I have Quadric Surface equation
I know A,B,C...
How can I plot my equation in matlab?
Your best bet is to produce a 3D contour plot of your function with a single contour at the function value 0. To do this with reasonable accuracy, compute your function F at a number of points x, y, z as follows:
gv = linspace(-30,30,50); % adjust for appropriate domain
[xx yy zz]=meshgrid(gv, gv, gv);
F = A*xx.*xx + B*yy.*yy + C*zz.*zz+ ... etc
figure
isosurface(xx, yy, zz, F, 0)
The reason to do it this way is that your function is typically multi-valued- that is, for a given value of X and Y there may be two possible answers for Z. By doing things this way you effectively bypass that problem - instructing matlab to put a surface anywhere that the function is zero.
Note that I gave an arbitrary vector gv for the grid - that is, the points on which the function is evaluated. To get an accurate and visually pleasing result you probably need around 50 points in each dimension within the range over which a solution is possible (this may be different in the three dimensions);
For example, with
F = xx.^2 + 2*yy.^2 + 0.5*zz.^2 + .4*xx.*yy + .5*xx.*zz + .6*yy.*zz + 7*xx + 8*yy + 9*zz - 100;
You get the following figure:
Related
I need to plot a parabola and ellipse. However the ellipse is giving me trouble. Can anyone help? The equations are: y = -5*x^2 + 2 and (x^2/16) + (y^2/2) = 4
I've tried this code but obviously I feel like like it isn't right.
x = linspace(-5, 5);
y1 = (x.^2/16) + (y.^2/2) - 1;
y2 = -5*x.^2 +2;
figure(1)
plot(x, y1)
hold on
plot(x, y2)
hold off
Firstly, you did not define a range variable x. Secondly, the ellipse won't pass the vertical line test and can't be plotted like a regular function f(x). Thirdly, your equation y1 = (x.^2/16) + (y.^2/2) - 1; is non-sensical because you have y on each side.
You could correct your method by defining a range variable x1 and x2 that each have appropriate ranges for the functions your plotting. What I mean by this is that you probably don't want the same range for each function, because the ellipse is undefined over most of the range that the parabola is defined. To plot the ellipse using f(x) you could observe that there are + and - values that are identical, using this fact you could plot your ellipse by two functions one to represent the top half and one to represent the bottom half, each of these would pass the vertical line test.
OR
You could utilize ezplot and have a nice time with it because it makes your life easier. Here is a solution.
ezplot('x^2/16+y^2/2-4'); axis equal; hold on
ezplot('-5*x^2+2-y')
There are multiple ways to plot an ellipse, e.g. you could also use a parametric representation of the equation.
In your approach though, when plotting functions using plot(x,y) command, you need to express your dependent variable (y) through independent variable (x). You defined the range for x, which is what you substitute into your equations in order to find y's. While for the parabola, the dependency of y from x is obvious, you forgot to derive such a relationship for the ellipse. In this case it will be +-sqrt((1 - x^2/16)*2). So in your approach, you'll have to take into account both negative and positive y's for the same value of x. Also there's discrepancy in your written equation for the ellipse (=4) and the one in Matlab code (=1).
x = linspace(-5, 5);
y1 = sqrt((1 - x.^2/16)*2);
y2 = -5*x.^2 +2;
figure(1)
plot(x, real(y1), 'r', x, -real(y1), 'r')
hold on
plot(x, y2)
hold off
Since the ellipse has real y's not on the whole x domain, if you want to plot only real parts, specify real(y1) or abs(y1) (even though Matlab does it for you, too). You can also dismiss complex numbers for certain x when computing y1, but you'll need a for-loop for that.
In order to make things simpler, you can check the function fimplicit, ezplot is not recommended according to Matlab's documentation. Or if you want to plot the ellipse in a parametric way, fplot will work, too.
Another (more classic) approach for parametric plotting is given here already, then you don't need any other functions than what you already use. I think it is the simplest and most elegant way to plot an ellipse.
You will not be able to generate points for the ellipse using a function f(x) from a Cartesian linspace range. Instead, you can still use linspace but for the angle in a polar notation, from 0 to 2*pi. You should also be able to easily adjust radius and offset on both axis on the cos and sin expressions.
x = linspace(-5, 5);
y2 = -5*x.^2 +2;
figure(1)
clf;
plot(x, y2)
hold on
a = linspace(0,2*pi);
x2 = 4*cos(a);
y2 = sqrt(2)*sin(a);
plot(x2, y2)
xlim([-5,5]);
ylim([-5,5]);
hold off
I have a parametric B-Spline surface, S
S=[x(:);y(:);z(:)];
Right now, I am plotting the surface by just plotting each column of S as a single point:
plot3(S(1,:),S(2,:),S(3,:),'.')
