How do i...how can I create an arc path from 3 point (p1-->p2-->p3) in 3D space?

I want to create an Arc path over 3 points in 3D space. I decided to draw a circle over them and then extract sector from p1 to p3 that passes through P2. 
circle equation is: 

    fc = @(a) center + cos(a).*(q1-center) + sin(a).*(q2-center);

in 3D plane for each point on the circle!

What I have tried:

<pre>I use this code but it did not extract sector from p1-->p2-->p3 !

    %Use n1 x n2 (where 'x' means the cross product) as the z-axis of the local CS
    n12 = cross((p1 - center),(p2 - center)); 
    n23 = cross((p3 - center),(p2 - center));
    n13 = cross((p3 - center),(p1 - center));
    n = [n12, n23, n13];
    %sign(n(1,:)--> find tow Orthogonal vectors, means cross product==1,
    %n./sign(n(1,:))--> make zero value column to NAN value!
    n = n./sign(n(1,:));
    idx = find(~all(isnan(n)),2);
    n = n(:,idx(1));
    n0 = n / norm(n);
    % Vectors to describe the plane, idx--> The index specifier is one of the input points
    q1 = P(:,idx(1));
    %Use (n1 x n2) x n1 as the y-axis of the local CS.
    q2 = center + cross(n0,(p1-center).').';
    %% Function to compute circle point at given angle
    fc = @(a) center + cos(a).*(q1-center) + sin(a).*(q2-center);
    %% Get angles of the original points for the circle formula
    a1 = angleFromPoint(center,p1,q1,q2);
    a2 = angleFromPoint(center,p2,q1,q2);
    a3 = angleFromPoint(center,p3,q1,q2);
    function ang = angleFromPoint(center,p,q1,q2)
    % Get the circle angle for point 'p'
    comp = @(a,b) dot(a,b)/norm(b);
    ang = atan( comp(p-center,q2-center)/comp(p-center,q1-center) );
    end

[![the output is:][1]][1]


  [1]: https://i.stack.imgur.com/QodeG.png

as you see, the direction of sector in output is not true! the direction is the opposite! Can anyone guide me? thanks a lot!