If a camera is looking at say 6 evenly spaced dots in the real world it would look like the image below if the camera is looking at the image straight on with no rotation in the x, y or z axis
The z-axis is perpendicular to the image sensor so rotation around the z-axis is simple, it's just a tilt of the image. If I were to rotate the camera (or objects being looked at) around the x axis (if the x-axis is up down) the rows and columns will no longer be parallel and would project off to a vanishing point, like this.
What I would like to do is take a 2 dimensional image of say, dots, and be able to apply different rotations around the x,y and z axes independently. I've experimented with reading my image in Matlab and multiplying by a rotation matrix, or even a full camera matrix but I can't figure out how to take a 2D image, simulate rotating it around the x axis and then saving that back to an image. So that my original grid of dots would look like the bottom image with lines going off to a vanishing point. I've seen some examples using imwarp but I didn't see how I can set the angle of rotation. I'm working on camera calibration so I really want to be able to specify an angle of rotation around each axis.
Thanks for any help.
Related
I have a 3D volume and I need to set some parts of it to zero.
The problem is that I don't know how to refer to the parts I want. I know the shape of the area I want to crop, but I need that area revolved around the Z axis.
A picture's worth a thousand words:
The image shows the cross section of a 3D matrix in the XZ plane, in the middle is the Z axis. The area I want to select (or set to zero) in the volume is the red area, revolved around the green axis, the Z axis.
I'd rather have a solution that doesn't have a very big memory dependency (such as using meshgrid would) as these matrices can get quite big. Else, a meshgrid solution with cylindrical coordinates wouldn't be too difficult to make, as #Luis suggests.
How can I select this area?
I would like to change the view of a 3D plot in matlab such that the y-axis points upward and the z-axis points to left. For example, consider the following plot:
Here the x-axis points forward, the y-axis points to the right and the z-axis points upward.
I would like to have the y-axis points upward and the z-axis points to the left instead. I tried to rotate the plot (using the figure window toolbar rotate button) but I could not get it to work. (It should just be a simple 90 degrees rotation about the x-axis)
Code to generate the plot:
membrane
view(100,50)
xlabel('x-axis');
ylabel('y-axis');
zlabel('z-axis');
grid on
Try using view. I don't have MATLAB available so I can't test it, but I think it can do what you want.
Example from the documentation:
Set the view along the y-axis, with the x-axis extending horizontally
and the z-axis extending vertically in the figure.
view([0 0]);
EDIT:
Try using three inputs to the view function. I can't experiment myself, but you should be able to do it if you choose the right values here.
From documentation:
view([x,y,z]) sets the view direction to the Cartesian coordinates x,
y, and z. The magnitude of (x,y,z) is ignored.
EDIT 2:
Check out camroll. I think camroll(90) (possibly in combination with view) will work.
From documentation:
camroll(dtheta) rotates the camera around the camera viewing axis by
the amounts specified in dtheta (in degrees). The viewing axis is the
line passing through the camera position and the camera target.
This was posted a while ago, but in case someone else is looking for ways to set y-axis as the vertical one here is a possible fix.
Manually: In the command window type cameratoolbar('show') which will open an interactive toolbar in your plot from which you could change the view. One of the options is to set a principle axis to x, y, or z.
Or in you script you could use cameratoolbar('SetCoordSys',coordsys) command which sets the principal axis of the camera motion. coordsys can be: x, y, z, or none.
http://uk.mathworks.com/help/matlab/ref/cameratoolbar.html
I have a 3D matrix of data in matlab, but I want to extract an arbitrarily rotated slice of data from that matrix and store it as a 2D matrix, which I can access. Similar to how the slice() function displays data sliced at any angle, except I would also like to be able to view and modify the data as if it were an array.
I have the coordinates of the pivot-point of the plane as well as the angles of rotation (in x, y and z axis), I have also calculated the equation of the plane in the form:
Ax + By + Cz = D
and can extract a 3D matrix containing only the data that fall on that plane, but I don't know how to then convert that into a simple 2D array.
Another way of doing it would be to somehow rotate the source matrix in the opposite direction of the angle of the plane, so as to line up the plane of data with the XY axis, and simply extract that portion of the matrix, but I do not know if rotating a matrix like that is possible.
