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.

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 26 time(s).

Best regards.
Alvaro.

I could rotate with breaking the equation. Is this natural?
rot.avi (3,007kb) downloaded 17 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.sm (23kb) downloaded 30 time(s).
projectionB.sm (35kb) downloaded 20 time(s).

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

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.

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.

The file has loaded and is working . Thank you.

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 15 time(s).



Best regards.
Alvaro.

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.


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

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 12 time(s).