I am trying to find the tangent lines from a given point outside a closed curve (not on the curve). The curve is defined as 2D x and y coordinates of points，shaped like an irregular ellipse for example.

If given a point by the user: (x0,y0) = (-30,80), how can I know the tangent points (obviously closest point among discrete points from the smooth curve) on curve (i.e. tangent lines from (x0,y0) to curve)?

Answer:

One possibility is to use numerical differentiation to find the tangent line at every point, and decide whether it passes "close enough" to the given point. However, one has to think hard about "close enough" to avoid getting either no matches or too many.

Here is another approach: consider the unit vectors pointing from the given point (x0,y0) to the points on the curve. Find the largest gap between them (the command convhull helps here). The vectors on both sides of the gap determine tangent lines.

In general this will find only two tangent lines, not all of them. But if the curve is convex, there are only two tangent lines anyway.

Here is an example of the tricky situations where the given point is within the convex hull of the curve.

The code that produced the above picture:

```
t = linspace(0,2*pi,100);
x = 10*cos(t) + sin(7*t);
y = 6*sin(t) + cos(13*t); % x,y describe the curve;
x0 = 4; y0 = 5; % given point
xn = (x-x0)./sqrt((x-x0).^2+(y-y0).^2); % unit vectors
yn = (y-y0)./sqrt((x-x0).^2+(y-y0).^2); % from x0,y0 to points on the curve
cvx = convhull(xn,yn); % convex hull of unit vectors
[~,i] = max(diff(xn(cvx)).^2+diff(yn(cvx)).^2); % largest gap in the hull
x1 = xn(cvx(i)); y1=yn(cvx(i)); % vectors on both sides
x2 = xn(cvx(i+1)); y2=yn(cvx(i+1)); % of the gap
plot(x,y)
hold on
s = linspace(0,10);
plot(x0+s*x1, y0+s*y1, 'r') % output
plot(x0+s*x2, y0+s*y2, 'r')
hold off
```

**Another approach**, which works fine if (x0,y0) is not within the convex hull of the curve.

Use `convhull`

to find the convex hull of the union of the curve and of the given points `(x0,y0)`

. The two edges of the convex hull that are incident to `(x0,y0)`

are tangent to the curve:

The code that produced the above picture:

```
t = linspace(0,2*pi,100);
x = 10*cos(t) + sin(7*t);
y = 6*sin(t) + cos(13*t); % x,y describe the curve;
x0 = 4; y0 = 8; % given point
xe = [x0, x]; ye = [y0, y]; % put all points together
cvx = convhull(xe,ye); % find convex hull
x1 = xe(cvx(2)); y1=ye(cvx(2)); % one neighbor of (x0,y0)
x2 = xe(cvx(end-1)); y2=ye(cvx(end-1)); % another neighbor
plot(x,y)
hold on
s = linspace(0,2);
plot(x0+s*(x1-x0), y0+s*(y1-y0), 'r') % plot the lines
plot(x0+s*(x2-x0), y0+s*(y2-y0), 'r')
hold off
```

matlab,matlab-figure

I'm struggling to plot multiple functions on one figure. Here is the code that I have: syms t a; a=0.9514; F1=0.5*sqrt(3*t^2); F2=-0.28375*t^2+1.155*a*(t-a)+1; F3=1; E1=diff(F1,t); E2=diff(F2,t); E3=diff(F3,t); I want to plot E1, E2 and E3, each only within a certain range, to make a "composite" line. I've tried plotting with ezplot...

arrays,matlab

I have two vectors, one of them stores the width dimension of a set of images and another one the height of these set of images. I want to use these values as two dimensional vectors [width height] and store them in a matrix. The first line, for instance, keeps...

matlab,loops,for-loop,while-loop,do-while

This is my one dimensional array A. containing 10 numbers A = [-8.92100000000000 10.6100000000000 1.33300000000000 ... -2.57400000000000 -4.52700000000000 9.63300000000000 ... 4.26200000000000 16.9580000000000 8.16900000000000 4.75100000000000]; I want the loop to go through like this; (calculating mean interval wise) - Interval length of 2,4,8 (a(1)+a(2))/2 - value stored in one block of...

matlab,image-processing

I have a labeled matrix containing two objects. How can I thicken an object to a curve? Actually I have the following image: and I want this: Each pixel of the resulting curve is the median of each column. But if you have another idea, it is acceptable, because I...

