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Offline Ber7  
#81 Posted : 04 December 2020 15:28:28(UTC)
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Very good job, Alvaro. Now gamma is an explicit function in Azimuth-Elevation coordinates.
I will use this function as it allows you to change the viewpoint in azimuth and elevation.
Thank you very much.
Fridel.
Offline grelkin2  
#82 Posted : 12 December 2020 19:00:16(UTC)
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Hmm. Someone told about parameterize equation.
System from #78
plos.avi (3,366kb) downloaded 20 time(s).
Offline Razonar  
#83 Posted : 15 December 2020 10:47:34(UTC)
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Originally Posted by: Ber7 Go to Quoted Post
Distance and projection of a point onto a parametric surface
...


Hi. Maybe it's cosmetic, or not, but the rotation matrix don't need the last column for the 2D projection. So, you don't have to use col (X*lambda, n), just multiply by lambda. That's clean up a lot the code. Also add your azimuth and elevation, which it's 145,48 degrees, without the need of Euler angles.

ParSur.sm (83kb) downloaded 22 time(s).

Best regards.
Alvaro.
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Offline Ber7  
#84 Posted : 15 December 2020 13:25:55(UTC)
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Thank you Alvaro. Two columns instead of three in the rotation matrix make it easy to convert a 3D plot to 2D.
Offline grelkin2  
#85 Posted : 17 December 2020 07:17:49(UTC)
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I could rotate with breaking the equation. Is this natural?
rot.avi (3,007kb) downloaded 13 time(s).
Offline grelkin2  
#86 Posted : 21 December 2020 21:15:45(UTC)
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Some ellipse
Ref
el.avi (1,171kb) downloaded 9 time(s).
Offline Ber7  
#87 Posted : 18 April 2021 20:18:45(UTC)
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Originally Posted by: Ber7 Go to Quoted Post
Distance and projection of a point onto a parametric surface


ParSur.sm (75kb) downloaded 31 time(s).
ParSur.pdf (620kb) downloaded 18 time(s).


Projection of a curve onto a surface
Computing the projection of a point onto a surface is to find a closest point
on the surface, and projection of a curve onto a surface is the locus of all
points on the curve project onto the surface.
projection (7).png

projection.sm (23kb) downloaded 26 time(s).
projectionB.sm (35kb) downloaded 16 time(s).

Edited by user 18 April 2022 17:47:02(UTC)  | Reason: Not specified

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Offline loha  
#88 Posted : 19 April 2021 09:53:00(UTC)
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Wow.
In fact, this whole series on the Draghilev method, 3D to 2D projections etc. is one of the most fascinating of this forum...
Offline Ber7  
#89 Posted : 19 April 2021 19:42:04(UTC)
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Тhank you for your interest in the Topic.
Remarks:
1,Unlike the previous examples, the last file does not use dragilev's method.
2.Bar structure analogy.A heavy hoop is pivotally attached to weightless rods
that rest on an uneven surface.The slope of each bar coincides with the surface
ormal at the foothold point. Consequently, the rods perceive only normal (compressive) load.
Offline Razonar  
#90 Posted : 20 April 2021 11:57:28(UTC)
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Hi Ber. As usual, your samples are amazing.

Originally Posted by: Ber7 Go to Quoted Post
...
1,Unlike the previous examples, the last file does not use dragilev's method.


It could be interesting convert it to Dragilev's method. I don't have enough time right now.

Originally Posted by: Ber7 Go to Quoted Post

2.Bar structure analogy.A heavy hoop is pivotally attached to weightless rods
that rest on an uneven surface.The slope of each bar coincides with the surface
ormal at the foothold point. Consequently, the rods perceive only normal (compressive) load.


Oh! I try to understand that, but can take a while. Well, I understand now why it could be important. In the mean time, here a faster version, with some margin notes.

projection.sm (63kb) downloaded 19 time(s).
projection.pdf (841kb) downloaded 12 time(s).

