How can I plot an elliptical paraboloid in MATLAB with surf() function, using parametric equations with 2 variables u and v? The equation looks like
r = {ucos{v}, u^2,5usin{v}}
I understand that I need to make a meshgrid from u and v, but what to do next?
You can do it the following way:
%// Create three function handles with the components of you function
fx = #(u,v) u.* cos(v); %// Notice that we use .*
fy = #(u,v) u.^2; %// and .^ because we want to apply
fz = #(u,v) 5.*u.*sin(v);%// multiplication and power component-wise.
%// Create vectors u and v within some range with 100 points each
u = linspace(-10,10, 100);
v = linspace(-pi,pi, 100);
%// Create a meshgrid from these ranges
[uu,vv] = meshgrid(u, v);
%// Create the surface plot using surf
surf(fx(uu,vv), fy(uu,vv), fz(uu,vv));
%// Optional: Interpolate the color and do not show the grid lines
shading interp;
%// Optional: Set the aspect ratio of the axes to 1:1:1 so proportions
%// are displayed correctly.
axis equal;
I added some annotation, because you seem to be new to Matlab.
Related
I'm wondering if anyone has any insight into why these two plot commands produce domains that are orders of magnitude different?
syms t
x1Axis = 0:.01:10;
fun1(t) = sin(t)
plot(sin(x1Axis))
hold on
y = sin(x1Axis)
plot(x1Axis, y)
fun1(t) is plotted "symbolically" while y is evaluated and plotted "discreetly". Should I be using a different plot method in the case of the first function?
No, you are not plotting the symbolic function correctly.
In your code, the instruction plot(sin(x1Axis)) is not a symbolic plot, but a numeric plot of the sine versus the index of each value.
From the plot documentation page:
plot(Y) creates a 2-D line plot of the data in Y versus the index of
each value.
If Y is a vector, then the x-axis scale ranges from 1 to length(Y).
To plot the symbolic function use fplot.
The following example will allow you to see that both the symbolic and numeric plots are the same:
xmin = 0;
xmax = 10;
% Symbolic Plot.
syms t
fun1(t) = sin(t);
fplot(fun1, [xmin xmax], '-r');
hold on;
% Numeric Plot.
x = xmin:.01:xmax;
y = sin(x);
plot(x, y, '--g');
% Add legend.
legend('Symbolic Plot', 'Numeric Plot', 'Location', 'north');
This is the result:
if the function F is available it is easy to draw surf plot i.e.
x=1:0.1:4;
y=1:0.1:4;
[X,Y]=meshgrid(x,y);
Z=sin(X).^2+cos(Y).^2;
surf(X,Y,Z);
view(2) ;
in my case I calculated F function using least square:
for example I have x and y vectors
x = [0 9.8312 77.1256 117.9810 99.9979];
y = [0 2754.5 4043.3 5376.3 5050.4];
the linear function of these two vector is define by
F= [1149.73 , 37.63];
therefore the estimation is equal to
z= [ones(5,1) x']*F';
which is
z = [1149.73 1519.67 4051.96 5589.35 4912.65];
and if it is plotted
plot(x,y,'b.');
hold on;plot(x,y,'b-');
hold on; plot(x,z,'-r');
The linear z ( red line) is showing correctly. Now I want to plot it for all possible combination of x and y using grid and I need to have a mesh for all inputs
[X,Y] = meshgrid(x,y);
but how to make the Z matrix to show the intensity plot of function Z? The Z suppose to have high intensity close to z value and less value far from it. I should suppose to get something like this
Thanks
P.S: the F is calculated using pinv (least square).
You have to interpolate the scattered data to plot it on grid. Here is a simple example for your x, y and z vectors
xi=linspace(min(x),max(x),100)
yi=linspace(min(y),max(y),100)
[XI YI]=meshgrid(xi,yi);
ZI = griddata(x,y,z,XI,YI);
contourf(XI,YI,ZI)
I have a problem and maybe you will be able to help me. Like in the title i have cross section data of a symmetric lens - coordinates s=-100:1:100 and height y - and I would like to create 3D plot the whole lens (x,y,z). Is there any build in function that helps with that? Thanks for help in advance!
