I am trying to plot random lines, starting from a specific radius of a sphere, but I only want the upper hemisphere, as shown in the image
So far I am able to create random starting points(but for R=15), random intersections, random slopes, but I don't know how to connect all these to plot the lines.
My code is
%Create the random starting points, slopes, intersections
tracks=input('Give me the number of muon tracks: ');
theta=180.*rand(tracks,1);
rho=15*ones(tracks,1);
startPoint = [theta rho];
[X,Y]=pol2cart(theta*pi/180,rho);
intersection =-6371+(2*6371).*rand(tracks,1);
slope = tand(360.*rand(tracks,1));
I know that I need only two elements to draw a line, but I kind of confused right now...
Any idea on how to do it?
Because you don't want MATLAB to join up all of your lines when you plot them, you need to plot them separately, in a loop, e.g., something like
theta = 2 * pi * rand(tracks, 2); % 2 rows of random points on a circle, in radians
X = cos(theta); Y = sin(theta);
close all;
figure;
hold on;
for nPlot = 1:tracks
plot(X(nPlot, :), Y(nPlot, :), 'r-o');
end
Note that this code also generates X and Y differently to your original - pol2cart and the above method both expect values in radians, not degrees.
Related
I'm plotting random lines and one circle as shown in the picture.
So I need to delete lines that located out of the circle and keep that's inside it. Also, if some lines have one point inside the circle and the other point outside the circle then I need to trim the outside part.
How can I do that?
Thank you in advance
I used this code
% plotting random lines
X1 = rand (8,8);
Y1 = rand (8,8);
figure
plot (X1,Y1)
hold on
% plotting the circle
R = 0.5;
angle = linspace(0,2*pi,180);
x= Rcos(angle);
y= Rsin(angle);
plot(x,y,'r')
axis equal
I am generating a scatter plot containing data from multiple sources, as displayed below.
I would like to be able to generate a curve surrounding an arbitrary query point and passing through points on scatter plot. Final goal is to calculate the area between the lines on the plot.
I have implemented solution using finding points with knnsearch in a circular fashion and then applying hampel filter to eliminate noise. In the example below, I have selected a point right about in the middle of the blue-shaded area. As you can see, the result is far from perfect, and I need more precision.
I am looking for something similar to boundary function, but to work from the inside of the point cloud, not from the outside.
Final goal is to calculate the area between the lines on the plot.
I would do it differently. Just take any two lines of the plot, calculate the area under the curves with some kind of numerical approximation (for example trapezoidal numerical integration), then subtract the areas and obtain the area between the lines.
Thank to idea in Trilarion's answer, I was able to come up with the better solution.
Note that I use notation for YZ plane instead of XY (to keep consistent with robot coordinate system).
Solution
Generate curves for each set of scatter data
% Scatter data is in iy and iz vectors.
curve = fit(iy, iz, 'smoothingspline', 'SmoothingParam', 0.5);
% Remove outliers.
fdata = feval(curve, iy);
I = abs(fdata - iz) > 0.5 * std(iz);
outliers = excludedata(iy, iz, 'indices', I);
% Final curve without outliers.
curve = fit(iy, iz, 'smoothingspline', 'Exclude', outliers, 'SmoothingParam', 0.5);
Plot curves and scatter data
% Color maps generated by MATLAB's colormap function.
h_curve = plot(curve);
set(h_curve, 'Color', color_map_light(i,:));
scatter(iy, iz, '.', 'MarkerFaceColor', color_map(i,:))
Let user provide an input by selecting points
User selects one point as a query point and two points for limits along Y axis. This is because some curves come close, but never intersect.
[cs_position.y, cs_position.z] = ginput(1);
[cs_area_limits, ~] = ginput(2);
if cs_area_limits(1) > cs_area_limits(2)
cs_area_limits = flipud(cs_area_limits);
end
plot_cross_section(cs_position);
Finally calculate and plot surface area
This section uses fantastic answer by Doresoom.
function [ ] = plot_cross_section(query_point)
%PLOT_CROSS_SECTION Calculates and plots cross-section area.