Best regards.
Alvaro.
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Offline Ber7  
#91 Posted : 20 April 2021 13:11:58(UTC)
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Hi,Alvaro.In my version 0.99.7610 your file is not loading. I will study your program
on PDF. your wonderful examples are very expressive and aesthetic . Thank you ,Fridel.
Offline Razonar  
#92 Posted : 20 April 2021 13:45:41(UTC)
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Originally Posted by: Ber7 Go to Quoted Post
Hi,Alvaro.In my version 0.99.7610 your file is not loading. I will study your program
on PDF. your wonderful examples are very expressive and aesthetic . Thank you ,Fridel.


Hi Fridel. I check the upload file, it's ok for me. But have something wrong, because I can't upload it to the cloud version: just it do nothing. I delete the text regions with math, and substitute them with the usual math region with a line, and then can upload: https://en.smath.com/cloud/worksheet/mgSbWNUw (obviously doesn't work there because the al_nleqsol plugin fails). Here the file:

projection_without_txt_region.sm (58kb) downloaded 23 time(s).

Best regards.
Alvaro.
Offline Ber7  
#93 Posted : 20 April 2021 14:11:17(UTC)
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The file has loaded and is working . Thank you.
Offline Ber7  
#94 Posted : 25 April 2021 14:57:00(UTC)
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IHi,Alvaro .In my version 0.99.7610 green dots are displayed
as unicode characters.Until I understand what is the reason.
Fridel.


Offline Razonar  
#95 Posted : 25 April 2021 19:46:25(UTC)
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Originally Posted by: Ber7 Go to Quoted Post
IHi,Alvaro .In my version 0.99.7610 green dots are displayed
as unicode characters.Until I understand what is the reason.
Fridel.



Hi Friedel. Nice, you're looking the matrix as hexadecimal. It could be better than reading it in binary, like in the movie. That, or this bug:

test.sm (3kb) downloaded 11 time(s).

Clipboard01.jpg

Best regards.
Alvaro.
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Offline grelkin2  
#96 Posted : 28 April 2021 06:54:59(UTC)
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Draghilev method with variation. Also working superb
dragvar.avi (5,016kb) downloaded 27 time(s).
Offline алексей_алексей  
#97 Posted : 08 October 2021 22:43:15(UTC)
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Offline алексей_алексей  
#98 Posted : 05 November 2021 17:13:35(UTC)
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Maple
1. 2

Offline grelkin2  
#99 Posted : 20 November 2021 12:38:40(UTC)
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Метод чувствителен к выбору начального положения. Существуют области устойчивости и неустойчивости. Области зависят от выбранной точности. Не все координаты из областей устойчивости дают все решения при смене знака у дополнительно введенного параметра.
[ENG]
The method is sensitive to the choice of initial position. There are regions of stability and instability. The regions depend on the chosen accuracy. Not all coordinates from the regions of stability give all solutions when the sign of the additionally introduced parameter changes.
На рис. pol1 представлены две кривые и точки. Красным и зеленым цветом показаны точки начального положения для расчета пересечения по методу Драгилева. Красный цвет означает, что в результате решения значение достигли Nan (т.е. бесконечности); зеленый, что решения не достигли Nan. На рис. pol2 представлено для красной точки А расчеты с достижением Nan.
[ENG]
Figure pol1 shows the two curves and points. Red and green show the initial position points for calculating the intersection by the Dragilev method. Red indicates that the solutions reached Nan (i.e., infinity); green indicates that the solutions did not reach Nan. Figure pol2 shows for red point A the calculations with reaching Nan.
pol1.png
pol2.png
На рис. pol3 представлены три кривые и точки. Третья кривая построена через зеленую точку B. Видно что она пересекает две начальные кривые в точках пересечения 1,2,3,4
[ENG]
Figure pol3 shows three curves and points. The third curve is drawn through the green point B. You can see that it intersects the two initial curves at the intersection points 1,2,3,4
pol3.png
На анимации представлено изменение кривой 2 и области устойчивости и неустойчивости
[ENG]
The animation shows the change of curve 2 and the region of stability and instability
pol.avi (3,911kb) downloaded 8 time(s).
Offline алексей_алексей  
#100 Posted : 04 November 2022 16:29:34(UTC)
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It turned out that Draghilev's method is capable of solving Diophantine equations.
Can be viewed here.
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