How to determine corresponding points between two 3d coordinate systems?

Hello,

I have a prism that is expressed in two different coordinate systems. Let's say I know the coordinates of all vertices of the prism in both coordinate systems and I have a point/set of points I only know coordinates of in one system. How would I determine the coordinates of those point(s) in the second coordinate system, or vice versa? In this example, the prism is the same scale in both systems, but I'm hoping to be able to convert between the two systems even if the scales were different if that makes sense.

figure

v1 = [1 0 0; 3 0 0; 3 2 0; 1 2 0; 1 0 1; 3 0 1];
faces = [1 2 3 4; 1 2 6 5; 3 4 5 6];
patch('Faces',faces,'Vertices',v1,'FaceAlpha',0.5);

hold on

v2 = [-1 3 5; -1 5 5; -1 5 3; -1 3 3; -2 3 5; -2 5 5];
patch('Faces',faces,'Vertices',v2,'FaceAlpha',0.3)

point1 = [4 0 0];
point2 = [-1 6 5];

scatter3(4,0,0,'o');
scatter3(-1,6,5,'o');
grid on;

Answer 1

[Matt J]

Using this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/26186-absolute-orientation-horn-s-method

v1 = [1 0 0; 3 0 0; 3 2 0; 1 2 0; 1 0 1; 3 0 1];
v2 = [-1 3 5; -1 5 5; -1 5 3; -1 3 3; -2 3 5; -2 5 5];
point1 = [4 0 0];


[reg,~,Error]=absor(v1',v2','doScale',1)

reg = struct with fields:
    R: [3×3 double]
    t: [3×1 double]
    s: 1.0000
    M: [4×4 double]
    q: [4×1 double]

Error = struct with fields:
    errlsq: 1.7200e-15
    errmax: 8.8818e-16

point2=point1*reg.R'*reg.s+reg.t'

point2 = 1×3

-1.0000 6.0000 5.0000

[Yavin Alwis]

Thank you!