Verified if a point is inside a surface matlab - matlab

I have a surface interpolating 3D points and I would like to test whether a point is inside or outside this surface.
I know the 3D coordinates of the point and the 3D coordinates of its nearest point on the surface.
For example:
scatter3(1.715710000000000e+02 ,-1.389280000000000e+02, -1.395990000000000e+02,'*','r') % point
hold on
scatter3(1.692480000000000e+02,-1.355325000000000e+02 ,-1.395429000000000e+02,'filled','y') % nearest surface point
hold on
or :
scatter3(1.780790000000000e+02, -1.505310000000000e+02, -1.481070000000000e+02,'*','r') % point
hold on
scatter3(1.795721000000000e+02,-1.346832000000000e+02, -1.499843000000000e+02,'filled','y') % nearest surface point
Plotting these points with surface, both these points seem to be within of the surface...
How can I prove it?
Thanks!

Related

How can I create a slice of a surface plot to create a line? (Matlab)

Given some function z = f(x,y), I'm interested in creating a (1D) line plot along an arbitrary cutting plane in x,y,z. How do I do this in Matlab? Slice, for example, provides a higher dimensional version (colormap of density data) but this is not what I'm looking for.
E.g.:
z = peaks(50);
surf(z);
%->plot z along some defined plane in x,y,z...
This has been asked before, e.g. here, but this is the answer given is for reducing 3D data to 2D data, and there is no obvious answer on googling. Thanks.
If the normal vector of the plane you want to slice your surface will always lay in the xy plane, then you can interpolate the data over your surface along the x,y coordinates that are in the slicing line, for example, let the plane be defined as going from the point (0,15) to the point (50,35)
% Create Data
z=peaks(50);
% Create x,y coordinates of the data
[x,y]=meshgrid(1:50);
% Plot Data and the slicing plane
surf(z);
hold on
patch([0,0,50,50],[15,15,35,35],[10,-10,-10,10],'w','FaceAlpha',0.7);
% Plot an arbitrary origin axis for the slicing plane, this will be relevant later
plot3([0,0],[15,15],[-10,10],'r','linewidth',3);
Since it is a plane, is relatively easy to obtain the x,y coordinates alogn the slicing plane with linspace, I'll get 100 points, and then interpolate those 100 points into the original data.
% Create x and y over the slicing plane
xq=linspace(0,50,100);
yq=linspace(15,35,100);
% Interpolate over the surface
zq=interp2(x,y,z,xq,yq);
Now that we have the values of z, we need against what to plot them against, that's where you need to define an arbitrary origin axis for your splicing plane, I defined mine at (0,15) for convenience sake, then calculate the distance of every x,y pair to this axis, and then we can plot the obtained z against this distance.
dq=sqrt((xq-0).^2 + (yq-15).^2);
plot(dq,zq)
axis([min(dq),max(dq),-10,10]) % to mantain a good perspective

Plotting a rectangular matrix into a circle

I have generated a rectangular matrix with the azimouth angle changing with rows and the radius changing as you change column. These are meant to represent the relative velocities experienced by a rotating helicopter blade. This produces a matrix called Vmat. I want to plot this to appears in a circle (representing the rotation of the blade)
So far I have tried
[R,T] = meshgrid(r,az);
[x,y] = pol2cart(T,R);
surf(x,y,Vmat(r,az));
which should produce a contoured surface showing velocity as it changes with azimouth angle and radius but it comes up with dimension errors.
I don't mind if it is a 2d contour plot or 3d plot i guess both would be written in a similar way.
Thanks
James
The error is in writing Vmat(r,az), presuming that these are actual values of radius and azimuth, not indexes into your radius and azimuth. If you want to take only a subset of Vmat that's a slightly different matter, but this should work:
[R,T] = meshgrid(r,az); % creates a grid in polar coordinates
[x,y] = pol2cart(T,R); % changes those to cartesian for surf
surf(x,y,Vmat);
Alternatively you could do a contour plot:
h = polar([0 2*pi], [0 max(r)]); % set up polar axes with right scale
delete(h) % remove line
hold on
contour(x,y,Vmat);

How to plot data points on top of what was previously plotted in MATLAB?

