# How to Interpolate between ROIs in 3D space

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Kyeong Min Kim on 8 Sep 2021
Edited: darova on 8 Sep 2021
In my code, I want to make code like "Manully Interpolate" in "Volume segmenter app".
The problem occurred when I proceeded in the following order.
1. Draw a star-shaped ROI on the 250th image and a 260th square-shaped ROI.
2. Use the "griddata" command to interpolate between ROIs.
3. In the 250th image, the star-shaped ROI in the before is transformed the pentagonal shape.
I want the star-shaped ROI in the 250th image become a square-shaped ROI as it goes to the 260th image.
My test code:
i=250;
[S.x,S.y,S.z] = ind2sub(size(VOI(:,:,i)),find(VOI(:,:,i) == 1));
S.z(:,1) = i;
i=260;
[E.x,E.y,E.z] = ind2sub(size(VOI(:,:,i)),find(VOI(:,:,i) == 1));
E.z(:,1) = i;
R.x = [S.x;E.x];
R.y = [S.y;E.y];
R.z = [S.z;E.z];
[M.Xq,M.Yq,M.Zq] = meshgrid(1:1:size(VOI,1),1:1:size(VOI,2),250:1:260);
Vq = griddata(R.x,R.y,R.z,ones(size(R.z)),M.Xq,M.Yq,M.Zq);
Vq(Vq>0)=1;
VOI(:,:,250:1:260) = Vq;
result: Thanks for all cooperation in advance.

darova on 8 Sep 2021
Edited: darova on 8 Sep 2021
t = linspace(0,2*pi,11)+pi/2;
r = 3 + sin(5*t); % create a start
[x,y] = pol2cart(t,r);
k = convhull(x,y); % find convhull (pentagon)
k(end) = []; % remove last duplicate point
% interpolate the star and pentagon to make the same number of points
p = [0 cumsum(hypot(diff(x),diff(y)))];
p1 = linspace(p(1),p(end));
x1 = interp1(p,x,p1);
y1 = interp1(p,y,p1);
x2 = interp1(p(k),x(k),p1);
y2 = interp1(p(k),y(k),p1);
% create surface
X = [x1;x2];
Y = [y1;y2];
Z = [x1*0;x2*0+5];
contour3(X,Y,Z,5,'linewidth',3)
surface(X,Y,Z,'edgecolor','none')
axis equal
light
view(45,45) R2021a

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