jtiernan2008
asked on
rotate a hyperbola in Matlab - code provided
https://www.experts-exchange.com/questions/24269123/Please-help-complete-the-following-Matlab-code-and-help-understand-it.html
following on from the above;
I understand the concept better now thanks to the link provided
the function xfm1 rotates a point on the locus of the hyperbola about 60 degrees from P(x',y') to P(x",y") around (xo,yo).
but I am stuck on how xfm1 below is incorporated into create_hyperbola as in the code box below;
Can someone please help
following on from the above;
I understand the concept better now thanks to the link provided
the function xfm1 rotates a point on the locus of the hyperbola about 60 degrees from P(x',y') to P(x",y") around (xo,yo).
but I am stuck on how xfm1 below is incorporated into create_hyperbola as in the code box below;
Can someone please help
% Program to plot the hyperbola
% y^2/a^2 - x^2/b^2 = 1
% The hyperbolae are open up/down, so that x is the independent variable
% for plotting. (Using the form x^2/a^2 - y^2/b^2 = 1 requires that y be
% the independent variable, which is awkward programming-wise.)
clear % all variables
figure(1), hold off % start a new figure
set(gca,'FontSize',14) % adjust fontsize
xmax = 30; ymax = 20;
x = linspace(-xmax,xmax,1001); % array of x values for plot : This function generates vector with 1001 points equally distributed between -xmax and xmax.
%1001 is probably to have 500 points on one side (>0), 500 on another side (<0) and to include 0 itself. So you will have
%more natural numbers.
a = 5; b = 3;
y=sqrt(((x.^2)./(b^2)+1).*a^2); % corresponding y values
plot(x,y)
hold on % add to current plot
plot(x,-y) % Plot other half of hyperbola
% plot the elipse
% y^2/a^2 - x^2/b^2 = 1
y=sqrt(((-x.^2)./(b^2)+1).*a^2); % corresponding y values
plot(x,y)
plot(x,-y) % Plot other half of elipse
axis([-xmax xmax -ymax ymax]) % specify axis limits
xlabel('x')
ylabel('y')
title(['Hyperbola and elipse $y^2/a^2 - x^2/b^2 = 1$;$y^2/a^2 + x^2/b^2 = 1$; $a$ = ', num2str(a), ...
', $b$ = ', num2str(b),';'],'Interpreter','latex')
% Add axes
plot([0 0],[-ymax ymax],'k') % y axis (black line - k)
plot([-xmax xmax],[0 0],'k') % x axis
f1=sqrt(a.^2+b.^2);
f2=-(sqrt(a.^2+b.^2));
plot([0 0],[f1 f2],'.')
text(0,f1,'\leftarrow +d','VerticalAlignment','middle','HorizontalAlignment','left')
text(0,f2,'\leftarrow -d','VerticalAlignment','middle','HorizontalAlignment','left')
f3=sqrt(a.^2-b.^2);
f4=-(sqrt(a.^2-b.^2));
plot([0 0],[f3 f4],'.')
text(0,f3,'\leftarrow +c','VerticalAlignment','middle','HorizontalAlignment','left')
text(0,f4,'\leftarrow -c','VerticalAlignment','middle','HorizontalAlignment','left')
text(0,a, '\leftarrow +a')
text(0,-a, '\leftarrow -a')
function [xout,yout] = xfm1(xin,yin,theta,x_offset,y_offset)
% Program to rotate and translate x,y values from x",y" to x,y space.
% Written to plot hyperbolas for time of arrival code.
% theta value assumed to be in radians.
% rotation matrix
xfm = [cos(theta) sin(theta); ...
-sin(theta) cos(theta)];
% make x,y values into a column vector
r_in = [xin; yin];
% rotate
r_out = xfm*r_in;
x = r_out(1,:); y = r_out(2,:);
xout = x + x_offset;
yout = y + y_offset;
ASKER
thanks, ok so I just invoke the function as long as it is in the same folder.
but how do i import the rotated values?
do I use x = linspace(-xmax,xmax,1001);
how do I use the function xfm1(xin,yin,theta,x_offse
thats where I am getting confused
but how do i import the rotated values?
do I use x = linspace(-xmax,xmax,1001);
how do I use the function xfm1(xin,yin,theta,x_offse
thats where I am getting confused
Add something like this to your code. x and y are coordinates for original hyperbola, you need to apply the function to every part of your figure.