matlab,plot,signals,circle

I have some random signal (for example sin signal) with the time scale. t=0:0.1:2*pi y=sin(t) plot(t,y) Now I want to draw this signal on this circle. So the time vector actually becomes an envelope of the circle. Envelope of the circle represents "y = 0" in cartesian coordinate system. Here...

matlab

A text file could be loaded as below: load sourceETA/Record1/result1.txt How can I use a variable in address of loading? For example (n is a variable): [load 'sourceETA/Record1/result',num2str(n),'.txt'] But the above code doesn't work! How do I do?...

arrays,matlab,math,for-loop,while-loop

This is my one dimensional array A, containing 10 numbers: A = [-8.92100000000000 10.6100000000000 1.33300000000000 ... -2.57400000000000 -4.52700000000000 9.63300000000000 ... 4.26200000000000 16.9580000000000 8.16900000000000 4.75100000000000]; I want the loop to go through like this; (calculating mean interval wise) - Interval length of 2,4,8 (a(1)+a(2))/2 - value stored in one block of...

matlab

I have the following matrix A in Matlab of dimension (m*d)x2 A=[1 1; 3 2; 8 3; ----- 9 1; 2 2; 5 3; ----- 6 1; 1 2; 4 3; ----- 8 1; 1 2; 5 3]; Hence m=max(A(:,2))=3 and d=4 is the number of submatrices in A of...

matlab,matrix,merge

I am trying to merge two matrices that share same values in multiple columns. The following matrices should exemplify my problem and provide a MWE. However, my data is very long size(500000, 4), therefore I am searching an efficient way to merge them. The data consists of option data where...

matlab,filtering,convolution

I'm trying to design a Wiener filter in Matlab for a deconvolution problem but I'm having a lot of problems. I have a gaussian white noise process with a variance of 1.2 and a impulse response which has length two. Its values are g(0) = 5 and g(1) = 4....

matlab

Is it possible to add statements in between the codes. For example: If I have a code like this, r(:,1) = a(:,1) - a(:,2); Then can I write it as, r(:,1) = a(:,1)("this is a constant") - a(:,2)("this is a variable"); ...

matlab,image-processing

I am trying to read all the images in the folder in MATLAB using this code flst=dir(str_Expfold); But it shows me output like this. which is not the sequence as i want. Can anyone please tell me how can i read all of them in sequence? for giving downmark, please...

matlab,matrix

I have a matrix looks like: 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 1 0 1 0 0 0 1 0 4 0 0 0 0 0 3 0 0 6 0 0 4...

math,javafx,geometry,coordinates

I have a line which has points (x1,y1) and (x2,y2). I wanted to attach a Button to it, it should align with the line by rotating based on the line segment points. I need some help in calculating the rotation angle for the Button.

string,matlab

I have a string "FDFACCFFFBDCGGHBBCFGE" . Could anyone help me to generate a new string with the same order but no element inside repeated twice. Thanks ! The expected output should be like this : "FDACBGHE"...

c++,matlab

Is there an alternative way to call a C++ class using MATLAB, and operate its methods on MATLAB variables?

matlab

my matlab version is 2012a. when I use fitcknn,has this error: Undefined function 'fitcknn' for input arguments of type 'cell'. how to calculate probability for each class for predicate with knn without fitcknn? after use this code, I want to calculate prob_estimates for each neighbors: knn = ClassificationKNN.fit(trainsample, trainlabel,'NumNeighbors',7); y...

matlab,system,equation

sorry if it already has a answer..i tried other links but it didn't understand i have 2 1*63 array .landa and v. each of their members are syms. and each v member is a function of all landa members.i have already calculated v members and they are all symbolic equations...

matlab

Hi I have data in MATLAB like this: F = 1.0000 1.0000 2.0000 1.0000 3.0000 1.0000 3.1416 9.0000 4.0000 1.0000 5.0000 1.0000 6.0000 1.0000 6.2832 9.0000 7.0000 1.0000 8.0000 1.0000 9.0000 1.0000 9.4248 9.0000 10.0000 1.0000 I am looking for a way to sum the data in specific intervals. Example...

arrays,matlab,matrix

I have matrix A and matrix B. Matrix A is 100*3. Matrix B is 10*3. I need to insert one row from matrix B each time in a sequence into matrix A after every 10th row. The result would be Matrix A with 110*3. How can I do this in...

