MATLAB: 3D matrix from 3D scatter points

3d matrixscatter3

Hi everyone,

I have tracked moving particles in a 3D space by storing their spatial coordinates positions in vectors. I.e. for a given time I have:

particle_x; particle_y; patricle_z;

specifying the x,y and z coordinates of each tracked particle/point. I can easily visualize these using scatter3 in Matlab, but from this, I would like to make 2D cuts and visualize the spread of points coinciding with certain planes. My idea was to create a 3D matrix of the whole 3D space and simply fill in a value ('1') where a particle is identified. However, I'm not really sure how to do this in a good way…

Since scatter3 can visualize the points in 3D, there has to be some sort of 3D matrix saved in the background, or? Or does anyone have a good idea of how I could do this? Any advice would be very much appreciated.

Thanks

/David

Best Answer

The conceptual method that springs to mind is to calculate the distance from each of your points to the plane you want, and plot the points that are within some tolerance of zero. (You probably don't want to require exactly zero distance, because of floating point arithmetic limitations.)

Search keywords like determine , distance , point , plane and the formula is easy to find.

Related Solutions

MATLAB: Finding a circle enclosing data points in a tilted plane

Hi Doctor61,

First, from your previous posts and this one I see that you're doing lots of stuff with 3d geometry. I think that you will find this FEX entry very very useful: http://www.mathworks.com/matlabcentral/fileexchange/24484

However, if I understand your problem correctly I think there's a simple answer. My understanding is that you have a set of planar points and you want to find the radius of a circle tilted to that plane that would enclose them.

If the points are indeed exactly coplanar, then a minimum bounding sphere of the points in 3D would actually have the same radius as the circle you describe.

In that case, let me point you towards: http://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects

It has a minboundsphere which would do the job.

If your points aren't exactly coplanar, then what you're actually talking about is a minimum bounding cylinder, tilted to align with the plane. In that case, I think that you'll find that the easiest way to answer the question is to:

rotate your points into a plane
get the minimum bounding circle of the local XY-coordinates

The good news is that with geom3d it's actually very easy to do this. If you don't have your plane (but you know 3 points lying on that plane), you can get it by:

myPlane = createPlane(P1, P2, P3);

Then you can get local coordinates of those points by transforming them:

Tform = createBasisTransform3d('global', myPlane);
PTS_WRT_PLANE = transformPoint3d(myPts, Tform);

At this point, your task of finding a minimum bounding circle gets quite a bit easier because we're only working in 2d. John D'Errico's suite of minimal-bounding-objects also has a minboundcircle.

Thanks, Sven.

MATLAB: How do you plot a 3D circle segment

Hi Laurence,

There is no built-in function to plot a segment of a circle. However, it is still possible to do with combinations of existing functions in MATLAB! Assuming that the center is defined as a point in Cartesian coordinates (X, Y, Z), you can add those values to the final x, y, z coordinates before plotting. Although it is easier to start with spherical coordinates, if you have Cartesian coordinates you can use the function cart2sph to convert them to spherical coordinates.

I was unsure if you wanted to plot a "slice" of the sphere that used the full range of the radius, the full range of phi, and the full range of theta, so I added the ability to select a smaller area to plot. Attached is my code to do so- hope this helps!

Best Answer

Related Solutions

MATLAB: Finding a circle enclosing data points in a tilted plane

MATLAB: How do you plot a 3D circle segment

Related Question