I am trying to set a number of vertex to define a very established path. The problem is that the nurbs spline that results from these vertex do not pass the control points. I'd need this spline to actually pass through the control points and I wondered if you know how this can be achieved? The image below, the line in red, represents what I want to achieve. :) Thank you so much.
To my best understanding NURBS curves do not precisely support what you wish to achieve and I could not find any options that would 100% bring the solution you wish for.
if it's necessary that the spline must cross the vertices, you may want to try Bezier curves instead of NURBS curves. While you will lose the convenience of the NURBS curves (Bezier curves being a bit more tedious to edit), you can be sure that the curve crosses the vertex.
If you don't want to use Beziers, but want to stay in NURBS curves instead, you can select the curve and navigate to "Active Spline" settings. From there you can reduce "Order U" to 2 and increase "Resolution U" to 12 or above, which will push the curve closer towards its control points. The trade-off is that you also lose the curvature from the curve itself, but you will have the curve following the control points.
Curves that run through moved control points...
This is basic and works in vers 2.77 so I imagine it should still work in 2.8+
To have your 'curve' pass through it's control points, as with a vector drawing, simply convert a Nurbs path to mesh and back again with Alt-C. If the path has already been curved the result will leave you with a multitude of control points but without Bezier properties.
They can however still be used to draw Bezier-like curves in Edit mode by enabling Proportional editing and dragging control points.
Shapekeys will animate these. In vers 2.77 animating control points with hooks can't use proportional editing and that makes things a lot harder.