Rigid body rotation of a set of points to align 3 on a plane

Hello All I have a set of points (X,Y,Z). I want to pick 3 points which have the smallest z co-ordinate and rotate all the points I have so that these 3 points lie on the X-Y plane or a plane parallel to it.

I have defined the XYZ triplet as variable XYZ XYZ=[X Y Z];

Next I translate the points so that the lowest point is at the origin. XYZ_sort=sortrows(XYZ,3); XYZ_sort(:,1)=XYZ_sort(:,1)-XYZ_sort(1,1); XYZ_sort(:,2)=XYZ_sort(:,2)-XYZ_sort(1,2); XYZ_sort(:,3)=XYZ_sort(:,3)-XYZ_sort(1,3);

Next I find the rotation matrix to rotate these points to align them with the X-Y plane. (Found this piece of code online) w = cross(XYZ_sort(2,:)-XYZ_sort(1,:),XYZ_sort(3,:)-XYZ_sort(1,:)); w = w/norm(w); R = [null(w),w.']; if det®<0, R(:,1:2) = R(:,2:-1:1); end

Now I multiply my original set of data with this rotation matrix XYZ_R=XYZ_sort*R;

It does align the 3 points so that they are on X-Y plane but the rest of the points do not seem to be rotated by same order. Can someone tell me what I am doing wrong and if they have an alternative way of doing this.

Thanks

Aditya