Slices through 3-D Volumes, formed by 1D-arrays

f=

I have a set of 1D - arrays and values of the inequality f.

I need to build a series of slices for any of the planes of this volume. I don't know how to do this in Matlab, because the data is in vector form. Please help.

[KSSV]

Your data lies in a sphere. You can make circular planes of required radius and center.

[Andrew Sol]

@KSSV And if the volume is different from a regular form, from a sphere, for example, as in this case? How to build slices automatically?

Answer 1

[Walter Roberson]

Nx = 50;
Ny = 51;
Nz = 52;

load f
load x
load y
load z

figure();
PointSize = 20;
scatter3(x, y, z, PointSize, f); colorbar();

minx = min(x); maxx = max(x);
miny = min(y); maxy = max(y);
minz = min(z); maxz = max(z);

xvec = linspace(minx, maxx, Nx);
yvec = linspace(miny, maxy, Ny);
zvec = linspace(minz, maxz, Nz);

[Xq, Yq, Zq] = meshgrid(xvec, yvec, zvec);

Fq = griddata(x, y, z, f, Xq, Yq, Zq);

Warning: Duplicate data points have been detected and removed - corresponding values have been averaged.

mask = Fq < 1/2 | Fq > 1;
Fq(mask) = nan;

figure();
sx = linspace(minx, maxx, 7);
sy = linspace(miny, maxy, 7);
sz = linspace(minz, maxz, 7);
H = slice(Xq, Yq, Zq, Fq, sx, sy, sz);
set(H, 'EdgeColor', 'none');

[Joe]

非常に正確な計算.

[Andrew Sol]

@Walter Roberson

Thank you for your answer. The method is good, I tested it, but what does not suit me is that some contours are formed very sloppy and rough. I suggest this way:

[X,Y,Z] = ndgrid(0:0.1:2,0:0.1:2,0:0.1:2);
F = X.^2+Y.^2+Z.^2;
idx = double((F>=1/2) & (F<=1));
idx(idx==0) = NaN;
F1=Z.*idx;
X1=X.*idx;
Y1=Y.*idx;
Z1=Z.*idx;
P = [X1(:),Y1(:),Z1(:),F1(:)]; 
plot3(P(:,1),P(:,2),P(:,3),'o','MarkerSize', 3);
axis square
grid on
hold on

Here the grid is formed evenly. In addition, if we look at the location of the points on the slices, we can see that the points can be placed clearly in the desired slice.

[x y] = meshgrid(0:0.1:2,0:0.1:2); % Generate x and y for XY-plane
Z2=Z1; % auxiliary data
Z2(Z2~=0.5) = NaN; % Generate data for z-slice = 0.5, for example
plot3(P(:,1), P(:,2), Z2(:),'+','MarkerSize', 5) % Plot the slice

What else I would like: draw a border around each such "slice", remove the dots inside and, if possible, project all of slices (with differentc olors) onto one plane (well, so that all slices lie on the same surface). I haven't succeeded yet, but I'm working on it.