If I'm understanding correctly, you have a 1-D array that you'd effectively like to 'sweep' around a circle to produce a 3-D plot. Here is an example of how to do that
% Some dummy data
Npts = 100;
z = sin(linspace(0, pi, Npts));
Nreps = 100; % How many times to repeat around circle
% Create polar meshgrid and convert to Cartesian
[r, theta] = meshgrid( ...
linspace(-length(z)/2, length(z)/2, Npts), ...
linspace(0, pi, Nreps));
[X, Y] = pol2cart(theta, r);
% Copy data Nreps times
Z = repmat(z, Nreps, 1);
% Plot!
surf(X, Y, Z)
Without more specs (such as if your y is a 2D matrix or a 1D array), it's not possible to give you the exact answer. However here is how you draw a surface in Matlab:
% create a meshgrid used as the independent variables of your surface
[sx, sy] = meshgrid(-100:100);
% if you have your own 2D matrix, ignore this line.
% if you have a formula, replace this line with your own formula
y = cos(sqrt(((sx/100).^2+(sy/100).^2)/2)*(pi/2));
% draw the surface
surf(sx, sy, y);
To have the opposite side as well, draw another surf on the same figure:
hold on;
surf(sx, sy, -y);
I have a dataset that describes a point cloud of a 3D cylinder (xx,yy,zz,C):
and I would like to make a surface plot from this dataset, similar to this
In order to do this I thought I could interpolate my scattered data using TriScatteredInterp onto a regular grid and then plot it using surf:
F = TriScatteredInterp(xx,yy,zz);
max_x = max(xx); min_x = min(xx);
max_y = max(yy); min_y = min(yy);
max_z = max(zz); min_z = min(zz);
xi = min_x:abs(stepSize):max_x;
yi = min_y:abs(stepSize):max_y;
zi = min_z:abs(stepSize):max_z;
[qx,qy] = meshgrid(xi,yi);
qz = F(qx,qy);
F = TriScatteredInterp(xx,yy,C);
qc = F(qx,qy);
figure
surf(qx,qy,qz,qc);
axis image
This works really well for convex and concave objects but ends in this for the cylinder:
Can anybody help me as to how to achieve a nicer plot?
Have you tried Delaunay triangulation?
http://www.mathworks.com/help/matlab/ref/delaunay.html
load seamount
tri = delaunay(x,y);
trisurf(tri,x,y,z);
There is also TriScatteredInterp
http://www.mathworks.com/help/matlab/ref/triscatteredinterp.html
ti = -2:.25:2;
[qx,qy] = meshgrid(ti,ti);
qz = F(qx,qy);
mesh(qx,qy,qz);
hold on;
plot3(x,y,z,'o');
I think what you are loking for is the Convex hull function. See its documentation.
K = convhull(X,Y,Z) returns the 3-D convex hull of the points (X,Y,Z),
where X, Y, and Z are column vectors. K is a triangulation
representing the boundary of the convex hull. K is of size mtri-by-3,
where mtri is the number of triangular facets. That is, each row of K
is a triangle defined in terms of the point indices.
Example in 2D
xx = -1:.05:1; yy = abs(sqrt(xx));
[x,y] = pol2cart(xx,yy);
k = convhull(x,y);
plot(x(k),y(k),'r-',x,y,'b+')
Use plot to plot the output of convhull in 2-D. Use trisurf or trimesh to plot the output of convhull in 3-D.
A cylinder is the collection of all points equidistant to a line. So you know that your xx, yy and zz data have one thing in common, and that is that they all should lie at an equal distance to the line of symmetry. You can use that to generate a new cylinder (line of symmetry taken to be z-axis in this example):
% best-fitting radius
% NOTE: only works if z-axis is cylinder's line of symmetry
R = mean( sqrt(xx.^2+yy.^2) );
% generate some cylinder
[x y z] = cylinder(ones(numel(xx),1));
% adjust z-range and set best-fitting radius
z = z * (max(zz(:))-min(zz(:))) + min(zz(:));
x=x*R;
y=y*R;
% plot cylinder
surf(x,y,z)
TriScatteredInterp is good for fitting 2D surfaces of the form z = f(x,y), where f is a single-valued function. It won't work to fit a point cloud like you have.
Since you're dealing with a cylinder, which is, in essence, a 2D surface, you can still use TriScatterdInterp if you convert to polar coordinates, and, say, fit radius as a function of angle and height--something like:
% convert to polar coordinates:
theta = atan2(yy,xx);
h = zz;
r = sqrt(xx.^2+yy.^2);
% fit radius as a function of theta and h
RFit = TriScatteredInterp(theta(:),h(:),r(:));
% define interpolation points
stepSize = 0.1;
ti = min(theta):abs(stepSize):max(theta);
hi = min(h):abs(stepSize):max(h);
[qx,qy] = meshgrid(ti,hi);
% find r values at points:
rfit = reshape(RFit(qx(:),qy(:)),size(qx));
% plot
surf(rfit.*cos(qx),rfit.*sin(qx),qy)
I have points in 3D space and their corresponding 2D image points. How can I make a mesh out of the 3D points, then texture the triangle faces formed by the mesh?