% query_point Query point.
% Find values on query point's Y on each of the curves.
z_values = cellfun(#(x, y) feval(x, y),...
curves, num2cell(ones(size(curves)) * query_point.y))
% Find which curves are right above and below the query point.
id_top = find(z_values >= query_point.z, 1, 'first')
id_bottom = find(z_values < query_point.z, 1, 'last')
if isempty(id_top) || isempty(id_bottom)
return
end
% Generate points along curves on the range over Y.
y_range = cs_area_limits(1):0.1:cs_area_limits(2);
z_top = feval(curves{id_top}, y_range).';
z_bottom = feval(curves{id_bottom}, y_range).';
% Plot area.
Y = [ y_range, fliplr(y_range) ];
Z = [ z_top, fliplr(z_bottom) ];
fill(Y, Z, 'b', 'LineStyle', 'none')
alpha 0.5
hold on
% Calculate area and show to user.
cs_area = polyarea(Y, Z);
area_string = sprintf('%.2f mm^2', cs_area);
text(0, -3, area_string, 'HorizontalAlignment', 'center')
end
Result
I have a binary image of a human. In MATLAB, boundary points and the center of the image are also defined, and they are two column matrices. Now I want to draw lines from the center to the boundary points so that I can obtain all points of intersection between these lines and the boundary of the image. How can I do that? Here is the code I have so far:
The code that is written just to get the one intersection point if anyone can help please
clear all
close all
clc
BW = im2bw(imread('C:\fyc-90_1-100.png'));
BW = imfill(BW,'holes');
[Bw m n]=preprocess(BW);
[bord sk pr_sk]=border_skeleton(BW);
boundry=bord;
L = bwlabel(BW);
s = regionprops(L, 'centroid');
centroids = cat(1, s.Centroid);
Step #1 - Generating your line
The first thing you need to do is figure out how to draw your line. To make this simple, let's assume that the centre of the human body is stored as an array of cen = [x1 y1] as you have said. Now, supposing you click anywhere in your image, you get another point linePt = [x2 y2]. Let's assume that both the x and y co-ordinates are the horizontal and vertical components respectively. We can find the slope and intercept of this line, then create points between these two points parameterized by the slope and intercept to generate your line points. One thing I will point out is that if we draw a slope with a vertical line, by definition the slope would be infinity. As such, we need to place in a check to see if we have this situation. If we do, we assume that all of the x points are the same, while y varies. Once you have your slope and intercept, simply create points in between the line. You'll have to choose how many points you want along this line yourself as I have no idea about the resolution of your image, nor how big you want the line to be. We will then store this into a variable called linePoints where the first column consists of x values and the second column consists of y values. In other words:
In other words, do this:
%// Define number of points
numPoints = 1000;
%// Recall the equation of the line: y = mx + b, m = (y2-y1)/(x2-x1)
if abs(cen(1) - linePt(1)) < 0.00001 %// If x points are close
yPts = linspace(cen(2), linePt(2), numPoints); %// y points are the ones that vary
xPts = cen(1)*ones(numPoints, 1); %//Make x points the same to make vertical line
else %// Normal case
slp = (cen(2) - linePt(2)) / cen(1) - linePt(1)); %// Solve for slope (m)
icept = cen(2) - slp*cen(1); %// Solve for intercept (b)
xPts = linspace(cen(1), linePt(1), numPoints); %// Vary the x points
yPts = slp*xPts + icept; %// Solve for the y points
end
linePoints = [xPts(:) yPts(:)]; %// Create point matrix
Step #2 - Finding points of intersection
Supposing you have a 2D array of points [x y] where x denotes the horizontal co-ordinates and y denotes the vertical co-ordinates of your line. We can simply find the distance between all of these points in your boundary with all of your points on the line. Should any of the points be under a certain threshold (like 0.0001 for example), then this indicates an intersection. Note that due to the crux of floating point data, we can't check to see if the distance is 0 due to the step size in between each discrete point in your data.
