Using matlab, I want to apply transform contain of rotate and translate to 2d points.
for example my points are:
points.x=[1 5 7 100 52];
points.y=[42 96 71 3 17];
points.angle=[2 6 7 9 4];
the value of rotate is:30 degree
the value of x_translate is 5.
the value of y_translate is 54.
can any body help me to write matlab code for apply this transform to my points and calculate new coordinate of points after transform?
I don't know what you mean by points.angle since the angle of the points with respect to origin (in a trigonometric sense) is already defined by atand2(y,x)
Here is the code:
clear;clc
oldCoord = [1 5 7 100 52;42 96 71 3 17];
newCoord = zeros(size(oldCoord));
theta = 30 * pi/180;
T = #(theta) [cos(theta), -sin(theta); sin(theta) , cos(theta)];
trans = [5;54];
for m = 1:size(oldCoord,2)
newCoord(:,m) = T(theta) * oldCoord(:,m) + trans;
end
Result:
oldCoord =
1 5 7 100 52
42 96 71 3 17
newCoord =
-15.1340 -38.6699 -24.4378 90.1025 41.5333
90.8731 139.6384 118.9878 106.5981 94.7224
Related
I am trying to follow this MATLAB example.
Please see Step 2, the example used a 128 * 27 matrix M2, and use affine transform to scale and rotate M2, the scale factor is 2.5. However, I expect the size of the result should be 67.5 * 128 (since 27 * 2.5 = 67.5, I do not think it works, but I have no idea how to handle double in this case), the actual result done by MATLAB is 66 * 128.
How to derive the 66 in this case?
I tried to change the scale factor to 2, and the result is 53 * 128, and I expect it to be 54 * 128 since 27 * 2 = 54.
load mri
M1 = D(:,64,:,:);
M2 = reshape(M1,[128 27]);
T0 = maketform('affine',[0 -2.5; 1 0; 0 0]);
res = imtransform(M2,T0,'cubic')
size(res) // 66 * 128
A matrix with 27 elements has coordinates going from 0 through 26 (these are the coordinates used by imtransform). After scaling by 2.5, these coordinates go from 0 through 26*2.5 = 65. To hold x-coordinates from 0 through 65 you need 66 elements.
For example, using the following code, I have a coordinate matrix with 3 cubical objects defined by 8 corners each, for a total of 24 coordinates. I apply a rotation to my coordinates, then delete the y coordinate to obtain a projection in the x-z plane. How do I calculate the area of these cubes in the x-z plane, ignoring gaps and accounting for overlap? I have tried using polyarea, but this doesn't seem to work.
clear all
clc
A=[-100 -40 50
-100 -40 0
-120 -40 50
-120 -40 0
-100 5 0
-100 5 50
-120 5 50
-120 5 0
-100 0 52
-100 0 52
20 0 5
20 0 5
-100 50 5
-100 50 5
20 50 52
20 50 52
-30 70 53
-30 70 0
5 70 0
5 70 53
-30 120 53
-30 120 0
5 120 53
5 120 0]; %3 Buildings Coordinate Matrix
theta=60; %Angle
rota = [cosd(theta) -sind(theta) 0; sind(theta) cosd(theta) 0; 0 0 1]; %Rotation matrix
R=A*rota; %rotates the matrix
R(:,2)=[];%deletes the y column
The first step will be to use convhull (as yar suggests) to get an outline of each projected polygonal region. It should be noted that a convex hull is appropriate to use here since you are dealing with cuboids, which are convex objects. I think you have an error in the coordinates for your second cuboid (located in A(9:16, :)), so I modified your code to the following:
A = [-100 -40 50
-100 -40 0
-120 -40 50
-120 -40 0
-100 5 0
-100 5 50
-120 5 50
-120 5 0
-100 0 52
-100 0 5
20 0 52
20 0 5
-100 50 5
-100 50 52
20 50 5
20 50 52
-30 70 53
-30 70 0
5 70 0
5 70 53
-30 120 53