When you call function in Matlab, input and output parameters names do not have to match those in function implementation.
BTW I think you made a wrong rotation matrix. No, it's correct, but rotate in not usual direction. It should be
xfm = [cos(theta) -sin(theta); ...
sin(theta) cos(theta)];
When you call function in Matlab, input and output parameters names do not have to match those in function implementation.
BTW I think you made a wrong rotation matrix. No, it's correct, but rotate in not usual direction. It should be
xfm = [cos(theta) -sin(theta); ...
sin(theta) cos(theta)];
theta=1; % in radians, 1 radian = 180/pi degrees
xoff=0;
yoff=0;
[xout,yout] = xfm1(x,y,theta,xoff,yoff);
plot(xout,yout)ASKER
Ok, I added this at the end of code but the plot does not seem to be correct as per page 4 of the tutorial... am I doing this wrong?
% Program to plot the hyperbola
% y^2/a^2 - x^2/b^2 = 1
% The hyperbolae are open up/down, so that x is the independent variable
% for plotting. (Using the form x^2/a^2 - y^2/b^2 = 1 requires that y be
% the independent variable, which is awkward programming-wise.)
clear % all variables
figure(1), hold off % start a new figure
set(gca,'FontSize',14) % adjust fontsize
xmax = 30; ymax = 20;
x = linspace(-xmax,xmax,1001); % array of x values for plot : This function generates vector with 1001 points equally distributed between -xmax and xmax.
%1001 is probably to have 500 points on one side (>0), 500 on another side (<0) and to include 0 itself. So you will have
%more natural numbers.
a = 5; b = 3;
y=sqrt(((x.^2)./(b^2)+1).*a^2); % corresponding y values
plot(x,y)
hold on % add to current plot
plot(x,-y) % Plot other half of hyperbola
% plot the elipse
% y^2/a^2 - x^2/b^2 = 1
y=sqrt(((-x.^2)./(b^2)+1).*a^2); % corresponding y values
plot(x,y)
plot(x,-y) % Plot other half of elipse
axis([-xmax xmax -ymax ymax]) % specify axis limits
xlabel('x')
ylabel('y')
title(['Hyperbola and elipse $y^2/a^2 - x^2/b^2 = 1$;$y^2/a^2 + x^2/b^2 = 1$; $a$ = ', num2str(a), ...
', $b$ = ', num2str(b),';'],'Interpreter','latex')
% Add axes
plot([0 0],[-ymax ymax],'k') % y axis (black line - k)
plot([-xmax xmax],[0 0],'k') % x axis
f1=sqrt(a.^2+b.^2);
f2=-(sqrt(a.^2+b.^2));
plot([0 0],[f1 f2],'.')
text(0,f1,'\leftarrow +d','VerticalAlignment','middle','HorizontalAlignment','left')
text(0,f2,'\leftarrow -d','VerticalAlignment','middle','HorizontalAlignment','left')
x1=10;
y1=sqrt(((x1.^2)./(b^2)+1).*a^2);
line([0 x1], [f1 y1],'color','r')
line([0 x1], [f2 y1],'color','r')
f3=sqrt(a.^2-b.^2);
f4=-(sqrt(a.^2-b.^2));
plot([0 0],[f3 f4],'.')
text(0,f3,'\leftarrow +c','VerticalAlignment','middle','HorizontalAlignment','left')
text(0,f4,'\leftarrow -c','VerticalAlignment','middle','HorizontalAlignment','left')
text(0,a, '\leftarrow +a')
text(0,-a, '\leftarrow -a')
theta=1; % in radians, 1 radian = 180/pi degrees
xoff=0;
yoff=0;
[xout,yout] = xfm1(x,y,theta,xoff,yoff);
plot(xout,yout)ASKER
tutorial
toa.pdf
toa.pdf
ASKER CERTIFIED SOLUTION
membership
This solution is only available to members.
To access this solution, you must be a member of Experts Exchange.
ASKER
Brilliant... yes I understand you invoke it through the plot function after defining the variables above...
I know how to get the focus points as well
thanks a million :)
I know how to get the focus points as well
thanks a million :)
You can read more about m-files, scripts and functions here:
http://www.mathworks.com/access/helpdesk/help/techdoc/matlab_prog/f7-38085.html
I should add, that function can be in the same m-file with another function, is it's nested function. If you are interested in this, see here:
http://www.mathworks.com/access/helpdesk/help/techdoc/matlab_prog/f4-39683.html