@zipit Thanks,this paper Parallel Transport Approach to Curve Framing
I will follow your suggestion to explore RMF. It may be that the language barrier prevents us from communicating well, but I still get a lot of help from your answer. I use Google translate

@zipit Hi, I came back a bit late.
I read the paper and watched the video. The video is understandable and the paper is still obscure. The effect of Parallel Transport is similar to some functions of c4d python utils.SplineHelp ().
The Parallel Transport method is useful, but using the control object to control the rotation of the joint (rotate around z) is still a bit unclear (in the picture below). The paper seems to mention some solutions such as (Animating rotation with quaternion curves) and (Fiber bundle twist reduction.)

@zipit Thank you for your patient reply, it really helped me a lot. I need to learn about PTF,This is a new point of knowledge for me, and I need some time to understand how it works. I will update the progress of the solution here.
Yes,rotation is banking ,in my method it points to the next object in the chain of objects，not use tangent

@r_gigante @zipit
The detailed explanation is shown below
“up interpolattion”


Try use "spline trail"

I read some papers, but always been very slow, just only expanded know, such as Frenet–Serret formulas etc. But I did not directly find a better way to replace my current method, and I have been looking for it.

Computation of Rotation Minimizing Frames This seems to be a good paper, I will read it carefully.

@m_magalhaes
ok,It's a bit complicated

Hello,
I rewritten spline ik due to some requirements, but I was stuck on the problem of rotation. I have tried to use up interpolation or spline trail, but there will still be their own problems. I also searched a lot paper, but did not find a clear solution, do you have any good ideas,or are these papers recommended?

welcome any ideas

@m_magalhaes Thanks for the explanation, can help me better understand how it works！

this version code can draw point but not be selected

    DRAWRESULT myplugin::Draw(BaseObject* op, DRAWPASS drawpass, BaseDraw* bd, BaseDrawHelp* bh)
    {
        if (drawpass != DRAWPASS::OBJECT)
            return SUPER::Draw(op, drawpass, bd, bh);
        BaseContainer* data = op->GetDataInstance();
        Float32 size = 10.0;
        Vector color = Vector(1.0);
        Vector pos = Vector();
        const Matrix& mg = bh->GetMg();
        const Int32 cnt = 1;
        bd->SetMatrix_Matrix(op, mg);
        bd->SetPen(color);
        bd->SetPointSize(size);
        bd->DrawPointArray(cnt,&static_cast<Vector32>(pos));
        return SUPER::Draw(op, drawpass, bd, bh);
    }

this version can draw and can be selected(only change return to --> return DRAWRESULT::OK)

    DRAWRESULT myplugin::Draw(BaseObject* op, DRAWPASS drawpass, BaseDraw* bd, BaseDrawHelp* bh)
    {
        if (drawpass != DRAWPASS::OBJECT)
            return SUPER::Draw(op, drawpass, bd, bh);
        BaseContainer* data = op->GetDataInstance();
        Float32 size = 10.0;
        Vector color = Vector(1.0);
        Vector pos = Vector();
        const Matrix& mg = bh->GetMg();
        const Int32 cnt = 1;
        bd->SetMatrix_Matrix(op, mg);
        bd->SetPen(color);
        bd->SetPointSize(size);
        bd->DrawPointArray(cnt,&static_cast<Vector32>(pos));
        //
        return DRAWRESULT::OK;
    }

@m_magalhaes I found the reason！

I used the example code like Draw manual

    return SUPER::Draw(op, drawpass, bd, bh);

if use return DRAWRESULT::OK; it can be selected by selection tool!

    return DRAWRESULT::OK;

it work,but why?

@m_magalhaes Thank you, this idea is good, I will to try it.

Below I show examples of drawing using the python plug-in and C ++ plug-in in the picture. I am not very clear why they have the difference between drawing can be selected (python) and drawing cannot be selected (c ++).

@PluginStudent Thanks for you help.

(initial() ->corrected -> Init() )

c++ ,i use DrawPointArray() to draw point,because i want to set custom color and point size.

in my python plugin use DrawPoints() to draw point in view,when selection tool select point(draw in view),the
plug_in Object can be selected.

just like null object(display can be selected)