-30 120 0
5 120 53
5 120 0];
theta = 60;
rota = [cosd(theta) -sind(theta) 0; sind(theta) cosd(theta) 0; 0 0 1];
R = A*rota;
And you can generate the polygonal outlines and visualize them like so:
nPerPoly = 8;
nPoly = size(R, 1)/nPerPoly;
xPoly = mat2cell(R(:, 1), nPerPoly.*ones(1, nPoly));
zPoly = mat2cell(R(:, 3), nPerPoly.*ones(1, nPoly));
C = cell(1, nPoly);
for iPoly = 1:nPoly
P = convhull(xPoly{iPoly}, zPoly{iPoly});
xPoly{iPoly} = xPoly{iPoly}(P);
zPoly{iPoly} = zPoly{iPoly}(P);
C{iPoly} = P([1:end-1; 2:end].')+nPerPoly.*(iPoly-1); % Constrained edges, needed later
end
figure();
colorOrder = get(gca, 'ColorOrder');
nColors = size(colorOrder, 1);
for iPoly = 1:nPoly
faceColor = colorOrder(rem(iPoly-1, nColors)+1, :);
patch(xPoly{iPoly}, zPoly{iPoly}, faceColor, 'EdgeColor', faceColor, 'FaceAlpha', 0.6);
hold on;
end
axis equal;
axis off;
And here's the plot:
If you wanted to calculate the area of each polygonal projection and add them up it would be very easy: just change the above loop to capture and sum the second output from the calls to convexhull:
totalArea = 0;
for iPoly = 1:nPoly
[~, cuboidArea] = convhull(xPoly{iPoly}, zPoly{iPoly});
totalArea = totalArea+cuboidArea;
end
However, if you want the area of the union of the polygons, you have to account for the overlap. You have a few alternatives. If you have the Mapping Toolbox then you could use the function polybool to get the outline, then use polyarea to compute its area. There are also utilities you can find on the MathWorks File Exchange (such as this and this). I'll show you another alternative here that uses delaunayTriangulation. First we can take the edge constraints C created above to use when creating a triangulation of the projected points:
oldState = warning('off', 'all');
DT = delaunayTriangulation(R(:, [1 3]), vertcat(C{:}));
warning(oldState);
This will automatically create new vertices where the constrained edges intersect. Unfortunately, it will also perform the triangulation on the convex hull of all the points, filling in spots that we don't want filled. Here's what the triangulation looks like:
figure();
triplot(DT, 'Color', 'k');
axis equal;
axis off;
We now have to identify the extra triangles we don't want and remove them. We can do this by finding the centroids of each triangle and using inpolygon to test if they are outside all 3 of our individual cuboid projections. We can then compute the areas of the remaining triangles and sum them up using polyarea, giving us the total area of the projection:
dtFaces = DT.ConnectivityList;
dtVertices = DT.Points;
meanX = mean(reshape(dtVertices(dtFaces, 1), size(dtFaces)), 2);
meanZ = mean(reshape(dtVertices(dtFaces, 2), size(dtFaces)), 2);
index = inpolygon(meanX, meanZ, xPoly{1}, zPoly{1});
for iPoly = 2:nPoly
index = index | inpolygon(meanX, meanZ, xPoly{iPoly}, zPoly{iPoly});
end
dtFaces = dtFaces(index, :);
xUnion = reshape(dtVertices(dtFaces, 1), size(dtFaces)).';
yUnion = reshape(dtVertices(dtFaces, 2), size(dtFaces)).';
totalArea = sum(polyarea(xUnion, yUnion));
And the total area for this example is:
totalArea =
9.970392341143055e+03
NOTE: The above code has been generalized for an arbitrary number of cuboids.
polyarea is the right way to go, but you need to call it on the convex hull of each projection. If not, you will have points in the centers of your projections and the result is not a "simple" polygon.