Note that the function trisurf that you were originally trying to use returns a handle to a patch object. If you look at the 'FaceColor' property for patch objects, you can see that there is no 'texturemap' option. That option is only valid for the 'FaceColor' property of surface objects. You will therefore have to find a way to plot your triangular surface as a surface object instead of a patch object. Here are two ways to approach this:
If your data is in a uniform grid...
If the coordinates of your surface data represent a uniform grid such that z is a rectangular set of points that span from xmin to xmax in the x-axis and ymin to ymax in the y-axis, you can plot it using surf instead of trisurf:
Z = ... % N-by-M matrix of data
x = linspace(xmin, xmax, size(Z, 2)); % x-coordinates for columns of Z
y = linspace(ymin, ymax, size(Z, 1)); % y-coordinates for rows of Z
[X, Y] = meshgrid(x, y); % Create meshes for x and y
C = imread('image1.jpg'); % Load RGB image
h = surf(X, Y, Z, flipdim(C, 1), ... % Plot surface (flips rows of C, if needed)
'FaceColor', 'texturemap', ...
'EdgeColor', 'none');
axis equal
In order to illustrate the results of the above code, I initialized the data as Z = peaks;, used the built-in sample image 'peppers.png', and set the x and y values to span from 1 to 16. This resulted in the following texture-mapped surface:
If your data is non-uniformly spaced...
If your data are not regularly spaced, you can create a set of regularly-spaced X and Y coordinates (as I did above using meshgrid) and then use one of the functions griddata or TriScatteredInterp to interpolate a regular grid of Z values from your irregular set of z values. I discuss how to use these two functions in my answer to another SO question. Here's a refined version of the code you posted using TriScatteredInterp (Note: as of R2013a scatteredInterpolant is the recommended alternative):
x = ... % Scattered x data
y = ... % Scattered y data
z = ... % Scattered z data
xmin = min(x);
xmax = max(x);
ymin = min(y);
ymax = max(y);
F = TriScatteredInterp(x(:), y(:), z(:)); % Create interpolant
N = 50; % Number of y values in uniform grid
M = 50; % Number of x values in uniform grid
xu = linspace(xmin, xmax, M); % Uniform x-coordinates
yu = linspace(ymin, ymax, N); % Uniform y-coordinates
[X, Y] = meshgrid(xu, yu); % Create meshes for xu and yu
Z = F(X, Y); % Evaluate interpolant (N-by-M matrix)
C = imread('image1.jpg'); % Load RGB image
h = surf(X, Y, Z, flipdim(C, 1), ... % Plot surface
'FaceColor', 'texturemap', ...
'EdgeColor', 'none');
axis equal
In this case, you have to first choose the values of N and M for the size of your matrix Z. In order to illustrate the results of the above code, I initialized the data for x, y, and z as follows and used the built-in sample image 'peppers.png':
x = rand(1, 100)-0.5; % 100 random values in the range -0.5 to 0.5
y = rand(1, 100)-0.5; % 100 random values in the range -0.5 to 0.5
z = exp(-(x.^2+y.^2)./0.125); % Values from a 2-D Gaussian distribution
This resulted in the following texture-mapped surface:
Notice that there are jagged edges near the corners of the surface. These are places where there were too few points for TriScatteredInterp to adequately fit an interpolated surface. The Z values at these points are therefore nan, resulting in the surface point not being plotted.
If your texture is already in the proper geometry you can just use regular old texture mapping.
The link to the MathWorks documentation of texture mapping:
http://www.mathworks.com/access/helpdesk/help/techdoc/visualize/f0-18164.html#f0-9250
Re-EDIT: Updated the code a little:
Try this approach (I just got it to work).
a=imread('image.jpg');
b=double(a)/255;
[x,y,z]=peaks(30); %# This is a surface maker that you do have
%# The matrix [x,y,z] is the representation of the surface.
surf(x,y,z,b,'FaceColor','texturemap') %# Try this with any image and you
%# should see a pretty explanatory
%# result. (Just copy and paste) ;)
So [x,y,z] is the 'surface' or rather a matrix containing a number of points in the form (x,y,z) that are on the surface. Notice that the image is stretched to fit the surface.