How to plot data points on top of what was previously plotted in MATLAB?
For example I have a 2D plot of a plane and points, and I plot
the points with scatter3 after I plot the plane with pcolor,
and the plane covers the points that are below it.
In the first image you can see the points by themselves. But when I plot
them together with the plane, the plane covers the points below it.
THanks
The issue is that you are using scatter3 instead of scatter and it is plotting against the 3rd dimension linearly which is why the points disappear half way down. They are actually just behind your plane.
Use uistack to bring data points on top of the plot of the plane. Something like
p1 = plot(...); % plot of data points (need to be on top of plane)
hold on;
p2 = plot(...); % plot of the plane
uistack(p1); % to bring data points on top of the plane
Try hold on. See http://www.mathworks.co.uk/help/matlab/ref/hold.html for more information.

Plotting 3xN matrix(N number of 3D points) on same graph using matlab

I've a 3xN matrix W where N is 50
W(1,1) is x coordinate of a point
W(2,1) is y coordinate of same point
W(3,1) is z coordinate of same point
Similarly:
W(1,2) is x coordinate of another point
W(2,2) is y coordinate of same point
W(3,2) is z coordinate of same point
....
Now I want to 3d plot all these 3d points on same figure using matlab. How can I plot all these
points on same figure?
Is it possible to plot this matrix using a single function call(in matlab)?
I know that plot3 can be used but it can be used for one graph at a time.
So plot3(v(1,1),v(1,2),v(1,3)); is just a single point. But how do I plot all N points?
Is there an easier and better method?
I guess you can use plot3(w(1,:),w(2,:),w(3,:)).

Plotting a surface from a set of interior 3D scatter points in MATLAB

I have a large (~60,000) set of triplet data points representing x,y, and z coordinates, which are scattered throughout a Cartesian volume.
I'm looking for a way to use Matlab to visualize the non-convex shape/volume described by the maximum extent of the points.
I can of course visualize the individual points using scatter3, but given the large number of points the details of the shape are obscured by the noise of the dots.
As an analogy, imagine that you filled a hour glass with spheres of random sizes such as BBs, ping pong balls, and kix and then were given the coordinates of the center of each of each object. How would you take those coordinates and visualize the shape of the hour glass containing them?
My example uses different sized objects because the spacing between data points is non-uniform and effectively random; it uses an hourglass because the shape is non-convex.
If your surface enclosing the points can be described as a convex polyhedron (i.e. like the surface of a cube or a dodecahedron, without concave pits or jagged pointy parts), then I would start by creating a 3-D Delaunay triangulation of the points. This will fill the volume around the points with a series of tetrahedral elements with the points as their vertices, and you can then find the set of triangular faces that form the outer shell of the volume using the convexHull method of the DelaunayTri class.
Here's an example that generates 200 random points uniformly distributed within the unit cube, creates a tetrahedral mesh for these points, then finds the 3-D convex hull for the volume:
interiorPoints = rand(200,3); %# Generate 200 3-D points
DT = DelaunayTri(interiorPoints); %# Create the tetrahedral mesh
hullFacets = convexHull(DT); %# Find the facets of the convex hull
%# Plot the scattered points:
subplot(2,2,1);
scatter3(interiorPoints(:,1),interiorPoints(:,2),interiorPoints(:,3),'.');
axis equal;
title('Interior points');
%# Plot the tetrahedral mesh:
subplot(2,2,2);
tetramesh(DT);
axis equal;
title('Tetrahedral mesh');
%# Plot the 3-D convex hull:
subplot(2,2,3);
trisurf(hullFacets,DT.X(:,1),DT.X(:,2),DT.X(:,3),'FaceColor','c')
axis equal;
title('Convex hull');
You could treat your data as a sample from a three-dimensional probability density, and estimate that density on a grid, e.g. via a 3d histogram, or better a 3d kernel density estimator. Then apply a threshold and extract the surface using isosurface.
Unfortunately, hist3 included in the Statistics Toolbox is (despite its name) just a 2d histogram, and ksdensity works only with 1d data, so you would have to implement 3d versions yourself.