I am trying to get a vector of different torque values with respect to speed of an electric motor. To do that I used some torque values at certain speeds and tried to fit a curve to them.
tpdata=[0 10 20 30 40 50 60 65 70 75 80 85 90 93.3 95.8 98 99 100];
pdata=[3.3 3.05 2.81 2.79 2.80 2.88 3.02 3.12 3.20 3.28 3.13 2.75 2.10 1.5 1 0.5 0.25 0];
I modified it according to my need
u=2880/690
ydata=pdata*3.65*u
tsdata=tpdata*30/u
I used the curve fitting tool to get the constants.
p1 = -2.4592e-20
p2 = 1.51e-16
p3 = -2.7946e-13
p4 = 2.3662e-10
p5 = -1.0391e-07
p6 = 2.3887e-05
p7 = -0.0024883
p8 = 0.035497
p9 = 50.272
I want to assign the solution of the fitted polynomial (from 1 rpm to 720 rpm) to a vector that I named as y (torque values)
I can get the solution plot but I cannot see them or assign them as a vector.
for i=1:720
y = p1*i^8 + p2*i^7 + p3*i^6 + p4*i^5 + p5*i^4 + p6*i^3 + p7*i^2 + p8*i + p9;
plot(i,y,'d');
hold on
grid on
end
When I add y=zeros(1,720) and change y to y(1,i) the script fails.
What is the reason of this?
You are saving the solution each time in y that is being overwritten in the next loop. You should probably do like this:
for i=1:720
y(i) = p1*i^8 + p2*i^7 + p3*i^6 + p4*i^5 + p5*i^4 + p6*i^3 + p7*i^2 + p8*i + p9;
end
plot(y,'d');
hold on
grid on
Now you get a vector y(1x720). You dont need to do y=zeros(1,720)...
I need to find the difference between positive and negative peaks where the difference is greater than +-3.
I am using findpeaks function in MATLAB to find the positive and negative peaks of the data.
In an example of my code:
[Ypos, Yposloc] = findpeaks(YT0);
[Yneg, Ynegloc] = findpeaks(YT0*-1);
Yneg = Yneg*-1;
Yposloc and Ynegloc return the locations of the positive and negative peaks in the data.
I want to concatenate Ypos and Yneg based on the order of the peaks.
For example, my peaks are
Ypos = [11 6 -10 -10 6 6 6 6 6 -5]
Yneg = [-12 -14 -11 -11 -11 5 5 5 -6]
Locations in YT0
Yposloc = [24 63 79 84 93 95 97 100 156]
Ynegloc = [11 51 78 81 85 94 96 99 154]
In this case, where both Yposloc and Ynegloc are 9x1, I can do the following;
nColumns = size(Yposs,2);
YTT0 = [Yneg, Ypos]';
YTT0 = reshape(YTT0(:),nColumns,[])';
YTT0 = diff(YTT0)
YT0Change = numel(YTT0(YTT0(:)>=3 | YTT0(:)<=-3));
Total changes that I am interested is 6
However, I need to concatenate Yneg and Ypos automatically, based on their locations. So I think I need to to do an if statement to figure out if my positive or negative peaks come first? Then, I am not sure how to tackle the problem of when Ypos and Yneg are different sizes.
I am running this script multiple times where data changes and the negative/positive peak order are constantly changing. Is there a simple way I can compare the peak locations or am I on the right track here?
I would check each minimum with both the previous and the next maxima. In order to do that you can first combine positive and negative peaks according to their order:
Y = zeros(1, max([Yposloc, Ynegloc]));
Yloc = zeros(size(Y));
Yloc(Yposloc) = Yposloc;
Yloc(Ynegloc) = Ynegloc;
Y(Yposloc) = Ypos; % I think you inserted one extra '6' in your code!