The result is this:
Unfortunately, by plotting individual points, we lose the sense of depth and curvy-ness when we look at this picture.
Any ideas on how to implement SURF or MESH command for a parametric surface? These functions seem to require a matrix representing a meshgrid which I dont think I can use since the X x Y domain of S is not a quadrilateral. However, I like the lighting and color interpolation that can be conveniently included when using these functions, as this would fix the visualization problem shown in figure above.
I am open to any other suggestions as well.
Thanks.
Without seeing your equations it's hard to offer an exact solution, but you can accomplish this by using fsurf (ezsurf if you have an older version of MATLAB).
There are specific sections regarding plotting parametric surfaces using ezsurf and fsurf
syms s t
r = 2 + sin(7*s + 5*t);
x = r*cos(s)*sin(t);
y = r*sin(s)*sin(t);
z = r*cos(t);
fsurf(x, y, z, [0 2*pi 0 pi]) % or ezsurf(x, y, z, [0 2*pi 0 pi])
If you want to have a piece-wise function, you can either write a custom function
function result = xval(s)
if s < 0.5
result = 1 - 2*s;
else
result = 2 * x - 1;
end
end
And pass a function handle to fsurf
fsurf(#xval, ...)
Or you can define x to be piece-wise using a little bit of manipulation of the function
x = (-1)^(s > 0.5) * (1 - 2*s)
I want to plot relations like y^2=x^2(x+3) in MATLAB without using ezplot or doing algebra to find each branch of the function.
Does anyone know how I can do this? I usually create a linspace and then create a function over the linspace. For example
x=linspace(-pi,pi,1001);
f=sin(x);
plot(x,f)
Can I do something similar for the relation I have provided?
What you could do is use solve and allow MATLAB's symbolic solver to symbolically solve for an expression of y in terms of x. Once you do this, you can use subs to substitute values of x into the expression found from solve and plot all of these together. Bear in mind that you will need to cast the result of subs with double because you want the numerical result of the substitution. Not doing this will still leave the answer in MATLAB's symbolic format, and it is incompatible for use when you want to plot the final points on your graph.
Also, what you'll need to do is that given equations like what you have posted above, you may have to loop over each solution, substitute your values of x into each, then add them to the plot.
Something like the following. Here, you also have control over the domain as you have desired:
syms x y;
eqn = solve('y^2 == x^2*(x+3)', 'y'); %// Solve for y, as an expression of x
xval = linspace(-1, 1, 1000);
%// Spawn a blank figure and remember stuff as we throw it in
figure;
hold on;
%// For as many solutions as we have...
for idx = 1 : numel(eqn)
%// Substitute our values of x into each solution
yval = double(subs(eqn(idx), xval));
%// Plot the points
plot(xval, yval);
end
%// Add a grid
grid;
Take special care of how I used solve. I specified y because I want to solve for y, which will give me an expression in terms of x. x is our independent variable, and so this is important. I then specify a grid of x points from -1 to 1 - exactly 1000 points actually. I spawn a blank figure, then for as many solutions to the equation that we have, we determine the output y values for each solution we have given the x values that I made earlier. I then plot these on a graph of these points. Note that I used hold on to add more points with each invocation to plot. If I didn't do this, the figure would refresh itself and only remember the most recent call to plot. You want to put all of the points on here generated from all of the solution. For some neatness, I threw a grid in.
This is what I get:
Ok I was about to write my answer and I just saw that #rayryeng proposed a similar idea (Good job Ray!) but here it goes. The idea is also to use solve to get an expression for y, then convert the symbolic function to an anonymous function and then plot it. The code is general for any number of solutions you get from solve:
clear
clc
close all
syms x y
FunXY = y^2 == x^2*(x+3);
%//Use solve to solve for y.
Y = solve(FunXY,y);
%// Create anonymous functions, stored in a cell array.
NumSol = numel(Y); %// Number of solutions.
