two put another mark. The angle is trisected at a certain 
approximation... Sound kosher? lol.

To do this for any given angle, try to rotate the compass at a speed 
such that it goes from start to end in 3 seconds. That should give an 
approximation.

;^)

Start at the beginning. This is zero time. Start rotating. At one second 
place a mark. At two seconds place a mark. At the third second, mark and 
stop.

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#50054

On 9/17/2021 3:16 PM, Chris M. Thomasson wrote:
> The trisector master recently received a massive head wound... It thinks 
> this crap is a solution. I coded this up to make you laugh, joke around. 
> Or, is it so stupid, it makes you accidentally spill coffee on your 
> keyboard? YIKES. Beware.

Zooming out on the bisector using circle intersections, and plotting my 
fractal on said intersections:

https://i.ibb.co/nwkMhpb/ct-bi-p4.png

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#50056

On 9/17/2021 3:16 PM, Chris M. Thomasson wrote:
> The trisector master recently received a massive head wound... It thinks 
> this crap is a solution. I coded this up to make you laugh, joke around. 
> Or, is it so stupid, it makes you accidentally spill coffee on your 
> keyboard? YIKES. Beware.
[...]
> I am wondering if this is worth a laugh at all...
> 
> YIKES! ;^)

Applied the seed circles that bisect an angle using intersecting circles 
to my hyper experimental vector field fractal growth algorihtm, and go this:

https://fractalforums.org/gallery/1612-200921082326.png

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#50095

On 9/19/2021 11:56 PM, Chris M. Thomasson wrote:
> On 9/17/2021 3:16 PM, Chris M. Thomasson wrote:
>> The trisector master recently received a massive head wound... It 
>> thinks this crap is a solution. I coded this up to make you laugh, 
>> joke around. Or, is it so stupid, it makes you accidentally spill 
>> coffee on your keyboard? YIKES. Beware.
> [...]
>> I am wondering if this is worth a laugh at all...
>>
>> YIKES! ;^)
> 
> Applied the seed circles that bisect an angle using intersecting circles 
> to my hyper experimental vector field fractal growth algorihtm, and go 
> this:
> 
> https://fractalforums.org/gallery/1612-200921082326.png

fun with color! Now, it seems like I can see more detail from 
generations one and two:

gen 1: https://fractalforums.org/gallery/1612-230921062812.png

gen 2: https://fractalforums.org/gallery/1612-230921065122.png

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