Interpolates 3D contours onto parallel 3D planes

I have a 3D matrix (250x3x7) where the 1st dimension are the data points, 2nd dimension the x,y,z coordinates, and 3rd dimension the slice location. This 3D matrix are the contours at each slice location and these contours are not parallel to each other. I wish to interpolate these contour onto some planes in 3D space. These planes are parallel to each other. I have the x,y,z coordinates of each pixel of these plane. The example in images below will explain it better. I want to interpolates those contours on those grey colour planes.

Images here: Image 1 - The contour and the plane

Image 2 - The set of contours and the planes. I want to interpolate these contours onto the grey color plane

I tried using interp3 to interpolate the contours with meshgrid, but I'm not sure how to interpolate it to a specific location (plane) in 3D space. Hope someone can help me with this. Do let me know if my question is not clear. Thanks!

[KSSV]

Images not opening....!

[Chen Onn Leong]

Hi @KSSV, I have reuploaded the images to google drive. Do have a look. Thanks.