How to plot a surface tangent to many points, or the smallest surface which covers all the points?

I want to plot a surface which covers many points in space.

The points are the solutions of a differential equation system.

I have tried different ways including the following:

1- I used meshgrid() and griddata() functions to generate uniformly distributed points and plot them using mesh() function. However, the figure was not so good.

2- In the same approach, I used the scatterInterpolant() function instead of griddata(), but the figure was worse than the first method.

3- I used convhull() and alphaShape() functions which worked in some cases, but in some others failed. As an example, I attach two figures here of the points and the obtained figure from this third method.

Moreover, in the cases in which the third idea works, I have problems with removing the black lines in the plotted surface. As you may see in the attached photo, there are many black lines in the plotted surface.

Any idea or help would be appreciated