matlab

So, I want to be able to look at (read: copy) MATLAB's NonLinearModel method of printing the regression results to the screen such as this. Nonlinear regression model: y ~ (alpha1 - alpha2*t^0.5) Estimated Coefficients: Estimate SE tStat pValue alpha1 1.0253 0.0082253 124.66 4.8823e-24 alpha2 0.0061783 0.00073277 8.4314 4.4834e-07 Number...

matlab,svm,auc

I'm having a weird problem in training an SVM with an RBF kernel in Matlab. The issue is that, when doing a grid search, using 10-fold cross-validation, for the C and Sigma values I always get AUC values equal to approximately .50 (varying between .48 and .54 depending) -- I...

matlab,regression

I am doing some bone segmentation whereas the result of this segmentation is points placed in a circular pattern around this bone. However as it is taken using a qCT scan, there is quite a lot noise (from e.g. flesh) on the points that i have. So the overall problem...

matlab

I have 20 column vectors in the workspace and I'd like them all to be contained within a cell array. They're all labelled data1, data2, data3,...data20. Is there a faster way to do this than: cell = {data1, data2, data3, data4, data5, data6, ...} all the way up to data20?...

matlab,simulink

I am working on a simple System Object in Matlab/Simulink. It looks like this : classdef realtime_header_detectorSO < matlab.System & matlab.system.mixin.Propagates % correlateHeader % % This template includes the minimum set of functions required % to define a System object with discrete state. properties Header %nrOfBitsInPreviousStep=0; s=100; d=zeros(1,s); end properties...

c,matlab,fopen,mex

I have a little experience with Matlab, but am new to the mex environment. What I am trying to do is to save some values I compute to a txt file in my C routine. For the sake of simplicity I am using the example arrayProduct.c from MathWork's Create C...

matlab,distribution,sampling,random-sample

How can I create a vector x in Matlab that has values between 0.8 and 1.2, randomly sampled from a: 1. Uniform 2. Normal distribution? There are a lot of functions dealing with distributions, but I'm having trouble using them properly....

matlab,matrix,multidimensional-array,scalar

I'm having problems multiplying specific values within my multidimensional matrix by a scalar. My matrix has the following dimension: size(comDatabe) = 5 10 3 397 10 The third dimension is an x-y-z coordinate frame. Something went wrong and now my y-axis is defined upside down for one subject (#8 out...

image,matlab,image-processing,mask,boundary

I'm trying to create a mask (or similar result) in order to erase pieces of a binary image that are not attached to the object surrounded by the boundary. I saw this thread (http://www.mathworks.com/matlabcentral/answers/120579-converting-boundary-to-mask) to do this from bwboundaries, but I'm having trouble making suitable changes to it. My goal...

matlab,image-processing

I have a binary matrix containing several binary objects and I want to bridge between them. Actually I have the following picture: And the result has to be like this: Is there any function or a shortcut way, other than loops, for this problem?...

matlab

What is the ellipsis for in this Matlab statement? frame = insertObjectAnnotation(frame, 'rectangle', ... bboxes, labels); ...I could not find in their online doc....

image,matlab,image-processing,computer-vision

I need to save a set of pre-processing images in matlab, resulting in grayscale images. The problem is the fact that these pre-processed images have pixel values higher than 255. If I save them with imwrite() as, for instance, .PNG files, does matlab normalize the values to be in [0,255]...

matlab,time-frequency

Code tfr = abs ( tfr ); [row_size, column_size] = size(tfr); tfr = tfr(1:round(row_size/2), 1:row_size); surf(tfr); view(2); I get in R2014b of OSX 10.10.3 Yosemite but rotating around shows that the cells should not be black Why is the output black? I wonder if this is a hardware problem or...

matlab,matrix,least-squares

How can I solve , where and and in the least squares sense in matlab? So I'd like to have the minimizing as output....

matlab,plot

I want to display three figures in a figure window. Assuming that I divide 2x2 regions. subplot(2,2,1) ---------+----------- | R1 | R2 | ---------+----------- | R3 | R4 | ---------+----------- I want to show a figure merging R1 and R3 ant other two in R2 and R4 I can display...

matlab,neural-network

How can I change "Validation Checks" value from 6 to higher or lower values using code? I have following code: % Create a Pattern Recognition Network hiddenLayerSize = ns; net = patternnet(hiddenLayerSize); net.divideParam.trainRatio = trRa/100; net.divideParam.valRatio = vaRa/100; net.divideParam.testRatio = teRa/100; % Train the Network [net,tr] = train(net,inputs,targets); % Test...

