2D图像通过垂直于视角的3D绘图

Question

so I want to include a 2D figure in a 3D plot and rotate the figure (with view([alpha beta])). As you can imagine, this would distord the surface plot. So basically I'm trying to figure out, how to adjust the surface plot to become perpendicular to the viewingangle (to see the figure as how it should be) and still being centered at the original location. I found something like

img = imread('galileo3.png');     % Load a sample image
xImage = [...]   % The x data for the image corners
yImage = [...]             % The y data for the image corners
zImage = [...]   % The z data for the image corners
surf(xImage,yImage,zImage,...    % Plot the surface
     'CData',img,...
     'FaceColor','texturemap');
view([phi theta]);

But what's the meaning of the image corners? And how would I adjust the original coordinates, to rotate the surface towards the viewingangle (but still being centered at the original location)?

Answer 1

You can use the viewmtx command to determine the proper transformation matrix. To make this work, you take all of your X, Y, and Z values and reshape them each into a single row. If your original data doesn't have Z values, set them to zero.

You have to reshape your transformed coordinates back to their previous shapes in order to use them in 'surf' commands, etc.

The transformation matrix is simply a function of the view so you can apply the same transformation to multiple data sets simply by making a new XYZ1 variable and multiplying again. That's also handy if you want to make an animation as you circle around a plot. You can just re-apply the transformation.

sizeX = size(X); % repeat for Y, Z;
X = reshape(X,1,numel(X)); % repeat for Y, Z;

XYZ1 = [X; Y; Z; ones(size(X))]; % it's important that you make this 4 rows

A = viewmtx(Azimuth, Elevation);
Transformed_XYZ = A * XYZ1; % you must left-multiply by A

X_Transformed = Transformed_XYZ(1,:); % rows 2 and 3 for Y and Z respectively
X_Transformed = reshape(X_transformed, sizeX); % putting X' into the same shape as X - repeat for Y and Z