Y(Ynegloc) = Yneg;
Y = Y(Yloc ~= 0) % this is the combined signal
Yloc = Yloc(Yloc ~= 0) % this is the combined locations
% Y =
%
% -12 11 -14 6 -11 -10 -11 -10 -11 6 5 6 5 6 5 6 -6 -5
%
% Yloc =
%
% 11 24 51 63 78 79 81 84 85 93 94 95 96 97 99 100 154 156
And then calculate the differences:
diff(Y)
% ans =
%
% 23 -25 20 -17 1 -1 1 -1 17 -1 1 -1 1 -1 1 -12 1
If you want changes of at least 6 units:
num = sum(abs(diff(Y)) > 6)
% num =
%
% 6
Ypos = [11 6 -10 -10 6 6 6 6 -5];
Yneg = [-12 -14 -11 -11 -11 5 5 5 -6];
Yposloc = [24 63 79 84 93 95 97 100 156];
Ynegloc = [11 51 78 81 85 94 96 99 154];
TOTAL=[Yposloc Ynegloc;Ypos Yneg];
%creatin a vector with positions in row 1 and values in row 2
[~,position]=sort(TOTAL(1,:));
%resort this matrix so the values are in the orginial order
TOTAL_sorted=TOTAL(:,position);
%look at the changes of the values
changes=diff(TOTAL_sorted(2,:));
if changes(1)>0
disp('First value was a Minimum')
else
disp('First value was a MAximum')
end
%same structure at the TOTAL matrix
%abs(changes)>3 produces a logical vector that shows where the absolute values was bigger
%than 3, in my opinon its rather intresting where the end is then were the start is
% thats why i add +1
Important_changes=TOTAL_sorted(:,find(abs(changes)>3)+1);
plot(TOTAL_sorted(1,:),TOTAL_sorted(2,:))
hold on
plot(Important_changes(1,:),Important_changes(2,:),...
'Marker','o','MarkerSize',10, 'LineStyle','none');
hold off
I am struggling with the concepts behind plotting a surface polar plot.
I am trying to plot the values measured by a sensor at a combination of different angles over a hemisphere.
I have an array containing the following information:
A(:,1) = azimuth values from 0 to 360º
A(:,2) = zenith values from 0 to 90º
A(:,3) = values measured at the combination of angles of A(:,1) and A(:,2)
For example, here is a snippet:
0 15 0.489502132167206
0 30 0.452957556748497
0 45 0.468147850273115
0 60 0.471115818950192
0 65 0.352532182508945
30 15 0.424997863795610
30 30 0.477814980942155
30 45 0.383999653859467
30 60 0.509625464595446
30 75 0.440940431784788
60 15 0.445028058361392
60 30 0.522388502880219
60 45 0.428092266657885
60 60 0.429315072676194
60 75 0.358172892912138
90 15 0.493704001125912
90 30 0.508762762699997
90 45 0.450598496609200
90 58 0.468523071441297
120 15 0.501619699042408
120 30 0.561755273071577
120 45 0.489660355057938
120 60 0.475478615354648
120 75 0.482572226928475
150 15 0.423716506205776
150 30 0.426735372570756
150 45 0.448548968227972
150 60 0.478055144126694
150 75 0.437389584937356
To clarify, here is a piece of code that shows the measurement points on a polar plot.
th = A(:,1)*pi/180
polar(th,A(:,2))
view([180 90])
This gives me the following plot:
I would like now to plot the same thing, but instead of the points, use the values of these points stored in A(:,3). Then, I would like to interpolate the data to get a colored surface.
After some research, I found that I need to interpolate my values over a grid, then translate to Cartesian coordinates. From there I do not know how to proceed. Could someone point me in the right direction?
I have trouble getting the concept of the interpolation, but this is what I have attempted:
x1 = linspace(0,2*pi,100)
x2 = linspace(0,90,100)
[XX,YY] = meshgrid(x1,x2)
[x,y] = pol2cart(th,A(:,2))
gr=griddata(x,y,A(:,3),XX,YY,'linear')
With this piece of code, your example data points are converted into cartesian coords, and then plotted as "lines". The two tips of a line are one data point and the origin.
az = bsxfun(#times, A(:,1), pi/180);
el = bsxfun(#times, A(:,2), pi/180);
r = A(:,3);
[x,y,z] = sph2cart(az,el,r);
cx = 0; % center of the sphere
cy = 0;
cz = 0;
X = [repmat(cx,1,length(x));x'];
Y = [repmat(cy,1,length(y));y'];
Z = [repmat(cz,1,length(z));z'];
Still thinking how to interpolate the data so you can draw a sphere. See my comments to your question.