matlab,typeconverter

I'm currently using a MATLAB to work and I need some help: I need to convert my output data (variable: units) be a double instead of a cell because I must perform a sum: units = inputdlg(question,title); sum = units + i; I've tried this code also but didn't solve...

excel,matlab,cluster-analysis,k-means,geo

I have 8 traveling consultants that need to visit 155 groups across the continental united states. Is there a way to find the optimal 8 regions based of drive time using k-means clustering? I see there are some methods implemented already for other data sets, but they are not based...

matlab,plot,legend,movie

i have a question regarding legend for movies. This is my code: fig = figure(); for i = 1: 70000 plot(signal1) hold on; plot([i,i],[-5,5]) plot(signal2,'r') hold off; title('\fontsize{14} my data'); legend('signal1','signal2'); axis tight; f(i) = getframe(fig); end The legend shows the same colors for the first two things I plot....

image,matlab,image-processing,image-segmentation

I have an image which I want to divide into overlapping blocks. I have set the box to be of size 8 rows and 8 columns, and the overlapping factor to be 4 rows/columns. This is what I have written to solve this: img = imread('a03-017-05.png'); overlap = 4 count...

matlab,plot

I have multiple 2D line plots in Matlab (they represent some wave moving through space). Each plot represents the wave at some time t. I want to animate through these plots (i.e. show the first plot for a fraction of a second, then show the next one, and the next,...

matlab,cell

I'm trying to equate each element to an array which correspond to cell element. To explain it more precisely, e.g A = {[1 1 1], [0 0 0 0 0], [1 1],[0 0 0 0 0]}; B = [0 1 0 0]; So the thing I want is : A=...

c++,geometry,quaternions,euler-angles

I've been trying to figure out the difference between these, and why ToEulerXYZ does not get the right rotation. Using MathGeoLib: axisX: x 0.80878228 float y -0.58810818 float z 0.00000000 float axisY: x 0.58811820 float y 0.80877501 float z 0.00000000 float axisZ: x 0.00000000 float y 0.00000000 float z 1.0000000...

matlab

I have a variable 'b'. Inside of b, I have 27X1 cell. In every cell there is some characters for example in 1x1 there is asdf, in 2x1 there is dfgh it's going on like this. I want that matlab creates mat files which names are asdf, dfgh and assign...

matlab,polynomial-math

I have the following code: syms z Gc=1.582*(1-0.3679*z^-1)/(1+.418*z^-1); Ghp=.3679*(z^-1)*(1+.718*z^-1)/((1-z^-1)*(1-.3679*z^-1)); T=(Gc*Ghp)/(1+Gc*Ghp); clipboard('copy', latex(simplifyFraction(T))); Which results in following for T: How can I normalise coefficients? I.e. I want the z2 in denominator and z in numerator to have the coefficient of 1. Is there any function in Matlab to do so?...

string,matlab,filenames

I am using the below mentioned code to get the file names of images according to their id's from images_1 text file as strings and use them to read the images from their directory image_count=1; for image_count=1:6 file=fopen('D:\Academics\New folder\CUB_200_2011\images_1.txt','r'); C = textscan(file, '%s'); original_image=imread('D:\Academics\New folder\CUB_200_2011\images\%s','C{1}{2*(image_count)}'); imshow(original_image) end I am able...

matlab,plot

I have a semilogarithmic plot which works so far with semilogx. Now I would like to change the tick labels. Now it says 10^8 10^9 ... 10^13, but I would like to see 1e8, 1e9, ... 1e13 on the x-axis. How can I change that? Cheers Manuel...

matlab,events,delay

In Matlab functions can be started at events,but occasionally, like with the resize function, the events are called in rapid order and the function is called many times in succession, which can cause weird behavior and lag. Is there a way to have it listen for the event but only...

java,android,image,matlab,jar

I managed to create a java package from a Matlab function (for image processing) using deploytool. I tested it in Eclipse and it runs perfectly. The problem is that I want to use this Matlab function for an Android Studio project and I can´t find any way to make it...

matlab,machine-learning

This is my implementation of CostFunctionJ: function J = CostFunctionJ(X,y,theta) m = size(X,1); predictions = X*theta; sqrErrors =(predictions - y).^2; J = 1/(2*m)* sum(sqrErrors); But when I try to enter the command in MATLAB as: >> X = [1 1; 1 2; 1 3]; >> y = [1; 2; 3];...