I'm also going to assume border_skeleton returns points of the same format. This method works without specifying what the centroid is. As such, I don't need to use the centroids in the method I'm proposing. Also, I'm going to assume that your line points are stored in a matrix called linePoints that is of the same type that I just talked about.
In other words, do this:
numBoundaryPoints = size(boundry, 1); %// boundary is misspelled in your code BTW
ptsIntersect = []; %// Store points of intersection here
for idx = 1 : numBoundaryPoints %// For each boundary point...
%//Obtain the i'th boundary point
pt = boundry(:,idx);
%//Get distances - This computes the Euclidean distance
%//between the i'th boundary point and all points along your line
dists = sqrt(sum(bsxfun(#minus, linePoints, pt).^2, 2));
%//Figure out which points intersect and store
ptsIntersect = [ptsIntersect; linePoints(dists < 0.0001, :)];
end
In the end, ptsIntersect will store all of the points along the boundary that intersect with this line. Take note that I have made a lot of assumptions here because you haven't (or seem reluctant to) give any more details than what you've specified in your comments.
Good luck.
Can you please help me document this Matlab code that is supposed to produce random shapes?? The wiggliness of the shapes is supposed to be controlled by the variable degree...
But how the rho (radius values) are produced... I can't really get it....
degree = 5;
numPoints = 1000;
blobWidth = 5;
theta = 0:(2*pi)/(numPoints-1):2*pi;
coeffs = rand(degree,1);
rho = zeros(size(theta));
for i = 1:degree
rho = rho + coeffs(i)*sin(i*theta);
end
phase = rand*2*pi;
[x,y] = pol2cart(theta+phase, rho+blobWidth);
plot(x,y)
axis equal
set(gca,'Visible','off')
theta = 0:(2*pi)/(numPoints-1):2*pi;
So this is just a vector of angles in a revolution, if you plot this theta against a constant rho (after calling pol2cart) you will get a circle:
r = ones(size(theta));
[x,y] = pol2cart(theta, r);
plot(x,y)
axis equal
This should be obvious if you understand what pol2cart does because you have a series of all the angles in a circle and a constant radius for all of them. If you don't understand that (i.e. polar coordinates) then that's a very basic mathematical concept you need to go and read up on your own before trying to understand this code.
OK so now a circle in cartesian coords is just a line in polar coords (i.e. plot(theta, r) noting that the horizontal axis now represents angle and the vertical represents radius). So if we want to randomly mess up our circle, we could randomly mess up our line. Using sin does this in a nice smooth way. Adding random frequencies of many sin waves adds less and less predictable "jitter". I think it would help you to understand if you add the following line to your code:
rho = zeros(size(theta));
hold all
for i = 1:degree
rho = rho + coeffs(i)*sin(i*theta);
plot(theta, rho)
end
and contrast this to (be sure to close your figure window before running this)
rho = zeros(size(theta));
hold all
for i = 1:degree
rho = rho + coeffs(i)*sin(i*theta);
plot(theta, coeffs(i)*sin(i*theta))
end
The second one shows you the different frequencies of sin waves used and the first shows how these sum to create unpredictable wavy lines. Now think of the pol2rect function as bending these lines around to make a "circle". If the line is dead straight you get a perfect circle, if it's wavy you get a "wavy" circle.
degree in your code just controls how many sin waves to add up.
finally phase = rand*2*pi; just randomly rotates your shape after it has been created.
Well, this was an amazing piece of code! But regarding rho. What is done is that you have a circle with base radius of 5 (blobwidth) and then you have a random offset coeffs. Then the offset is added to rho in rho = rho + coeffs(i)*sin(i*theta);. This means that the first loop an offset is added to the circle with frequency 1Hz. This then yields a constant offset. The next loop the frequency increases to 2Hz. Then the offset will be added to every second point and the offset may be negative as well. Then it goes on like this. Finally the coordinate is transformed to polar.