I hope this hasn't been answered elsewhere, I've been googling it all day, but none of the problems seem to exactly match mine.
Thanks
You can take a look at the code here. I think the function is similar to what you are trying to solve.
The function extracts an arbitrary plane from a volume given the size of the plane, the center point of the plane, and the plane normal, i.e. [A,B,C]. It also outputs the volumetric index and coordinate of each pixel on the plane.
Aha! May have just solved it myself.
To produce the plane equation I rotate a normal vector of (0,0,1) using rotation matrices and then find D. If I also rotate the following vectors:
(1,0,0) //step in the x direction of our 2D array
and
(0,1,0) //step in the y direction of our 2D array
I'll have the gradients that denote how much my coordinates in x,y,z have to change before I step to the next column in my array, or to the next row.
I'll mock this up ASAP and mark it as the answer if it works
EDIT: Ok slight alteration, when I'm rotating my vectors I should also rotate the point in 3D space that represents the xyz coordinates of x=0,y=0,z=0 (although I'm rotating around the centre of the structure, so it's actually -sizex/2,-sizey/2,-sizez/2, where size is the size of the data, and then I simply add size/2 to each coordinate after the rotations to translate it back to where it should be).
Now that I have the gradient change in 3D as I increase the x coordinate of my 2D array and the gradient change as I increase the y coordinate, I can simply loop through all possible x and y coordinates (the resulting array will be 50x50 for a 50x50x50 array, I'm not sure what it will be for irregular sizes, which I'll need to work out eventually) in my 2D array and calculate the resulting 3D coordinates on my plane in the data. My rotated corner value serves as the starting point. Hooray!
Just got to work out a good test for this encompassing all angles and then I'll approve this as an answer
I have an image loaded from disk as a texture, and a same-sized matrix d which has the corresponding depths.
How can I use surf to show me the image as a 3d-model? Simply taking
surf(depthMatrix, img);
doesn't give a nice result since
the camera looks not from the x-y plane in z-direction
It looks fairly black
It doesn't look that smooth although my depth matrix is actually smoothed out when I show it using imshow(depthMatrix, []);
You can use texture mapping to display your image on your surface like so:
surf(depthMatrix,img,... %# depthMatrix is z data, img is an image
'FaceColor','texturemap',... %# Use texture mapping
'EdgeColor','none'); %# Turn off edge coloring
And to address your 3 points:
You can adjust your camera angle with the mouse by pressing the button on the figure, which turns on interactive 3-D rotation. You can also turn interactive rotation on using the function ROTATE3D, or you can change the camera view without the mouse using the function VIEW.
Your plot was looking black because edges are drawn as black lines by default, and there were probably a lot of them.
You can adjust the axis scaling and limits to make your surface appear smoother. For example, axis equal will make data units the same for all 3 axes, so your z axis (which ranges from 0 to 25) will be flattened significantly since your other two axes span ranges in the hundreds. Alternatively, in your call to SURF you can specify x and y data to use for the values on those axes, which can ultimately help you to better adjust the relative scaling between those axes and the z axis.
I know Matlab has a function called cylinder to create the points for a cylinder when number of points along the circumference, and the radius length. What if I don't want a unit cylinder, and also don't want it to center at the default axis (for example along z-axis)? What would be the easiest approach to create such a cylinder? Thanks in advance.
The previous answer is fine, but you can get matlab to do more of the work for you (because the results of cylinder separate x,y,z components you need to work a little to do the matrix multiplication for the rotation). To have the center of base of the cylinder at [x0 y0 z0], scaled by [xf yf xf] (use xf=yf unless you want an elliptic cylinder), use:
[x y z] = cylinder;
h=mesh(x*xf+x0,y*yf+y0,z*zf+z0)
If you also want to rotate it so it isn't aligned along the z-axis, use rotate. For example, to rotate about the x-axis by 90 degrees, so it's aligned along the y-axis, use:
rotate(h,[1 0 0],90)
Multiply the points by your favourite combination of a scaling matrix, a translation matrix, and a rotation matrix.