How to plot a 3D cube based if i have the coordinates of the 8 surrounding nodes?

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Dimitris K 2021-11-3

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回答： Eric 2024-7-25

采纳的回答： Kelly Kearney

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Hello community,

I want to plot a 3d cube based on the coordinates of my geometry (8 nodes). The coordinates of my cube are:

coord=[0    0    0;
       0.5  0    0;
       0.5  0.5  0;
       0    0.5  0;
       0    0    0.5;
       0.5  0    0.5;
       0.5  0.5  0.5;
       0    0.5  0.5;];

Thanks a lot in advance.

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Answer 1

Kelly Kearney 2021-11-4

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To expand on Star Strider's answer, in your example, you've specified a list of coordinates, but you haven't told Matlab how they should be connected. Based on your original example, the following array of row indices defines the faces of your cube:

coord = [...
  0    0;
5  0    0;
5  0.5  0;
  0.5  0;
  0    0.5;
5  0    0.5;
5  0.5  0.5;
  0.5  0.5;];
idx = [4 8 5 1 4; 1 5 6 2 1; 2 6 7 3 2; 3 7 8 4 3; 5 8 7 6 5; 1 4 3 2 1]';

To plot, substitute the coordinates:

xc = coord(:,1);

yc = coord(:,2);

zc = coord(:,3);

ax(1) = subplot(2,1,1);

patch(xc(idx), yc(idx), zc(idx), 'r', 'facealpha', 0.1);

view(3);

% Deformed

coord2 = coord + rand(size(coord))*0.1;

xc = coord2(:,1);

yc = coord2(:,2);

zc = coord2(:,3);

ax(2) = subplot(2,1,2);

patch(xc(idx), yc(idx), zc(idx), 'r', 'facealpha', 0.1);

view(3);

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Kelly Kearney 2021-11-4

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Multi-faceted patches can be defined a few different ways. The most straightforward is by defining the x, y, and z coordinates as arrays where each column describes a different face (i.e. a polygon). That's the syntax I used above.

idx = [4 8 5 1 4; 1 5 6 2 1; 2 6 7 3 2; 3 7 8 4 3; 5 8 7 6 5; 1 4 3 2 1]'
idx = 5×6
   1     2     3     5     1
   5     6     7     8     4
   6     7     8     7     3
   2     3     4     6     2
   1     2     3     5     1

idx says to create a polygon connecting vertices 4-8-5-1-4, then one connecting 1-5-6-2-1, etc., with the coordinates for those vertices defined by the rows of coord. By indexing into each of the columns of coord, you get a set of x/y/z coordinates for each face with the same ordering.

Alternatively, you can use face/vertex input, where you define the coordinates of the vertices and the connectivity of the faces separately. This allows you to skip the step of expanding the x/y/z coordinate matrices yourself. In this example, that would look like:

patch('vertices', coord, 'faces', idx', 'facecolor', 'r', 'facealpha', 0.1)

(For some reason, in face/vertex mode, the rows of the face input array define each face, as opposed to the columns in x/y/z input, hence the transposition of idx). I actually prefer this syntax because it's more compact, but it can be more confusing for new users.

Kelly Kearney 2021-11-5

编辑：Kelly Kearney 2021-11-5

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Those numbers indicate that your deformations are about 6 orders of magnitude smaller than the cube edge lengths... so yeah, that won't be visible to the naked eye. If you just want to use this as a visual aid, then I suppose you could scale up the deformations, although then you lose the "real" aspect ratio of the cube. To sync the axes, just set the axis limits appropriately:

% Original cube

coord = [...

0 0 0;

0.5 0 0;

0.5 0.5 0;

0 0.5 0;

0 0 0.5;

0.5 0 0.5;

0.5 0.5 0.5;

0 0.5 0.5;];

idx = [4 8 5 1 4; 1 5 6 2 1; 2 6 7 3 2; 3 7 8 4 3; 5 8 7 6 5; 1 4 3 2 1]';

% Deformed cube

coord2 = [...

0 0 0

0.500001990189944 0 0

0.500001990189944 0.500001990189944 0

0 0.500001990189944 0

0 0 0.499993366033520

0.500001990189944 0 0.499993366033520

0.500001990189944 0.500001990189944 0.499993366033520

0 0.500001990189944 0.499993366033520];

% Deformation

dc = coord - coord2;

% Plot

ax(1) = subplot(1,2,1);

patch('vertices', coord, 'faces', idx', 'facecolor', 'r', 'facealpha', 0.1);

view(3);

ax(2) = subplot(1,2,2);

patch('vertices', coord+dc*1e5, 'faces', idx', 'facecolor', 'r', 'facealpha', 0.1);

view(3);

lim = [-0.1 0.6];

set(ax, 'xlim', [-0.1 0.6], ...

'ylim', [-0.1 0.6], ...

'zlim', [-0.1 1.2], ...

'dataaspectratio', [1 1 1]); % last one same as "axis equal"

Simson Hutagalung 2022-6-24

how if those coordinate data from excel?

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Answer 2

Eric 2024-7-25

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Another route using the 'surf' function:

x = 0.5*[ 1 1 1 1 1; 1 1 -1 -1 1;1 1 -1 -1 1;1 1 1 1 1];

y = 0.5*[ 1 -1 -1 1 1; 1 -1 -1 1 1;1 -1 -1 1 1;1 -1 -1 1 1];

z = 0.5*[-1 -1 -1 -1 -1;-1 -1 -1 -1 -1;1 1 1 1 1;1 1 1 1 1];

% Plow

fig = figure("Name","cube");

surf(x,y,z,'FaceColor','g')

set(fig.CurrentAxes,"XLim",[-1 1],"YLim",[-1 1],"ZLim",[-1 1]);

xlabel("x")

ylabel("y")

zlabel("z")

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How to plot a 3D cube based if i have the coordinates of the 8 surrounding nodes?

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How to plot a 3D cube based if i have the coordinates of the 8 surrounding nodes?

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