A few comments though. The most readable and the easiest way to create theta is to use linspace. And also, since rho is overwritten in the loop, you may as well define it just as rho = 0;
i just started with my master thesis and i already am in trouble with my capability/understanding of matlab.
The thing is, i have a trajectory on a surface of a planet/moon whatever (a .mat with the time, and the coordinates. Then i have some .mat with time and the measurement at that time.
I am able to plot this as a color coded trajectory (using the measurement and the coordinates) in scatter(). This works awesomely nice.
However my problem is that i need something more sophisticated.
I now need to take the trajectory and instead of color-coding it, i am supposed to add the graph (value) of the measurement (which is given for each point) to the trajectory (which is not always a straight line). I will added a little sketch to explain what i want. The red arrow shows what i want to add to my plot and the green shows what i have.
You can always transform your data yourself: (using the same notation as #Shai)
x = 0:0.1:10;
y = x;
m = 10*sin(x);
So what you need is the vector normal to the curve at each datapoint:
dx = diff(x); % backward finite differences for 2:end points
dx = [dx(1) dx]; % forward finite difference for 1th point
dy = diff(y);
dy = [dy(1) dy];
curve_tang = [dx ; dy];
% rotate tangential vectors 90° counterclockwise
curve_norm = [-dy; dx];
% normalize the vectors:
nrm_cn = sqrt(sum(abs(curve_norm).^2,1));
curve_norm = curve_norm ./ repmat(sqrt(sum(abs(curve_norm).^2,1)),2,1);
Multiply that vector with the measurement (m), offset it with the datapoint coordinates and you're done:
mx = x + curve_norm(1,:).*m;
my = y + curve_norm(2,:).*m;
plot it with:
figure; hold on
axis equal;
scatter(x,y,[],m);
plot(mx,my)
which is imo exactly what you want. This example has just a straight line as coordinates, but this code can handle any curve just fine:
x=0:0.1:10;y=x.^2;m=sin(x);
t=0:pi/50:2*pi;x=5*cos(t);y=5*sin(t);m=sin(5*t);
If I understand your question correctly, what you need is to rotate your actual data around an origin point at a certain angle. This is pretty simple, as you only need to multiply the coordinates by a rotation matrix. You can then use hold on and plot to overlay your plot with the rotated points, as suggested in the comments.
Example
First, let's generate some data that resembles yours and create a scatter plot:
% # Generate some data
t = -20:0.1:20;
idx = (t ~= 0);
y = ones(size(t));
y(idx) = abs(sin(t(idx)) ./ t(idx)) .^ 0.25;
% # Create a scatter plot
x = 1:numel(y);
figure
scatter(x, x, 10, y, 'filled')
Now let's rotate the points (specified by the values of x and y) around (0, 0) at a 45° angle:
P = [x(:) * sqrt(2), y(:) * 100] * [1, 1; -1, 1] / sqrt(2);
and then plot them on top of the scatter plot:
hold on
axis square
plot(P(:, 1), P(:, 2))
Note the additional things have been done here for visualization purposes:
The final x-coordinates have been stretched (by sqrt(2)) to the appropriate length.
The final y-coordinates have been magnified (by 100) so that the rotated plot stands out.
The axes have been squared to avoid distortion.
This is what you should get:
It seems like you are interested in 3D plotting.
If I understand your question correctly, you have a 2D curve represented as [x(t), y(t)].
Additionally, you have some value m(t) for each point.
Thus we are looking at the plot of a 3D curve [x(t) y(t) m(t)].
you can easily achieve this using
plot3( x, y, m ); % assuming x,y, and m are sorted w.r.t t
alternatively, you can use the 3D version of scatter
scatter3( x, y, m );
pick your choice.
Nice plot BTW.
Good luck with your thesis.