G = cell(1,NumSol);
for k = 1:NumSol
G{k} = matlabFunction(Y(k))
end
%// Plot the functions...
figure
hold on
for PlotCounter = 1:NumSol
fplot(G{PlotCounter},[-pi,pi])
end
hold off
The result is the following:
n = 1000;
[x y] = meshgrid(linspace(-3,3,n),linspace(-3,3,n));
z = nan(n,n);
z = (y .^ 2 <= x .^2 .* (x + 3) + .1);
z = z & (y .^ 2 >= x .^2 .* (x + 3) - .1);
contour(x,y,z)
It's probably not what you want, but I it's pretty cool!
Basically, I have a function f(X,Y) that would return one value for each X,Y that I give. Is there any function in matlab where I can pass the function f, the ranges for X,Y so that it plots a 3d graph showing the magnitude of f (along the z axis) for all values within the given range.
ezplot3, does this kind of, but it takes only one parameter 't'. I am very new to matlab and am trying my best to learn it fast, but I couldnt find much regarding this. Any help would be appreciated
Keep in mind, that with matlab, you're never really plotting "functions"; You're plotting arrays/vectors. So instead of trying to plot g = f(X,Y), you'll actually by plotting the vectors X, Y, and g, where X and Y are your original inputs and g is a vector containing your outputs.
I'm having a hard time visualizing what exactly you're trying to plot but basically, you can follow any standard matlab plotting example such as: http://web.cecs.pdx.edu/~gerry/MATLAB/plotting/plotting.html
It does not produce a 3D plot, but I have found the 2D scatter plot useful for this kind of task before:
scatter(x, y, 5, z)
Where z is the value of the function at the point (x, y) will produce something similar to what you want. Its perhaps not quite as pretty as a full 3D plot but can be used to good effect.
See:
http://www.mathworks.com/matlabcentral/fileexchange/35287-matlab-plot-gallery-scatter-plot-2d/content/html/Scatter_Plot_2D.html
Here is some (very ugly) code I put together to demonstrate the difference:
j=1;
y = -100:1:100;
for i = -100:1:100
y = [y -100:1:100];
count = 0;
while count < 202;
x(j) = i;
j = j+1;
count = count + 1;
end
end
z = (abs(x) + abs(y));
figure(1)
scatter(x, y, 10, z)
h=colorbar;
figure(2)
ezsurf('(abs(x) + abs(y))')
Well, this is what I was going for : http://www.mathworks.com/help/matlab/ref/ezsurf.html
if i do this
ezsurf('f(x,y)');
I get the 3d graph I wanted.
Thanks anyways!
I'm trying to do a scatter plot with a line of best fit in matlab, I can get a scatter plot using either scatter(x1,x2) or scatterplot(x1,x2) but the basic fitting option is shadowed out and lsline returns the error 'No allowed line types found. Nothing done'
Any help would be great,
Thanks,
Jon.
lsline is only available in the Statistics Toolbox, do you have the statistics toolbox? A more general solution might be to use polyfit.
You need to use polyfit to fit a line to your data. Suppose you have some data in y and you have corresponding domain values in x, (ie you have data approximating y = f(x) for arbitrary f) then you can fit a linear curve as follows:
p = polyfit(x,y,1); % p returns 2 coefficients fitting r = a_1 * x + a_2
r = p(1) .* x + p(2); % compute a new vector r that has matching datapoints in x
% now plot both the points in y and the curve fit in r
plot(x, y, 'x');
hold on;
plot(x, r, '-');
hold off;
Note that if you want to fit an arbitrary polynomial to your data you can do so by changing the last parameter of polyfit to be the dimensionality of the curvefit. Suppose we call this dimension d, you'll receive back d+1 coefficients in p, which represent a polynomial conforming to an estimate of f(x):
f(x) = p(1) * x^d + p(2) * x^(d-1) + ... + p(d)*x + p(d+1)
Edit, as noted in a comment you can also use polyval to compute r, its syntax would like like this:
r = polyval(p, x);
Infs, NaNs, and imaginaryparts of complex numbers are ignored in the data.
Curve Fitting Tool provides a flexible graphical user interfacewhere you can interactively fit curves and surfaces to data and viewplots. You can:
Create, plot, and compare multiple fits
Use linear or nonlinear regression, interpolation,local smoothing regression, or custom equations
View goodness-of-fit statistics, display confidenceintervals and residuals, remove outliers and assess fits with validationdata
Automatically generate code for fitting and plottingsurfaces, or export fits to workspace for further analysis